Question

Question 1: Write a Yacc program that takes boolean expressions as input and produces the truth value of the expressions. The following grammar for boolean expressions:

bexpr → bexpr or bterm | bterm

bterm → bterm and bfactor | bfactor

bfactor→ not bfactor|( bexpr ) | true | false

Answer 1

Parse tree for the sentence:

Grammar generates all boolean expressions,

<bexpr> <bterm> <bfactor> NOT <bfactors "" <bexpr> <bexpr> OR <bfactor> <bfactor FALSE <bterm> TRUE

bexpr => bterm => bfactor => not bfactor => not (bexpr) => not (bexpr or bterm)

=> not (bterm or bterm) => not (bfactor or bfactor) => not (true or false)

By traversing the tree, the tree generated will lead to bfactor which will generates all boolean expression.

bexpr=> bterm=> bfactor=> true

bexpr=> bterm=> bfactor=>false

bexpr=> bterm=> bfactor=> not bfactor=> not true

bexpr=> bterm=> bfactor=> not bfactor=> not false

bexpr=> bexpr or bterm=> bterm or bterm=> bfactor or bfactor=> true or false

bexpr=> bexpr and bterm=> bterm and bterm=> bfactor and bfactor=> true and false

bexpr => bterm => bfactor => not bfactor => not (bexpr) => not (bexpr or bterm)

=> not (bterm or bterm) => not (bfactor or bfactor) => not (true or false)

Yacc program that takes boolean expressions as input and produces the truth value of the expressions:

test.l %{ #include "y.tab.h" %} AND [Aa][Nn][Dd] OR [Oo][Rr] NOT [Nn][Oo][Tt] op '&' | '|' | "!" %% [a-zA-Z] {return ALPHA;} [\t]+ ; [\n] {return '\n';} {AND} { return (AND); } {OR} { return (OR); } {NOT} { return (NOT); } [Tt][Rr][Uu][Ee] { yylval = 1; return (boolean); } [Ff][Aa][Ll][Ss][Ee] { yylval = 0; return (boolean); } . {();} %%

test.y %{ #include<stdio.h> #include<stdlib.h> int yylex(); %} %token ALPHA AND OR NOT TRUE FALSE boolean %left "&" "|" %right '!' %% program: bexpr '\n' {if ($1 >= 1) { printf("TRUE\n"); exit(0); } else{ printf("FALSE\n"); exit(0); } | ; bexpr: bexpr "|""|" bterm { $$ = $1 || $3; } | bterm { $$ = $1; } ; bterm: bterm "&""&" bfactor { $$ = $1 && $3; } | bfactor { $$ = $1; } ; bfactor: '!' bfactor { $$ = ! $2; } | '(' bexpr ')' { $$ = $2; } | TRUE { $$ = $1; } | FALSE {$$ = $1; } | boolean { $$ = $1; } ; %% int main() { printf("Enter your truth statement\n"); yyparse(); return 0; }