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Info file bison.info, produced by Makeinfo, -*- Text -*- from input
file bison.texinfo.

This file documents the Bison parser generator.

Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.

Permission is granted to copy and distribute modified versions of
this manual under the conditions for verbatim copying, provided also
that the sections entitled ``GNU General Public License'' and
``Conditions for Using Bison'' are included exactly as in the
original, and provided that the entire resulting derived work is
distributed under the terms of a permission notice identical to this
one.

Permission is granted to copy and distribute translations of this
manual into another language, under the above conditions for modified
versions, except that the sections entitled ``GNU General Public
License'', ``Conditions for Using Bison'' and this permission notice
may be included in translations approved by the Free Software
Foundation instead of in the original English.

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* Menu:

* Introduction::
* Conditions::
* Copying:: The GNU General Public License says
how you can copy and share Bison

Tutorial sections:
* Concepts:: Basic concepts for understanding Bison.
* Examples:: Three simple explained examples of using Bison.

Reference sections:
* Grammar File:: Writing Bison declarations and rules.
* Interface:: C-language interface to the parser function `yyparse'.
* Algorithm:: How the Bison parser works at run-time.
* Error Recovery:: Writing rules for error recovery.
* Context Dependency::What to do if your language syntax is too
messy for Bison to handle straightforwardly.
* Debugging:: Debugging Bison parsers that parse wrong.
* Invocation:: How to run Bison (to produce the parser source file).
* Table of Symbols:: All the keywords of the Bison language are explained.
* Glossary:: Basic concepts are explained.
* Index:: Cross-references to the text.

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Introduction
************

"Bison" is a general-purpose parser generator which converts a
grammar description 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 basically written by Robert Corbett, and made
Yacc-compatible by Richard Stallman.

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Conditions for Using Bison
**************************

Bison grammars can be used only in programs that are free software.
This is in contrast to what happens with the GNU C compiler and the
other GNU programming tools.

The reason Bison is special is that 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.)

As a result, the Bison parser file is covered by the same copying
conditions that cover Bison itself and the rest of the GNU system:
any program containing it has to be distributed under the standard
GNU copying conditions.

Occasionally people who would like to use Bison to develop
proprietary programs complain about this.

We don't particularly sympathize with their complaints. The purpose
of the GNU project is to promote the right to share software and the
practice of sharing software; it is a means of changing society. The
people who complain are planning to be uncooperative toward the rest
of the world; why should they deserve our help in doing so?

However, it's possible that a change in these conditions might
encourage computer companies to use and distribute the GNU system.
If so, then we might decide to change the terms on `yyparse' as a
matter of the strategy of promoting the right to share. Such a
change would be irrevocable. Since we stand by the copying
permissions we have announced, we cannot withdraw them once given.

We mustn't make an irrevocable change hastily. We have to wait until
there is a complete GNU system and there has been time to learn how
this issue affects its reception.

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GNU GENERAL PUBLIC LICENSE
**************************

Version 1, February 1989

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

Preamble
=========

The license agreements of most software companies try to keep users
at the mercy of those companies. By contrast, our 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.
The General Public License applies to the Free Software Foundation's
software and to any other program whose authors commit to using it.
You can use it for your programs, too.

When we speak of free software, we are referring to freedom, not
price. Specifically, the General Public License is designed to make
sure that you have the freedom to give away or sell copies of free
software, 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 a 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 tell them 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.

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

TERMS AND CONDITIONS

1. This License Agreement 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 work containing the Program or a portion of it,
either verbatim or with modifications. Each licensee is
addressed as ``you''.

2. You may copy and distribute verbatim copies of the Program's
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conspicuously and appropriately publish on each copy an
appropriate copyright notice and disclaimer of warranty; keep
intact all the notices that refer to this General Public License
and to the absence of any warranty; and give any other
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3. You may modify your copy or copies of the Program or any portion
of it, and copy and distribute such modifications under the
terms of Paragraph 1 above, provided that you also do the
following:

* cause the modified files to carry prominent notices stating
that you changed the files and the date of any change; and

* cause the whole of any work that you distribute or publish,
that in whole or in part contains the Program or any part
thereof, either with or without modifications, to be
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of this General Public License (except that you may choose
to grant warranty protection to some or all third parties,
at your option).

* If the modified program normally reads commands
interactively when run, you must cause it, when started
running for such interactive use in the simplest and most
usual 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
General Public License.

* 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.

Mere aggregation of another independent work with the Program
(or its derivative) on a volume of a storage or distribution
medium does not bring the other work under the scope of these
terms.

4. You may copy and distribute the Program (or a portion or
derivative of it, under Paragraph 2) in object code or
executable form under the terms of Paragraphs 1 and 2 above
provided that you also do one of the following:

* accompany it with the complete corresponding
machine-readable source code, which must be distributed
under the terms of Paragraphs 1 and 2 above; or,

* accompany it with a written offer, valid for at least three
years, to give any third party free (except for a nominal
charge for the cost of distribution) a complete
machine-readable copy of the corresponding source code, to
be distributed under the terms of Paragraphs 1 and 2 above;
or,

* accompany it with the information you received as to where
the corresponding source code may be obtained. (This
alternative is allowed only for noncommercial distribution
and only if you received the program in object code or
executable form alone.)

Source code for a work means the preferred form of the work for
making modifications to it. For an executable file, complete
source code means all the source code for all modules it
contains; but, as a special exception, it need not include
source code for modules which are standard libraries that
accompany the operating system on which the executable file
runs, or for standard header files or definitions files that
accompany that operating system.

5. You may not copy, modify, sublicense, distribute or transfer the
Program except as expressly provided under this General Public
License. Any attempt otherwise to copy, modify, sublicense,
distribute or transfer the Program is void, and will
automatically terminate your rights to use the Program under
this License. However, parties who have received copies, or
rights to use copies, from you under this General Public License
will not have their licenses terminated so long as such parties
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6. By copying, distributing or modifying the Program (or any work
based on the Program) you indicate your acceptance of this
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7. Each time you redistribute the Program (or any work based on the
Program), the recipient automatically receives a license from
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subject to these terms and conditions. You may not impose any
further restrictions on the recipients' exercise of the rights
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8. The Free Software Foundation may publish revised and/or new
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you may choose any version ever published by the Free Software
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9. If you wish to incorporate parts of the Program into other free
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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
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NO WARRANTY

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WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE
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END OF TERMS AND CONDITIONS

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 humanity, 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) 19YY 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 1, 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., 675 Mass Ave, Cambridge, MA 02139, 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 a sample; alter the names:

Yoyodyne, Inc., hereby disclaims all copyright interest in the
program `Gnomovision' (a program to direct compilers to make passes
at assemblers) written by James Hacker.

SIGNATURE OF TY COON, 1 April 1989
Ty Coon, President of Vice

That's all there is to it!

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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.

* Menu:

* Language and Grammar:: Languages and context-free grammars,
as mathematical ideas.
* Grammar in Bison:: How we represent grammars for Bison's sake.
* Semantic Values:: Each token or syntactic grouping can have
a semantic value (the value of an integer,
the name of an identifier, etc.).
* Semantic Actions:: Each rule can have an action containing C code.
* Bison Parser:: What are Bison's input and output,
how is the output used?
* Stages:: Stages in writing and running Bison grammars.
* Grammar Layout:: Overall structure of a Bison grammar file.

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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.

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 (x) /* identifier, open-paren, */
/* identifier, close-paren */
int x; /* keyword `int', identifier, semicolon */
{ /* 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.

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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. *Note Grammar File::.

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. *Note 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.

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 ';'
;

*Note Rules::.

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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". *Note Semantics::, for details.

The token type is a terminal symbol defined in the grammar, such as
`INTEGER_CONSTANT', `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 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.

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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. *Note 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.

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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. *Note Lexical::.

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. *Note Interface::.

Aside from the token type names and the symbols in the actions you
write, all variable and function names used in the Bison parser file
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.

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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
(*note Grammar File::.). 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 (*note
Lexical::.). 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.

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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:

%{
C DECLARATIONS
%}

BISON DECLARATIONS

%%
GRAMMAR RULES
%%
ADDITIONAL C CODE

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

The C declarations 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.

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 additional C code can contain any C code you want to use. Often
the definition of the lexical analyzer `yylex' goes here, plus
subroutines called by the actions in the grammar rules. In a simple
program, all the rest of the program can go here.

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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.

You can copy these examples out of the Info file and into a source
file to try them.

* Menu:

* RPN Calc:: Reverse polish notation calculator;
a first example with no operator precedence.
* Infix Calc:: Infix (algebraic) notation calculator.
Operator precedence is introduced.
* Simple Error Recovery:: Continuing after syntax errors.
* Multi-function Calc:: Calculator with memory and trig functions.
It uses multiple data-types for semantic values.
* Exercises:: Ideas for improving the multi-function calculator.

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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.

* Menu:

* Decls: Rpcalc Decls. Bison and C declarations for rpcalc.
* Rules: Rpcalc Rules. Grammar Rules for rpcalc, with explanation.
* Input: Rpcalc Input. Explaining the rules for `input'.
* Line: Rpcalc Line. Explaining the rules for `line'.
* Expr: Rpcalc Expr. Explaining the rules for `expr'.
* Lexer: Rpcalc Lexer. The lexical analyzer.
* Main: Rpcalc Main. The controlling function.
* Error: Rpcalc Error. The error reporting function.
* Gen: Rpcalc Gen. Running Bison on the grammar file.
* Comp: Rpcalc Compile. Run the C compiler on the output code.

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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>
%}

%token NUM

%% /* Grammar rules and actions follow */

The C declarations section (*note C Declarations::.) contains two
preprocessor directives.

The `#define' directive defines the macro `YYSTYPE', thus specifying
the C data type for semantic values of both tokens and groupings
(*note Value Type::.). 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 second section, Bison declarations, provides information to Bison
about the token types (*note Bison Declarations::.). 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.

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File: bison.info, Node: Rpcalc Rules, Next: Rpcalc Input, Prev: Rpcalc Decls, Up: RPN Calc

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. *Note 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.

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File: bison.info, Node: Rpcalc Input, Next: Rpcalc Line, Prev: Rpcalc Rules, Up: RPN Calc

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. *Note Recursion::.

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
file.

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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.

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File: bison.info, Node: Rpcalc Expr, Next: Rpcalc Lexer, Prev: Rpcalc Line, Up: RPN Calc

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. *Note 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 whitespace 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.

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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. *Note Lexical::.

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 the ASCII code for that
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; *note Rpcalc Decls::..)

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

Here is the code for the lexical analyzer:

/* Lexical analyzer returns a double floating point number on the
stack and the token NUM, or the ASCII character read if not a
number. Skips all blanks and tabs, returns 0 for EOF. */

#include <ctype.h>

yylex ()
{
int c;

while ((c = getchar ()) == ' ' || c == '\t') /* skip white space */
;
if (c == '.' || isdigit (c)) /* process numbers */
{
ungetc (c, stdin);
scanf ("%lf", &yylval);
return NUM;
}
if (c == EOF) /* return end-of-file */
return 0;
return c; /* return single chars */
}

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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.

main ()
{
yyparse ();
}

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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
`"parse error"'). It is up to the programmer to supply `yyerror'
(*note Interface::.), so here is the definition we will use:

#include <stdio.h>

yyerror (s) /* Called by yyparse on error */
char *s;
{
printf ("%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
(*note 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 in the first
example.

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File: bison.info, Node: Rpcalc Gen, Next: Rpcalc Compile, Prev: Rpcalc Error, Up: RPN Calc

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 ``additional C code'' section of the file (*note Grammar
Layout::.).

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.

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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 rpcalc.tab.c -lm -o rpcalc

# 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
%

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