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Info file bison.info, produced by Makeinfo, -*- Text -*- from input file bison.texinfo. This file documents the Bison parser generator. Copyright (C) 1988, 1989, 1990 Free Software Foundation, Inc. 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. File: bison.info, Node: Top, Next: Introduction, Prev: (DIR), Up: (DIR) This manual documents version 1.16 of Bison. * 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. File: bison.info, Node: Introduction, Next: Conditions, Prev: 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. This edition corresponds to version 1.16 of Bison. File: bison.info, Node: Conditions, Next: Copying, Prev: Introduction, Up: Top 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. File: bison.info, Node: Copying, Next: Concepts, Prev: Conditions, Up: Top GNU GENERAL PUBLIC LICENSE ************************** Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 675 Mass Ave, Cambridge, MA 02139, 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. 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TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 1. 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. 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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 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., 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 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. File: bison.info, Node: Concepts, Next: Examples, Prev: Copying, Up: Top 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. File: bison.info, Node: Language and Grammar, Next: Grammar in Bison, Prev: Concepts, Up: Concepts 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. Not all context-free languages can be handled by Bison, only those that are LALR(1). In brief, this means that 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). *Note Mysterious Reduce/Reduce Conflicts: Mystery Conflicts, for more information on this. 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. File: bison.info, Node: Grammar in Bison, Next: Semantic Values, Prev: Language and Grammar, Up: Concepts 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::. File: bison.info, Node: Semantic Values, Next: Semantic Actions, Prev: Grammar in Bison, Up: Concepts 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', `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. File: bison.info, Node: Semantic Actions, Next: Bison Parser, Prev: Semantic Values, Up: Concepts 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. File: bison.info, Node: Bison Parser, Next: Stages, Prev: Semantic Actions, Up: Concepts 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. File: bison.info, Node: Stages, Next: Grammar Layout, Prev: Bison Parser, Up: Concepts 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. File: bison.info, Node: Grammar Layout, Prev: Stages, Up: Concepts 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. File: bison.info, Node: Examples, Next: Grammar File, Prev: Concepts, Up: Top 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. File: bison.info, Node: RPN Calc, Next: Infix Calc, Prev: Examples, Up: Examples 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. File: bison.info, Node: Rpcalc Decls, Next: Rpcalc Rules, Prev: RPN calc, Up: RPN calc 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. 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. 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. File: bison.info, Node: Rpcalc Line, Next: Rpcalc Expr, Prev: Rpcalc Input, Up: RPN Calc 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 `$$'. As a consequence, the semantic value associated with the `line' is uninitialized (its value will be unpredictable). This would be a bug if that value were ever used, but we don't use it: once rpcalc has printed the value of the user's input line, that value is no longer needed. File: bison.info, Node: Rpcalc Expr, Next: Rpcalc Lexer, Prev: Rpcalc Line, Up: RPN Calc Explanation of `expr' ..................... The `exp' grouping has several rules, one for each kind of expression. The first rule handles the simplest expressions: those that are just numbers. The second handles an addition-expression, which looks like two expressions followed by a plus-sign. The third handles subtraction, and so on. exp: NUM | exp exp '+' { $$ = $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.