# Bison '2.0' (DJGPP port 2005-02-18 (r1))

## Table of Contents

- Bison
- Introduction
- Conditions for Using Bison
- GNU GENERAL PUBLIC LICENSE
  - Preamble
  - Appendix: How to Apply These Terms to Your New Programs
- 1 The Concepts of Bison
  - 1.1 Languages and Context-Free Grammars
  - 1.2 From Formal Rules to Bison Input
  - 1.3 Semantic Values
  - 1.4 Semantic Actions
  - 1.5 Writing GLR Parsers
    - 1.5.1 Using GLR on Unambiguous Grammars
    - 1.5.2 Using GLR to Resolve Ambiguities
    - 1.5.3 Considerations when Compiling GLR Parsers
  - 1.6 Locations
  - 1.7 Bison Output: the Parser File
  - 1.8 Stages in Using Bison
  - 1.9 The Overall Layout of a Bison Grammar
- 2 Examples
  - 2.1 Reverse Polish Notation Calculator
    - 2.1.1 Declarations for `rpcalc`
    - 2.1.2 Grammar Rules for `rpcalc`
      - 2.1.2.1 Explanation of `input`
      - 2.1.2.2 Explanation of `line`
      - 2.1.2.3 Explanation of `expr`
    - 2.1.3 The `rpcalc` Lexical Analyzer
    - 2.1.4 The Controlling Function
    - 2.1.5 The Error Reporting Routine
    - 2.1.6 Running Bison to Make the Parser
    - 2.1.7 Compiling the Parser File
  - 2.2 Infix Notation Calculator: `calc`
  - 2.3 Simple Error Recovery
  - 2.4 Location Tracking Calculator: `ltcalc`
    - 2.4.1 Declarations for `ltcalc`
    - 2.4.2 Grammar Rules for `ltcalc`
    - 2.4.3 The `ltcalc` Lexical Analyzer.
  - 2.5 Multi-Function Calculator: `mfcalc`
    - 2.5.1 Declarations for `mfcalc`
    - 2.5.2 Grammar Rules for `mfcalc`
    - 2.5.3 The `mfcalc` Symbol Table
  - 2.6 Exercises
- 3 Bison Grammar Files
  - 3.1 Outline of a Bison Grammar
    - 3.1.1 The prologue
    - 3.1.2 The Bison Declarations Section
    - 3.1.3 The Grammar Rules Section
    - 3.1.4 The epilogue
  - 3.2 Symbols, Terminal and Nonterminal
  - 3.3 Syntax of Grammar Rules
  - 3.4 Recursive Rules
  - 3.5 Defining Language Semantics
    - 3.5.1 Data Types of Semantic Values
    - 3.5.2 More Than One Value Type
    - 3.5.3 Actions
    - 3.5.4 Data Types of Values in Actions
    - 3.5.5 Actions in Mid-Rule
  - 3.6 Tracking Locations
    - 3.6.1 Data Type of Locations
    - 3.6.2 Actions and Locations
    - 3.6.3 Default Action for Locations
  - 3.7 Bison Declarations
    - 3.7.1 Token Type Names
    - 3.7.2 Operator Precedence
    - 3.7.3 The Collection of Value Types
    - 3.7.4 Nonterminal Symbols
    - 3.7.5 Performing Actions before Parsing
    - 3.7.6 Freeing Discarded Symbols
    - 3.7.7 Suppressing Conflict Warnings
    - 3.7.8 The Start-Symbol
    - 3.7.9 A Pure (Reentrant) Parser
    - 3.7.10 Bison Declaration Summary
  - 3.8 Multiple Parsers in the Same Program
- 4 Parser C-Language Interface
  - 4.1 The Parser Function `yyparse`
  - 4.2 The Lexical Analyzer Function `yylex`
    - 4.2.1 Calling Convention for `yylex`
    - 4.2.2 Semantic Values of Tokens
    - 4.2.3 Textual Locations of Tokens
    - 4.2.4 Calling Conventions for Pure Parsers
  - 4.3 The Error Reporting Function `yyerror`
  - 4.4 Special Features for Use in Actions
- 5 The Bison Parser Algorithm
  - 5.1 Look-Ahead Tokens
  - 5.2 Shift/Reduce Conflicts
  - 5.3 Operator Precedence
    - 5.3.1 When Precedence is Needed
    - 5.3.2 Specifying Operator Precedence
    - 5.3.3 Precedence Examples
    - 5.3.4 How Precedence Works
  - 5.4 Context-Dependent Precedence
  - 5.5 Parser States
  - 5.6 Reduce/Reduce Conflicts
  - 5.7 Mysterious Reduce/Reduce Conflicts
  - 5.8 Generalized LR (GLR) Parsing
  - 5.9 Stack Overflow, and How to Avoid It
- 6 Error Recovery
- 7 Handling Context Dependencies
  - 7.1 Semantic Info in Token Types
  - 7.2 Lexical Tie-ins
  - 7.3 Lexical Tie-ins and Error Recovery
- 8 Debugging Your Parser
  - 8.1 Understanding Your Parser
  - 8.2 Tracing Your Parser
- 9 Invoking Bison
  - 9.1 Bison Options
  - 9.2 Option Cross Key
  - 9.3 Yacc Library
- 10 Frequently Asked Questions
  - 10.1 Parser Stack Overflow
  - 10.2 How Can I Reset the Parser
  - 10.3 Strings are Destroyed
  - 10.4 C++ Parsers
  - 10.5 Implementing Gotos/Loops
- Appendix A Bison Symbols
- Appendix B Glossary
- Appendix C Copying This Manual
  - C.1 GNU Free Documentation License
    - C.1.1 ADDENDUM: How to use this License for your documents
- Index

Next: Introduction, Up: (dir)

## Bison

This manual is for GNU Bison (version '2.0' (DJGPP port 2005-02-18 (r1)), 22 December 2004), the GNU parser generator.

Copyright © 1988, 1989, 1990, 1991, 1992, 1993, 1995, 1998, 1999, 2000, 2001, 2002, 2003, 2004 Free Software Foundation, Inc.

> Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation; with no Invariant Sections, with the Front-Cover texts being “A GNU Manual,” and with the Back-Cover Texts as in (a) below. A copy of the license is included in the section entitled “GNU Free Documentation License.”

> (a) The FSF's Back-Cover Text is: “You have freedom to copy and modify this GNU Manual, like GNU software. Copies published by the Free Software Foundation raise funds for GNU development.”

Tutorial sections:

Reference sections:

--- The Detailed Node Listing ---

The Concepts of Bison

Writing GLR Parsers

Examples

Reverse Polish Notation Calculator

Grammar Rules for `rpcalc`

Location Tracking Calculator: `ltcalc`

Multi-Function Calculator: `mfcalc`

Bison Grammar Files

Outline of a Bison Grammar

Defining Language Semantics

Tracking Locations

Bison Declarations

Parser C-Language Interface

The Lexical Analyzer Function `yylex`

The Bison Parser Algorithm

Operator Precedence

Handling Context Dependencies

Debugging Your Parser

Invoking Bison

Frequently Asked Questions

Copying This Manual

Next: Conditions, Previous: Top, Up: Top

## Introduction

Bison is a general-purpose parser generator that converts a grammar description for an LALR(1) context-free grammar into a C program to parse that grammar. Once you are proficient with Bison, you may use it to develop a wide range of language parsers, from those used in simple desk calculators to complex programming languages.

Bison is upward compatible with Yacc: all properly-written Yacc grammars ought to work with Bison with no change. Anyone familiar with Yacc should be able to use Bison with little trouble. You need to be fluent in C programming in order to use Bison or to understand this manual.

We begin with tutorial chapters that explain the basic concepts of using Bison and show three explained examples, each building on the last. If you don't know Bison or Yacc, start by reading these chapters. Reference chapters follow which describe specific aspects of Bison in detail.

Bison was written primarily by Robert Corbett; Richard Stallman made it Yacc-compatible. Wilfred Hansen of Carnegie Mellon University added multi-character string literals and other features.

This edition corresponds to version '2.0' (DJGPP port 2005-02-18 (r1)) of Bison.

Next: Copying, Previous: Introduction, Up: Top

## Conditions for Using Bison

As of Bison version 1.24, we have changed the distribution terms for `yyparse` to permit using Bison's output in nonfree programs when Bison is generating C code for LALR(1) parsers. Formerly, these parsers could be used only in programs that were free software.

The other GNU programming tools, such as the GNU C compiler, have never had such a requirement. They could always be used for nonfree software. The reason Bison was different was not due to a special policy decision; it resulted from applying the usual General Public License to all of the Bison source code.

The output of the Bison utility—the Bison parser file—contains a verbatim copy of a sizable piece of Bison, which is the code for the `yyparse` function. (The actions from your grammar are inserted into this function at one point, but the rest of the function is not changed.) When we applied the GPL terms to the code for `yyparse`, the effect was to restrict the use of Bison output to free software.

We didn't change the terms because of sympathy for people who want to make software proprietary. Software should be free. But we concluded that limiting Bison's use to free software was doing little to encourage people to make other software free. So we decided to make the practical conditions for using Bison match the practical conditions for using the other GNU tools.

This exception applies only when Bison is generating C code for an LALR(1) parser; otherwise, the GPL terms operate as usual. You can tell whether the exception applies to your .c output file by inspecting it to see whether it says “As a special exception, when this file is copied by Bison into a Bison output file, you may use that output file without restriction.”

Next: Concepts, Previous: Conditions, Up: Top

## GNU GENERAL PUBLIC LICENSE

Version 2, June 1991

         Copyright © 1989, 1991 Free Software Foundation, Inc.
         59 Temple Place - Suite 330, Boston, MA  02111-1307, USA

         Everyone is permitted to copy and distribute verbatim copies
         of this license document, but changing it is not allowed.

### Preamble

The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software—to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too.

When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things.

To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it.

For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights.

We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software.

Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations.

Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all.

The precise terms and conditions for copying, distribution and modification follow.

0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The “Program”, below, refers to any such program or work, and a “work based on the Program” means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term “modification”.) Each licensee is addressed as “you”.

   Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does.

1. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program.

   You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee.

2. You may modify your copy or copies of the Program or any portion of it, thus forming a work based on the Program, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions:
   1. You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change.
   2. You must cause any work that you distribute or publish, that in whole or in part contains or is derived from the Program or any part thereof, to be licensed as a whole at no charge to all third parties under the terms of this License.
   3. If the modified program normally reads commands interactively when run, you must cause it, when started running for such interactive use in the most ordinary way, to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty (or else, saying that you provide a warranty) and that users may redistribute the program under these conditions, and telling the user how to view a copy of this License. (Exception: if the Program itself is interactive but does not normally print such an announcement, your work based on the Program is not required to print an announcement.)

   These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it.

   Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program.

   In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License.

3. You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following:
   1. Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or,
   2. Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or,
   3. Accompany it with the information you received as to the offer to distribute corresponding source code. (This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer, in accord with Subsection b above.)

   The source code for a work means the preferred form of the work for making modifications to it. For an executable work, complete source code means all the source code for all modules it contains, plus any associated interface definition files, plus the scripts used to control compilation and installation of the executable. However, as a special exception, the source code distributed need not include anything that is normally distributed (in either source or binary form) with the major components (compiler, kernel, and so on) of the operating system on which the executable runs, unless that component itself accompanies the executable.

   If distribution of executable or object code is made by offering access to copy from a designated place, then offering equivalent access to copy the source code from the same place counts as distribution of the source code, even though third parties are not compelled to copy the source along with the object code.

4. You may not copy, modify, sublicense, or distribute the Program except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense or distribute the Program is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance.
5. You are not required to accept this License, since you have not signed it. However, nothing else grants you permission to modify or distribute the Program or its derivative works. These actions are prohibited by law if you do not accept this License. Therefore, by modifying or distributing the Program (or any work based on the Program), you indicate your acceptance of this License to do so, and all its terms and conditions for copying, distributing or modifying the Program or works based on it.
6. Each time you redistribute the Program (or any work based on the Program), the recipient automatically receives a license from the original licensor to copy, distribute or modify the Program subject to these terms and conditions. You may not impose any further restrictions on the recipients' exercise of the rights granted herein. You are not responsible for enforcing compliance by third parties to this License.
7. If, as a consequence of a court judgment or allegation of patent infringement or for any other reason (not limited to patent issues), conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not distribute the Program at all. For example, if a patent license would not permit royalty-free redistribution of the Program by all those who receive copies directly or indirectly through you, then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program.

   If any portion of this section is held invalid or unenforceable under any particular circumstance, the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances.

   It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice.

   This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License.

8. If the distribution and/or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces, the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries, so that distribution is permitted only in or among countries not thus excluded. In such case, this License incorporates the limitation as if written in the body of this License.
9. The Free Software Foundation may publish revised and/or new versions of the General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns.

   Each version is given a distinguishing version number. If the Program specifies a version number of this License which applies to it and “any later version”, you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation.

10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally.
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM “AS IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

### Appendix: How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the “copyright” line and a pointer to where the full notice is found.

         one line to give the program's name and a brief idea of what it does.
         Copyright (C) yyyy  name of author

         This program is free software; you can redistribute it and/or modify
         it under the terms of the GNU General Public License as published by
         the Free Software Foundation; either version 2 of the License, or
         (at your option) any later version.

         This program is distributed in the hope that it will be useful,
         but WITHOUT ANY WARRANTY; without even the implied warranty of
         MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
         GNU General Public License for more details.

         You should have received a copy of the GNU General Public License
         along with this program; if not, write to the Free Software
         Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

Also add information on how to contact you by electronic and paper mail.

If the program is interactive, make it output a short notice like this when it starts in an interactive mode:

         Gnomovision version 69, Copyright (C) 19yy name of author
         Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
         This is free software, and you are welcome to redistribute it
         under certain conditions; type `show c' for details.

The hypothetical commands show w and show c should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than show w and show c; they could even be mouse-clicks or menu items—whatever suits your program.

You should also get your employer (if you work as a programmer) or your school, if any, to sign a “copyright disclaimer” for the program, if necessary. Here is a sample; alter the names:

         Yoyodyne, Inc., hereby disclaims all copyright interest in the program
         `Gnomovision' (which makes passes at compilers) written by James Hacker.

         signature of Ty Coon, 1 April 1989
         Ty Coon, President of Vice

This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License.

Next: Examples, Previous: Copying, Up: Top

## 1 The Concepts of Bison

This chapter introduces many of the basic concepts without which the details of Bison will not make sense. If you do not already know how to use Bison or Yacc, we suggest you start by reading this chapter carefully.

Next: Grammar in Bison, Up: Concepts

### 1.1 Languages and Context-Free Grammars

In order for Bison to parse a language, it must be described by a context-free grammar. This means that you specify one or more syntactic groupings and give rules for constructing them from their parts. For example, in the C language, one kind of grouping is called an `expression'. One rule for making an expression might be, “An expression can be made of a minus sign and another expression”. Another would be, “An expression can be an integer”. As you can see, rules are often recursive, but there must be at least one rule which leads out of the recursion.

The most common formal system for presenting such rules for humans to read is Backus-Naur Form or “BNF”, which was developed in order to specify the language Algol 60. Any grammar expressed in BNF is a context-free grammar. The input to Bison is essentially machine-readable BNF.

There are various important subclasses of context-free grammar. Although it can handle almost all context-free grammars, Bison is optimized for what are called LALR(1) grammars. In brief, in these grammars, it must be possible to tell how to parse any portion of an input string with just a single token of look-ahead. Strictly speaking, that is a description of an LR(1) grammar, and LALR(1) involves additional restrictions that are hard to explain simply; but it is rare in actual practice to find an LR(1) grammar that fails to be LALR(1). See Mysterious Reduce/Reduce Conflicts, for more information on this.

Parsers for LALR(1) grammars are deterministic, meaning roughly that the next grammar rule to apply at any point in the input is uniquely determined by the preceding input and a fixed, finite portion (called a look-ahead) of the remaining input. A context-free grammar can be ambiguous, meaning that there are multiple ways to apply the grammar rules to get the some inputs. Even unambiguous grammars can be non-deterministic, meaning that no fixed look-ahead always suffices to determine the next grammar rule to apply. With the proper declarations, Bison is also able to parse these more general context-free grammars, using a technique known as GLR parsing (for Generalized LR). Bison's GLR parsers are able to handle any context-free grammar for which the number of possible parses of any given string is finite.

In the formal grammatical rules for a language, each kind of syntactic unit or grouping is named by a symbol. Those which are built by grouping smaller constructs according to grammatical rules are called nonterminal symbols; those which can't be subdivided are called terminal symbols or token types. We call a piece of input corresponding to a single terminal symbol a token, and a piece corresponding to a single nonterminal symbol a grouping.

We can use the C language as an example of what symbols, terminal and nonterminal, mean. The tokens of C are identifiers, constants (numeric and string), and the various keywords, arithmetic operators and punctuation marks. So the terminal symbols of a grammar for C include `identifier', `number', `string', plus one symbol for each keyword, operator or punctuation mark: `if', `return', `const', `static', `int', `char', `plus-sign', `open-brace', `close-brace', `comma' and many more. (These tokens can be subdivided into characters, but that is a matter of lexicography, not grammar.)

Here is a simple C function subdivided into tokens:

         int             /* keyword `int' */
         square (int x)  /* identifier, open-paren, keyword `int', identifier, close-paren */
         {               /* open-brace */
           return x * x; /* keyword `return', identifier, asterisk, identifier, semicolon */
         }               /* close-brace */

The syntactic groupings of C include the expression, the statement, the declaration, and the function definition. These are represented in the grammar of C by nonterminal symbols `expression', `statement', `declaration' and `function definition'. The full grammar uses dozens of additional language constructs, each with its own nonterminal symbol, in order to express the meanings of these four. The example above is a function definition; it contains one declaration, and one statement. In the statement, each x is an expression and so is x * x.

Each nonterminal symbol must have grammatical rules showing how it is made out of simpler constructs. For example, one kind of C statement is the `return` statement; this would be described with a grammar rule which reads informally as follows:

> A `statement' can be made of a `return' keyword, an `expression' and a `semicolon'.

There would be many other rules for `statement', one for each kind of statement in C.

One nonterminal symbol must be distinguished as the special one which defines a complete utterance in the language. It is called the start symbol. In a compiler, this means a complete input program. In the C language, the nonterminal symbol `sequence of definitions and declarations' plays this role.

For example, 1 + 2 is a valid C expression—a valid part of a C program—but it is not valid as an entire C program. In the context-free grammar of C, this follows from the fact that `expression' is not the start symbol.

The Bison parser reads a sequence of tokens as its input, and groups the tokens using the grammar rules. If the input is valid, the end result is that the entire token sequence reduces to a single grouping whose symbol is the grammar's start symbol. If we use a grammar for C, the entire input must be a `sequence of definitions and declarations'. If not, the parser reports a syntax error.

Next: Semantic Values, Previous: Language and Grammar, Up: Concepts

### 1.2 From Formal Rules to Bison Input

A formal grammar is a mathematical construct. To define the language for Bison, you must write a file expressing the grammar in Bison syntax: a Bison grammar file. See Bison Grammar Files.

A nonterminal symbol in the formal grammar is represented in Bison input as an identifier, like an identifier in C. By convention, it should be in lower case, such as `expr`, `stmt` or `declaration`.

The Bison representation for a terminal symbol is also called a token type. Token types as well can be represented as C-like identifiers. By convention, these identifiers should be upper case to distinguish them from nonterminals: for example, `INTEGER`, `IDENTIFIER`, `IF` or `RETURN`. A terminal symbol that stands for a particular keyword in the language should be named after that keyword converted to upper case. The terminal symbol `error` is reserved for error recovery. See Symbols.

A terminal symbol can also be represented as a character literal, just like a C character constant. You should do this whenever a token is just a single character (parenthesis, plus-sign, etc.): use that same character in a literal as the terminal symbol for that token.

A third way to represent a terminal symbol is with a C string constant containing several characters. See Symbols, for more information.

The grammar rules also have an expression in Bison syntax. For example, here is the Bison rule for a C `return` statement. The semicolon in quotes is a literal character token, representing part of the C syntax for the statement; the naked semicolon, and the colon, are Bison punctuation used in every rule.

         stmt:   RETURN expr ';'
                 ;

See Syntax of Grammar Rules.

Next: Semantic Actions, Previous: Grammar in Bison, Up: Concepts

### 1.3 Semantic Values

A formal grammar selects tokens only by their classifications: for example, if a rule mentions the terminal symbol `integer constant', it means that any integer constant is grammatically valid in that position. The precise value of the constant is irrelevant to how to parse the input: if x+4 is grammatical then x+1 or x+3989 is equally grammatical.

But the precise value is very important for what the input means once it is parsed. A compiler is useless if it fails to distinguish between 4, 1 and 3989 as constants in the program! Therefore, each token in a Bison grammar has both a token type and a semantic value. See Defining Language Semantics, for details.

The token type is a terminal symbol defined in the grammar, such as `INTEGER`, `IDENTIFIER` or `','`. It tells everything you need to know to decide where the token may validly appear and how to group it with other tokens. The grammar rules know nothing about tokens except their types.

The semantic value has all the rest of the information about the meaning of the token, such as the value of an integer, or the name of an identifier. (A token such as `','` which is just punctuation doesn't need to have any semantic value.)

For example, an input token might be classified as token type `INTEGER` and have the semantic value 4. Another input token might have the same token type `INTEGER` but value 3989. When a grammar rule says that `INTEGER` is allowed, either of these tokens is acceptable because each is an `INTEGER`. When the parser accepts the token, it keeps track of the token's semantic value.

Each grouping can also have a semantic value as well as its nonterminal symbol. For example, in a calculator, an expression typically has a semantic value that is a number. In a compiler for a programming language, an expression typically has a semantic value that is a tree structure describing the meaning of the expression.

Next: GLR Parsers, Previous: Semantic Values, Up: Concepts

### 1.4 Semantic Actions

In order to be useful, a program must do more than parse input; it must also produce some output based on the input. In a Bison grammar, a grammar rule can have an action made up of C statements. Each time the parser recognizes a match for that rule, the action is executed. See Actions.

Most of the time, the purpose of an action is to compute the semantic value of the whole construct from the semantic values of its parts. For example, suppose we have a rule which says an expression can be the sum of two expressions. When the parser recognizes such a sum, each of the subexpressions has a semantic value which describes how it was built up. The action for this rule should create a similar sort of value for the newly recognized larger expression.

For example, here is a rule that says an expression can be the sum of two subexpressions:

         expr: expr '+' expr   { $$ = $1 + $3; }
                 ;

The action says how to produce the semantic value of the sum expression from the values of the two subexpressions.

Next: Locations Overview, Previous: Semantic Actions, Up: Concepts

### 1.5 Writing GLR Parsers

In some grammars, Bison's standard LALR(1) parsing algorithm cannot decide whether to apply a certain grammar rule at a given point. That is, it may not be able to decide (on the basis of the input read so far) which of two possible reductions (applications of a grammar rule) applies, or whether to apply a reduction or read more of the input and apply a reduction later in the input. These are known respectively as reduce/reduce conflicts (see Reduce/Reduce), and shift/reduce conflicts (see Shift/Reduce).

To use a grammar that is not easily modified to be LALR(1), a more general parsing algorithm is sometimes necessary. If you include `%glr-parser` among the Bison declarations in your file (see Grammar Outline), the result is a Generalized LR (GLR) parser. These parsers handle Bison grammars that contain no unresolved conflicts (i.e., after applying precedence declarations) identically to LALR(1) parsers. However, when faced with unresolved shift/reduce and reduce/reduce conflicts, GLR parsers use the simple expedient of doing both, effectively cloning the parser to follow both possibilities. Each of the resulting parsers can again split, so that at any given time, there can be any number of possible parses being explored. The parsers proceed in lockstep; that is, all of them consume (shift) a given input symbol before any of them proceed to the next. Each of the cloned parsers eventually meets one of two possible fates: either it runs into a parsing error, in which case it simply vanishes, or it merges with another parser, because the two of them have reduced the input to an identical set of symbols.

During the time that there are multiple parsers, semantic actions are recorded, but not performed. When a parser disappears, its recorded semantic actions disappear as well, and are never performed. When a reduction makes two parsers identical, causing them to merge, Bison records both sets of semantic actions. Whenever the last two parsers merge, reverting to the single-parser case, Bison resolves all the outstanding actions either by precedences given to the grammar rules involved, or by performing both actions, and then calling a designated user-defined function on the resulting values to produce an arbitrary merged result.

Next: Merging GLR Parses, Up: GLR Parsers

#### 1.5.1 Using GLR on Unambiguous Grammars

In the simplest cases, you can use the GLR algorithm to parse grammars that are unambiguous, but fail to be LALR(1). Such grammars typically require more than one symbol of look-ahead, or (in rare cases) fall into the category of grammars in which the LALR(1) algorithm throws away too much information (they are in LR(1), but not LALR(1), Mystery Conflicts).

Consider a problem that arises in the declaration of enumerated and subrange types in the programming language Pascal. Here are some examples:

         type subrange = lo .. hi;
         type enum = (a, b, c);

The original language standard allows only numeric literals and constant identifiers for the subrange bounds (lo and hi), but Extended Pascal (ISO/IEC 10206) and many other Pascal implementations allow arbitrary expressions there. This gives rise to the following situation, containing a superfluous pair of parentheses:

         type subrange = (a) .. b;

Compare this to the following declaration of an enumerated type with only one value:

         type enum = (a);

(These declarations are contrived, but they are syntactically valid, and more-complicated cases can come up in practical programs.)

These two declarations look identical until the .. token. With normal LALR(1) one-token look-ahead it is not possible to decide between the two forms when the identifier a is parsed. It is, however, desirable for a parser to decide this, since in the latter case a must become a new identifier to represent the enumeration value, while in the former case a must be evaluated with its current meaning, which may be a constant or even a function call.

You could parse (a) as an “unspecified identifier in parentheses”, to be resolved later, but this typically requires substantial contortions in both semantic actions and large parts of the grammar, where the parentheses are nested in the recursive rules for expressions.

You might think of using the lexer to distinguish between the two forms by returning different tokens for currently defined and undefined identifiers. But if these declarations occur in a local scope, and a is defined in an outer scope, then both forms are possible—either locally redefining a, or using the value of a from the outer scope. So this approach cannot work.

A simple solution to this problem is to declare the parser to use the GLR algorithm. When the GLR parser reaches the critical state, it merely splits into two branches and pursues both syntax rules simultaneously. Sooner or later, one of them runs into a parsing error. If there is a .. token before the next ;, the rule for enumerated types fails since it cannot accept .. anywhere; otherwise, the subrange type rule fails since it requires a .. token. So one of the branches fails silently, and the other one continues normally, performing all the intermediate actions that were postponed during the split.

If the input is syntactically incorrect, both branches fail and the parser reports a syntax error as usual.

The effect of all this is that the parser seems to “guess” the correct branch to take, or in other words, it seems to use more look-ahead than the underlying LALR(1) algorithm actually allows for. In this example, LALR(2) would suffice, but also some cases that are not LALR(k) for any k can be handled this way.

In general, a GLR parser can take quadratic or cubic worst-case time, and the current Bison parser even takes exponential time and space for some grammars. In practice, this rarely happens, and for many grammars it is possible to prove that it cannot happen. The present example contains only one conflict between two rules, and the type-declaration context containing the conflict cannot be nested. So the number of branches that can exist at any time is limited by the constant 2, and the parsing time is still linear.

Here is a Bison grammar corresponding to the example above. It parses a vastly simplified form of Pascal type declarations.

         %token TYPE DOTDOT ID

         %left '+' '-'
         %left '*' '/'

         %%

         type_decl : TYPE ID '=' type ';'
              ;

         type : '(' id_list ')'
              | expr DOTDOT expr
              ;

         id_list : ID
              | id_list ',' ID
              ;

         expr : '(' expr ')'
              | expr '+' expr
              | expr '-' expr
              | expr '*' expr
              | expr '/' expr
              | ID
              ;

When used as a normal LALR(1) grammar, Bison correctly complains about one reduce/reduce conflict. In the conflicting situation the parser chooses one of the alternatives, arbitrarily the one declared first. Therefore the following correct input is not recognized:

         type t = (a) .. b;

The parser can be turned into a GLR parser, while also telling Bison to be silent about the one known reduce/reduce conflict, by adding these two declarations to the Bison input file (before the first %%):

         %glr-parser
         %expect-rr 1

No change in the grammar itself is required. Now the parser recognizes all valid declarations, according to the limited syntax above, transparently. In fact, the user does not even notice when the parser splits.

So here we have a case where we can use the benefits of GLR, almost without disadvantages. Even in simple cases like this, however, there are at least two potential problems to beware. First, always analyze the conflicts reported by Bison to make sure that GLR splitting is only done where it is intended. A GLR parser splitting inadvertently may cause problems less obvious than an LALR parser statically choosing the wrong alternative in a conflict. Second, consider interactions with the lexer (see Semantic Tokens) with great care. Since a split parser consumes tokens without performing any actions during the split, the lexer cannot obtain information via parser actions. Some cases of lexer interactions can be eliminated by using GLR to shift the complications from the lexer to the parser. You must check the remaining cases for correctness.

In our example, it would be safe for the lexer to return tokens based on their current meanings in some symbol table, because no new symbols are defined in the middle of a type declaration. Though it is possible for a parser to define the enumeration constants as they are parsed, before the type declaration is completed, it actually makes no difference since they cannot be used within the same enumerated type declaration.

Next: Compiler Requirements, Previous: Simple GLR Parsers, Up: GLR Parsers

#### 1.5.2 Using GLR to Resolve Ambiguities

Let's consider an example, vastly simplified from a C++ grammar.

         %{
           #include <stdio.h>
           #define YYSTYPE char const *
           int yylex (void);
           void yyerror (char const *);
         %}

         %token TYPENAME ID

         %right '='
         %left '+'

         %glr-parser

         %%

         prog :
              | prog stmt   { printf ("\n"); }
              ;

         stmt : expr ';'  %dprec 1
              | decl      %dprec 2
              ;

         expr : ID               { printf ("%s ", $$); }
              | TYPENAME '(' expr ')'
                                 { printf ("%s <cast> ", $1); }
              | expr '+' expr    { printf ("+ "); }
              | expr '=' expr    { printf ("= "); }
              ;

         decl : TYPENAME declarator ';'
                                 { printf ("%s <declare> ", $1); }
              | TYPENAME declarator '=' expr ';'
                                 { printf ("%s <init-declare> ", $1); }
              ;

         declarator : ID         { printf ("\"%s\" ", $1); }
              | '(' declarator ')'
              ;

This models a problematic part of the C++ grammar—the ambiguity between certain declarations and statements. For example,

         T (x) = y+z;

parses as either an `expr` or a `stmt` (assuming that T is recognized as a `TYPENAME` and x as an `ID`). Bison detects this as a reduce/reduce conflict between the rules `expr : ID` and `declarator : ID`, which it cannot resolve at the time it encounters `x` in the example above. Since this is a GLR parser, it therefore splits the problem into two parses, one for each choice of resolving the reduce/reduce conflict. Unlike the example from the previous section (see Simple GLR Parsers), however, neither of these parses “dies,” because the grammar as it stands is ambiguous. One of the parsers eventually reduces `stmt : expr ';'` and the other reduces `stmt : decl`, after which both parsers are in an identical state: they've seen prog stmt and have the same unprocessed input remaining. We say that these parses have merged.

At this point, the GLR parser requires a specification in the grammar of how to choose between the competing parses. In the example above, the two `%dprec` declarations specify that Bison is to give precedence to the parse that interprets the example as a `decl`, which implies that `x` is a declarator. The parser therefore prints

         "x" y z + T <init-declare>

The `%dprec` declarations only come into play when more than one parse survives. Consider a different input string for this parser:

         T (x) + y;

This is another example of using GLR to parse an unambiguous construct, as shown in the previous section (see Simple GLR Parsers). Here, there is no ambiguity (this cannot be parsed as a declaration). However, at the time the Bison parser encounters `x`, it does not have enough information to resolve the reduce/reduce conflict (again, between `x` as an `expr` or a `declarator`). In this case, no precedence declaration is used. Again, the parser splits into two, one assuming that `x` is an `expr`, and the other assuming `x` is a `declarator`. The second of these parsers then vanishes when it sees `+`, and the parser prints

         x T <cast> y +

Suppose that instead of resolving the ambiguity, you wanted to see all the possibilities. For this purpose, you must merge the semantic actions of the two possible parsers, rather than choosing one over the other. To do so, you could change the declaration of `stmt` as follows:

         stmt : expr ';'  %merge <stmtMerge>
              | decl      %merge <stmtMerge>
              ;

and define the `stmtMerge` function as:

         static YYSTYPE
         stmtMerge (YYSTYPE x0, YYSTYPE x1)
         {
           printf ("<OR> ");
           return "";
         }

with an accompanying forward declaration in the C declarations at the beginning of the file:

         %{
           #define YYSTYPE char const *
           static YYSTYPE stmtMerge (YYSTYPE x0, YYSTYPE x1);
         %}

With these declarations, the resulting parser parses the first example as both an `expr` and a `decl`, and prints

         "x" y z + T <init-declare> x T <cast> y z + = <OR>

Bison requires that all of the productions that participate in any particular merge have identical %merge clauses. Otherwise, the ambiguity would be unresolvable, and the parser will report an error during any parse that results in the offending merge.

Previous: Merging GLR Parses, Up: GLR Parsers

#### 1.5.3 Considerations when Compiling GLR Parsers

The GLR parsers require a compiler for ISO C89 or later. In addition, they use the `inline` keyword, which is not C89, but is C99 and is a common extension in pre-C99 compilers. It is up to the user of these parsers to handle portability issues. For instance, if using Autoconf and the Autoconf macro `AC_C_INLINE`, a mere

         %{
           #include <config.h>
         %}

will suffice. Otherwise, we suggest

         %{
           #if __STDC_VERSION__ < 199901 && ! defined __GNUC__ && ! defined inline
            #define inline
           #endif
         %}

Next: Bison Parser, Previous: GLR Parsers, Up: Concepts

### 1.6 Locations

Many applications, like interpreters or compilers, have to produce verbose and useful error messages. To achieve this, one must be able to keep track of the textual location, or location, of each syntactic construct. Bison provides a mechanism for handling these locations.

Each token has a semantic value. In a similar fashion, each token has an associated location, but the type of locations is the same for all tokens and groupings. Moreover, the output parser is equipped with a default data structure for storing locations (see Locations, for more details).

Like semantic values, locations can be reached in actions using a dedicated set of constructs. In the example above, the location of the whole grouping is `@$`, while the locations of the subexpressions are `@1` and `@3`.

When a rule is matched, a default action is used to compute the semantic value of its left hand side (see Actions). In the same way, another default action is used for locations. However, the action for locations is general enough for most cases, meaning there is usually no need to describe for each rule how `@$` should be formed. When building a new location for a given grouping, the default behavior of the output parser is to take the beginning of the first symbol, and the end of the last symbol.

Next: Stages, Previous: Locations Overview, Up: Concepts

### 1.7 Bison Output: the Parser File

When you run Bison, you give it a Bison grammar file as input. The output is a C source file that parses the language described by the grammar. This file is called a Bison parser. Keep in mind that the Bison utility and the Bison parser are two distinct programs: the Bison utility is a program whose output is the Bison parser that becomes part of your program.

The job of the Bison parser is to group tokens into groupings according to the grammar rules—for example, to build identifiers and operators into expressions. As it does this, it runs the actions for the grammar rules it uses.

The tokens come from a function called the lexical analyzer that you must supply in some fashion (such as by writing it in C). The Bison parser calls the lexical analyzer each time it wants a new token. It doesn't know what is “inside” the tokens (though their semantic values may reflect this). Typically the lexical analyzer makes the tokens by parsing characters of text, but Bison does not depend on this. See The Lexical Analyzer Function `yylex`.

The Bison parser file is C code which defines a function named `yyparse` which implements that grammar. This function does not make a complete C program: you must supply some additional functions. One is the lexical analyzer. Another is an error-reporting function which the parser calls to report an error. In addition, a complete C program must start with a function called `main`; you have to provide this, and arrange for it to call `yyparse` or the parser will never run. See Parser C-Language Interface.

Aside from the token type names and the symbols in the actions you write, all symbols defined in the Bison parser file itself begin with yy or YY. This includes interface functions such as the lexical analyzer function `yylex`, the error reporting function `yyerror` and the parser function `yyparse` itself. This also includes numerous identifiers used for internal purposes. Therefore, you should avoid using C identifiers starting with yy or YY in the Bison grammar file except for the ones defined in this manual.

In some cases the Bison parser file includes system headers, and in those cases your code should respect the identifiers reserved by those headers. On some non-GNU hosts, `<alloca.h>`, `<stddef.h>`, and `<stdlib.h>` are included as needed to declare memory allocators and related types. Other system headers may be included if you define `YYDEBUG` to a nonzero value (see Tracing Your Parser).

Next: Grammar Layout, Previous: Bison Parser, Up: Concepts

### 1.8 Stages in Using Bison

The actual language-design process using Bison, from grammar specification to a working compiler or interpreter, has these parts:

1. Formally specify the grammar in a form recognized by Bison (see Bison Grammar Files). For each grammatical rule in the language, describe the action that is to be taken when an instance of that rule is recognized. The action is described by a sequence of C statements.
2. Write a lexical analyzer to process input and pass tokens to the parser. The lexical analyzer may be written by hand in C (see The Lexical Analyzer Function `yylex`). It could also be produced using Lex, but the use of Lex is not discussed in this manual.
3. Write a controlling function that calls the Bison-produced parser.
4. Write error-reporting routines.

To turn this source code as written into a runnable program, you must follow these steps:

1. Run Bison on the grammar to produce the parser.
2. Compile the code output by Bison, as well as any other source files.
3. Link the object files to produce the finished product.

Previous: Stages, Up: Concepts

### 1.9 The Overall Layout of a Bison Grammar

The input file for the Bison utility is a Bison grammar file. The general form of a Bison grammar file is as follows:

         %{
         Prologue
         %}

         Bison declarations

         %%
         Grammar rules
         %%
         Epilogue

The %%, %{ and %} are punctuation that appears in every Bison grammar file to separate the sections.

The prologue may define types and variables used in the actions. You can also use preprocessor commands to define macros used there, and use `#include` to include header files that do any of these things. You need to declare the lexical analyzer `yylex` and the error printer `yyerror` here, along with any other global identifiers used by the actions in the grammar rules.

The Bison declarations declare the names of the terminal and nonterminal symbols, and may also describe operator precedence and the data types of semantic values of various symbols.

The grammar rules define how to construct each nonterminal symbol from its parts.

The epilogue can contain any code you want to use. Often the definitions of functions declared in the prologue go here. In a simple program, all the rest of the program can go here.

Next: Grammar File, Previous: Concepts, Up: Top

## 2 Examples

Now we show and explain three sample programs written using Bison: a reverse polish notation calculator, an algebraic (infix) notation calculator, and a multi-function calculator. All three have been tested under BSD Unix 4.3; each produces a usable, though limited, interactive desk-top calculator.

These examples are simple, but Bison grammars for real programming languages are written the same way.

Next: Infix Calc, Up: Examples

### 2.1 Reverse Polish Notation Calculator

The first example is that of a simple double-precision reverse polish notation calculator (a calculator using postfix operators). This example provides a good starting point, since operator precedence is not an issue. The second example will illustrate how operator precedence is handled.

The source code for this calculator is named rpcalc.y. The .y extension is a convention used for Bison input files.

Next: Rpcalc Rules, Up: RPN Calc

#### 2.1.1 Declarations for `rpcalc`

Here are the C and Bison declarations for the reverse polish notation calculator. As in C, comments are placed between /*...*/.

         /* Reverse polish notation calculator.  */

         %{
           #define YYSTYPE double
           #include <math.h>
           int yylex (void);
           void yyerror (char const *);
         %}

         %token NUM

         %% /* Grammar rules and actions follow.  */

The declarations section (see The prologue) contains two preprocessor directives and two forward declarations.

The `#define` directive defines the macro `YYSTYPE`, thus specifying the C data type for semantic values of both tokens and groupings (see Data Types of Semantic Values). The Bison parser will use whatever type `YYSTYPE` is defined as; if you don't define it, `int` is the default. Because we specify `double`, each token and each expression has an associated value, which is a floating point number.

The `#include` directive is used to declare the exponentiation function `pow`.

The forward declarations for `yylex` and `yyerror` are needed because the C language requires that functions be declared before they are used. These functions will be defined in the epilogue, but the parser calls them so they must be declared in the prologue.

The second section, Bison declarations, provides information to Bison about the token types (see The Bison Declarations Section). Each terminal symbol that is not a single-character literal must be declared here. (Single-character literals normally don't need to be declared.) In this example, all the arithmetic operators are designated by single-character literals, so the only terminal symbol that needs to be declared is `NUM`, the token type for numeric constants.

Next: Rpcalc Lexer, Previous: Rpcalc Decls, Up: RPN Calc

#### 2.1.2 Grammar Rules for `rpcalc`

Here are the grammar rules for the reverse polish notation calculator.

         input:    /* empty */
                 | input line
         ;

         line:     '\n'
                 | exp '\n'      { printf ("\t%.10g\n", $1); }
         ;

         exp:      NUM           { $$ = $1;           }
                 | exp exp '+'   { $$ = $1 + $2;      }
                 | exp exp '-'   { $$ = $1 - $2;      }
                 | exp exp '*'   { $$ = $1 * $2;      }
                 | exp exp '/'   { $$ = $1 / $2;      }
                  /* Exponentiation */
                 | exp exp '^'   { $$ = pow ($1, $2); }
                  /* Unary minus    */
                 | exp 'n'       { $$ = -$1;          }
         ;
         %%

The groupings of the rpcalc “language” defined here are the expression (given the name `exp`), the line of input (`line`), and the complete input transcript (`input`). Each of these nonterminal symbols has several alternate rules, joined by the | punctuator which is read as “or”. The following sections explain what these rules mean.

The semantics of the language is determined by the actions taken when a grouping is recognized. The actions are the C code that appears inside braces. See Actions.

You must specify these actions in C, but Bison provides the means for passing semantic values between the rules. In each action, the pseudo-variable `$$` stands for the semantic value for the grouping that the rule is going to construct. Assigning a value to `$$` is the main job of most actions. The semantic values of the components of the rule are referred to as `$1`, `$2`, and so on.

Next: Rpcalc Line, Up: Rpcalc Rules

##### 2.1.2.1 Explanation of `input`

Consider the definition of `input`:

         input:    /* empty */
                 | input line
         ;

This definition reads as follows: “A complete input is either an empty string, or a complete input followed by an input line”. Notice that “complete input” is defined in terms of itself. This definition is said to be left recursive since `input` appears always as the leftmost symbol in the sequence. See Recursive Rules.

The first alternative is empty because there are no symbols between the colon and the first |; this means that `input` can match an empty string of input (no tokens). We write the rules this way because it is legitimate to type `Ctrl-d` right after you start the calculator. It's conventional to put an empty alternative first and write the comment /* empty */ in it.

The second alternate rule (`input line`) handles all nontrivial input. It means, “After reading any number of lines, read one more line if possible.” The left recursion makes this rule into a loop. Since the first alternative matches empty input, the loop can be executed zero or more times.

The parser function `yyparse` continues to process input until a grammatical error is seen or the lexical analyzer says there are no more input tokens; we will arrange for the latter to happen at end-of-input.

Next: Rpcalc Expr, Previous: Rpcalc Input, Up: Rpcalc Rules

##### 2.1.2.2 Explanation of `line`

Now consider the definition of `line`:

         line:     '\n'
                 | exp '\n'  { printf ("\t%.10g\n", $1); }
         ;

The first alternative is a token which is a newline character; this means that rpcalc accepts a blank line (and ignores it, since there is no action). The second alternative is an expression followed by a newline. This is the alternative that makes rpcalc useful. The semantic value of the `exp` grouping is the value of `$1` because the `exp` in question is the first symbol in the alternative. The action prints this value, which is the result of the computation the user asked for.

This action is unusual because it does not assign a value to `$$`. As a consequence, the semantic value associated with the `line` is uninitialized (its value will be unpredictable). This would be a bug if that value were ever used, but we don't use it: once rpcalc has printed the value of the user's input line, that value is no longer needed.

Previous: Rpcalc Line, Up: Rpcalc Rules

##### 2.1.2.3 Explanation of `expr`

The `exp` grouping has several rules, one for each kind of expression. The first rule handles the simplest expressions: those that are just numbers. The second handles an addition-expression, which looks like two expressions followed by a plus-sign. The third handles subtraction, and so on.

         exp:      NUM
                 | exp exp '+'     { $$ = $1 + $2;    }
                 | exp exp '-'     { $$ = $1 - $2;    }
                 ...
                 ;

We have used | to join all the rules for `exp`, but we could equally well have written them separately:

         exp:      NUM ;
         exp:      exp exp '+'     { $$ = $1 + $2;    } ;
         exp:      exp exp '-'     { $$ = $1 - $2;    } ;
                 ...

Most of the rules have actions that compute the value of the expression in terms of the value of its parts. For example, in the rule for addition, `$1` refers to the first component `exp` and `$2` refers to the second one. The third component, `'+'`, has no meaningful associated semantic value, but if it had one you could refer to it as `$3`. When `yyparse` recognizes a sum expression using this rule, the sum of the two subexpressions' values is produced as the value of the entire expression. See Actions.

You don't have to give an action for every rule. When a rule has no action, Bison by default copies the value of `$1` into `$$`. This is what happens in the first rule (the one that uses `NUM`).

The formatting shown here is the recommended convention, but Bison does not require it. You can add or change white space as much as you wish. For example, this:

         exp   : NUM | exp exp '+' {$$ = $1 + $2; } | ... ;

means the same thing as this:

         exp:      NUM
                 | exp exp '+'    { $$ = $1 + $2; }
                 | ...
         ;

The latter, however, is much more readable.

Next: Rpcalc Main, Previous: Rpcalc Rules, Up: RPN Calc

#### 2.1.3 The `rpcalc` Lexical Analyzer

The lexical analyzer's job is low-level parsing: converting characters or sequences of characters into tokens. The Bison parser gets its tokens by calling the lexical analyzer. See The Lexical Analyzer Function `yylex`.

Only a simple lexical analyzer is needed for the RPN calculator. This lexical analyzer skips blanks and tabs, then reads in numbers as `double` and returns them as `NUM` tokens. Any other character that isn't part of a number is a separate token. Note that the token-code for such a single-character token is the character itself.

The return value of the lexical analyzer function is a numeric code which represents a token type. The same text used in Bison rules to stand for this token type is also a C expression for the numeric code for the type. This works in two ways. If the token type is a character literal, then its numeric code is that of the character; you can use the same character literal in the lexical analyzer to express the number. If the token type is an identifier, that identifier is defined by Bison as a C macro whose definition is the appropriate number. In this example, therefore, `NUM` becomes a macro for `yylex` to use.

The semantic value of the token (if it has one) is stored into the global variable `yylval`, which is where the Bison parser will look for it. (The C data type of `yylval` is `YYSTYPE`, which was defined at the beginning of the grammar; see Declarations for `rpcalc`.)

A token type code of zero is returned if the end-of-input is encountered. (Bison recognizes any nonpositive value as indicating end-of-input.)

Here is the code for the lexical analyzer:

         /* The lexical analyzer returns a double floating point
            number on the stack and the token NUM, or the numeric code
            of the character read if not a number.  It skips all blanks
            and tabs, and returns 0 for end-of-input.  */

         #include <ctype.h>

         int
         yylex (void)
         {
           int c;

           /* Skip white space.  */
           while ((c = getchar ()) == ' ' || c == '\t')
             ;
           /* Process numbers.  */
           if (c == '.' || isdigit (c))
             {
               ungetc (c, stdin);
               scanf ("%lf", &yylval);
               return NUM;
             }
           /* Return end-of-input.  */
           if (c == EOF)
             return 0;
           /* Return a single char.  */
           return c;
         }

Next: Rpcalc Error, Previous: Rpcalc Lexer, Up: RPN Calc

#### 2.1.4 The Controlling Function

In keeping with the spirit of this example, the controlling function is kept to the bare minimum. The only requirement is that it call `yyparse` to start the process of parsing.

         int
         main (void)
         {
           return yyparse ();
         }

Next: Rpcalc Gen, Previous: Rpcalc Main, Up: RPN Calc

#### 2.1.5 The Error Reporting Routine

When `yyparse` detects a syntax error, it calls the error reporting function `yyerror` to print an error message (usually but not always `"syntax error"`). It is up to the programmer to supply `yyerror` (see Parser C-Language Interface), so here is the definition we will use:

         #include <stdio.h>

         /* Called by yyparse on error.  */
         void
         yyerror (char const *s)
         {
           fprintf (stderr, "%s\n", s);
         }

After `yyerror` returns, the Bison parser may recover from the error and continue parsing if the grammar contains a suitable error rule (see Error Recovery). Otherwise, `yyparse` returns nonzero. We have not written any error rules in this example, so any invalid input will cause the calculator program to exit. This is not clean behavior for a real calculator, but it is adequate for the first example.

Next: Rpcalc Compile, Previous: Rpcalc Error, Up: RPN Calc

#### 2.1.6 Running Bison to Make the Parser

Before running Bison to produce a parser, we need to decide how to arrange all the source code in one or more source files. For such a simple example, the easiest thing is to put everything in one file. The definitions of `yylex`, `yyerror` and `main` go at the end, in the epilogue of the file (see The Overall Layout of a Bison Grammar).

For a large project, you would probably have several source files, and use `make` to arrange to recompile them.

With all the source in a single file, you use the following command to convert it into a parser file:

         bison file_name.y

In this example the file was called rpcalc.y (for “Reverse Polish calculator”). Bison produces a file named file_name.tab.c, removing the .y from the original file name. The file output by Bison contains the source code for `yyparse`. The additional functions in the input file (`yylex`, `yyerror` and `main`) are copied verbatim to the output.

Previous: Rpcalc Gen, Up: RPN Calc

#### 2.1.7 Compiling the Parser File

Here is how to compile and run the parser file:

         # List files in current directory.
         $ ls
         rpcalc.tab.c  rpcalc.y

         # Compile the Bison parser.
         # -lm tells compiler to search math library for pow.
         $ cc -lm -o rpcalc rpcalc.tab.c

         # List files again.
         $ ls
         rpcalc  rpcalc.tab.c  rpcalc.y

The file rpcalc now contains the executable code. Here is an example session using `rpcalc`.

         $ rpcalc
         4 9 +
         13
         3 7 + 3 4 5 *+-
         -13
         3 7 + 3 4 5 * + - n              Note the unary minus, n
         13
         5 6 / 4 n +
         -3.166666667
         3 4 ^                            Exponentiation
         81
         ^D                               End-of-file indicator
         $

Next: Simple Error Recovery, Previous: RPN Calc, Up: Examples

### 2.2 Infix Notation Calculator: `calc`

We now modify rpcalc to handle infix operators instead of postfix. Infix notation involves the concept of operator precedence and the need for parentheses nested to arbitrary depth. Here is the Bison code for calc.y, an infix desk-top calculator.

         /* Infix notation calculator.  */

         %{
           #define YYSTYPE double
           #include <math.h>
           #include <stdio.h>
           int yylex (void);
           void yyerror (char const *);
         %}

         /* Bison declarations.  */
         %token NUM
         %left '-' '+'
         %left '*' '/'
         %left NEG     /* negation--unary minus */
         %right '^'    /* exponentiation */

         %% /* The grammar follows.  */
         input:    /* empty */
                 | input line
         ;

         line:     '\n'
                 | exp '\n'  { printf ("\t%.10g\n", $1); }
         ;

         exp:      NUM                { $$ = $1;         }
                 | exp '+' exp        { $$ = $1 + $3;    }
                 | exp '-' exp        { $$ = $1 - $3;    }
                 | exp '*' exp        { $$ = $1 * $3;    }
                 | exp '/' exp        { $$ = $1 / $3;    }
                 | '-' exp  %prec NEG { $$ = -$2;        }
                 | exp '^' exp        { $$ = pow ($1, $3); }
                 | '(' exp ')'        { $$ = $2;         }
         ;
         %%

The functions `yylex`, `yyerror` and `main` can be the same as before.

There are two important new features shown in this code.

In the second section (Bison declarations), `%left` declares token types and says they are left-associative operators. The declarations `%left` and `%right` (right associativity) take the place of `%token` which is used to declare a token type name without associativity. (These tokens are single-character literals, which ordinarily don't need to be declared. We declare them here to specify the associativity.)

Operator precedence is determined by the line ordering of the declarations; the higher the line number of the declaration (lower on the page or screen), the higher the precedence. Hence, exponentiation has the highest precedence, unary minus (`NEG`) is next, followed by * and /, and so on. See Operator Precedence.

The other important new feature is the `%prec` in the grammar section for the unary minus operator. The `%prec` simply instructs Bison that the rule | '-' exp has the same precedence as `NEG`—in this case the next-to-highest. See Context-Dependent Precedence.

Here is a sample run of calc.y:

         $ calc
         4 + 4.5 - (34/(8*3+-3))
         6.880952381
         -56 + 2
         -54
         3 ^ 2
         9

Next: Location Tracking Calc, Previous: Infix Calc, Up: Examples

### 2.3 Simple Error Recovery

Up to this point, this manual has not addressed the issue of error recovery—how to continue parsing after the parser detects a syntax error. All we have handled is error reporting with `yyerror`. Recall that by default `yyparse` returns after calling `yyerror`. This means that an erroneous input line causes the calculator program to exit. Now we show how to rectify this deficiency.

The Bison language itself includes the reserved word `error`, which may be included in the grammar rules. In the example below it has been added to one of the alternatives for `line`:

         line:     '\n'
                 | exp '\n'   { printf ("\t%.10g\n", $1); }
                 | error '\n' { yyerrok;                  }
         ;

This addition to the grammar allows for simple error recovery in the event of a syntax error. If an expression that cannot be evaluated is read, the error will be recognized by the third rule for `line`, and parsing will continue. (The `yyerror` function is still called upon to print its message as well.) The action executes the statement `yyerrok`, a macro defined automatically by Bison; its meaning is that error recovery is complete (see Error Recovery). Note the difference between `yyerrok` and `yyerror`; neither one is a misprint.

This form of error recovery deals with syntax errors. There are other kinds of errors; for example, division by zero, which raises an exception signal that is normally fatal. A real calculator program must handle this signal and use `longjmp` to return to `main` and resume parsing input lines; it would also have to discard the rest of the current line of input. We won't discuss this issue further because it is not specific to Bison programs.

Next: Multi-function Calc, Previous: Simple Error Recovery, Up: Examples

### 2.4 Location Tracking Calculator: `ltcalc`

This example extends the infix notation calculator with location tracking. This feature will be used to improve the error messages. For the sake of clarity, this example is a simple integer calculator, since most of the work needed to use locations will be done in the lexical analyzer.

Next: Ltcalc Rules, Up: Location Tracking Calc

#### 2.4.1 Declarations for `ltcalc`

The C and Bison declarations for the location tracking calculator are the same as the declarations for the infix notation calculator.

         /* Location tracking calculator.  */

         %{
           #define YYSTYPE int
           #include <math.h>
           int yylex (void);
           void yyerror (char const *);
         %}

         /* Bison declarations.  */
         %token NUM

         %left '-' '+'
         %left '*' '/'
         %left NEG
         %right '^'

         %% /* The grammar follows.  */

Note there are no declarations specific to locations. Defining a data type for storing locations is not needed: we will use the type provided by default (see Data Types of Locations), which is a four member structure with the following integer fields: `first_line`, `first_column`, `last_line` and `last_column`.

Next: Ltcalc Lexer, Previous: Ltcalc Decls, Up: Location Tracking Calc

#### 2.4.2 Grammar Rules for `ltcalc`

Whether handling locations or not has no effect on the syntax of your language. Therefore, grammar rules for this example will be very close to those of the previous example: we will only modify them to benefit from the new information.

Here, we will use locations to report divisions by zero, and locate the wrong expressions or subexpressions.

         input   : /* empty */
                 | input line
         ;

         line    : '\n'
                 | exp '\n' { printf ("%d\n", $1); }
         ;

         exp     : NUM           { $$ = $1; }
                 | exp '+' exp   { $$ = $1 + $3; }
                 | exp '-' exp   { $$ = $1 - $3; }
                 | exp '*' exp   { $$ = $1 * $3; }
                 | exp '/' exp
                     {
                       if ($3)
                         $$ = $1 / $3;
                       else
                         {
                           $$ = 1;
                           fprintf (stderr, "%d.%d-%d.%d: division by zero",
                                    @3.first_line, @3.first_column,
                                    @3.last_line, @3.last_column);
                         }
                     }
                 | '-' exp %preg NEG     { $$ = -$2; }
                 | exp '^' exp           { $$ = pow ($1, $3); }
                 | '(' exp ')'           { $$ = $2; }

This code shows how to reach locations inside of semantic actions, by using the pseudo-variables `@`n for rule components, and the pseudo-variable `@$` for groupings.

We don't need to assign a value to `@$`: the output parser does it automatically. By default, before executing the C code of each action, `@$` is set to range from the beginning of `@1` to the end of `@`n, for a rule with n components. This behavior can be redefined (see Default Action for Locations), and for very specific rules, `@$` can be computed by hand.

Previous: Ltcalc Rules, Up: Location Tracking Calc

#### 2.4.3 The `ltcalc` Lexical Analyzer.

Until now, we relied on Bison's defaults to enable location tracking. The next step is to rewrite the lexical analyzer, and make it able to feed the parser with the token locations, as it already does for semantic values.

To this end, we must take into account every single character of the input text, to avoid the computed locations of being fuzzy or wrong:

         int
         yylex (void)
         {
           int c;

           /* Skip white space.  */
           while ((c = getchar ()) == ' ' || c == '\t')
             ++yylloc.last_column;

           /* Step.  */
           yylloc.first_line = yylloc.last_line;
           yylloc.first_column = yylloc.last_column;

           /* Process numbers.  */
           if (isdigit (c))
             {
               yylval = c - '0';
               ++yylloc.last_column;
               while (isdigit (c = getchar ()))
                 {
                   ++yylloc.last_column;
                   yylval = yylval * 10 + c - '0';
                 }
               ungetc (c, stdin);
               return NUM;
             }

           /* Return end-of-input.  */
           if (c == EOF)
             return 0;

           /* Return a single char, and update location.  */
           if (c == '\n')
             {
               ++yylloc.last_line;
               yylloc.last_column = 0;
             }
           else
             ++yylloc.last_column;
           return c;
         }

Basically, the lexical analyzer performs the same processing as before: it skips blanks and tabs, and reads numbers or single-character tokens. In addition, it updates `yylloc`, the global variable (of type `YYLTYPE`) containing the token's location.

Now, each time this function returns a token, the parser has its number as well as its semantic value, and its location in the text. The last needed change is to initialize `yylloc`, for example in the controlling function:

         int
         main (void)
         {
           yylloc.first_line = yylloc.last_line = 1;
           yylloc.first_column = yylloc.last_column = 0;
           return yyparse ();
         }

Remember that computing locations is not a matter of syntax. Every character must be associated to a location update, whether it is in valid input, in comments, in literal strings, and so on.

Next: Exercises, Previous: Location Tracking Calc, Up: Examples

### 2.5 Multi-Function Calculator: `mfcalc`

Now that the basics of Bison have been discussed, it is time to move on to a more advanced problem. The above calculators provided only five functions, +, -, *, / and ^. It would be nice to have a calculator that provides other mathematical functions such as `sin`, `cos`, etc.

It is easy to add new operators to the infix calculator as long as they are only single-character literals. The lexical analyzer `yylex` passes back all nonnumber characters as tokens, so new grammar rules suffice for adding a new operator. But we want something more flexible: built-in functions whose syntax has this form:

         function_name (argument)

At the same time, we will add memory to the calculator, by allowing you to create named variables, store values in them, and use them later. Here is a sample session with the multi-function calculator:

         $ mfcalc
         pi = 3.141592653589
         3.1415926536
         sin(pi)
         0.0000000000
         alpha = beta1 = 2.3
         2.3000000000
         alpha
         2.3000000000
         ln(alpha)
         0.8329091229
         exp(ln(beta1))
         2.3000000000
         $

Note that multiple assignment and nested function calls are permitted.

Next: Mfcalc Rules, Up: Multi-function Calc

#### 2.5.1 Declarations for `mfcalc`

Here are the C and Bison declarations for the multi-function calculator.

         %{
           #include <math.h>  /* For math functions, cos(), sin(), etc.  */
           #include "calc.h"  /* Contains definition of `symrec'.  */
           int yylex (void);
           void yyerror (char const *);
         %}
         %union {
           double    val;   /* For returning numbers.  */
           symrec  *tptr;   /* For returning symbol-table pointers.  */
         }
         %token <val>  NUM        /* Simple double precision number.  */
         %token <tptr> VAR FNCT   /* Variable and Function.  */
         %type  <val>  exp

         %right '='
         %left '-' '+'
         %left '*' '/'
         %left NEG     /* negation--unary minus */
         %right '^'    /* exponentiation */
         %% /* The grammar follows.  */

The above grammar introduces only two new features of the Bison language. These features allow semantic values to have various data types (see More Than One Value Type).

The `%union` declaration specifies the entire list of possible types; this is instead of defining `YYSTYPE`. The allowable types are now double-floats (for `exp` and `NUM`) and pointers to entries in the symbol table. See The Collection of Value Types.

Since values can now have various types, it is necessary to associate a type with each grammar symbol whose semantic value is used. These symbols are `NUM`, `VAR`, `FNCT`, and `exp`. Their declarations are augmented with information about their data type (placed between angle brackets).

The Bison construct `%type` is used for declaring nonterminal symbols, just as `%token` is used for declaring token types. We have not used `%type` before because nonterminal symbols are normally declared implicitly by the rules that define them. But `exp` must be declared explicitly so we can specify its value type. See Nonterminal Symbols.

Next: Mfcalc Symtab, Previous: Mfcalc Decl, Up: Multi-function Calc

#### 2.5.2 Grammar Rules for `mfcalc`

Here are the grammar rules for the multi-function calculator. Most of them are copied directly from `calc`; three rules, those which mention `VAR` or `FNCT`, are new.

         input:   /* empty */
                 | input line
         ;

         line:
                   '\n'
                 | exp '\n'   { printf ("\t%.10g\n", $1); }
                 | error '\n' { yyerrok;                  }
         ;

         exp:      NUM                { $$ = $1;                         }
                 | VAR                { $$ = $1->value.var;              }
                 | VAR '=' exp        { $$ = $3; $1->value.var = $3;     }
                 | FNCT '(' exp ')'   { $$ = (*($1->value.fnctptr))($3); }
                 | exp '+' exp        { $$ = $1 + $3;                    }
                 | exp '-' exp        { $$ = $1 - $3;                    }
                 | exp '*' exp        { $$ = $1 * $3;                    }
                 | exp '/' exp        { $$ = $1 / $3;                    }
                 | '-' exp  %prec NEG { $$ = -$2;                        }
                 | exp '^' exp        { $$ = pow ($1, $3);               }
                 | '(' exp ')'        { $$ = $2;                         }
         ;
         /* End of grammar.  */
         %%

Previous: Mfcalc Rules, Up: Multi-function Calc

#### 2.5.3 The `mfcalc` Symbol Table

The multi-function calculator requires a symbol table to keep track of the names and meanings of variables and functions. This doesn't affect the grammar rules (except for the actions) or the Bison declarations, but it requires some additional C functions for support.

The symbol table itself consists of a linked list of records. Its definition, which is kept in the header calc.h, is as follows. It provides for either functions or variables to be placed in the table.

         /* Function type.  */
         typedef double (*func_t) (double);

         /* Data type for links in the chain of symbols.  */
         struct symrec
         {
           char *name;  /* name of symbol */
           int type;    /* type of symbol: either VAR or FNCT */
           union
           {
             double var;      /* value of a VAR */
             func_t fnctptr;  /* value of a FNCT */
           } value;
           struct symrec *next;  /* link field */
         };

         typedef struct symrec symrec;

         /* The symbol table: a chain of `struct symrec'.  */
         extern symrec *sym_table;

         symrec *putsym (char const *, func_t);
         symrec *getsym (char const *);

The new version of `main` includes a call to `init_table`, a function that initializes the symbol table. Here it is, and `init_table` as well:

         #include <stdio.h>

         /* Called by yyparse on error.  */
         void
         yyerror (char const *s)
         {
           printf ("%s\n", s);
         }

         struct init
         {
           char const *fname;
           double (*fnct) (double);
         };

         struct init const arith_fncts[] =
         {
           "sin",  sin,
           "cos",  cos,
           "atan", atan,
           "ln",   log,
           "exp",  exp,
           "sqrt", sqrt,
           0, 0
         };

         /* The symbol table: a chain of `struct symrec'.  */
         symrec *sym_table;

         /* Put arithmetic functions in table.  */
         void
         init_table (void)
         {
           int i;
           symrec *ptr;
           for (i = 0; arith_fncts[i].fname != 0; i++)
             {
               ptr = putsym (arith_fncts[i].fname, FNCT);
               ptr->value.fnctptr = arith_fncts[i].fnct;
             }
         }

         int
         main (void)
         {
           init_table ();
           return yyparse ();
         }

By simply editing the initialization list and adding the necessary include files, you can add additional functions to the calculator.

Two important functions allow look-up and installation of symbols in the symbol table. The function `putsym` is passed a name and the type (`VAR` or `FNCT`) of the object to be installed. The object is linked to the front of the list, and a pointer to the object is returned. The function `getsym` is passed the name of the symbol to look up. If found, a pointer to that symbol is returned; otherwise zero is returned.

         symrec *
         putsym (char const *sym_name, int sym_type)
         {
           symrec *ptr;
           ptr = (symrec *) malloc (sizeof (symrec));
           ptr->name = (char *) malloc (strlen (sym_name) + 1);
           strcpy (ptr->name,sym_name);
           ptr->type = sym_type;
           ptr->value.var = 0; /* Set value to 0 even if fctn.  */
           ptr->next = (struct symrec *)sym_table;
           sym_table = ptr;
           return ptr;
         }

         symrec *
         getsym (char const *sym_name)
         {
           symrec *ptr;
           for (ptr = sym_table; ptr != (symrec *) 0;
                ptr = (symrec *)ptr->next)
             if (strcmp (ptr->name,sym_name) == 0)
               return ptr;
           return 0;
         }

The function `yylex` must now recognize variables, numeric values, and the single-character arithmetic operators. Strings of alphanumeric characters with a leading non-digit are recognized as either variables or functions depending on what the symbol table says about them.

The string is passed to `getsym` for look up in the symbol table. If the name appears in the table, a pointer to its location and its type (`VAR` or `FNCT`) is returned to `yyparse`. If it is not already in the table, then it is installed as a `VAR` using `putsym`. Again, a pointer and its type (which must be `VAR`) is returned to `yyparse`.

No change is needed in the handling of numeric values and arithmetic operators in `yylex`.

         #include <ctype.h>

         int
         yylex (void)
         {
           int c;

           /* Ignore white space, get first nonwhite character.  */
           while ((c = getchar ()) == ' ' || c == '\t');

           if (c == EOF)
             return 0;

           /* Char starts a number => parse the number.         */
           if (c == '.' || isdigit (c))
             {
               ungetc (c, stdin);
               scanf ("%lf", &yylval.val);
               return NUM;
             }

           /* Char starts an identifier => read the name.       */
           if (isalpha (c))
             {
               symrec *s;
               static char *symbuf = 0;
               static int length = 0;
               int i;

               /* Initially make the buffer long enough
                  for a 40-character symbol name.  */
               if (length == 0)
                 length = 40, symbuf = (char *)malloc (length + 1);

               i = 0;
               do
                 {
                   /* If buffer is full, make it bigger.        */
                   if (i == length)
                     {
                       length *= 2;
                       symbuf = (char *) realloc (symbuf, length + 1);
                     }
                   /* Add this character to the buffer.         */
                   symbuf[i++] = c;
                   /* Get another character.                    */
                   c = getchar ();
                 }
               while (isalnum (c));

               ungetc (c, stdin);
               symbuf[i] = '\0';

               s = getsym (symbuf);
               if (s == 0)
                 s = putsym (symbuf, VAR);
               yylval.tptr = s;
               return s->type;
             }

           /* Any other character is a token by itself.        */
           return c;
         }

This program is both powerful and flexible. You may easily add new functions, and it is a simple job to modify this code to install predefined variables such as `pi` or `e` as well.

Previous: Multi-function Calc, Up: Examples

### 2.6 Exercises

1. Add some new functions from math.h to the initialization list.
2. Add another array that contains constants and their values. Then modify `init_table` to add these constants to the symbol table. It will be easiest to give the constants type `VAR`.
3. Make the program report an error if the user refers to an uninitialized variable in any way except to store a value in it.

Next: Interface, Previous: Examples, Up: Top

## 3 Bison Grammar Files

Bison takes as input a context-free grammar specification and produces a C-language function that recognizes correct instances of the grammar.

The Bison grammar input file conventionally has a name ending in .y. See Invoking Bison.

Next: Symbols, Up: Grammar File

### 3.1 Outline of a Bison Grammar

A Bison grammar file has four main sections, shown here with the appropriate delimiters:

         %{
           Prologue
         %}

         Bison declarations

         %%
         Grammar rules
         %%

         Epilogue

Comments enclosed in /* ... */ may appear in any of the sections. As a GNU extension, // introduces a comment that continues until end of line.

Next: Bison Declarations, Up: Grammar Outline

#### 3.1.1 The prologue

The Prologue section contains macro definitions and declarations of functions and variables that are used in the actions in the grammar rules. These are copied to the beginning of the parser file so that they precede the definition of `yyparse`. You can use #include to get the declarations from a header file. If you don't need any C declarations, you may omit the %{ and %} delimiters that bracket this section.

You may have more than one Prologue section, intermixed with the Bison declarations. This allows you to have C and Bison declarations that refer to each other. For example, the `%union` declaration may use types defined in a header file, and you may wish to prototype functions that take arguments of type `YYSTYPE`. This can be done with two Prologue blocks, one before and one after the `%union` declaration.

         %{
           #include <stdio.h>
           #include "ptypes.h"
         %}

         %union {
           long int n;
           tree t;  /* tree is defined in ptypes.h. */
         }

         %{
           static void print_token_value (FILE *, int, YYSTYPE);
           #define YYPRINT(F, N, L) print_token_value (F, N, L)
         %}

         ...

Next: Grammar Rules, Previous: Prologue, Up: Grammar Outline

#### 3.1.2 The Bison Declarations Section

The Bison declarations section contains declarations that define terminal and nonterminal symbols, specify precedence, and so on. In some simple grammars you may not need any declarations. See Bison Declarations.

Next: Epilogue, Previous: Bison Declarations, Up: Grammar Outline

#### 3.1.3 The Grammar Rules Section

The grammar rules section contains one or more Bison grammar rules, and nothing else. See Syntax of Grammar Rules.

There must always be at least one grammar rule, and the first %% (which precedes the grammar rules) may never be omitted even if it is the first thing in the file.

Previous: Grammar Rules, Up: Grammar Outline

#### 3.1.4 The epilogue

The Epilogue is copied verbatim to the end of the parser file, just as the Prologue is copied to the beginning. This is the most convenient place to put anything that you want to have in the parser file but which need not come before the definition of `yyparse`. For example, the definitions of `yylex` and `yyerror` often go here. Because C requires functions to be declared before being used, you often need to declare functions like `yylex` and `yyerror` in the Prologue, even if you define them int he Epilogue. See Parser C-Language Interface.

If the last section is empty, you may omit the %% that separates it from the grammar rules.

The Bison parser itself contains many macros and identifiers whose names start with yy or YY, so it is a good idea to avoid using any such names (except those documented in this manual) in the epilogue of the grammar file.

Next: Rules, Previous: Grammar Outline, Up: Grammar File

### 3.2 Symbols, Terminal and Nonterminal

Symbols in Bison grammars represent the grammatical classifications of the language.

A terminal symbol (also known as a token type) represents a class of syntactically equivalent tokens. You use the symbol in grammar rules to mean that a token in that class is allowed. The symbol is represented in the Bison parser by a numeric code, and the `yylex` function returns a token type code to indicate what kind of token has been read. You don't need to know what the code value is; you can use the symbol to stand for it.

A nonterminal symbol stands for a class of syntactically equivalent groupings. The symbol name is used in writing grammar rules. By convention, it should be all lower case.

Symbol names can contain letters, digits (not at the beginning), underscores and periods. Periods make sense only in nonterminals.

There are three ways of writing terminal symbols in the grammar:

- A named token type is written with an identifier, like an identifier in C. By convention, it should be all upper case. Each such name must be defined with a Bison declaration such as `%token`. See Token Type Names.
- A character token type (or literal character token) is written in the grammar using the same syntax used in C for character constants; for example, `'+'` is a character token type. A character token type doesn't need to be declared unless you need to specify its semantic value data type (see Data Types of Semantic Values), associativity, or precedence (see Operator Precedence).

  By convention, a character token type is used only to represent a token that consists of that particular character. Thus, the token type `'+'` is used to represent the character + as a token. Nothing enforces this convention, but if you depart from it, your program will confuse other readers.

  All the usual escape sequences used in character literals in C can be used in Bison as well, but you must not use the null character as a character literal because its numeric code, zero, signifies end-of-input (see Calling Convention for `yylex`). Also, unlike standard C, trigraphs have no special meaning in Bison character literals, nor is backslash-newline allowed.

- A literal string token is written like a C string constant; for example, `"<="` is a literal string token. A literal string token doesn't need to be declared unless you need to specify its semantic value data type (see Value Type), associativity, or precedence (see Precedence).

  You can associate the literal string token with a symbolic name as an alias, using the `%token` declaration (see Token Declarations). If you don't do that, the lexical analyzer has to retrieve the token number for the literal string token from the `yytname` table (see Calling Convention).

  Warning: literal string tokens do not work in Yacc.

  By convention, a literal string token is used only to represent a token that consists of that particular string. Thus, you should use the token type `"<="` to represent the string <= as a token. Bison does not enforce this convention, but if you depart from it, people who read your program will be confused.

  All the escape sequences used in string literals in C can be used in Bison as well, except that you must not use a null character within a string literal. Also, unlike Standard C, trigraphs have no special meaning in Bison string literals, nor is backslash-newline allowed. A literal string token must contain two or more characters; for a token containing just one character, use a character token (see above).

How you choose to write a terminal symbol has no effect on its grammatical meaning. That depends only on where it appears in rules and on when the parser function returns that symbol.

The value returned by `yylex` is always one of the terminal symbols, except that a zero or negative value signifies end-of-input. Whichever way you write the token type in the grammar rules, you write it the same way in the definition of `yylex`. The numeric code for a character token type is simply the positive numeric code of the character, so `yylex` can use the identical value to generate the requisite code, though you may need to convert it to `unsigned char` to avoid sign-extension on hosts where `char` is signed. Each named token type becomes a C macro in the parser file, so `yylex` can use the name to stand for the code. (This is why periods don't make sense in terminal symbols.) See Calling Convention for `yylex`.

If `yylex` is defined in a separate file, you need to arrange for the token-type macro definitions to be available there. Use the -d option when you run Bison, so that it will write these macro definitions into a separate header file name.tab.h which you can include in the other source files that need it. See Invoking Bison.

If you want to write a grammar that is portable to any Standard C host, you must use only non-null character tokens taken from the basic execution character set of Standard C. This set consists of the ten digits, the 52 lower- and upper-case English letters, and the characters in the following C-language string:

         "\a\b\t\n\v\f\r !\"#%&'()*+,-./:;<=>?[\\]^_{|}~"

The `yylex` function and Bison must use a consistent character set and encoding for character tokens. For example, if you run Bison in an ASCII environment, but then compile and run the resulting program in an environment that uses an incompatible character set like EBCDIC, the resulting program may not work because the tables generated by Bison will assume ASCII numeric values for character tokens. It is standard practice for software distributions to contain C source files that were generated by Bison in an ASCII environment, so installers on platforms that are incompatible with ASCII must rebuild those files before compiling them.

The symbol `error` is a terminal symbol reserved for error recovery (see Error Recovery); you shouldn't use it for any other purpose. In particular, `yylex` should never return this value. The default value of the error token is 256, unless you explicitly assigned 256 to one of your tokens with a `%token` declaration.

Next: Recursion, Previous: Symbols, Up: Grammar File

### 3.3 Syntax of Grammar Rules

A Bison grammar rule has the following general form:

         result: components...
                 ;

where result is the nonterminal symbol that this rule describes, and components are various terminal and nonterminal symbols that are put together by this rule (see Symbols).

For example,

         exp:      exp '+' exp
                 ;

says that two groupings of type `exp`, with a + token in between, can be combined into a larger grouping of type `exp`.

White space in rules is significant only to separate symbols. You can add extra white space as you wish.

Scattered among the components can be actions that determine the semantics of the rule. An action looks like this:

         {C statements}

Usually there is only one action and it follows the components. See Actions.

Multiple rules for the same result can be written separately or can be joined with the vertical-bar character | as follows:

They are still considered distinct rules even when joined in this way.

If components in a rule is empty, it means that result can match the empty string. For example, here is how to define a comma-separated sequence of zero or more `exp` groupings:

         expseq:   /* empty */
                 | expseq1
                 ;

         expseq1:  exp
                 | expseq1 ',' exp
                 ;

It is customary to write a comment /* empty */ in each rule with no components.

Next: Semantics, Previous: Rules, Up: Grammar File

### 3.4 Recursive Rules

A rule is called recursive when its result nonterminal appears also on its right hand side. Nearly all Bison grammars need to use recursion, because that is the only way to define a sequence of any number of a particular thing. Consider this recursive definition of a comma-separated sequence of one or more expressions:

         expseq1:  exp
                 | expseq1 ',' exp
                 ;

Since the recursive use of `expseq1` is the leftmost symbol in the right hand side, we call this left recursion. By contrast, here the same construct is defined using right recursion:

         expseq1:  exp
                 | exp ',' expseq1
                 ;

Any kind of sequence can be defined using either left recursion or right recursion, but you should always use left recursion, because it can parse a sequence of any number of elements with bounded stack space. Right recursion uses up space on the Bison stack in proportion to the number of elements in the sequence, because all the elements must be shifted onto the stack before the rule can be applied even once. See The Bison Parser Algorithm, for further explanation of this.

Indirect or mutual recursion occurs when the result of the rule does not appear directly on its right hand side, but does appear in rules for other nonterminals which do appear on its right hand side.

For example:

         expr:     primary
                 | primary '+' primary
                 ;

         primary:  constant
                 | '(' expr ')'
                 ;

defines two mutually-recursive nonterminals, since each refers to the other.

Next: Locations, Previous: Recursion, Up: Grammar File

### 3.5 Defining Language Semantics

The grammar rules for a language determine only the syntax. The semantics are determined by the semantic values associated with various tokens and groupings, and by the actions taken when various groupings are recognized.

For example, the calculator calculates properly because the value associated with each expression is the proper number; it adds properly because the action for the grouping x + y is to add the numbers associated with x and y.

Next: Multiple Types, Up: Semantics

#### 3.5.1 Data Types of Semantic Values

In a simple program it may be sufficient to use the same data type for the semantic values of all language constructs. This was true in the RPN and infix calculator examples (see Reverse Polish Notation Calculator).

Bison's default is to use type `int` for all semantic values. To specify some other type, define `YYSTYPE` as a macro, like this:

         #define YYSTYPE double

This macro definition must go in the prologue of the grammar file (see Outline of a Bison Grammar).

Next: Actions, Previous: Value Type, Up: Semantics

#### 3.5.2 More Than One Value Type

In most programs, you will need different data types for different kinds of tokens and groupings. For example, a numeric constant may need type `int` or `long int`, while a string constant needs type `char *`, and an identifier might need a pointer to an entry in the symbol table.

To use more than one data type for semantic values in one parser, Bison requires you to do two things:

- Specify the entire collection of possible data types, with the `%union` Bison declaration (see The Collection of Value Types).
- Choose one of those types for each symbol (terminal or nonterminal) for which semantic values are used. This is done for tokens with the `%token` Bison declaration (see Token Type Names) and for groupings with the `%type` Bison declaration (see Nonterminal Symbols).

Next: Action Types, Previous: Multiple Types, Up: Semantics

#### 3.5.3 Actions

An action accompanies a syntactic rule and contains C code to be executed each time an instance of that rule is recognized. The task of most actions is to compute a semantic value for the grouping built by the rule from the semantic values associated with tokens or smaller groupings.

An action consists of C statements surrounded by braces, much like a compound statement in C. An action can contain any sequence of C statements. Bison does not look for trigraphs, though, so if your C code uses trigraphs you should ensure that they do not affect the nesting of braces or the boundaries of comments, strings, or character literals.

An action can be placed at any position in the rule; it is executed at that position. Most rules have just one action at the end of the rule, following all the components. Actions in the middle of a rule are tricky and used only for special purposes (see Actions in Mid-Rule).

The C code in an action can refer to the semantic values of the components matched by the rule with the construct `$`n, which stands for the value of the nth component. The semantic value for the grouping being constructed is `$$`. Bison translates both of these constructs into expressions of the appropriate type when it copies the actions into the parser file. `$$` is translated to a modifiable lvalue, so it can be assigned to.

Here is a typical example:

         exp:    ...
                 | exp '+' exp
                     { $$ = $1 + $3; }

This rule constructs an `exp` from two smaller `exp` groupings connected by a plus-sign token. In the action, `$1` and `$3` refer to the semantic values of the two component `exp` groupings, which are the first and third symbols on the right hand side of the rule. The sum is stored into `$$` so that it becomes the semantic value of the addition-expression just recognized by the rule. If there were a useful semantic value associated with the + token, it could be referred to as `$2`.

Note that the vertical-bar character | is really a rule separator, and actions are attached to a single rule. This is a difference with tools like Flex, for which | stands for either “or”, or “the same action as that of the next rule”. In the following example, the action is triggered only when b is found:

         a-or-b: 'a'|'b'   { a_or_b_found = 1; };

If you don't specify an action for a rule, Bison supplies a default: `$$ = $1`. Thus, the value of the first symbol in the rule becomes the value of the whole rule. Of course, the default action is valid only if the two data types match. There is no meaningful default action for an empty rule; every empty rule must have an explicit action unless the rule's value does not matter.

`$`n with n zero or negative is allowed for reference to tokens and groupings on the stack before those that match the current rule. This is a very risky practice, and to use it reliably you must be certain of the context in which the rule is applied. Here is a case in which you can use this reliably:

         foo:      expr bar '+' expr  { ... }
                 | expr bar '-' expr  { ... }
                 ;

         bar:      /* empty */
                 { previous_expr = $0; }
                 ;

As long as `bar` is used only in the fashion shown here, `$0` always refers to the `expr` which precedes `bar` in the definition of `foo`.

Next: Mid-Rule Actions, Previous: Actions, Up: Semantics

#### 3.5.4 Data Types of Values in Actions

If you have chosen a single data type for semantic values, the `$$` and `$`n constructs always have that data type.

If you have used `%union` to specify a variety of data types, then you must declare a choice among these types for each terminal or nonterminal symbol that can have a semantic value. Then each time you use `$$` or `$`n, its data type is determined by which symbol it refers to in the rule. In this example,

         exp:    ...
                 | exp '+' exp
                     { $$ = $1 + $3; }

`$1` and `$3` refer to instances of `exp`, so they all have the data type declared for the nonterminal symbol `exp`. If `$2` were used, it would have the data type declared for the terminal symbol `'+'`, whatever that might be.

Alternatively, you can specify the data type when you refer to the value, by inserting <type> after the $ at the beginning of the reference. For example, if you have defined types as shown here:

         %union {
           int itype;
           double dtype;
         }

then you can write `$<itype>1` to refer to the first subunit of the rule as an integer, or `$<dtype>1` to refer to it as a double.

Previous: Action Types, Up: Semantics

#### 3.5.5 Actions in Mid-Rule

Occasionally it is useful to put an action in the middle of a rule. These actions are written just like usual end-of-rule actions, but they are executed before the parser even recognizes the following components.

A mid-rule action may refer to the components preceding it using `$`n, but it may not refer to subsequent components because it is run before they are parsed.

The mid-rule action itself counts as one of the components of the rule. This makes a difference when there is another action later in the same rule (and usually there is another at the end): you have to count the actions along with the symbols when working out which number n to use in `$`n.

The mid-rule action can also have a semantic value. The action can set its value with an assignment to `$$`, and actions later in the rule can refer to the value using `$`n. Since there is no symbol to name the action, there is no way to declare a data type for the value in advance, so you must use the $<...>n construct to specify a data type each time you refer to this value.

There is no way to set the value of the entire rule with a mid-rule action, because assignments to `$$` do not have that effect. The only way to set the value for the entire rule is with an ordinary action at the end of the rule.

Here is an example from a hypothetical compiler, handling a `let` statement that looks like let (variable) statement and serves to create a variable named variable temporarily for the duration of statement. To parse this construct, we must put variable into the symbol table while statement is parsed, then remove it afterward. Here is how it is done:

         stmt:   LET '(' var ')'
                         { $<context>$ = push_context ();
                           declare_variable ($3); }
                 stmt    { $$ = $6;
                           pop_context ($<context>5); }

As soon as let (variable) has been recognized, the first action is run. It saves a copy of the current semantic context (the list of accessible variables) as its semantic value, using alternative `context` in the data-type union. Then it calls `declare_variable` to add the new variable to that list. Once the first action is finished, the embedded statement `stmt` can be parsed. Note that the mid-rule action is component number 5, so the stmt is component number 6.

After the embedded statement is parsed, its semantic value becomes the value of the entire `let`-statement. Then the semantic value from the earlier action is used to restore the prior list of variables. This removes the temporary `let`-variable from the list so that it won't appear to exist while the rest of the program is parsed.

Taking action before a rule is completely recognized often leads to conflicts since the parser must commit to a parse in order to execute the action. For example, the following two rules, without mid-rule actions, can coexist in a working parser because the parser can shift the open-brace token and look at what follows before deciding whether there is a declaration or not:

         compound: '{' declarations statements '}'
                 | '{' statements '}'
                 ;

But when we add a mid-rule action as follows, the rules become nonfunctional:

         compound: { prepare_for_local_variables (); }
                   '{' declarations statements '}'
                 | '{' statements '}'
                 ;

Now the parser is forced to decide whether to run the mid-rule action when it has read no farther than the open-brace. In other words, it must commit to using one rule or the other, without sufficient information to do it correctly. (The open-brace token is what is called the look-ahead token at this time, since the parser is still deciding what to do about it. See Look-Ahead Tokens.)

You might think that you could correct the problem by putting identical actions into the two rules, like this:

         compound: { prepare_for_local_variables (); }
                   '{' declarations statements '}'
                 | { prepare_for_local_variables (); }
                   '{' statements '}'
                 ;

But this does not help, because Bison does not realize that the two actions are identical. (Bison never tries to understand the C code in an action.)

If the grammar is such that a declaration can be distinguished from a statement by the first token (which is true in C), then one solution which does work is to put the action after the open-brace, like this:

         compound: '{' { prepare_for_local_variables (); }
                   declarations statements '}'
                 | '{' statements '}'
                 ;

Now the first token of the following declaration or statement, which would in any case tell Bison which rule to use, can still do so.

Another solution is to bury the action inside a nonterminal symbol which serves as a subroutine:

         subroutine: /* empty */
                   { prepare_for_local_variables (); }
                 ;

         compound: subroutine
                   '{' declarations statements '}'
                 | subroutine
                   '{' statements '}'
                 ;

Now Bison can execute the action in the rule for `subroutine` without deciding which rule for `compound` it will eventually use. Note that the action is now at the end of its rule. Any mid-rule action can be converted to an end-of-rule action in this way, and this is what Bison actually does to implement mid-rule actions.

Next: Declarations, Previous: Semantics, Up: Grammar File

### 3.6 Tracking Locations

Though grammar rules and semantic actions are enough to write a fully functional parser, it can be useful to process some additional information, especially symbol locations.

The way locations are handled is defined by providing a data type, and actions to take when rules are matched.

Next: Actions and Locations, Up: Locations

#### 3.6.1 Data Type of Locations

Defining a data type for locations is much simpler than for semantic values, since all tokens and groupings always use the same type.

The type of locations is specified by defining a macro called `YYLTYPE`. When `YYLTYPE` is not defined, Bison uses a default structure type with four members:

         typedef struct YYLTYPE
         {
           int first_line;
           int first_column;
           int last_line;
           int last_column;
         } YYLTYPE;

Next: Location Default Action, Previous: Location Type, Up: Locations

#### 3.6.2 Actions and Locations

Actions are not only useful for defining language semantics, but also for describing the behavior of the output parser with locations.

The most obvious way for building locations of syntactic groupings is very similar to the way semantic values are computed. In a given rule, several constructs can be used to access the locations of the elements being matched. The location of the nth component of the right hand side is `@`n, while the location of the left hand side grouping is `@$`.

Here is a basic example using the default data type for locations:

         exp:    ...
                 | exp '/' exp
                     {
                       @$.first_column = @1.first_column;
                       @$.first_line = @1.first_line;
                       @$.last_column = @3.last_column;
                       @$.last_line = @3.last_line;
                       if ($3)
                         $$ = $1 / $3;
                       else
                         {
                           $$ = 1;
                           fprintf (stderr,
                                    "Division by zero, l%d,c%d-l%d,c%d",
                                    @3.first_line, @3.first_column,
                                    @3.last_line, @3.last_column);
                         }
                     }

As for semantic values, there is a default action for locations that is run each time a rule is matched. It sets the beginning of `@$` to the beginning of the first symbol, and the end of `@$` to the end of the last symbol.

With this default action, the location tracking can be fully automatic. The example above simply rewrites this way:

         exp:    ...
                 | exp '/' exp
                     {
                       if ($3)
                         $$ = $1 / $3;
                       else
                         {
                           $$ = 1;
                           fprintf (stderr,
                                    "Division by zero, l%d,c%d-l%d,c%d",
                                    @3.first_line, @3.first_column,
                                    @3.last_line, @3.last_column);
                         }
                     }

Previous: Actions and Locations, Up: Locations

#### 3.6.3 Default Action for Locations

Actually, actions are not the best place to compute locations. Since locations are much more general than semantic values, there is room in the output parser to redefine the default action to take for each rule. The `YYLLOC_DEFAULT` macro is invoked each time a rule is matched, before the associated action is run. It is also invoked while processing a syntax error, to compute the error's location.

Most of the time, this macro is general enough to suppress location dedicated code from semantic actions.

The `YYLLOC_DEFAULT` macro takes three parameters. The first one is the location of the grouping (the result of the computation). When a rule is matched, the second parameter identifies locations of all right hand side elements of the rule being matched, and the third parameter is the size of the rule's right hand side. When processing a syntax error, the second parameter identifies locations of the symbols that were discarded during error processing, and the third parameter is the number of discarded symbols.

By default, `YYLLOC_DEFAULT` is defined this way:

         # define YYLLOC_DEFAULT(Current, Rhs, N)                                \
             do                                                                  \
               if (N)                                                            \
                 {                                                               \
                   (Current).first_line   = YYRHSLOC(Rhs, 1).first_line;         \
                   (Current).first_column = YYRHSLOC(Rhs, 1).first_column;       \
                   (Current).last_line    = YYRHSLOC(Rhs, N).last_line;          \
                   (Current).last_column  = YYRHSLOC(Rhs, N).last_column;        \
                 }                                                               \
               else                                                              \
                 {                                                               \
                   (Current).first_line   = (Current).last_line   =              \
                     YYRHSLOC(Rhs, 0).last_line;                                 \
                   (Current).first_column = (Current).last_column =              \
                     YYRHSLOC(Rhs, 0).last_column;                               \
                 }                                                               \
             while (0)

where `YYRHSLOC (rhs, k)` is the location of the kth symbol in rhs when k is positive, and the location of the symbol just before the reduction when k and n are both zero.

When defining `YYLLOC_DEFAULT`, you should consider that:

- All arguments are free of side-effects. However, only the first one (the result) should be modified by `YYLLOC_DEFAULT`.
- For consistency with semantic actions, valid indexes within the right hand side range from 1 to n. When n is zero, only 0 is a valid index, and it refers to the symbol just before the reduction. During error processing n is always positive.
- Your macro should parenthesize its arguments, if need be, since the actual arguments may not be surrounded by parentheses. Also, your macro should expand to something that can be used as a single statement when it is followed by a semicolon.

Next: Multiple Parsers, Previous: Locations, Up: Grammar File

### 3.7 Bison Declarations

The Bison declarations section of a Bison grammar defines the symbols used in formulating the grammar and the data types of semantic values. See Symbols.

All token type names (but not single-character literal tokens such as `'+'` and `'*'`) must be declared. Nonterminal symbols must be declared if you need to specify which data type to use for the semantic value (see More Than One Value Type).

The first rule in the file also specifies the start symbol, by default. If you want some other symbol to be the start symbol, you must declare it explicitly (see Languages and Context-Free Grammars).

Next: Precedence Decl, Up: Declarations

#### 3.7.1 Token Type Names

The basic way to declare a token type name (terminal symbol) is as follows:

         %token name

Bison will convert this into a `#define` directive in the parser, so that the function `yylex` (if it is in this file) can use the name name to stand for this token type's code.

Alternatively, you can use `%left`, `%right`, or `%nonassoc` instead of `%token`, if you wish to specify associativity and precedence. See Operator Precedence.

You can explicitly specify the numeric code for a token type by appending a decimal or hexadecimal integer value in the field immediately following the token name:

         %token NUM 300
         %token XNUM 0x12d // a GNU extension

It is generally best, however, to let Bison choose the numeric codes for all token types. Bison will automatically select codes that don't conflict with each other or with normal characters.

In the event that the stack type is a union, you must augment the `%token` or other token declaration to include the data type alternative delimited by angle-brackets (see More Than One Value Type).

For example:

         %union {              /* define stack type */
           double val;
           symrec *tptr;
         }
         %token <val> NUM      /* define token NUM and its type */

You can associate a literal string token with a token type name by writing the literal string at the end of a `%token` declaration which declares the name. For example:

         %token arrow "=>"

For example, a grammar for the C language might specify these names with equivalent literal string tokens:

         %token  <operator>  OR      "||"
         %token  <operator>  LE 134  "<="
         %left  OR  "<="

Once you equate the literal string and the token name, you can use them interchangeably in further declarations or the grammar rules. The `yylex` function can use the token name or the literal string to obtain the token type code number (see Calling Convention).

Next: Union Decl, Previous: Token Decl, Up: Declarations

#### 3.7.2 Operator Precedence

Use the `%left`, `%right` or `%nonassoc` declaration to declare a token and specify its precedence and associativity, all at once. These are called precedence declarations. See Operator Precedence, for general information on operator precedence.

The syntax of a precedence declaration is the same as that of `%token`: either

         %left symbols...

or

         %left <type> symbols...

And indeed any of these declarations serves the purposes of `%token`. But in addition, they specify the associativity and relative precedence for all the symbols:

- The associativity of an operator op determines how repeated uses of the operator nest: whether x op y op z is parsed by grouping x with y first or by grouping y with z first. `%left` specifies left-associativity (grouping x with y first) and `%right` specifies right-associativity (grouping y with z first). `%nonassoc` specifies no associativity, which means that x op y op z is considered a syntax error.
- The precedence of an operator determines how it nests with other operators. All the tokens declared in a single precedence declaration have equal precedence and nest together according to their associativity. When two tokens declared in different precedence declarations associate, the one declared later has the higher precedence and is grouped first.

Next: Type Decl, Previous: Precedence Decl, Up: Declarations

#### 3.7.3 The Collection of Value Types

The `%union` declaration specifies the entire collection of possible data types for semantic values. The keyword `%union` is followed by a pair of braces containing the same thing that goes inside a `union` in C.

For example:

         %union {
           double val;
           symrec *tptr;
         }

This says that the two alternative types are `double` and `symrec *`. They are given names `val` and `tptr`; these names are used in the `%token` and `%type` declarations to pick one of the types for a terminal or nonterminal symbol (see Nonterminal Symbols).

As an extension to POSIX, a tag is allowed after the `union`. For example:

         %union value {
           double val;
           symrec *tptr;
         }

specifies the union tag `value`, so the corresponding C type is `union value`. If you do not specify a tag, it defaults to `YYSTYPE`.

Note that, unlike making a `union` declaration in C, you need not write a semicolon after the closing brace.

Next: Initial Action Decl, Previous: Union Decl, Up: Declarations

#### 3.7.4 Nonterminal Symbols

When you use `%union` to specify multiple value types, you must declare the value type of each nonterminal symbol for which values are used. This is done with a `%type` declaration, like this:

         %type <type> nonterminal...

Here nonterminal is the name of a nonterminal symbol, and type is the name given in the `%union` to the alternative that you want (see The Collection of Value Types). You can give any number of nonterminal symbols in the same `%type` declaration, if they have the same value type. Use spaces to separate the symbol names.

You can also declare the value type of a terminal symbol. To do this, use the same `<`type`>` construction in a declaration for the terminal symbol. All kinds of token declarations allow `<`type`>`.

Next: Destructor Decl, Previous: Type Decl, Up: Declarations

#### 3.7.5 Performing Actions before Parsing

Sometimes your parser needs to perform some initializations before parsing. The `%initial-action` directive allows for such arbitrary code.

— Directive: %initial-action { code }

> Declare that the code must be invoked before parsing each time `yyparse` is called. The code may use `$$` and `@$` — initial value and location of the look-ahead — and the `%parse-param`.

For instance, if your locations use a file name, you may use

         %parse-param { const char *filename };
         %initial-action
         {
           @$.begin.filename = @$.end.filename = filename;
         };

Next: Expect Decl, Previous: Initial Action Decl, Up: Declarations

#### 3.7.6 Freeing Discarded Symbols

Some symbols can be discarded by the parser. For instance, during error recovery (see Error Recovery), embarrassing symbols already pushed on the stack, and embarrassing tokens coming from the rest of the file are thrown away until the parser falls on its feet. If these symbols convey heap based information, this memory is lost. While this behavior can be tolerable for batch parsers, such as in compilers, it is not for possibly “never ending” parsers such as shells, or implementations of communication protocols.

The `%destructor` directive allows for the definition of code that is called when a symbol is thrown away.

— Directive: %destructor { code } symbols

> Declare that the code must be invoked for each of the symbols that will be discarded by the parser. The code should use `$$` to designate the semantic value associated to the symbols. The additional parser parameters are also available (see The Parser Function `yyparse`).

> Warning: as of Bison 1.875, this feature is still considered as experimental, as there was not enough user feedback. In particular, the syntax might still change.

For instance:

         %union
         {
           char *string;
         }
         %token <string> STRING
         %type  <string> string
         %destructor { free ($$); } STRING string

guarantees that when a `STRING` or a `string` will be discarded, its associated memory will be freed.

Note that in the future, Bison might also consider that right hand side members that are not mentioned in the action can be destroyed. For instance, in:

         comment: "/*" STRING "*/";

the parser is entitled to destroy the semantic value of the `string`. Of course, this will not apply to the default action; compare:

         typeless: string;  // $$ = $1 does not apply; $1 is destroyed.
         typefull: string;  // $$ = $1 applies, $1 is not destroyed.

Discarded symbols are the following:

- stacked symbols popped during the first phase of error recovery,
- incoming terminals during the second phase of error recovery,
- the current look-ahead when the parser aborts (either via an explicit call to `YYABORT`, or as a consequence of a failed error recovery).

Next: Start Decl, Previous: Destructor Decl, Up: Declarations

#### 3.7.7 Suppressing Conflict Warnings

Bison normally warns if there are any conflicts in the grammar (see Shift/Reduce Conflicts), but most real grammars have harmless shift/reduce conflicts which are resolved in a predictable way and would be difficult to eliminate. It is desirable to suppress the warning about these conflicts unless the number of conflicts changes. You can do this with the `%expect` declaration.

The declaration looks like this:

         %expect n

Here n is a decimal integer. The declaration says there should be no warning if there are n shift/reduce conflicts and no reduce/reduce conflicts. The usual warning is given if there are either more or fewer conflicts, or if there are any reduce/reduce conflicts.

For normal LALR(1) parsers, reduce/reduce conflicts are more serious, and should be eliminated entirely. Bison will always report reduce/reduce conflicts for these parsers. With GLR parsers, however, both shift/reduce and reduce/reduce are routine (otherwise, there would be no need to use GLR parsing). Therefore, it is also possible to specify an expected number of reduce/reduce conflicts in GLR parsers, using the declaration:

         %expect-rr n

In general, using `%expect` involves these steps:

- Compile your grammar without `%expect`. Use the -v option to get a verbose list of where the conflicts occur. Bison will also print the number of conflicts.
- Check each of the conflicts to make sure that Bison's default resolution is what you really want. If not, rewrite the grammar and go back to the beginning.
- Add an `%expect` declaration, copying the number n from the number which Bison printed.

Now Bison will stop annoying you if you do not change the number of conflicts, but it will warn you again if changes in the grammar result in more or fewer conflicts.

Next: Pure Decl, Previous: Expect Decl, Up: Declarations

#### 3.7.8 The Start-Symbol

Bison assumes by default that the start symbol for the grammar is the first nonterminal specified in the grammar specification section. The programmer may override this restriction with the `%start` declaration as follows:

         %start symbol

Next: Decl Summary, Previous: Start Decl, Up: Declarations

#### 3.7.9 A Pure (Reentrant) Parser

A reentrant program is one which does not alter in the course of execution; in other words, it consists entirely of pure (read-only) code. Reentrancy is important whenever asynchronous execution is possible; for example, a non-reentrant program may not be safe to call from a signal handler. In systems with multiple threads of control, a non-reentrant program must be called only within interlocks.

Normally, Bison generates a parser which is not reentrant. This is suitable for most uses, and it permits compatibility with Yacc. (The standard Yacc interfaces are inherently nonreentrant, because they use statically allocated variables for communication with `yylex`, including `yylval` and `yylloc`.)

Alternatively, you can generate a pure, reentrant parser. The Bison declaration `%pure-parser` says that you want the parser to be reentrant. It looks like this:

         %pure-parser

The result is that the communication variables `yylval` and `yylloc` become local variables in `yyparse`, and a different calling convention is used for the lexical analyzer function `yylex`. See Calling Conventions for Pure Parsers, for the details of this. The variable `yynerrs` also becomes local in `yyparse` (see The Error Reporting Function `yyerror`). The convention for calling `yyparse` itself is unchanged.

Whether the parser is pure has nothing to do with the grammar rules. You can generate either a pure parser or a nonreentrant parser from any valid grammar.

Previous: Pure Decl, Up: Declarations

#### 3.7.10 Bison Declaration Summary

Here is a summary of the declarations used to define a grammar:

— Directive: %union

> Declare the collection of data types that semantic values may have (see The Collection of Value Types).

— Directive: %token

> Declare a terminal symbol (token type name) with no precedence or associativity specified (see Token Type Names).

— Directive: %right

> Declare a terminal symbol (token type name) that is right-associative (see Operator Precedence).

— Directive: %left

> Declare a terminal symbol (token type name) that is left-associative (see Operator Precedence).

— Directive: %nonassoc

> Declare a terminal symbol (token type name) that is nonassociative (see Operator Precedence). Using it in a way that would be associative is a syntax error.

— Directive: %type

> Declare the type of semantic values for a nonterminal symbol (see Nonterminal Symbols).

— Directive: %start

> Specify the grammar's start symbol (see The Start-Symbol).

— Directive: %expect

> Declare the expected number of shift-reduce conflicts (see Suppressing Conflict Warnings).

In order to change the behavior of bison, use the following directives:
— Directive: %debug

> In the parser file, define the macro `YYDEBUG` to 1 if it is not already defined, so that the debugging facilities are compiled.

See Tracing Your Parser.
— Directive: %defines

> Write a header file containing macro definitions for the token type names defined in the grammar as well as a few other declarations. If the parser output file is named name.c then this file is named name.h.

> Unless `YYSTYPE` is already defined as a macro, the output header declares `YYSTYPE`. Therefore, if you are using a `%union` (see More Than One Value Type) with components that require other definitions, or if you have defined a `YYSTYPE` macro (see Data Types of Semantic Values), you need to arrange for these definitions to be propagated to all modules, e.g., by putting them in a prerequisite header that is included both by your parser and by any other module that needs `YYSTYPE`.

> Unless your parser is pure, the output header declares `yylval` as an external variable. See A Pure (Reentrant) Parser.

> If you have also used locations, the output header declares `YYLTYPE` and `yylloc` using a protocol similar to that of `YYSTYPE` and `yylval`. See Tracking Locations.

> This output file is normally essential if you wish to put the definition of `yylex` in a separate source file, because `yylex` typically needs to be able to refer to the above-mentioned declarations and to the token type codes. See Semantic Values of Tokens.

— Directive: %destructor

> Specifying how the parser should reclaim the memory associated to discarded symbols. See Freeing Discarded Symbols.

— Directive: %file-prefix="prefix"

> Specify a prefix to use for all Bison output file names. The names are chosen as if the input file were named prefix.y.

— Directive: %locations

> Generate the code processing the locations (see Special Features for Use in Actions). This mode is enabled as soon as the grammar uses the special @n tokens, but if your grammar does not use it, using %locations allows for more accurate syntax error messages.

— Directive: %name-prefix="prefix"

> Rename the external symbols used in the parser so that they start with prefix instead of yy. The precise list of symbols renamed is `yyparse`, `yylex`, `yyerror`, `yynerrs`, `yylval`, `yylloc`, `yychar`, `yydebug`, and possible `yylloc`. For example, if you use %name-prefix="c_", the names become `c_parse`, `c_lex`, and so on. See Multiple Parsers in the Same Program.

— Directive: %no-parser

> Do not include any C code in the parser file; generate tables only. The parser file contains just `#define` directives and static variable declarations.

> This option also tells Bison to write the C code for the grammar actions into a file named filename.act, in the form of a brace-surrounded body fit for a `switch` statement.

— Directive: %no-lines

> Don't generate any `#line` preprocessor commands in the parser file. Ordinarily Bison writes these commands in the parser file so that the C compiler and debuggers will associate errors and object code with your source file (the grammar file). This directive causes them to associate errors with the parser file, treating it an independent source file in its own right.

— Directive: %output="filename"

> Specify the filename for the parser file.

— Directive: %pure-parser

> Request a pure (reentrant) parser program (see A Pure (Reentrant) Parser).

— Directive: %token-table

> Generate an array of token names in the parser file. The name of the array is `yytname`; `yytname[`i`]` is the name of the token whose internal Bison token code number is i. The first three elements of `yytname` correspond to the predefined tokens `"$end"`, `"error"`, and `"$undefined"`; after these come the symbols defined in the grammar file.

> For single-character literal tokens and literal string tokens, the name in the table includes the single-quote or double-quote characters: for example, `"'+'"` is a single-character literal and `"\"<=\""` is a literal string token. All the characters of the literal string token appear verbatim in the string found in the table; even double-quote characters are not escaped. For example, if the token consists of three characters *"*, its string in `yytname` contains "*"*". (In C, that would be written as `"\"*\"*\""`).

> When you specify `%token-table`, Bison also generates macro definitions for macros `YYNTOKENS`, `YYNNTS`, and `YYNRULES`, and `YYNSTATES`:

> `YYNTOKENS`
>   The highest token number, plus one.
> `YYNNTS`
>   The number of nonterminal symbols.
> `YYNRULES`
>   The number of grammar rules,
> `YYNSTATES`
>   The number of parser states (see Parser States).

— Directive: %verbose

> Write an extra output file containing verbose descriptions of the parser states and what is done for each type of look-ahead token in that state. See Understanding Your Parser, for more information.

— Directive: %yacc

> Pretend the option --yacc was given, i.e., imitate Yacc, including its naming conventions. See Bison Options, for more.

Previous: Declarations, Up: Grammar File

### 3.8 Multiple Parsers in the Same Program

Most programs that use Bison parse only one language and therefore contain only one Bison parser. But what if you want to parse more than one language with the same program? Then you need to avoid a name conflict between different definitions of `yyparse`, `yylval`, and so on.

The easy way to do this is to use the option -p prefix (see Invoking Bison). This renames the interface functions and variables of the Bison parser to start with prefix instead of yy. You can use this to give each parser distinct names that do not conflict.

The precise list of symbols renamed is `yyparse`, `yylex`, `yyerror`, `yynerrs`, `yylval`, `yylloc`, `yychar` and `yydebug`. For example, if you use -p c, the names become `cparse`, `clex`, and so on.

All the other variables and macros associated with Bison are not renamed. These others are not global; there is no conflict if the same name is used in different parsers. For example, `YYSTYPE` is not renamed, but defining this in different ways in different parsers causes no trouble (see Data Types of Semantic Values).

The -p option works by adding macro definitions to the beginning of the parser source file, defining `yyparse` as prefix `parse`, and so on. This effectively substitutes one name for the other in the entire parser file.

Next: Algorithm, Previous: Grammar File, Up: Top

## 4 Parser C-Language Interface

The Bison parser is actually a C function named `yyparse`. Here we describe the interface conventions of `yyparse` and the other functions that it needs to use.

Keep in mind that the parser uses many C identifiers starting with yy and YY for internal purposes. If you use such an identifier (aside from those in this manual) in an action or in epilogue in the grammar file, you are likely to run into trouble.

Next: Lexical, Up: Interface

### 4.1 The Parser Function `yyparse`

You call the function `yyparse` to cause parsing to occur. This function reads tokens, executes actions, and ultimately returns when it encounters end-of-input or an unrecoverable syntax error. You can also write an action which directs `yyparse` to return immediately without reading further.

— Function: int yyparse (void)

> The value returned by `yyparse` is 0 if parsing was successful (return is due to end-of-input).

> The value is 1 if parsing failed (return is due to a syntax error).

In an action, you can cause immediate return from `yyparse` by using these macros:

— Macro: YYACCEPT

> Return immediately with value 0 (to report success).

— Macro: YYABORT

> Return immediately with value 1 (to report failure).

If you use a reentrant parser, you can optionally pass additional parameter information to it in a reentrant way. To do so, use the declaration `%parse-param`:

— Directive: %parse-param {argument-declaration}

> Declare that an argument declared by `argument-declaration` is an additional `yyparse` argument. The argument-declaration is used when declaring functions or prototypes. The last identifier in argument-declaration must be the argument name.

Here's an example. Write this in the parser:

         %parse-param {int *nastiness}
         %parse-param {int *randomness}

Then call the parser like this:

         {
           int nastiness, randomness;
           ...  /* Store proper data in nastiness and randomness.  */
           value = yyparse (&nastiness, &randomness);
           ...
         }

In the grammar actions, use expressions like this to refer to the data:

         exp: ...    { ...; *randomness += 1; ... }

Next: Error Reporting, Previous: Parser Function, Up: Interface

### 4.2 The Lexical Analyzer Function `yylex`

The lexical analyzer function, `yylex`, recognizes tokens from the input stream and returns them to the parser. Bison does not create this function automatically; you must write it so that `yyparse` can call it. The function is sometimes referred to as a lexical scanner.

In simple programs, `yylex` is often defined at the end of the Bison grammar file. If `yylex` is defined in a separate source file, you need to arrange for the token-type macro definitions to be available there. To do this, use the -d option when you run Bison, so that it will write these macro definitions into a separate header file name.tab.h which you can include in the other source files that need it. See Invoking Bison.

Next: Token Values, Up: Lexical

#### 4.2.1 Calling Convention for `yylex`

The value that `yylex` returns must be the positive numeric code for the type of token it has just found; a zero or negative value signifies end-of-input.

When a token is referred to in the grammar rules by a name, that name in the parser file becomes a C macro whose definition is the proper numeric code for that token type. So `yylex` can use the name to indicate that type. See Symbols.

When a token is referred to in the grammar rules by a character literal, the numeric code for that character is also the code for the token type. So `yylex` can simply return that character code, possibly converted to `unsigned char` to avoid sign-extension. The null character must not be used this way, because its code is zero and that signifies end-of-input.

Here is an example showing these things:

         int
         yylex (void)
         {
           ...
           if (c == EOF)    /* Detect end-of-input.  */
             return 0;
           ...
           if (c == '+' || c == '-')
             return c;      /* Assume token type for `+' is '+'.  */
           ...
           return INT;      /* Return the type of the token.  */
           ...
         }

This interface has been designed so that the output from the `lex` utility can be used without change as the definition of `yylex`.

If the grammar uses literal string tokens, there are two ways that `yylex` can determine the token type codes for them:

- If the grammar defines symbolic token names as aliases for the literal string tokens, `yylex` can use these symbolic names like all others. In this case, the use of the literal string tokens in the grammar file has no effect on `yylex`.
- `yylex` can find the multicharacter token in the `yytname` table. The index of the token in the table is the token type's code. The name of a multicharacter token is recorded in `yytname` with a double-quote, the token's characters, and another double-quote. The token's characters are not escaped in any way; they appear verbatim in the contents of the string in the table.

  Here's code for looking up a token in `yytname`, assuming that the characters of the token are stored in `token_buffer`.

                for (i = 0; i < YYNTOKENS; i++)
                  {
                    if (yytname[i] != 0
                        && yytname[i][0] == '"'
                        && ! strncmp (yytname[i] + 1, token_buffer,
                                      strlen (token_buffer))
                        && yytname[i][strlen (token_buffer) + 1] == '"'
                        && yytname[i][strlen (token_buffer) + 2] == 0)
                      break;
                  }

  The `yytname` table is generated only if you use the `%token-table` declaration. See Decl Summary.

Next: Token Locations, Previous: Calling Convention, Up: Lexical

#### 4.2.2 Semantic Values of Tokens

In an ordinary (non-reentrant) parser, the semantic value of the token must be stored into the global variable `yylval`. When you are using just one data type for semantic values, `yylval` has that type. Thus, if the type is `int` (the default), you might write this in `yylex`:

           ...
           yylval = value;  /* Put value onto Bison stack.  */
           return INT;      /* Return the type of the token.  */
           ...

When you are using multiple data types, `yylval`'s type is a union made from the `%union` declaration (see The Collection of Value Types). So when you store a token's value, you must use the proper member of the union. If the `%union` declaration looks like this:

         %union {
           int intval;
           double val;
           symrec *tptr;
         }

then the code in `yylex` might look like this:

           ...
           yylval.intval = value; /* Put value onto Bison stack.  */
           return INT;            /* Return the type of the token.  */
           ...

Next: Pure Calling, Previous: Token Values, Up: Lexical

#### 4.2.3 Textual Locations of Tokens

If you are using the @n-feature (see Tracking Locations) in actions to keep track of the textual locations of tokens and groupings, then you must provide this information in `yylex`. The function `yyparse` expects to find the textual location of a token just parsed in the global variable `yylloc`. So `yylex` must store the proper data in that variable.

By default, the value of `yylloc` is a structure and you need only initialize the members that are going to be used by the actions. The four members are called `first_line`, `first_column`, `last_line` and `last_column`. Note that the use of this feature makes the parser noticeably slower.

The data type of `yylloc` has the name `YYLTYPE`.

Previous: Token Locations, Up: Lexical

#### 4.2.4 Calling Conventions for Pure Parsers

When you use the Bison declaration `%pure-parser` to request a pure, reentrant parser, the global communication variables `yylval` and `yylloc` cannot be used. (See A Pure (Reentrant) Parser.) In such parsers the two global variables are replaced by pointers passed as arguments to `yylex`. You must declare them as shown here, and pass the information back by storing it through those pointers.

         int
         yylex (YYSTYPE *lvalp, YYLTYPE *llocp)
         {
           ...
           *lvalp = value;  /* Put value onto Bison stack.  */
           return INT;      /* Return the type of the token.  */
           ...
         }

If the grammar file does not use the @ constructs to refer to textual locations, then the type `YYLTYPE` will not be defined. In this case, omit the second argument; `yylex` will be called with only one argument.

If you wish to pass the additional parameter data to `yylex`, use `%lex-param` just like `%parse-param` (see Parser Function).

— Directive: lex-param {argument-declaration}

> Declare that `argument-declaration` is an additional `yylex` argument declaration.

For instance:

         %parse-param {int *nastiness}
         %lex-param   {int *nastiness}
         %parse-param {int *randomness}

results in the following signature:

         int yylex   (int *nastiness);
         int yyparse (int *nastiness, int *randomness);

If `%pure-parser` is added:

         int yylex   (YYSTYPE *lvalp, int *nastiness);
         int yyparse (int *nastiness, int *randomness);

and finally, if both `%pure-parser` and `%locations` are used:

         int yylex   (YYSTYPE *lvalp, YYLTYPE *llocp, int *nastiness);
         int yyparse (int *nastiness, int *randomness);

Next: Action Features, Previous: Lexical, Up: Interface

### 4.3 The Error Reporting Function `yyerror`

The Bison parser detects a syntax error or parse error whenever it reads a token which cannot satisfy any syntax rule. An action in the grammar can also explicitly proclaim an error, using the macro `YYERROR` (see Special Features for Use in Actions).

The Bison parser expects to report the error by calling an error reporting function named `yyerror`, which you must supply. It is called by `yyparse` whenever a syntax error is found, and it receives one argument. For a syntax error, the string is normally `"syntax error"`.

If you invoke the directive `%error-verbose` in the Bison declarations section (see The Bison Declarations Section), then Bison provides a more verbose and specific error message string instead of just plain `"syntax error"`.

The parser can detect one other kind of error: stack overflow. This happens when the input contains constructions that are very deeply nested. It isn't likely you will encounter this, since the Bison parser extends its stack automatically up to a very large limit. But if overflow happens, `yyparse` calls `yyerror` in the usual fashion, except that the argument string is `"parser stack overflow"`.

The following definition suffices in simple programs:

         void
         yyerror (char const *s)
         {
           fprintf (stderr, "%s\n", s);
         }

After `yyerror` returns to `yyparse`, the latter will attempt error recovery if you have written suitable error recovery grammar rules (see Error Recovery). If recovery is impossible, `yyparse` will immediately return 1.

Obviously, in location tracking pure parsers, `yyerror` should have an access to the current location. This is indeed the case for the GLR parsers, but not for the Yacc parser, for historical reasons. I.e., if %locations %pure-parser is passed then the prototypes for `yyerror` are:

         void yyerror (char const *msg);                 /* Yacc parsers.  */
         void yyerror (YYLTYPE *locp, char const *msg);  /* GLR parsers.   */

If %parse-param {int *nastiness} is used, then:

         void yyerror (int *nastiness, char const *msg);  /* Yacc parsers.  */
         void yyerror (int *nastiness, char const *msg);  /* GLR parsers.   */

Finally, GLR and Yacc parsers share the same `yyerror` calling convention for absolutely pure parsers, i.e., when the calling convention of `yylex` and the calling convention of `%pure-parser` are pure. I.e.:

         /* Location tracking.  */
         %locations
         /* Pure yylex.  */
         %pure-parser
         %lex-param   {int *nastiness}
         /* Pure yyparse.  */
         %parse-param {int *nastiness}
         %parse-param {int *randomness}

results in the following signatures for all the parser kinds:

         int yylex (YYSTYPE *lvalp, YYLTYPE *llocp, int *nastiness);
         int yyparse (int *nastiness, int *randomness);
         void yyerror (YYLTYPE *locp,
                       int *nastiness, int *randomness,
                       char const *msg);

The prototypes are only indications of how the code produced by Bison uses `yyerror`. Bison-generated code always ignores the returned value, so `yyerror` can return any type, including `void`. Also, `yyerror` can be a variadic function; that is why the message is always passed last.

Traditionally `yyerror` returns an `int` that is always ignored, but this is purely for historical reasons, and `void` is preferable since it more accurately describes the return type for `yyerror`.

The variable `yynerrs` contains the number of syntax errors encountered so far. Normally this variable is global; but if you request a pure parser (see A Pure (Reentrant) Parser) then it is a local variable which only the actions can access.

Previous: Error Reporting, Up: Interface

### 4.4 Special Features for Use in Actions

Here is a table of Bison constructs, variables and macros that are useful in actions.

— Variable: $$

> Acts like a variable that contains the semantic value for the grouping made by the current rule. See Actions.

— Variable: $n

> Acts like a variable that contains the semantic value for the nth component of the current rule. See Actions.

— Variable: $<typealt>$

> Like `$$` but specifies alternative typealt in the union specified by the `%union` declaration. See Data Types of Values in Actions.

— Variable: $<typealt>n

> Like `$`n but specifies alternative typealt in the union specified by the `%union` declaration. See Data Types of Values in Actions.

— Macro: YYABORT;

> Return immediately from `yyparse`, indicating failure. See The Parser Function `yyparse`.

— Macro: YYACCEPT;

> Return immediately from `yyparse`, indicating success. See The Parser Function `yyparse`.

— Macro: YYBACKUP (token, value);

> Unshift a token. This macro is allowed only for rules that reduce a single value, and only when there is no look-ahead token. It is also disallowed in GLR parsers. It installs a look-ahead token with token type token and semantic value value; then it discards the value that was going to be reduced by this rule.

> If the macro is used when it is not valid, such as when there is a look-ahead token already, then it reports a syntax error with a message cannot back up and performs ordinary error recovery.

> In either case, the rest of the action is not executed.

— Macro: YYEMPTY

> Value stored in `yychar` when there is no look-ahead token.

— Macro: YYERROR;

> Cause an immediate syntax error. This statement initiates error recovery just as if the parser itself had detected an error; however, it does not call `yyerror`, and does not print any message. If you want to print an error message, call `yyerror` explicitly before the YYERROR; statement. See Error Recovery.

— Macro: YYRECOVERING

> This macro stands for an expression that has the value 1 when the parser is recovering from a syntax error, and 0 the rest of the time. See Error Recovery.

— Variable: yychar

> Variable containing the current look-ahead token. (In a pure parser, this is actually a local variable within `yyparse`.) When there is no look-ahead token, the value `YYEMPTY` is stored in the variable. See Look-Ahead Tokens.

— Macro: yyclearin;

> Discard the current look-ahead token. This is useful primarily in error rules. See Error Recovery.

— Macro: yyerrok;

> Resume generating error messages immediately for subsequent syntax errors. This is useful primarily in error rules. See Error Recovery.

— Value: @$

> Acts like a structure variable containing information on the textual location of the grouping made by the current rule. See Tracking Locations.

— Value: @n

> Acts like a structure variable containing information on the textual location of the nth component of the current rule. See Tracking Locations.

Next: Error Recovery, Previous: Interface, Up: Top

## 5 The Bison Parser Algorithm

As Bison reads tokens, it pushes them onto a stack along with their semantic values. The stack is called the parser stack. Pushing a token is traditionally called shifting.

For example, suppose the infix calculator has read 1 + 5 *, with a 3 to come. The stack will have four elements, one for each token that was shifted.

But the stack does not always have an element for each token read. When the last n tokens and groupings shifted match the components of a grammar rule, they can be combined according to that rule. This is called reduction. Those tokens and groupings are replaced on the stack by a single grouping whose symbol is the result (left hand side) of that rule. Running the rule's action is part of the process of reduction, because this is what computes the semantic value of the resulting grouping.

For example, if the infix calculator's parser stack contains this:

         1 + 5 * 3

and the next input token is a newline character, then the last three elements can be reduced to 15 via the rule:

         expr: expr '*' expr;

Then the stack contains just these three elements:

         1 + 15

At this point, another reduction can be made, resulting in the single value 16. Then the newline token can be shifted.

The parser tries, by shifts and reductions, to reduce the entire input down to a single grouping whose symbol is the grammar's start-symbol (see Languages and Context-Free Grammars).

This kind of parser is known in the literature as a bottom-up parser.

Next: Shift/Reduce, Up: Algorithm

### 5.1 Look-Ahead Tokens

The Bison parser does not always reduce immediately as soon as the last n tokens and groupings match a rule. This is because such a simple strategy is inadequate to handle most languages. Instead, when a reduction is possible, the parser sometimes “looks ahead” at the next token in order to decide what to do.

When a token is read, it is not immediately shifted; first it becomes the look-ahead token, which is not on the stack. Now the parser can perform one or more reductions of tokens and groupings on the stack, while the look-ahead token remains off to the side. When no more reductions should take place, the look-ahead token is shifted onto the stack. This does not mean that all possible reductions have been done; depending on the token type of the look-ahead token, some rules may choose to delay their application.

Here is a simple case where look-ahead is needed. These three rules define expressions which contain binary addition operators and postfix unary factorial operators (!), and allow parentheses for grouping.

         expr:     term '+' expr
                 | term
                 ;

         term:     '(' expr ')'
                 | term '!'
                 | NUMBER
                 ;

Suppose that the tokens 1 + 2 have been read and shifted; what should be done? If the following token is ), then the first three tokens must be reduced to form an `expr`. This is the only valid course, because shifting the ) would produce a sequence of symbols `term ')'`, and no rule allows this.

If the following token is !, then it must be shifted immediately so that 2 ! can be reduced to make a `term`. If instead the parser were to reduce before shifting, 1 + 2 would become an `expr`. It would then be impossible to shift the ! because doing so would produce on the stack the sequence of symbols `expr '!'`. No rule allows that sequence.

The current look-ahead token is stored in the variable `yychar`. See Special Features for Use in Actions.

Next: Precedence, Previous: Look-Ahead, Up: Algorithm

### 5.2 Shift/Reduce Conflicts

Suppose we are parsing a language which has if-then and if-then-else statements, with a pair of rules like this:

         if_stmt:
                   IF expr THEN stmt
                 | IF expr THEN stmt ELSE stmt
                 ;

Here we assume that `IF`, `THEN` and `ELSE` are terminal symbols for specific keyword tokens.

When the `ELSE` token is read and becomes the look-ahead token, the contents of the stack (assuming the input is valid) are just right for reduction by the first rule. But it is also legitimate to shift the `ELSE`, because that would lead to eventual reduction by the second rule.

This situation, where either a shift or a reduction would be valid, is called a shift/reduce conflict. Bison is designed to resolve these conflicts by choosing to shift, unless otherwise directed by operator precedence declarations. To see the reason for this, let's contrast it with the other alternative.

Since the parser prefers to shift the `ELSE`, the result is to attach the else-clause to the innermost if-statement, making these two inputs equivalent:

         if x then if y then win (); else lose;

         if x then do; if y then win (); else lose; end;

But if the parser chose to reduce when possible rather than shift, the result would be to attach the else-clause to the outermost if-statement, making these two inputs equivalent:

         if x then if y then win (); else lose;

         if x then do; if y then win (); end; else lose;

The conflict exists because the grammar as written is ambiguous: either parsing of the simple nested if-statement is legitimate. The established convention is that these ambiguities are resolved by attaching the else-clause to the innermost if-statement; this is what Bison accomplishes by choosing to shift rather than reduce. (It would ideally be cleaner to write an unambiguous grammar, but that is very hard to do in this case.) This particular ambiguity was first encountered in the specifications of Algol 60 and is called the “dangling `else`” ambiguity.

To avoid warnings from Bison about predictable, legitimate shift/reduce conflicts, use the `%expect` n declaration. There will be no warning as long as the number of shift/reduce conflicts is exactly n. See Suppressing Conflict Warnings.

The definition of `if_stmt` above is solely to blame for the conflict, but the conflict does not actually appear without additional rules. Here is a complete Bison input file that actually manifests the conflict:

         %token IF THEN ELSE variable
         %%
         stmt:     expr
                 | if_stmt
                 ;

         if_stmt:
                   IF expr THEN stmt
                 | IF expr THEN stmt ELSE stmt
                 ;

         expr:     variable
                 ;

Next: Contextual Precedence, Previous: Shift/Reduce, Up: Algorithm

### 5.3 Operator Precedence

Another situation where shift/reduce conflicts appear is in arithmetic expressions. Here shifting is not always the preferred resolution; the Bison declarations for operator precedence allow you to specify when to shift and when to reduce.

Next: Using Precedence, Up: Precedence

#### 5.3.1 When Precedence is Needed

Consider the following ambiguous grammar fragment (ambiguous because the input 1 - 2 * 3 can be parsed in two different ways):

         expr:     expr '-' expr
                 | expr '*' expr
                 | expr '<' expr
                 | '(' expr ')'
                 ...
                 ;

Suppose the parser has seen the tokens 1, - and 2; should it reduce them via the rule for the subtraction operator? It depends on the next token. Of course, if the next token is ), we must reduce; shifting is invalid because no single rule can reduce the token sequence - 2 ) or anything starting with that. But if the next token is * or <, we have a choice: either shifting or reduction would allow the parse to complete, but with different results.

To decide which one Bison should do, we must consider the results. If the next operator token op is shifted, then it must be reduced first in order to permit another opportunity to reduce the difference. The result is (in effect) 1 - (2 op 3). On the other hand, if the subtraction is reduced before shifting op, the result is (1 - 2) op 3. Clearly, then, the choice of shift or reduce should depend on the relative precedence of the operators - and op: * should be shifted first, but not <.

What about input such as 1 - 2 - 5; should this be (1 - 2) - 5 or should it be 1 - (2 - 5)? For most operators we prefer the former, which is called left association. The latter alternative, right association, is desirable for assignment operators. The choice of left or right association is a matter of whether the parser chooses to shift or reduce when the stack contains 1 - 2 and the look-ahead token is -: shifting makes right-associativity.

Next: Precedence Examples, Previous: Why Precedence, Up: Precedence

#### 5.3.2 Specifying Operator Precedence

Bison allows you to specify these choices with the operator precedence declarations `%left` and `%right`. Each such declaration contains a list of tokens, which are operators whose precedence and associativity is being declared. The `%left` declaration makes all those operators left-associative and the `%right` declaration makes them right-associative. A third alternative is `%nonassoc`, which declares that it is a syntax error to find the same operator twice “in a row”.

The relative precedence of different operators is controlled by the order in which they are declared. The first `%left` or `%right` declaration in the file declares the operators whose precedence is lowest, the next such declaration declares the operators whose precedence is a little higher, and so on.

Next: How Precedence, Previous: Using Precedence, Up: Precedence

#### 5.3.3 Precedence Examples

In our example, we would want the following declarations:

         %left '<'
         %left '-'
         %left '*'

In a more complete example, which supports other operators as well, we would declare them in groups of equal precedence. For example, `'+'` is declared with `'-'`:

         %left '<' '>' '=' NE LE GE
         %left '+' '-'
         %left '*' '/'

(Here `NE` and so on stand for the operators for “not equal” and so on. We assume that these tokens are more than one character long and therefore are represented by names, not character literals.)

Previous: Precedence Examples, Up: Precedence

#### 5.3.4 How Precedence Works

The first effect of the precedence declarations is to assign precedence levels to the terminal symbols declared. The second effect is to assign precedence levels to certain rules: each rule gets its precedence from the last terminal symbol mentioned in the components. (You can also specify explicitly the precedence of a rule. See Context-Dependent Precedence.)

Finally, the resolution of conflicts works by comparing the precedence of the rule being considered with that of the look-ahead token. If the token's precedence is higher, the choice is to shift. If the rule's precedence is higher, the choice is to reduce. If they have equal precedence, the choice is made based on the associativity of that precedence level. The verbose output file made by -v (see Invoking Bison) says how each conflict was resolved.

Not all rules and not all tokens have precedence. If either the rule or the look-ahead token has no precedence, then the default is to shift.

Next: Parser States, Previous: Precedence, Up: Algorithm

### 5.4 Context-Dependent Precedence

Often the precedence of an operator depends on the context. This sounds outlandish at first, but it is really very common. For example, a minus sign typically has a very high precedence as a unary operator, and a somewhat lower precedence (lower than multiplication) as a binary operator.

The Bison precedence declarations, `%left`, `%right` and `%nonassoc`, can only be used once for a given token; so a token has only one precedence declared in this way. For context-dependent precedence, you need to use an additional mechanism: the `%prec` modifier for rules.

The `%prec` modifier declares the precedence of a particular rule by specifying a terminal symbol whose precedence should be used for that rule. It's not necessary for that symbol to appear otherwise in the rule. The modifier's syntax is:

         %prec terminal-symbol

and it is written after the components of the rule. Its effect is to assign the rule the precedence of terminal-symbol, overriding the precedence that would be deduced for it in the ordinary way. The altered rule precedence then affects how conflicts involving that rule are resolved (see Operator Precedence).

Here is how `%prec` solves the problem of unary minus. First, declare a precedence for a fictitious terminal symbol named `UMINUS`. There are no tokens of this type, but the symbol serves to stand for its precedence:

         ...
         %left '+' '-'
         %left '*'
         %left UMINUS

Now the precedence of `UMINUS` can be used in specific rules:

         exp:    ...
                 | exp '-' exp
                 ...
                 | '-' exp %prec UMINUS

Next: Reduce/Reduce, Previous: Contextual Precedence, Up: Algorithm

### 5.5 Parser States

The function `yyparse` is implemented using a finite-state machine. The values pushed on the parser stack are not simply token type codes; they represent the entire sequence of terminal and nonterminal symbols at or near the top of the stack. The current state collects all the information about previous input which is relevant to deciding what to do next.

Each time a look-ahead token is read, the current parser state together with the type of look-ahead token are looked up in a table. This table entry can say, “Shift the look-ahead token.” In this case, it also specifies the new parser state, which is pushed onto the top of the parser stack. Or it can say, “Reduce using rule number n.” This means that a certain number of tokens or groupings are taken off the top of the stack, and replaced by one grouping. In other words, that number of states are popped from the stack, and one new state is pushed.

There is one other alternative: the table can say that the look-ahead token is erroneous in the current state. This causes error processing to begin (see Error Recovery).

Next: Mystery Conflicts, Previous: Parser States, Up: Algorithm

### 5.6 Reduce/Reduce Conflicts

A reduce/reduce conflict occurs if there are two or more rules that apply to the same sequence of input. This usually indicates a serious error in the grammar.

For example, here is an erroneous attempt to define a sequence of zero or more `word` groupings.

         sequence: /* empty */
                         { printf ("empty sequence\n"); }
                 | maybeword
                 | sequence word
                         { printf ("added word %s\n", $2); }
                 ;

         maybeword: /* empty */
                         { printf ("empty maybeword\n"); }
                 | word
                         { printf ("single word %s\n", $1); }
                 ;

The error is an ambiguity: there is more than one way to parse a single `word` into a `sequence`. It could be reduced to a `maybeword` and then into a `sequence` via the second rule. Alternatively, nothing-at-all could be reduced into a `sequence` via the first rule, and this could be combined with the `word` using the third rule for `sequence`.

There is also more than one way to reduce nothing-at-all into a `sequence`. This can be done directly via the first rule, or indirectly via `maybeword` and then the second rule.

You might think that this is a distinction without a difference, because it does not change whether any particular input is valid or not. But it does affect which actions are run. One parsing order runs the second rule's action; the other runs the first rule's action and the third rule's action. In this example, the output of the program changes.

Bison resolves a reduce/reduce conflict by choosing to use the rule that appears first in the grammar, but it is very risky to rely on this. Every reduce/reduce conflict must be studied and usually eliminated. Here is the proper way to define `sequence`:

         sequence: /* empty */
                         { printf ("empty sequence\n"); }
                 | sequence word
                         { printf ("added word %s\n", $2); }
                 ;

Here is another common error that yields a reduce/reduce conflict:

         sequence: /* empty */
                 | sequence words
                 | sequence redirects
                 ;

         words:    /* empty */
                 | words word
                 ;

         redirects:/* empty */
                 | redirects redirect
                 ;

The intention here is to define a sequence which can contain either `word` or `redirect` groupings. The individual definitions of `sequence`, `words` and `redirects` are error-free, but the three together make a subtle ambiguity: even an empty input can be parsed in infinitely many ways!

Consider: nothing-at-all could be a `words`. Or it could be two `words` in a row, or three, or any number. It could equally well be a `redirects`, or two, or any number. Or it could be a `words` followed by three `redirects` and another `words`. And so on.

Here are two ways to correct these rules. First, to make it a single level of sequence:

         sequence: /* empty */
                 | sequence word
                 | sequence redirect
                 ;

Second, to prevent either a `words` or a `redirects` from being empty:

         sequence: /* empty */
                 | sequence words
                 | sequence redirects
                 ;

         words:    word
                 | words word
                 ;

         redirects:redirect
                 | redirects redirect
                 ;

Next: Generalized LR Parsing, Previous: Reduce/Reduce, Up: Algorithm

### 5.7 Mysterious Reduce/Reduce Conflicts

Sometimes reduce/reduce conflicts can occur that don't look warranted. Here is an example:

         %token ID

         %%
         def:    param_spec return_spec ','
                 ;
         param_spec:
                      type
                 |    name_list ':' type
                 ;
         return_spec:
                      type
                 |    name ':' type
                 ;
         type:        ID
                 ;
         name:        ID
                 ;
         name_list:
                      name
                 |    name ',' name_list
                 ;

It would seem that this grammar can be parsed with only a single token of look-ahead: when a `param_spec` is being read, an `ID` is a `name` if a comma or colon follows, or a `type` if another `ID` follows. In other words, this grammar is LR(1).

However, Bison, like most parser generators, cannot actually handle all LR(1) grammars. In this grammar, two contexts, that after an `ID` at the beginning of a `param_spec` and likewise at the beginning of a `return_spec`, are similar enough that Bison assumes they are the same. They appear similar because the same set of rules would be active—the rule for reducing to a `name` and that for reducing to a `type`. Bison is unable to determine at that stage of processing that the rules would require different look-ahead tokens in the two contexts, so it makes a single parser state for them both. Combining the two contexts causes a conflict later. In parser terminology, this occurrence means that the grammar is not LALR(1).

In general, it is better to fix deficiencies than to document them. But this particular deficiency is intrinsically hard to fix; parser generators that can handle LR(1) grammars are hard to write and tend to produce parsers that are very large. In practice, Bison is more useful as it is now.

When the problem arises, you can often fix it by identifying the two parser states that are being confused, and adding something to make them look distinct. In the above example, adding one rule to `return_spec` as follows makes the problem go away:

         %token BOGUS
         ...
         %%
         ...
         return_spec:
                      type
                 |    name ':' type
                 /* This rule is never used.  */
                 |    ID BOGUS
                 ;

This corrects the problem because it introduces the possibility of an additional active rule in the context after the `ID` at the beginning of `return_spec`. This rule is not active in the corresponding context in a `param_spec`, so the two contexts receive distinct parser states. As long as the token `BOGUS` is never generated by `yylex`, the added rule cannot alter the way actual input is parsed.

In this particular example, there is another way to solve the problem: rewrite the rule for `return_spec` to use `ID` directly instead of via `name`. This also causes the two confusing contexts to have different sets of active rules, because the one for `return_spec` activates the altered rule for `return_spec` rather than the one for `name`.

         param_spec:
                      type
                 |    name_list ':' type
                 ;
         return_spec:
                      type
                 |    ID ':' type
                 ;

Next: Stack Overflow, Previous: Mystery Conflicts, Up: Algorithm

### 5.8 Generalized LR (GLR) Parsing

Bison produces deterministic parsers that choose uniquely when to reduce and which reduction to apply based on a summary of the preceding input and on one extra token of look-ahead. As a result, normal Bison handles a proper subset of the family of context-free languages. Ambiguous grammars, since they have strings with more than one possible sequence of reductions cannot have deterministic parsers in this sense. The same is true of languages that require more than one symbol of look-ahead, since the parser lacks the information necessary to make a decision at the point it must be made in a shift-reduce parser. Finally, as previously mentioned (see Mystery Conflicts), there are languages where Bison's particular choice of how to summarize the input seen so far loses necessary information.

When you use the %glr-parser declaration in your grammar file, Bison generates a parser that uses a different algorithm, called Generalized LR (or GLR). A Bison GLR parser uses the same basic algorithm for parsing as an ordinary Bison parser, but behaves differently in cases where there is a shift-reduce conflict that has not been resolved by precedence rules (see Precedence) or a reduce-reduce conflict. When a GLR parser encounters such a situation, it effectively splits into a several parsers, one for each possible shift or reduction. These parsers then proceed as usual, consuming tokens in lock-step. Some of the stacks may encounter other conflicts and split further, with the result that instead of a sequence of states, a Bison GLR parsing stack is what is in effect a tree of states.

In effect, each stack represents a guess as to what the proper parse is. Additional input may indicate that a guess was wrong, in which case the appropriate stack silently disappears. Otherwise, the semantics actions generated in each stack are saved, rather than being executed immediately. When a stack disappears, its saved semantic actions never get executed. When a reduction causes two stacks to become equivalent, their sets of semantic actions are both saved with the state that results from the reduction. We say that two stacks are equivalent when they both represent the same sequence of states, and each pair of corresponding states represents a grammar symbol that produces the same segment of the input token stream.

Whenever the parser makes a transition from having multiple states to having one, it reverts to the normal LALR(1) parsing algorithm, after resolving and executing the saved-up actions. At this transition, some of the states on the stack will have semantic values that are sets (actually multisets) of possible actions. The parser tries to pick one of the actions by first finding one whose rule has the highest dynamic precedence, as set by the %dprec declaration. Otherwise, if the alternative actions are not ordered by precedence, but there the same merging function is declared for both rules by the %merge declaration, Bison resolves and evaluates both and then calls the merge function on the result. Otherwise, it reports an ambiguity.

It is possible to use a data structure for the GLR parsing tree that permits the processing of any LALR(1) grammar in linear time (in the size of the input), any unambiguous (not necessarily LALR(1)) grammar in quadratic worst-case time, and any general (possibly ambiguous) context-free grammar in cubic worst-case time. However, Bison currently uses a simpler data structure that requires time proportional to the length of the input times the maximum number of stacks required for any prefix of the input. Thus, really ambiguous or non-deterministic grammars can require exponential time and space to process. Such badly behaving examples, however, are not generally of practical interest. Usually, non-determinism in a grammar is local—the parser is “in doubt” only for a few tokens at a time. Therefore, the current data structure should generally be adequate. On LALR(1) portions of a grammar, in particular, it is only slightly slower than with the default Bison parser.

For a more detailed exposition of GLR parsers, please see: Elizabeth Scott, Adrian Johnstone and Shamsa Sadaf Hussain, Tomita-Style Generalised LR Parsers, Royal Holloway, University of London, Department of Computer Science, TR-00-12, http://www.cs.rhul.ac.uk/research/languages/publications/tomita_style_1.ps, (2000-12-24).

Previous: Generalized LR Parsing, Up: Algorithm

### 5.9 Stack Overflow, and How to Avoid It

The Bison parser stack can overflow if too many tokens are shifted and not reduced. When this happens, the parser function `yyparse` returns a nonzero value, pausing only to call `yyerror` to report the overflow.

Because Bison parsers have growing stacks, hitting the upper limit usually results from using a right recursion instead of a left recursion, See Recursive Rules.

By defining the macro `YYMAXDEPTH`, you can control how deep the parser stack can become before a stack overflow occurs. Define the macro with a value that is an integer. This value is the maximum number of tokens that can be shifted (and not reduced) before overflow.

The stack space allowed is not necessarily allocated. If you specify a large value for `YYMAXDEPTH`, the parser actually allocates a small stack at first, and then makes it bigger by stages as needed. This increasing allocation happens automatically and silently. Therefore, you do not need to make `YYMAXDEPTH` painfully small merely to save space for ordinary inputs that do not need much stack.

However, do not allow `YYMAXDEPTH` to be a value so large that arithmetic overflow could occur when calculating the size of the stack space. Also, do not allow `YYMAXDEPTH` to be less than `YYINITDEPTH`.

The default value of `YYMAXDEPTH`, if you do not define it, is 10000.

You can control how much stack is allocated initially by defining the macro `YYINITDEPTH` to a positive integer. For the C LALR(1) parser, this value must be a compile-time constant unless you are assuming C99 or some other target language or compiler that allows variable-length arrays. The default is 200.

Do not allow `YYINITDEPTH` to be a value so large that arithmetic overflow would occur when calculating the size of the stack space. Also, do not allow `YYINITDEPTH` to be greater than `YYMAXDEPTH`.

Because of semantical differences between C and C++, the LALR(1) parsers in C produced by Bison by compiled as C++ cannot grow. In this precise case (compiling a C parser as C++) you are suggested to grow `YYINITDEPTH`. In the near future, a C++ output output will be provided which addresses this issue.

Next: Context Dependency, Previous: Algorithm, Up: Top

## 6 Error Recovery

It is not usually acceptable to have a program terminate on a syntax error. For example, a compiler should recover sufficiently to parse the rest of the input file and check it for errors; a calculator should accept another expression.

In a simple interactive command parser where each input is one line, it may be sufficient to allow `yyparse` to return 1 on error and have the caller ignore the rest of the input line when that happens (and then call `yyparse` again). But this is inadequate for a compiler, because it forgets all the syntactic context leading up to the error. A syntax error deep within a function in the compiler input should not cause the compiler to treat the following line like the beginning of a source file.

You can define how to recover from a syntax error by writing rules to recognize the special token `error`. This is a terminal symbol that is always defined (you need not declare it) and reserved for error handling. The Bison parser generates an `error` token whenever a syntax error happens; if you have provided a rule to recognize this token in the current context, the parse can continue.

For example:

         stmnts:  /* empty string */
                 | stmnts '\n'
                 | stmnts exp '\n'
                 | stmnts error '\n'

The fourth rule in this example says that an error followed by a newline makes a valid addition to any `stmnts`.

What happens if a syntax error occurs in the middle of an `exp`? The error recovery rule, interpreted strictly, applies to the precise sequence of a `stmnts`, an `error` and a newline. If an error occurs in the middle of an `exp`, there will probably be some additional tokens and subexpressions on the stack after the last `stmnts`, and there will be tokens to read before the next newline. So the rule is not applicable in the ordinary way.

But Bison can force the situation to fit the rule, by discarding part of the semantic context and part of the input. First it discards states and objects from the stack until it gets back to a state in which the `error` token is acceptable. (This means that the subexpressions already parsed are discarded, back to the last complete `stmnts`.) At this point the `error` token can be shifted. Then, if the old look-ahead token is not acceptable to be shifted next, the parser reads tokens and discards them until it finds a token which is acceptable. In this example, Bison reads and discards input until the next newline so that the fourth rule can apply. Note that discarded symbols are possible sources of memory leaks, see Freeing Discarded Symbols, for a means to reclaim this memory.

The choice of error rules in the grammar is a choice of strategies for error recovery. A simple and useful strategy is simply to skip the rest of the current input line or current statement if an error is detected:

         stmnt: error ';'  /* On error, skip until ';' is read.  */

It is also useful to recover to the matching close-delimiter of an opening-delimiter that has already been parsed. Otherwise the close-delimiter will probably appear to be unmatched, and generate another, spurious error message:

         primary:  '(' expr ')'
                 | '(' error ')'
                 ...
                 ;

Error recovery strategies are necessarily guesses. When they guess wrong, one syntax error often leads to another. In the above example, the error recovery rule guesses that an error is due to bad input within one `stmnt`. Suppose that instead a spurious semicolon is inserted in the middle of a valid `stmnt`. After the error recovery rule recovers from the first error, another syntax error will be found straightaway, since the text following the spurious semicolon is also an invalid `stmnt`.

To prevent an outpouring of error messages, the parser will output no error message for another syntax error that happens shortly after the first; only after three consecutive input tokens have been successfully shifted will error messages resume.

Note that rules which accept the `error` token may have actions, just as any other rules can.

You can make error messages resume immediately by using the macro `yyerrok` in an action. If you do this in the error rule's action, no error messages will be suppressed. This macro requires no arguments; yyerrok; is a valid C statement.

The previous look-ahead token is reanalyzed immediately after an error. If this is unacceptable, then the macro `yyclearin` may be used to clear this token. Write the statement yyclearin; in the error rule's action.

For example, suppose that on a syntax error, an error handling routine is called that advances the input stream to some point where parsing should once again commence. The next symbol returned by the lexical scanner is probably correct. The previous look-ahead token ought to be discarded with yyclearin;.

The macro `YYRECOVERING` stands for an expression that has the value 1 when the parser is recovering from a syntax error, and 0 the rest of the time. A value of 1 indicates that error messages are currently suppressed for new syntax errors.

Next: Debugging, Previous: Error Recovery, Up: Top

## 7 Handling Context Dependencies

The Bison paradigm is to parse tokens first, then group them into larger syntactic units. In many languages, the meaning of a token is affected by its context. Although this violates the Bison paradigm, certain techniques (known as kludges) may enable you to write Bison parsers for such languages.

(Actually, “kludge” means any technique that gets its job done but is neither clean nor robust.)

Next: Lexical Tie-ins, Up: Context Dependency

### 7.1 Semantic Info in Token Types

The C language has a context dependency: the way an identifier is used depends on what its current meaning is. For example, consider this:

         foo (x);

This looks like a function call statement, but if `foo` is a typedef name, then this is actually a declaration of `x`. How can a Bison parser for C decide how to parse this input?

The method used in GNU C is to have two different token types, `IDENTIFIER` and `TYPENAME`. When `yylex` finds an identifier, it looks up the current declaration of the identifier in order to decide which token type to return: `TYPENAME` if the identifier is declared as a typedef, `IDENTIFIER` otherwise.

The grammar rules can then express the context dependency by the choice of token type to recognize. `IDENTIFIER` is accepted as an expression, but `TYPENAME` is not. `TYPENAME` can start a declaration, but `IDENTIFIER` cannot. In contexts where the meaning of the identifier is not significant, such as in declarations that can shadow a typedef name, either `TYPENAME` or `IDENTIFIER` is accepted—there is one rule for each of the two token types.

This technique is simple to use if the decision of which kinds of identifiers to allow is made at a place close to where the identifier is parsed. But in C this is not always so: C allows a declaration to redeclare a typedef name provided an explicit type has been specified earlier:

         typedef int foo, bar, lose;
         static foo (bar);        /* redeclare bar as static variable */
         static int foo (lose);   /* redeclare foo as function */

Unfortunately, the name being declared is separated from the declaration construct itself by a complicated syntactic structure—the “declarator”.

As a result, part of the Bison parser for C needs to be duplicated, with all the nonterminal names changed: once for parsing a declaration in which a typedef name can be redefined, and once for parsing a declaration in which that can't be done. Here is a part of the duplication, with actions omitted for brevity:

         initdcl:
                   declarator maybeasm '='
                   init
                 | declarator maybeasm
                 ;

         notype_initdcl:
                   notype_declarator maybeasm '='
                   init
                 | notype_declarator maybeasm
                 ;

Here `initdcl` can redeclare a typedef name, but `notype_initdcl` cannot. The distinction between `declarator` and `notype_declarator` is the same sort of thing.

There is some similarity between this technique and a lexical tie-in (described next), in that information which alters the lexical analysis is changed during parsing by other parts of the program. The difference is here the information is global, and is used for other purposes in the program. A true lexical tie-in has a special-purpose flag controlled by the syntactic context.

Next: Tie-in Recovery, Previous: Semantic Tokens, Up: Context Dependency

### 7.2 Lexical Tie-ins

One way to handle context-dependency is the lexical tie-in: a flag which is set by Bison actions, whose purpose is to alter the way tokens are parsed.

For example, suppose we have a language vaguely like C, but with a special construct hex (hex-expr). After the keyword `hex` comes an expression in parentheses in which all integers are hexadecimal. In particular, the token a1b must be treated as an integer rather than as an identifier if it appears in that context. Here is how you can do it:

         %{
           int hexflag;
           int yylex (void);
           void yyerror (char const *);
         %}
         %%
         ...
         expr:   IDENTIFIER
                 | constant
                 | HEX '('
                         { hexflag = 1; }
                   expr ')'
                         { hexflag = 0;
                            $$ = $4; }
                 | expr '+' expr
                         { $$ = make_sum ($1, $3); }
                 ...
                 ;

         constant:
                   INTEGER
                 | STRING
                 ;

Here we assume that `yylex` looks at the value of `hexflag`; when it is nonzero, all integers are parsed in hexadecimal, and tokens starting with letters are parsed as integers if possible.

The declaration of `hexflag` shown in the prologue of the parser file is needed to make it accessible to the actions (see The Prologue). You must also write the code in `yylex` to obey the flag.

Previous: Lexical Tie-ins, Up: Context Dependency

### 7.3 Lexical Tie-ins and Error Recovery

Lexical tie-ins make strict demands on any error recovery rules you have. See Error Recovery.

The reason for this is that the purpose of an error recovery rule is to abort the parsing of one construct and resume in some larger construct. For example, in C-like languages, a typical error recovery rule is to skip tokens until the next semicolon, and then start a new statement, like this:

         stmt:   expr ';'
                 | IF '(' expr ')' stmt { ... }
                 ...
                 error ';'
                         { hexflag = 0; }
                 ;

If there is a syntax error in the middle of a hex (expr) construct, this error rule will apply, and then the action for the completed hex (expr) will never run. So `hexflag` would remain set for the entire rest of the input, or until the next `hex` keyword, causing identifiers to be misinterpreted as integers.

To avoid this problem the error recovery rule itself clears `hexflag`.

There may also be an error recovery rule that works within expressions. For example, there could be a rule which applies within parentheses and skips to the close-parenthesis:

         expr:   ...
                 | '(' expr ')'
                         { $$ = $2; }
                 | '(' error ')'
                 ...

If this rule acts within the `hex` construct, it is not going to abort that construct (since it applies to an inner level of parentheses within the construct). Therefore, it should not clear the flag: the rest of the `hex` construct should be parsed with the flag still in effect.

What if there is an error recovery rule which might abort out of the `hex` construct or might not, depending on circumstances? There is no way you can write the action to determine whether a `hex` construct is being aborted or not. So if you are using a lexical tie-in, you had better make sure your error recovery rules are not of this kind. Each rule must be such that you can be sure that it always will, or always won't, have to clear the flag.

Next: Invocation, Previous: Context Dependency, Up: Top

## 8 Debugging Your Parser

Developing a parser can be a challenge, especially if you don't understand the algorithm (see The Bison Parser Algorithm). Even so, sometimes a detailed description of the automaton can help (see Understanding Your Parser), or tracing the execution of the parser can give some insight on why it behaves improperly (see Tracing Your Parser).

Next: Tracing, Up: Debugging

### 8.1 Understanding Your Parser

As documented elsewhere (see The Bison Parser Algorithm) Bison parsers are shift/reduce automata. In some cases (much more frequent than one would hope), looking at this automaton is required to tune or simply fix a parser. Bison provides two different representation of it, either textually or graphically (as a VCG file).

The textual file is generated when the options --report or --verbose are specified, see See Invoking Bison. Its name is made by removing .tab.c or .c from the parser output file name, and adding .output instead. Therefore, if the input file is foo.y, then the parser file is called foo.tab.c by default. As a consequence, the verbose output file is called foo.output.

The following grammar file, calc.y, will be used in the sequel:

         %token NUM STR
         %left '+' '-'
         %left '*'
         %%
         exp: exp '+' exp
            | exp '-' exp
            | exp '*' exp
            | exp '/' exp
            | NUM
            ;
         useless: STR;
         %%

bison reports:

         calc.y: warning: 1 useless nonterminal and 1 useless rule
         calc.y:11.1-7: warning: useless nonterminal: useless
         calc.y:11.10-12: warning: useless rule: useless: STR
         calc.y: conflicts: 7 shift/reduce

When given --report=state, in addition to calc.tab.c, it creates a file calc.output with contents detailed below. The order of the output and the exact presentation might vary, but the interpretation is the same.

The first section includes details on conflicts that were solved thanks to precedence and/or associativity:

         Conflict in state 8 between rule 2 and token '+' resolved as reduce.
         Conflict in state 8 between rule 2 and token '-' resolved as reduce.
         Conflict in state 8 between rule 2 and token '*' resolved as shift.

    ...

The next section lists states that still have conflicts.

         State 8 conflicts: 1 shift/reduce
         State 9 conflicts: 1 shift/reduce
         State 10 conflicts: 1 shift/reduce
         State 11 conflicts: 4 shift/reduce

The next section reports useless tokens, nonterminal and rules. Useless nonterminals and rules are removed in order to produce a smaller parser, but useless tokens are preserved, since they might be used by the scanner (note the difference between “useless” and “not used” below):

         Useless nonterminals:
            useless

         Terminals which are not used:
            STR

         Useless rules:
         #6     useless: STR;

The next section reproduces the exact grammar that Bison used:

         Grammar

           Number, Line, Rule
             0   5 $accept -> exp $end
             1   5 exp -> exp '+' exp
             2   6 exp -> exp '-' exp
             3   7 exp -> exp '*' exp
             4   8 exp -> exp '/' exp
             5   9 exp -> NUM

and reports the uses of the symbols:

         Terminals, with rules where they appear

         $end (0) 0
         '*' (42) 3
         '+' (43) 1
         '-' (45) 2
         '/' (47) 4
         error (256)
         NUM (258) 5

         Nonterminals, with rules where they appear

         $accept (8)
             on left: 0
         exp (9)
             on left: 1 2 3 4 5, on right: 0 1 2 3 4

Bison then proceeds onto the automaton itself, describing each state with it set of items, also known as pointed rules. Each item is a production rule together with a point (marked by .) that the input cursor.

         state 0

             $accept  ->  . exp $   (rule 0)

             NUM         shift, and go to state 1

             exp         go to state 2

This reads as follows: “state 0 corresponds to being at the very beginning of the parsing, in the initial rule, right before the start symbol (here, `exp`). When the parser returns to this state right after having reduced a rule that produced an `exp`, the control flow jumps to state 2. If there is no such transition on a nonterminal symbol, and the look-ahead is a `NUM`, then this token is shifted on the parse stack, and the control flow jumps to state 1. Any other look-ahead triggers a syntax error.”

Even though the only active rule in state 0 seems to be rule 0, the report lists `NUM` as a look-ahead token because `NUM` can be at the beginning of any rule deriving an `exp`. By default Bison reports the so-called core or kernel of the item set, but if you want to see more detail you can invoke bison with --report=itemset to list all the items, include those that can be derived:

         state 0

             $accept  ->  . exp $   (rule 0)
             exp  ->  . exp '+' exp   (rule 1)
             exp  ->  . exp '-' exp   (rule 2)
             exp  ->  . exp '*' exp   (rule 3)
             exp  ->  . exp '/' exp   (rule 4)
             exp  ->  . NUM   (rule 5)

             NUM         shift, and go to state 1

             exp         go to state 2

In the state 1...

         state 1

             exp  ->  NUM .   (rule 5)

             $default    reduce using rule 5 (exp)

the rule 5, exp: NUM;, is completed. Whatever the look-ahead token ($default), the parser will reduce it. If it was coming from state 0, then, after this reduction it will return to state 0, and will jump to state 2 (exp: go to state 2).

         state 2

             $accept  ->  exp . $   (rule 0)
             exp  ->  exp . '+' exp   (rule 1)
             exp  ->  exp . '-' exp   (rule 2)
             exp  ->  exp . '*' exp   (rule 3)
             exp  ->  exp . '/' exp   (rule 4)

             $           shift, and go to state 3
             '+'         shift, and go to state 4
             '-'         shift, and go to state 5
             '*'         shift, and go to state 6
             '/'         shift, and go to state 7

In state 2, the automaton can only shift a symbol. For instance, because of the item exp -> exp . '+' exp, if the look-ahead if +, it will be shifted on the parse stack, and the automaton control will jump to state 4, corresponding to the item exp -> exp '+' . exp. Since there is no default action, any other token than those listed above will trigger a syntax error.

The state 3 is named the final state, or the accepting state:

         state 3

             $accept  ->  exp $ .   (rule 0)

             $default    accept

the initial rule is completed (the start symbol and the end of input were read), the parsing exits successfully.

The interpretation of states 4 to 7 is straightforward, and is left to the reader.

         state 4

             exp  ->  exp '+' . exp   (rule 1)

             NUM         shift, and go to state 1

             exp         go to state 8

         state 5

             exp  ->  exp '-' . exp   (rule 2)

             NUM         shift, and go to state 1

             exp         go to state 9

         state 6

             exp  ->  exp '*' . exp   (rule 3)

             NUM         shift, and go to state 1

             exp         go to state 10

         state 7

             exp  ->  exp '/' . exp   (rule 4)

             NUM         shift, and go to state 1

             exp         go to state 11

As was announced in beginning of the report, State 8 conflicts: 1 shift/reduce:

         state 8

             exp  ->  exp . '+' exp   (rule 1)
             exp  ->  exp '+' exp .   (rule 1)
             exp  ->  exp . '-' exp   (rule 2)
             exp  ->  exp . '*' exp   (rule 3)
             exp  ->  exp . '/' exp   (rule 4)

             '*'         shift, and go to state 6
             '/'         shift, and go to state 7

             '/'         [reduce using rule 1 (exp)]
             $default    reduce using rule 1 (exp)

Indeed, there are two actions associated to the look-ahead /: either shifting (and going to state 7), or reducing rule 1. The conflict means that either the grammar is ambiguous, or the parser lacks information to make the right decision. Indeed the grammar is ambiguous, as, since we did not specify the precedence of /, the sentence NUM + NUM / NUM can be parsed as NUM + (NUM / NUM), which corresponds to shifting /, or as (NUM + NUM) / NUM, which corresponds to reducing rule 1.

Because in LALR(1) parsing a single decision can be made, Bison arbitrarily chose to disable the reduction, see Shift/Reduce Conflicts. Discarded actions are reported in between square brackets.

Note that all the previous states had a single possible action: either shifting the next token and going to the corresponding state, or reducing a single rule. In the other cases, i.e., when shifting and reducing is possible or when several reductions are possible, the look-ahead is required to select the action. State 8 is one such state: if the look-ahead is * or / then the action is shifting, otherwise the action is reducing rule 1. In other words, the first two items, corresponding to rule 1, are not eligible when the look-ahead token is *, since we specified that * has higher precedence than +. More generally, some items are eligible only with some set of possible look-ahead tokens. When run with --report=look-ahead, Bison specifies these look-ahead tokens:

         state 8

             exp  ->  exp . '+' exp  [$, '+', '-', '/']   (rule 1)
             exp  ->  exp '+' exp .  [$, '+', '-', '/']   (rule 1)
             exp  ->  exp . '-' exp   (rule 2)
             exp  ->  exp . '*' exp   (rule 3)
             exp  ->  exp . '/' exp   (rule 4)

             '*'         shift, and go to state 6
             '/'         shift, and go to state 7

             '/'         [reduce using rule 1 (exp)]
             $default    reduce using rule 1 (exp)

The remaining states are similar:

         state 9

             exp  ->  exp . '+' exp   (rule 1)
             exp  ->  exp . '-' exp   (rule 2)
             exp  ->  exp '-' exp .   (rule 2)
             exp  ->  exp . '*' exp   (rule 3)
             exp  ->  exp . '/' exp   (rule 4)

             '*'         shift, and go to state 6
             '/'         shift, and go to state 7

             '/'         [reduce using rule 2 (exp)]
             $default    reduce using rule 2 (exp)

         state 10

             exp  ->  exp . '+' exp   (rule 1)
             exp  ->  exp . '-' exp   (rule 2)
             exp  ->  exp . '*' exp   (rule 3)
             exp  ->  exp '*' exp .   (rule 3)
             exp  ->  exp . '/' exp   (rule 4)

             '/'         shift, and go to state 7

             '/'         [reduce using rule 3 (exp)]
             $default    reduce using rule 3 (exp)

         state 11

             exp  ->  exp . '+' exp   (rule 1)
             exp  ->  exp . '-' exp   (rule 2)
             exp  ->  exp . '*' exp   (rule 3)
             exp  ->  exp . '/' exp   (rule 4)
             exp  ->  exp '/' exp .   (rule 4)

             '+'         shift, and go to state 4
             '-'         shift, and go to state 5
             '*'         shift, and go to state 6
             '/'         shift, and go to state 7

             '+'         [reduce using rule 4 (exp)]
             '-'         [reduce using rule 4 (exp)]
             '*'         [reduce using rule 4 (exp)]
             '/'         [reduce using rule 4 (exp)]
             $default    reduce using rule 4 (exp)

Observe that state 11 contains conflicts not only due to the lack of precedence of / with respect to +, -, and *, but also because the associativity of / is not specified.

Previous: Understanding, Up: Debugging

### 8.2 Tracing Your Parser

If a Bison grammar compiles properly but doesn't do what you want when it runs, the `yydebug` parser-trace feature can help you figure out why.

There are several means to enable compilation of trace facilities:

the macro `YYDEBUG`
  Define the macro `YYDEBUG` to a nonzero value when you compile the parser. This is compliant with POSIX Yacc. You could use -DYYDEBUG=1 as a compiler option or you could put #define YYDEBUG 1 in the prologue of the grammar file (see The Prologue).
the option -t, --debug
  Use the -t option when you run Bison (see Invoking Bison). This is POSIX compliant too.
the directive %debug
  Add the `%debug` directive (see Bison Declaration Summary). This is a Bison extension, which will prove useful when Bison will output parsers for languages that don't use a preprocessor. Unless POSIX and Yacc portability matter to you, this is the preferred solution.

We suggest that you always enable the debug option so that debugging is always possible.

The trace facility outputs messages with macro calls of the form `YYFPRINTF (stderr,` format`,` args`)` where format and args are the usual `printf` format and arguments. If you define `YYDEBUG` to a nonzero value but do not define `YYFPRINTF`, `<stdio.h>` is automatically included and `YYPRINTF` is defined to `fprintf`.

Once you have compiled the program with trace facilities, the way to request a trace is to store a nonzero value in the variable `yydebug`. You can do this by making the C code do it (in `main`, perhaps), or you can alter the value with a C debugger.

Each step taken by the parser when `yydebug` is nonzero produces a line or two of trace information, written on `stderr`. The trace messages tell you these things:

- Each time the parser calls `yylex`, what kind of token was read.
- Each time a token is shifted, the depth and complete contents of the state stack (see Parser States).
- Each time a rule is reduced, which rule it is, and the complete contents of the state stack afterward.

To make sense of this information, it helps to refer to the listing file produced by the Bison -v option (see Invoking Bison). This file shows the meaning of each state in terms of positions in various rules, and also what each state will do with each possible input token. As you read the successive trace messages, you can see that the parser is functioning according to its specification in the listing file. Eventually you will arrive at the place where something undesirable happens, and you will see which parts of the grammar are to blame.

The parser file is a C program and you can use C debuggers on it, but it's not easy to interpret what it is doing. The parser function is a finite-state machine interpreter, and aside from the actions it executes the same code over and over. Only the values of variables show where in the grammar it is working.

The debugging information normally gives the token type of each token read, but not its semantic value. You can optionally define a macro named `YYPRINT` to provide a way to print the value. If you define `YYPRINT`, it should take three arguments. The parser will pass a standard I/O stream, the numeric code for the token type, and the token value (from `yylval`).

Here is an example of `YYPRINT` suitable for the multi-function calculator (see Declarations for `mfcalc`):

         %{
           static void print_token_value (FILE *, int, YYSTYPE);
           #define YYPRINT(file, type, value) print_token_value (file, type, value)
         %}

         ... %% ... %% ...

         static void
         print_token_value (FILE *file, int type, YYSTYPE value)
         {
           if (type == VAR)
             fprintf (file, "%s", value.tptr->name);
           else if (type == NUM)
             fprintf (file, "%d", value.val);
         }

Next: Table of Symbols, Previous: Debugging, Up: Top

## 9 Invoking Bison

The usual way to invoke Bison is as follows:

         bison infile

Here infile is the grammar file name, which usually ends in .y. The parser file's name is made by replacing the .y with .tab.c. Thus, the bison foo.y filename yields foo.tab.c, and the bison hack/foo.y filename yields hack/foo.tab.c. It's also possible, in case you are writing C++ code instead of C in your grammar file, to name it foo.ypp or foo.y++. Then, the output files will take an extension like the given one as input (respectively foo.tab.cpp and foo.tab.c++). This feature takes effect with all options that manipulate filenames like -o or -d.

For example :

         bison -d infile.yxx

will produce infile.tab.cxx and infile.tab.hxx, and

         bison -d -o output.c++ infile.y

will produce output.c++ and outfile.h++.

For compatibility with POSIX, the standard Bison distribution also contains a shell script called yacc that invokes Bison with the -y option.

Next: Option Cross Key, Up: Invocation

### 9.1 Bison Options

Bison supports both traditional single-letter options and mnemonic long option names. Long option names are indicated with -- instead of -. Abbreviations for option names are allowed as long as they are unique. When a long option takes an argument, like --file-prefix, connect the option name and the argument with =.

Here is a list of options that can be used with Bison, alphabetized by short option. It is followed by a cross key alphabetized by long option.

Operations modes:

-h
--help
  Print a summary of the command-line options to Bison and exit.
-V
--version
  Print the version number of Bison and exit.
-y
--yacc
  Equivalent to -o y.tab.c; the parser output file is called y.tab.c, and the other outputs are called y.output and y.tab.h. The purpose of this option is to imitate Yacc's output file name conventions. Thus, the following shell script can substitute for Yacc, and the Bison distribution contains such a script for compatibility with POSIX:

                #! /bin/sh
                bison -y "$@"

Tuning the parser:

-S file
--skeleton=file
  Specify the skeleton to use. You probably don't need this option unless you are developing Bison.
-t
--debug
  In the parser file, define the macro `YYDEBUG` to 1 if it is not already defined, so that the debugging facilities are compiled. See Tracing Your Parser.
--locations
  Pretend that `%locations` was specified. See Decl Summary.
-p prefix
--name-prefix=prefix
  Pretend that `%name-prefix="`prefix`"` was specified. See Decl Summary.
-l
--no-lines
  Don't put any `#line` preprocessor commands in the parser file. Ordinarily Bison puts them in the parser file so that the C compiler and debuggers will associate errors with your source file, the grammar file. This option causes them to associate errors with the parser file, treating it as an independent source file in its own right.
-n
--no-parser
  Pretend that `%no-parser` was specified. See Decl Summary.
-k
--token-table
  Pretend that `%token-table` was specified. See Decl Summary.

Adjust the output:

-d
--defines
  Pretend that `%defines` was specified, i.e., write an extra output file containing macro definitions for the token type names defined in the grammar, as well as a few other declarations. See Decl Summary.
--defines=defines-file
  Same as above, but save in the file defines-file.
-b file-prefix
--file-prefix=prefix
  Pretend that `%verbose` was specified, i.e, specify prefix to use for all Bison output file names. See Decl Summary.
-r things
--report=things
  Write an extra output file containing verbose description of the comma separated list of things among:
  `state`
    Description of the grammar, conflicts (resolved and unresolved), and LALR automaton.
  `look-ahead`
    Implies `state` and augments the description of the automaton with each rule's look-ahead set.
  `itemset`
    Implies `state` and augments the description of the automaton with the full set of items for each state, instead of its core only.

  For instance, on the following grammar

-v
--verbose
  Pretend that `%verbose` was specified, i.e, write an extra output file containing verbose descriptions of the grammar and parser. See Decl Summary.
-o filename
--output=filename
  Specify the filename for the parser file.

  The other output files' names are constructed from filename as described under the -v and -d options.

-g
  Output a VCG definition of the LALR(1) grammar automaton computed by Bison. If the grammar file is foo.y, the VCG output file will be foo.vcg.
--graph=graph-file
  The behavior of –graph is the same than -g. The only difference is that it has an optional argument which is the name of the output graph filename.

Next: Yacc Library, Previous: Bison Options, Up: Invocation

### 9.2 Option Cross Key

Here is a list of options, alphabetized by long option, to help you find the corresponding short option.

Previous: Option Cross Key, Up: Invocation

### 9.3 Yacc Library

The Yacc library contains default implementations of the `yyerror` and `main` functions. These default implementations are normally not useful, but POSIX requires them. To use the Yacc library, link your program with the -ly option. Note that Bison's implementation of the Yacc library is distributed under the terms of the GNU General Public License (see Copying).

If you use the Yacc library's `yyerror` function, you should declare `yyerror` as follows:

         int yyerror (char const *);

Bison ignores the `int` value returned by this `yyerror`. If you use the Yacc library's `main` function, your `yyparse` function should have the following type signature:

         int yyparse (void);

Next: Copying This Manual, Previous: Glossary, Up: Top

## 10 Frequently Asked Questions

Several questions about Bison come up occasionally. Here some of them are addressed.

Next: How Can I Reset the Parser, Up: FAQ

### 10.1 Parser Stack Overflow

         My parser returns with error with a parser stack overflow
         message.  What can I do?

This question is already addressed elsewhere, See Recursive Rules.

Next: Strings are Destroyed, Previous: Parser Stack Overflow, Up: FAQ

### 10.2 How Can I Reset the Parser

The following phenomenon has several symptoms, resulting in the following typical questions:

         I invoke yyparse several times, and on correct input it works
         properly; but when a parse error is found, all the other calls fail
         too.  How can I reset the error flag of yyparse?

or

         My parser includes support for an #include-like feature, in
         which case I run yyparse from yyparse.  This fails
         although I did specify I needed a %pure-parser.

These problems typically come not from Bison itself, but from Lex-generated scanners. Because these scanners use large buffers for speed, they might not notice a change of input file. As a demonstration, consider the following source file, first-line.l:

    %{
    #include <stdio.h>
    #include <stdlib.h>
    %}
    %%
    .*\n    ECHO; return 1;
    %%
    int
    yyparse (char const *file)
    {
      yyin = fopen (file, "r");
      if (!yyin)
        exit (2);
      /* One token only.  */
      yylex ();
      if (fclose (yyin) != 0)
        exit (3);
      return 0;
    }

    int
    main (void)
    {
      yyparse ("input");
      yyparse ("input");
      return 0;
    }

If the file input contains

    input:1: Hello,
    input:2: World!

then instead of getting the first line twice, you get:

         $ flex -ofirst-line.c first-line.l
         $ gcc  -ofirst-line   first-line.c -ll
         $ ./first-line
         input:1: Hello,
         input:2: World!

Therefore, whenever you change `yyin`, you must tell the Lex-generated scanner to discard its current buffer and switch to the new one. This depends upon your implementation of Lex; see its documentation for more. For Flex, it suffices to call YY_FLUSH_BUFFER after each change to `yyin`. If your Flex-generated scanner needs to read from several input streams to handle features like include files, you might consider using Flex functions like yy_switch_to_buffer that manipulate multiple input buffers.

If your Flex-generated scanner uses start conditions (see Start conditions (The Flex Manual)), you might also want to reset the scanner's state, i.e., go back to the initial start condition, through a call to BEGIN (0).

Next: C++ Parsers, Previous: How Can I Reset the Parser, Up: FAQ

### 10.3 Strings are Destroyed

         My parser seems to destroy old strings, or maybe it loses track of
         them.  Instead of reporting "foo", "bar", it reports
         "bar", "bar", or even "foo\nbar", "bar".

This error is probably the single most frequent “bug report” sent to Bison lists, but is only concerned with a misunderstanding of the role of scanner. Consider the following Lex code:

    %{
    #include <stdio.h>
    char *yylval = NULL;
    %}
    %%
    .*    yylval = yytext; return 1;
    \n    /* IGNORE */
    %%
    int
    main ()
    {
      /* Similar to using $1, $2 in a Bison action.  */
      char *fst = (yylex (), yylval);
      char *snd = (yylex (), yylval);
      printf ("\"%s\", \"%s\"\n", fst, snd);
      return 0;
    }

If you compile and run this code, you get:

         $ flex -osplit-lines.c split-lines.l
         $ gcc  -osplit-lines   split-lines.c -ll
         $ printf 'one\ntwo\n' | ./split-lines
         "one
         two", "two"

this is because `yytext` is a buffer provided for reading in the action, but if you want to keep it, you have to duplicate it (e.g., using `strdup`). Note that the output may depend on how your implementation of Lex handles `yytext`. For instance, when given the Lex compatibility option -l (which triggers the option %array) Flex generates a different behavior:

         $ flex -l -osplit-lines.c split-lines.l
         $ gcc     -osplit-lines   split-lines.c -ll
         $ printf 'one\ntwo\n' | ./split-lines
         "two", "two"

Next: Implementing Gotos/Loops, Previous: Strings are Destroyed, Up: FAQ

### 10.4 C++ Parsers

         How can I generate parsers in C++?

We are working on a C++ output for Bison, but unfortunately, for lack of time, the skeleton is not finished. It is functional, but in numerous respects, it will require additional work which might break backward compatibility. Since the skeleton for C++ is not documented, we do not consider ourselves bound to this interface, nevertheless, as much as possible we will try to keep compatibility.

Another possibility is to use the regular C parsers, and to compile them with a C++ compiler. This works properly, provided that you bear some simple C++ rules in mind, such as not including “real classes” (i.e., structure with constructors) in unions. Therefore, in the `%union`, use pointers to classes.

Previous: C++ Parsers, Up: FAQ

### 10.5 Implementing Gotos/Loops

         My simple calculator supports variables, assignments, and functions,
         but how can I implement gotos, or loops?

Although very pedagogical, the examples included in the document blur the distinction to make between the parser—whose job is to recover the structure of a text and to transmit it to subsequent modules of the program—and the processing (such as the execution) of this structure. This works well with so called straight line programs, i.e., precisely those that have a straightforward execution model: execute simple instructions one after the others.

If you want a richer model, you will probably need to use the parser to construct a tree that does represent the structure it has recovered; this tree is usually called the abstract syntax tree, or AST for short. Then, walking through this tree, traversing it in various ways, will enable treatments such as its execution or its translation, which will result in an interpreter or a compiler.

This topic is way beyond the scope of this manual, and the reader is invited to consult the dedicated literature.

Next: Glossary, Previous: Invocation, Up: Top

## Appendix A Bison Symbols

— Variable: @$

> In an action, the location of the left-hand side of the rule. See Locations Overview.

— Variable: @n

> In an action, the location of the n-th symbol of the right-hand side of the rule. See Locations Overview.

— Variable: $$

> In an action, the semantic value of the left-hand side of the rule. See Actions.

— Variable: $n

> In an action, the semantic value of the n-th symbol of the right-hand side of the rule. See Actions.

— Delimiter: %%

> Delimiter used to separate the grammar rule section from the Bison declarations section or the epilogue. See The Overall Layout of a Bison Grammar.

— Delimiter: %{code%}

> All code listed between %{ and %} is copied directly to the output file uninterpreted. Such code forms the prologue of the input file. See Outline of a Bison Grammar.

— Construct: /*...*/

> Comment delimiters, as in C.

— Delimiter: :

> Separates a rule's result from its components. See Syntax of Grammar Rules.

— Delimiter: ;

> Terminates a rule. See Syntax of Grammar Rules.

— Delimiter: |

> Separates alternate rules for the same result nonterminal. See Syntax of Grammar Rules.

— Symbol: $accept

> The predefined nonterminal whose only rule is $accept: start $end, where start is the start symbol. See The Start-Symbol. It cannot be used in the grammar.

— Directive: %debug

> Equip the parser for debugging. See Decl Summary.

— Directive: %defines

> Bison declaration to create a header file meant for the scanner. See Decl Summary.

— Directive: %destructor

> Specifying how the parser should reclaim the memory associated to discarded symbols. See Freeing Discarded Symbols.

— Directive: %dprec

> Bison declaration to assign a precedence to a rule that is used at parse time to resolve reduce/reduce conflicts. See Writing GLR Parsers.

— Symbol: $end

> The predefined token marking the end of the token stream. It cannot be used in the grammar.

— Symbol: error

> A token name reserved for error recovery. This token may be used in grammar rules so as to allow the Bison parser to recognize an error in the grammar without halting the process. In effect, a sentence containing an error may be recognized as valid. On a syntax error, the token `error` becomes the current look-ahead token. Actions corresponding to `error` are then executed, and the look-ahead token is reset to the token that originally caused the violation. See Error Recovery.

— Directive: %error-verbose

> Bison declaration to request verbose, specific error message strings when `yyerror` is called.

— Directive: %file-prefix="prefix"

> Bison declaration to set the prefix of the output files. See Decl Summary.

— Directive: %glr-parser

> Bison declaration to produce a GLR parser. See Writing GLR Parsers.

— Directive: %initial-action

> Run user code before parsing. See Performing Actions before Parsing.

— Directive: %left

> Bison declaration to assign left associativity to token(s). See Operator Precedence.

— Directive: %lex-param {argument-declaration}

> Bison declaration to specifying an additional parameter that `yylex` should accept. See Calling Conventions for Pure Parsers.

— Directive: %merge

> Bison declaration to assign a merging function to a rule. If there is a reduce/reduce conflict with a rule having the same merging function, the function is applied to the two semantic values to get a single result. See Writing GLR Parsers.

— Directive: %name-prefix="prefix"

> Bison declaration to rename the external symbols. See Decl Summary.

— Directive: %no-lines

> Bison declaration to avoid generating `#line` directives in the parser file. See Decl Summary.

— Directive: %nonassoc

> Bison declaration to assign non-associativity to token(s). See Operator Precedence.

— Directive: %output="filename"

> Bison declaration to set the name of the parser file. See Decl Summary.

— Directive: %parse-param {argument-declaration}

> Bison declaration to specifying an additional parameter that `yyparse` should accept. See The Parser Function `yyparse`.

— Directive: %prec

> Bison declaration to assign a precedence to a specific rule. See Context-Dependent Precedence.

— Directive: %pure-parser

> Bison declaration to request a pure (reentrant) parser. See A Pure (Reentrant) Parser.

— Directive: %right

> Bison declaration to assign right associativity to token(s). See Operator Precedence.

— Directive: %start

> Bison declaration to specify the start symbol. See The Start-Symbol.

— Directive: %token

> Bison declaration to declare token(s) without specifying precedence. See Token Type Names.

— Directive: %token-table

> Bison declaration to include a token name table in the parser file. See Decl Summary.

— Directive: %type

> Bison declaration to declare nonterminals. See Nonterminal Symbols.

— Symbol: $undefined

> The predefined token onto which all undefined values returned by `yylex` are mapped. It cannot be used in the grammar, rather, use `error`.

— Directive: %union

> Bison declaration to specify several possible data types for semantic values. See The Collection of Value Types.

— Macro: YYABORT

> Macro to pretend that an unrecoverable syntax error has occurred, by making `yyparse` return 1 immediately. The error reporting function `yyerror` is not called. See The Parser Function `yyparse`.

— Macro: YYACCEPT

> Macro to pretend that a complete utterance of the language has been read, by making `yyparse` return 0 immediately. See The Parser Function `yyparse`.

— Macro: YYBACKUP

> Macro to discard a value from the parser stack and fake a look-ahead token. See Special Features for Use in Actions.

— Variable: yychar

> External integer variable that contains the integer value of the current look-ahead token. (In a pure parser, it is a local variable within `yyparse`.) Error-recovery rule actions may examine this variable. See Special Features for Use in Actions.

— Variable: yyclearin

> Macro used in error-recovery rule actions. It clears the previous look-ahead token. See Error Recovery.

— Macro: YYDEBUG

> Macro to define to equip the parser with tracing code. See Tracing Your Parser.

— Variable: yydebug

> External integer variable set to zero by default. If `yydebug` is given a nonzero value, the parser will output information on input symbols and parser action. See Tracing Your Parser.

— Macro: yyerrok

> Macro to cause parser to recover immediately to its normal mode after a syntax error. See Error Recovery.

— Macro: YYERROR

> Macro to pretend that a syntax error has just been detected: call `yyerror` and then perform normal error recovery if possible (see Error Recovery), or (if recovery is impossible) make `yyparse` return 1. See Error Recovery.

— Function: yyerror

> User-supplied function to be called by `yyparse` on error. See The Error Reporting Function `yyerror`.

— Macro: YYERROR_VERBOSE

> An obsolete macro that you define with `#define` in the prologue to request verbose, specific error message strings when `yyerror` is called. It doesn't matter what definition you use for `YYERROR_VERBOSE`, just whether you define it. Using `%error-verbose` is preferred.

— Macro: YYINITDEPTH

> Macro for specifying the initial size of the parser stack. See Stack Overflow.

— Function: yylex

> User-supplied lexical analyzer function, called with no arguments to get the next token. See The Lexical Analyzer Function `yylex`.

— Macro: YYLEX_PARAM

> An obsolete macro for specifying an extra argument (or list of extra arguments) for `yyparse` to pass to `yylex`. he use of this macro is deprecated, and is supported only for Yacc like parsers. See Calling Conventions for Pure Parsers.

— Variable: yylloc

> External variable in which `yylex` should place the line and column numbers associated with a token. (In a pure parser, it is a local variable within `yyparse`, and its address is passed to `yylex`.) You can ignore this variable if you don't use the @ feature in the grammar actions. See Textual Locations of Tokens.

— Type: YYLTYPE

> Data type of `yylloc`; by default, a structure with four members. See Data Types of Locations.

— Variable: yylval

> External variable in which `yylex` should place the semantic value associated with a token. (In a pure parser, it is a local variable within `yyparse`, and its address is passed to `yylex`.) See Semantic Values of Tokens.

— Macro: YYMAXDEPTH

> Macro for specifying the maximum size of the parser stack. See Stack Overflow.

— Variable: yynerrs

> Global variable which Bison increments each time there is a syntax error. (In a pure parser, it is a local variable within `yyparse`.) See The Error Reporting Function `yyerror`.

— Function: yyparse

> The parser function produced by Bison; call this function to start parsing. See The Parser Function `yyparse`.

— Macro: YYPARSE_PARAM

> An obsolete macro for specifying the name of a parameter that `yyparse` should accept. The use of this macro is deprecated, and is supported only for Yacc like parsers. See Calling Conventions for Pure Parsers.

— Macro: YYRECOVERING

> Macro whose value indicates whether the parser is recovering from a syntax error. See Special Features for Use in Actions.

— Macro: YYSTACK_USE_ALLOCA

> Macro used to control the use of `alloca` when the C LALR(1) parser needs to extend its stacks. If defined to 0, the parser will use `malloc` to extend its stacks. If defined to 1, the parser will use `alloca`. Values other than 0 and 1 are reserved for future Bison extensions. If not defined, `YYSTACK_USE_ALLOCA` defaults to 0.

> If you define `YYSTACK_USE_ALLOCA` to 1, it is your responsibility to make sure that `alloca` is visible, e.g., by using GCC or by including `<stdlib.h>`. Furthermore, in the all-too-common case where your code may run on a host with a limited stack and with unreliable stack-overflow checking, you should set `YYMAXDEPTH` to a value that cannot possibly result in unchecked stack overflow on any of your target hosts when `alloca` is called. You can inspect the code that Bison generates in order to determine the proper numeric values. This will require some expertise in low-level implementation details.

— Type: YYSTYPE

> Data type of semantic values; `int` by default. See Data Types of Semantic Values.

Next: FAQ, Previous: Table of Symbols, Up: Top

## Appendix B Glossary

Backus-Naur Form (BNF; also called “Backus Normal Form”)
  Formal method of specifying context-free grammars originally proposed by John Backus, and slightly improved by Peter Naur in his 1960-01-02 committee document contributing to what became the Algol 60 report. See Languages and Context-Free Grammars.
Context-free grammars
  Grammars specified as rules that can be applied regardless of context. Thus, if there is a rule which says that an integer can be used as an expression, integers are allowed anywhere an expression is permitted. See Languages and Context-Free Grammars.
Dynamic allocation
  Allocation of memory that occurs during execution, rather than at compile time or on entry to a function.
Empty string
  Analogous to the empty set in set theory, the empty string is a character string of length zero.
Finite-state stack machine
  A “machine” that has discrete states in which it is said to exist at each instant in time. As input to the machine is processed, the machine moves from state to state as specified by the logic of the machine. In the case of the parser, the input is the language being parsed, and the states correspond to various stages in the grammar rules. See The Bison Parser Algorithm.
Generalized LR (GLR)
  A parsing algorithm that can handle all context-free grammars, including those that are not LALR(1). It resolves situations that Bison's usual LALR(1) algorithm cannot by effectively splitting off multiple parsers, trying all possible parsers, and discarding those that fail in the light of additional right context. See Generalized LR Parsing.
Grouping
  A language construct that is (in general) grammatically divisible; for example, `expression' or `declaration' in C. See Languages and Context-Free Grammars.
Infix operator
  An arithmetic operator that is placed between the operands on which it performs some operation.
Input stream
  A continuous flow of data between devices or programs.
Language construct
  One of the typical usage schemas of the language. For example, one of the constructs of the C language is the `if` statement. See Languages and Context-Free Grammars.
Left associativity
  Operators having left associativity are analyzed from left to right: a+b+c first computes a+b and then combines with c. See Operator Precedence.
Left recursion
  A rule whose result symbol is also its first component symbol; for example, expseq1 : expseq1 ',' exp;. See Recursive Rules.
Left-to-right parsing
  Parsing a sentence of a language by analyzing it token by token from left to right. See The Bison Parser Algorithm.
Lexical analyzer (scanner)
  A function that reads an input stream and returns tokens one by one. See The Lexical Analyzer Function `yylex`.
Lexical tie-in
  A flag, set by actions in the grammar rules, which alters the way tokens are parsed. See Lexical Tie-ins.
Literal string token
  A token which consists of two or more fixed characters. See Symbols.
Look-ahead token
  A token already read but not yet shifted. See Look-Ahead Tokens.
LALR(1)
  The class of context-free grammars that Bison (like most other parser generators) can handle; a subset of LR(1). See Mysterious Reduce/Reduce Conflicts.
LR(1)
  The class of context-free grammars in which at most one token of look-ahead is needed to disambiguate the parsing of any piece of input.
Nonterminal symbol
  A grammar symbol standing for a grammatical construct that can be expressed through rules in terms of smaller constructs; in other words, a construct that is not a token. See Symbols.
Parser
  A function that recognizes valid sentences of a language by analyzing the syntax structure of a set of tokens passed to it from a lexical analyzer.
Postfix operator
  An arithmetic operator that is placed after the operands upon which it performs some operation.
Reduction
  Replacing a string of nonterminals and/or terminals with a single nonterminal, according to a grammar rule. See The Bison Parser Algorithm.
Reentrant
  A reentrant subprogram is a subprogram which can be in invoked any number of times in parallel, without interference between the various invocations. See A Pure (Reentrant) Parser.
Reverse polish notation
  A language in which all operators are postfix operators.
Right recursion
  A rule whose result symbol is also its last component symbol; for example, expseq1: exp ',' expseq1;. See Recursive Rules.
Semantics
  In computer languages, the semantics are specified by the actions taken for each instance of the language, i.e., the meaning of each statement. See Defining Language Semantics.
Shift
  A parser is said to shift when it makes the choice of analyzing further input from the stream rather than reducing immediately some already-recognized rule. See The Bison Parser Algorithm.
Single-character literal
  A single character that is recognized and interpreted as is. See From Formal Rules to Bison Input.
Start symbol
  The nonterminal symbol that stands for a complete valid utterance in the language being parsed. The start symbol is usually listed as the first nonterminal symbol in a language specification. See The Start-Symbol.
Symbol table
  A data structure where symbol names and associated data are stored during parsing to allow for recognition and use of existing information in repeated uses of a symbol. See Multi-function Calc.
Syntax error
  An error encountered during parsing of an input stream due to invalid syntax. See Error Recovery.
Token
  A basic, grammatically indivisible unit of a language. The symbol that describes a token in the grammar is a terminal symbol. The input of the Bison parser is a stream of tokens which comes from the lexical analyzer. See Symbols.
Terminal symbol
  A grammar symbol that has no rules in the grammar and therefore is grammatically indivisible. The piece of text it represents is a token. See Languages and Context-Free Grammars.

Next: Index, Previous: FAQ, Up: Top

## Appendix C Copying This Manual

Up: Copying This Manual

### C.1 GNU Free Documentation License

Version 1.2, November 2002

         Copyright © 2000,2001,2002 Free Software Foundation, Inc.
         59 Temple Place, Suite 330, Boston, MA  02111-1307, USA

         Everyone is permitted to copy and distribute verbatim copies
         of this license document, but changing it is not allowed.

0. PREAMBLE

   The purpose of this License is to make a manual, textbook, or other functional and useful document free in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others.

   This License is a kind of “copyleft”, which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software.

   We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference.

1. APPLICABILITY AND DEFINITIONS

   This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The “Document”, below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as “you”. You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law.

   A “Modified Version” of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language.

   A “Secondary Section” is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document's overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.

   The “Invariant Sections” are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none.

   The “Cover Texts” are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words.

   A “Transparent” copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public, that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to thwart or discourage subsequent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of text. A copy that is not “Transparent” is called “Opaque”.

   Examples of suitable formats for Transparent copies include plain ascii without markup, Texinfo input format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image formats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and edited only by proprietary word processors, SGML or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some word processors for output purposes only.

   The “Title Page” means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, “Title Page” means the text near the most prominent appearance of the work's title, preceding the beginning of the body of the text.

   A section “Entitled XYZ” means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as “Acknowledgements”, “Dedications”, “Endorsements”, or “History”.) To “Preserve the Title” of such a section when you modify the Document means that it remains a section “Entitled XYZ” according to this definition.

   The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License.

2. VERBATIM COPYING

   You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3.

   You may also lend copies, under the same conditions stated above, and you may publicly display copies.

3. COPYING IN QUANTITY

   If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document's license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects.

   If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.

   If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public.

   It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document.

4. MODIFICATIONS

   You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

   1. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission.
   2. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement.
   3. State on the Title page the name of the publisher of the Modified Version, as the publisher.
   4. Preserve all the copyright notices of the Document.
   5. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.
   6. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below.
   7. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document's license notice.
   8. Include an unaltered copy of this License.
   9. Preserve the section Entitled “History”, Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled “History” in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.
   10. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the “History” section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.
   11. For any section Entitled “Acknowledgements” or “Dedications”, Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.
   12. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.
   13. Delete any section Entitled “Endorsements”. Such a section may not be included in the Modified Version.
   14. Do not retitle any existing section to be Entitled “Endorsements” or to conflict in title with any Invariant Section.
   15. Preserve any Warranty Disclaimers.

   If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version's license notice. These titles must be distinct from any other section titles.

   You may add a section Entitled “Endorsements”, provided it contains nothing but endorsements of your Modified Version by various parties—for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.

   You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.

   The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.

5. COMBINING DOCUMENTS

   You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

   The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.

   In the combination, you must combine any sections Entitled “History” in the various original documents, forming one section Entitled “History”; likewise combine any sections Entitled “Acknowledgements”, and any sections Entitled “Dedications”. You must delete all sections Entitled “Endorsements.”

6. COLLECTIONS OF DOCUMENTS

   You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.

   You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.

7. AGGREGATION WITH INDEPENDENT WORKS

   A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an “aggregate” if the copyright resulting from the compilation is not used to limit the legal rights of the compilation's users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.

   If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document's Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

8. TRANSLATION

   Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.

   If a section in the Document is Entitled “Acknowledgements”, “Dedications”, or “History”, the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.

9. TERMINATION

   You may not copy, modify, sublicense, or distribute the Document except as expressly provided for under this License. Any other attempt to copy, modify, sublicense or distribute the Document is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance.

10. FUTURE REVISIONS OF THIS LICENSE

    The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.

    Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License “or any later version” applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation.

#### C.1.1 ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:

           Copyright (C)  year  your name.
           Permission is granted to copy, distribute and/or modify this document
           under the terms of the GNU Free Documentation License, Version 1.2
           or any later version published by the Free Software Foundation;
           with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
           A copy of the license is included in the section entitled ``GNU
           Free Documentation License''.

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the “with...Texts.” line with this:

             with the Invariant Sections being list their titles, with
             the Front-Cover Texts being list, and with the Back-Cover Texts
             being list.

If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.

Previous: Copying This Manual, Up: Top

## Index

- abstract syntax tree: Implementing Gotos/Loops
- action: Actions
- action data types: Action Types
- action features summary: Action Features
- actions in mid-rule: Mid-Rule Actions
- actions, location: Actions and Locations
- actions, semantic: Semantic Actions
- additional C code section: Epilogue
- algorithm of parser: Algorithm
- ambiguous grammars: Language and Grammar
- ambiguous grammars: Generalized LR Parsing
- associativity: Why Precedence
- AST: Implementing Gotos/Loops
- Backus-Naur form: Language and Grammar
- Bison declaration summary: Decl Summary
- Bison declarations: Declarations
- Bison declarations (introduction): Bison Declarations
- Bison grammar: Grammar in Bison
- Bison invocation: Invocation
- Bison parser: Bison Parser
- Bison parser algorithm: Algorithm
- Bison symbols, table of: Table of Symbols
- Bison utility: Bison Parser
- BNF: Language and Grammar
- C code, section for additional: Epilogue
- C-language interface: Interface
- `calc`: Infix Calc
- calculator, infix notation: Infix Calc
- calculator, location tracking: Location Tracking Calc
- calculator, multi-function: Multi-function Calc
- calculator, simple: RPN Calc
- character token: Symbols
- compiling the parser: Rpcalc Compile
- conflicts: Shift/Reduce
- conflicts: Merging GLR Parses
- conflicts: GLR Parsers
- conflicts: Simple GLR Parsers
- conflicts, reduce/reduce: Reduce/Reduce
- conflicts, suppressing warnings of: Expect Decl
- context-dependent precedence: Contextual Precedence
- context-free grammar: Language and Grammar
- controlling function: Rpcalc Main
- core, item set: Understanding
- dangling `else`: Shift/Reduce
- data type of locations: Location Type
- data types in actions: Action Types
- data types of semantic values: Value Type
- debugging: Tracing
- declaration summary: Decl Summary
- declarations: Prologue
- declarations section: Prologue
- declarations, Bison: Declarations
- declarations, Bison (introduction): Bison Declarations
- declaring literal string tokens: Token Decl
- declaring operator precedence: Precedence Decl
- declaring the start symbol: Start Decl
- declaring token type names: Token Decl
- declaring value types: Union Decl
- declaring value types, nonterminals: Type Decl
- default action: Actions
- default data type: Value Type
- default location type: Location Type
- default stack limit: Stack Overflow
- default start symbol: Start Decl
- defining language semantics: Semantics
- discarded symbols: Destructor Decl
- `else`, dangling: Shift/Reduce
- epilogue: Epilogue
- error recovery: Error Recovery
- error recovery, simple: Simple Error Recovery
- error reporting function: Error Reporting
- error reporting routine: Rpcalc Error
- examples, simple: Examples
- exercises: Exercises
- FDL, GNU Free Documentation License: GNU Free Documentation License
- file format: Grammar Layout
- finite-state machine: Parser States
- formal grammar: Grammar in Bison
- format of grammar file: Grammar Layout
- freeing discarded symbols: Destructor Decl
- frequently asked questions: FAQ
- generalized LR (GLR) parsing: Language and Grammar
- generalized LR (GLR) parsing: GLR Parsers
- generalized LR (GLR) parsing: Generalized LR Parsing
- generalized LR (GLR) parsing, ambiguous grammars: Merging GLR Parses
- generalized LR (GLR) parsing, unambiguous grammars: Simple GLR Parsers
- glossary: Glossary
- GLR parsers and `inline`: Compiler Requirements
- GLR parsing: Generalized LR Parsing
- GLR parsing: Language and Grammar
- GLR parsing: GLR Parsers
- GLR parsing, ambiguous grammars: Merging GLR Parses
- GLR parsing, unambiguous grammars: Simple GLR Parsers
- grammar file: Grammar Layout
- grammar rule syntax: Rules
- grammar rules section: Grammar Rules
- grammar, Bison: Grammar in Bison
- grammar, context-free: Language and Grammar
- grouping, syntactic: Language and Grammar
- infix notation calculator: Infix Calc
- `inline`: Compiler Requirements
- interface: Interface
- introduction: Introduction
- invoking Bison: Invocation
- item: Understanding
- item set core: Understanding
- kernel, item set: Understanding
- LALR(1): Mystery Conflicts
- LALR(1) grammars: Language and Grammar
- language semantics, defining: Semantics
- layout of Bison grammar: Grammar Layout
- left recursion: Recursion
- lexical analyzer: Lexical
- lexical analyzer, purpose: Bison Parser
- lexical analyzer, writing: Rpcalc Lexer
- lexical tie-in: Lexical Tie-ins
- literal string token: Symbols
- literal token: Symbols
- location: Locations Overview
- location: Locations
- location actions: Actions and Locations
- location tracking calculator: Location Tracking Calc
- location, textual: Locations
- location, textual: Locations Overview
- look-ahead token: Look-Ahead
- LR(1): Mystery Conflicts
- LR(1) grammars: Language and Grammar
- `ltcalc`: Location Tracking Calc
- main function in simple example: Rpcalc Main
- `mfcalc`: Multi-function Calc
- mid-rule actions: Mid-Rule Actions
- multi-function calculator: Multi-function Calc
- multicharacter literal: Symbols
- mutual recursion: Recursion
- non-deterministic parsing: Language and Grammar
- non-deterministic parsing: Generalized LR Parsing
- nonterminal symbol: Symbols
- nonterminal, useless: Understanding
- operator precedence: Precedence
- operator precedence, declaring: Precedence Decl
- options for invoking Bison: Invocation
- overflow of parser stack: Stack Overflow
- parse error: Error Reporting
- parser: Bison Parser
- parser stack: Algorithm
- parser stack overflow: Stack Overflow
- parser state: Parser States
- pointed rule: Understanding
- polish notation calculator: RPN Calc
- precedence declarations: Precedence Decl
- precedence of operators: Precedence
- precedence, context-dependent: Contextual Precedence
- precedence, unary operator: Contextual Precedence
- preventing warnings about conflicts: Expect Decl
- Prologue: Prologue
- pure parser: Pure Decl
- questions: FAQ
- recovery from errors: Error Recovery
- recursive rule: Recursion
- reduce/reduce conflict: Reduce/Reduce
- reduce/reduce conflicts: GLR Parsers
- reduce/reduce conflicts: Merging GLR Parses
- reduce/reduce conflicts: Simple GLR Parsers
- reduction: Algorithm
- reentrant parser: Pure Decl
- reverse polish notation: RPN Calc
- right recursion: Recursion
- `rpcalc`: RPN Calc
- rule syntax: Rules
- rule, pointed: Understanding
- rule, useless: Understanding
- rules section for grammar: Grammar Rules
- running Bison (introduction): Rpcalc Gen
- semantic actions: Semantic Actions
- semantic value: Semantic Values
- semantic value type: Value Type
- shift/reduce conflicts: Shift/Reduce
- shift/reduce conflicts: Simple GLR Parsers
- shift/reduce conflicts: GLR Parsers
- shifting: Algorithm
- simple examples: Examples
- single-character literal: Symbols
- stack overflow: Stack Overflow
- stack, parser: Algorithm
- stages in using Bison: Stages
- start symbol: Language and Grammar
- start symbol, declaring: Start Decl
- state (of parser): Parser States
- string token: Symbols
- summary, action features: Action Features
- summary, Bison declaration: Decl Summary
- suppressing conflict warnings: Expect Decl
- symbol: Symbols
- symbol table example: Mfcalc Symtab
- symbols (abstract): Language and Grammar
- symbols in Bison, table of: Table of Symbols
- syntactic grouping: Language and Grammar
- syntax error: Error Reporting
- syntax of grammar rules: Rules
- terminal symbol: Symbols
- textual location: Locations Overview
- textual location: Locations
- token: Language and Grammar
- token type: Symbols
- token type names, declaring: Token Decl
- token, useless: Understanding
- tracing the parser: Tracing
- unary operator precedence: Contextual Precedence
- useless nonterminal: Understanding
- useless rule: Understanding
- useless token: Understanding
- using Bison: Stages
- value type, semantic: Value Type
- value types, declaring: Union Decl
- value types, nonterminals, declaring: Type Decl
- value, semantic: Semantic Values
- warnings, preventing: Expect Decl
- writing a lexical analyzer: Rpcalc Lexer