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1. Consider the following lambda expression (\\lambda~x.~(\\lambda~y.y+x) ((\\la

ID: 3724662 • Letter: 1

Question

1. Consider the following lambda expression (lambda~x.~(lambda~y.y+x) ((lambda~z.z+x)x) 3) ( x . ( y . y + x ) ( ( z . z + x ) x ) 3 ) What is the outcome after the first reduction step that eliminates the right-most lambda?

a. ((lambda~y.y+3) ((lambda~z.z+3)3))

b. (lambda~x.~((lambda~z.z+x)x)+x) 3)

c. (lambda~x.~(x+x+x) 3)

d. ((lambda~y.y+3) (3+3))

e. none of the above

2. Consider the following lambda expression

What is the outcome after the first reduction step that eliminates the left-most lambda?

e. none of the above

Does using a sequence of left-most or a sequence of right-most reductions of lambda expressions always yields the same normal form (if it exists)?

a.

Explanation / Answer

Hi.. Please check below.

1. Consider the following lambda expression (lambda~x.~(lambda~y.y+x) ((lambda~z.z+x)x) 3) ( x . ( y . y + x ) ( ( z . z + x ) x ) 3 ) What is the outcome after the first reduction step that eliminates the right-most lambda?

a. ((lambda~y.y+3) ((lambda~z.z+3)3))

b. (lambda~x.~((lambda~z.z+x)x)+x) 3)

c. (lambda~x.~(x+x+x) 3)

d. ((lambda~y.y+3) (3+3))

e. none of the above

Answer: c

(lambda~x.~(x+x+x) 3)

2. Consider the following lambda expression

(lambda~x.~(lambda~y.y+x) ((lambda~z.z+x)x) 3)( x. ( y.y+x)(( z.z+x)x)3)( x. ( y.y+x)(( z.z+x)x)3)

What is the outcome after the first reduction step that eliminates the left-most lambda?

a. (lambda~x.~((lambda~z.z+x)x)+x) 3)

b. This answer is set as correct

c. ((lambda~y.y+3) (3+3))

d. (lambda~x.~(x+x+x) 3)

e. none of the above

Answer: c

((lambda~y.y+3) (3+3))

Does using a sequence of left-most or a sequence of right-most reductions of lambda expressions always yields the same normal form (if it exists)?

a. True

b. False

Answer: True

Please check above and let me know any issues. Thank you. All the best.