We will keep the same operators as the postfix calculator, but we will give them their usual associativity (left), precedence (* and / before + and ) and we will also need brackets.
($CS2121/e*/infix1/*
)
%{ /* C declarations used in actions */ #include <stdio.h> %} /* yacc definitions */ %union {int a_number;} %start line %type <a_number> exp term factor number digit %% /*descriptions of expected inputs corresponding actions (in C)*/ line : exp ';' '\n' {printf ("result is %d\n", $1);} ; exp : term {$$ = $1;}  exp '+' term {$$ = $1 + $3;}  exp '' term {$$ = $1  $3;} ; term : factor {$$ = $1;}  term '*' factor {$$ = $1 * $3;}  term '/' factor {$$ = $1 / $3;} ; factor : number {$$ = $1;}  '(' exp ')' {$$ = $2;} ; number : digit {$$ = $1;}  number digit {$$ = $1*10 + $2;} ; digit : '0' {$$ = 0;}  '1' {$$ = 1;}  '2' {$$ = 2;}  '3' {$$ = 3;}  '4' {$$ = 4;}  '5' {$$ = 5;}  '6' {$$ = 6;}  '7' {$$ = 7;}  '8' {$$ = 8;}  '9' {$$ = 9;} ; %% /* C code */ int main (void) {return yyparse ( );} int yylex (void) {return getchar ( );} void yyerror (char *s) {fprintf (stderr, "%s\n", s);}
name : names and 'single character's  alternatives ;
%start line 
means the whole input should match line 
%union 
lists all possible types for values associated with parts of the grammar and gives each a fieldname 
%type 
gives an individual type for the values associated with each part of the grammar, 
using the fieldnames from the %union declaration 
$$ 
resulting value for any part of the grammar 
$1 , $2 , etc. 
values from subparts of the grammar 
yyparse 
routine created by YACC from (expected input, action) lists. 
(It actually returns a value indicating if it failed to recognise the input.)  
yylex 
routine called by yyparse for all its input. 
We are using getchar, which just reads characters from the input.  
yyerror 
routine called by yyparse whenever it detects an error in its input. 
BYACC : calc.y calc.c
GCC : calc.c calc
calc : expression result
YACC has other facilities, some of which we will use elsewhere, but those described above are among the most important. Further details and examples can be found in the readings (3.10).
Unfortunately, YACC cannot represent numbers as [09]+
nor
easily obtain the corresponding value, nor can it easily be used to ignore
white space and comments. Therefore, we need to use both LEX and
YACC together; LEX for the simple parts (e.g. numbers,
white space, comments)
and YACC for more complex parts (e.g. expressions).
YACC code for infix calculator using LEX and YACC
($CS2121/e*/infix2/*
):
%{ #include <stdio.h> %} %union {int a_number;} %start line %token <a_number> number %type <a_number> exp term factor %% line : exp ';' {printf ("result is %d\n", $1);} ; exp : term {$$ = $1;}  exp '+' term {$$ = $1 + $3;}  exp '' term {$$ = $1  $3;} ; term : factor {$$ = $1;}  term '*' factor {$$ = $1 * $3;}  term '/' factor {$$ = $1 / $3;} ; factor : number {$$ = $1;}  '(' exp ')' {$$ = $2;} ; %% int main (void) {return yyparse ( );} void yyerror (char *s) {fprintf (stderr, "%s\n", s);}
LEX code for infix calculator using LEX and YACC
($CS2121/e*/infix2/*
):
%{ #include "y.tab.h" %} %% [09]+ {yylval.a_number = atoi(yytext); return number;} [ \t\n] ; [+*/();] {return yytext[0];} . {ECHO; yyerror ("unexpected character");} %% int yywrap (void) {return 1;}
%token 
declare each grammar rule used by YACC that is recognised by LEX and give type of value 
y.tab.h 
gives LEX the names and type declarations etc. from YACC 
yylval 
name used for values set in LEX e.g. 
yylval.a_number = atoi (yytext); 

yylval.a_name = findname (yytext); 
BYACC : calcy.y calcy.c + y.tab.h
GCC : calcy.c calcy.o
FLEX : calcl.l + y.tab.h calcl.c
GCC : calcl.c calcl.o
GCC : calcl.o + calcy.o calc
calc : expression result
Using a tool like YACC, infix, postfix and prefix expressions are equally simple to implement  it automatically checks that we have the correct number and layout of operands. We will see in the next section that YACC can also cope with precedence and associativity.
We now have two different ways of describing patterns in text  regular expressions and BNF  and two different tools to deal with them  LEX and YACC. Why don't we just use the better of these two and forget the other one? Any pattern we can describe using regular expressions can also be described using BNF, but not viceversa, so in this sense BNF is the more powerful of the two notations. However, that power has a price, both in terms of how hard it can be to write the BNF (e.g. recognising numbers), and in terms of how poorly YACC performs compared with LEX.
As we have seen in the example programs, both LEX and YACC can be used independantly of each other. In fact, on many occasions I have written small textprocessing programs just using LEX. However, if I was going to deal with a real programming language I would always use LEX and YACC together, partly for performance reasons, but mainly because it makes writing the patterns (and their actions) much simpler if it can be divided into these two parts.
This notational convenience is particularly obvious in two simple and common
situations: recognising sets of characters using e.g. [09]
or
[AZ]
, and recognising spaces and comments which then must be discarded
(e.g. a bonus in the third lab exercise).
'=' '+' '*'
etc. in the descriptions of
expected inputs for YACC, when we don't have to for LEX?
'+'
and '*'
in
YACC, we can not use multicharacter strings like 'mod'
.
Extend the calculator in 3.6 to include
multicharacter operators like mod
and div
.
5
sqrt ( expression )
.
AA...ABB...B
,
i.e. any number of A
s followed by any number of B
s. Would it
be better to use LEX or YACC to recognise it?
A
s and
B
s  now which is best?
A
s, B
s and
C
s?
Louden: chs. 4.2, 4.6
Johnson
Levine, Mason & Brown: chs. 1, 3, 7
Capon & Jinks: chs. 8.1, 8.4, 8.5
Aho, Sethi & Ullman: chs. 4.9, 2.12.5