(Beta Reductions). For each of the following, give the resulting expression afte

Question

(Beta Reductions). For each of the following, give the resulting expression after executing a beta reduction (with renaming only if needed) of the highlighted redex

Problem 3 (Beta Reductions). For each of the following, give the resulting expression after executing a beta reduction (with renaming only if needed) of the highlighted redex Example 1: for the expression (Xx. t )t' your answer should be (Xx. x ) (Xx. x x) // beta reduction Example 2: for the expression (Ax t' your answer should be // beta reduction

Explanation / Answer

Solution:

b and c is done, please repost others.

b)

=> ( x. x x. y. x x) x. y x

=> (( x. x ( x y. x x )) ( x. y x ))

=> (( x. y x ) ( x y. x x ))

=> ( y ( x y. x x ))

c)

=> ( x. x z. y. x x ) x. y z

=> (( x. x ( z y. x x )) ( x. y z))

=> (( x. y z) ( a a. ( x. y z ) ( x. y z )))

=> ( y z )

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