[4203] Compiler Theory Sheet # 3-Answers

Transcription

1 El-Shourouk cademy cad. Year : 2012 / 2013 Higher Institute for Computer & Term : Second Information Technology Year : Fourth Department of Computer Science [4203] Compiler Theory Sheet # 3-nswers 1- Write down an unambiguous grammar that generates the set of strings { s;, s;s;, s;s;s;,... } and give leftmost and rightmost derivation for the string s;s; using your grammar. stmt-sequence s ; stmt-sequence s; Left most derivation (1) stmt-sequence => s;stmt-sequence (2) => s;s; Right most derivation (1) stmt-sequence => s;stmt-sequence (2) => s;s; leftmost will be the same as rightmost derivation for s;s; 2- Given the grammar ( ) a- describe the language it generates generates the strings of all "balanced parentheses." a- Description : This grammar produces an infinite set of strings of the characters ( and ) in which 0 or more ( ) can be generated and each ( ) can contain 0 or more ( ) inside. b- show that it is ambiguous b- consider the expression ( ) ( ) ( ) It has 2 different parse trees Parse Tree(1) ( ) ( ) ( ) 1

2 Parse Tree(2) ( ) ( ) ( ) So, this grammar is ambiguous 3- Given the grammar exp exp addop term term addop + - term term multop factor factor multop * factor ( exp ) number write down leftmost derivation, rightmost derivation, parse tree, and abstract syntax tree for the following arithmetic expressions: a- 3+4*56 b- 3* ( ) c- 3- ( 4+5*6 ) a-for The expression 3+4*5-6 a. The leftmost derivation exp exp addop term exp addop term addop term term addop term addop term factor addop term addop term number addop term addop term number + term addop term number + term multop factor addop term number + factor multop factor addop term number + number multop factor addop term number + number * factor addop term number + number * number addop term number + number * number term number + number * number factor number + number * number number -For the expression 3*(4-5+6) - leftmost derivation 2

3 exp term term multop factor factor multop factor number multop factor number multop ( exp ) number * ( exp ) number * ( exp addop term ) number * ( exp addop term addop term ) number * ( term addop term addop term) number * ( factor addop term addop term) number * ( number addop term addop term) number * ( number term addop term) number * ( number factor addop term) number * ( number number addop term) number * ( number number + term) number * ( number number + factor ) number * ( number number + number ) c- for the expression 3-(4+5*6) - leftmost derivation exp exp addop term term addop term factor addop term number addop term number term number factor number ( exp ) number ( exp addop term ) number ( term addop term ) number ( factor addop term ) number ( number addop term ) number ( number +term) number ( number + term multop factor ) number ( number + factor multop factor) number ( number + number multop factor) number ( number + number * factor ) number ( number + number * number) 3

4 4- The following grammar generates all regular expressions over the alphabet of letters rexp rexp rexp rexp rexp rexp * ( rexp ) letter a- give a derivation for the regular expressions ( ab b )* using this grammar. (1) rexp => rexp * [exp rexp * ] (2) rexp => ( rexp ) * [exp ( rexp ) ] (3) => (rexp rexp ) * [exp rexp rexp] (4) => (rexp rexp rexp ) * [exp rexp rexp] (5) => (letter rexp rexp ) * [exp letter] (6) =>( a rexp rexp) * [letter a] (7) =>( a letter rexp) * [exp letter] (8) =>( a b rexp) [letter b] (9) =>( a b rexp) [exp letter] (10) =>( a b b) [letter c] b- Show that this grammar is ambiguous b- this grammar is ambiguous because it generates 2 different parse trees for the expression ab c c- Rewrite this grammar to establish the correct precedence of the operators rexp rexp rterm rterm rterm rterm rfactor rfactor rfactor rfactor * (rexp) letter d- What associativity does your answer in part c give to the binary operator? why? d- the associativity is left because a series of operators with same precedence will be evaluated from left to right 4

5 5- Write an unambiguous grammar for Boolean expressions that includes the constants true and false, and the operator and,or,not and parentheses. Be sure to give or lowest precedence and give the not the highest precedence.lso allow repeated not s. Similar to the arithmetic expression example <b-expression> <b-expression> <orop> <b-term> b-term <b-term> <b-term> ND <not-factor> not-factor <not-factor> NOT<not-factor> b-factor <b-factor> (<b-expression>) <b-literal> <b-variable> bexp bexp or term b term or b term b term and notfactor notfactor and && notfactor not bfactor b factor not! b factor (b exp ) b literal bliteral true false 6- Consider the following grammar represent simplified LISP like expressions Lexp list number identifier list ( -seq ) -seq -seq a- write a leftmost and rightmost derivation for the string ( a 23 (m x y )) Left most derivation (1) Lexp => list [Lexp list] (2) => (-seq ) [list ( -seq )] (3) => (-seq ) [-seq -seq ] (4) => (-seq ) [-seq -seq ] (5) => (-seq ) [-seq -seq ] (6) => ( ) [-seq ] (7) => ( ) [Lexp ] (8) => (identifier ) [ identifier] (9) => (identifier ) [Lexp ] (10) => (identifier number ) [ number] (11) => (identifier number list) [Lexp list] (12) => (identifier number (-seq )) [list ( -seq )] (13) => (identifier number (-seq )) [-seq -seq ] (14) => (identifier number (-seq )) [-seq -seq ] (15) => (identifier number ( )) [-seq ] (16) => (identifier number ( )) [ ] (17) => (identifier number (identifier )) [ identifier] (18) => (identifier number (identifier )) [ ] (19) => (identifier number (identifier identifier )) [ identifier] (20) => (identifier number (identifier identifier )) [ ] (21) => (identifier number (identifier identifier identifier )) [ identifier] b- draw a parse tree for the strings of part (a) 5

6 b- parse tree list ( ) list ( ) letter number lettetr lettetr lettetr 6

7 7- Given the following grammar statement if-stmt other if-stmt if( exp ) statement else-part else-part else statement exp 0 1 a- draw a parse tree for the string if (0) if(1) other else else other a- parse tree statement If-stmt if ( exp ) statement Else-part else statement 0 other if ( exp ) statement Else-part 1 other else statement 7

8 b- what is the purpose of 2 else s b- the purpose of 2 else is to match with 2 if c- is similar code permissible in C and C#? explain c- this code is permissible in C 8- What is dangling else problem and how can we solve it. Refer to lecture notes 8