quiz4-example-soln-fall11

quiz4-example-soln-fall11 - &-expressions as much as...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CMSC330 Fall 2011 Example Quiz #4 Solution 1. (14 pts) Parsing Consider the following grammar: S aA | A A bS | ca a. (6 pts) Compute First sets for S and A First(A) = First(bS) ± First(ca) = {b, c} First(S) = First(aA) ± First(A) = {a, b, c} b. (12 pts) Write a predictive, recursive descent parser for the grammar parse_S( ) { if (lookahead == “a”) { // S aA match(“a”); parse_A( ); } else if ((lookahead == “b”) || (lookahead == “c”)) { // S A parse_A( ); } else error( ); } parse_A( ) { if (lookahead == “b”) { // A bS match(“b”); parse_S( ); } else if (lookahead == “c”) { // S aA match(“c”); match(“a”); } else error( ); }
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. (16 pts) Lambda calculus Circle all free (unbound) variables in the following & -expression a. (2 pts) ( a. a ( b. b a ) a b ) a ( a. a ( b. b a ) a b ) a Evaluate the following
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: &-expressions as much as possible. Show each beta-reduction b. (3 pts) ( & x. & y.y x) a ( & z.z) b ( & x . & y.y x) a ( & z.z) b ± ( & y .y a) ( & z.z) b ± (( & z .z) a) b ± a b c. (3 pts) ( & y. & x. x y) x a b ( & y. & x . x y) x a b ± ( & y . & z. z y) x a b ± ( & z . z x) a b ± a x b d. (8 pts) Using encodings, show 3*1 =>* 3. Show each beta-reduction. =>* indicates 0 or more steps of beta-reduction 3*1 => & x.(3 (1 x)) => & x.(3 (( & f . & y.f y) x)) => & x.(3 ( & y.x y)) => & x.( & f. & y.f (f (f y)) ( & y.x y)) => & x.( & y.( & y.x y) (( & y.x y) (( & y .x y) y))) => & x.( & y.( & y.x y) (( & y .x y) (x y))) => & x.( & y.( & y .x y) (x (x y))) => & x.( & y.x (x (x y))) => 3 M * N = & x.(M (N x)) 1 = & f. & y.f y 2 = & f. & y.f (f y) 3 = & f. & y.f (f (f y)) 4 = & f. & y.f (f (f (f y)))...
View Full Document

This note was uploaded on 01/13/2012 for the course CMSC 330 taught by Professor Staff during the Fall '08 term at Maryland.

Page1 / 2

quiz4-example-soln-fall11 - &-expressions as much as...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online