Here are the definitions pre-loaded for working on assignment 3: let true = \x y. x in let false = \x y. y in let and = \l r. l (r true false) false in let makePair = \f s g. g f s in let fst = true in let snd = false in let nil = makePair true meh in let isNil = \x. x fst in let makeList = \h t. makePair false (makePair h t) in let head = \l. isNil l err (l snd fst) in let tail = \l. isNil l err (l snd snd) in let mylist = makeList 1 (makeList 2 (makeList 3 nil)) in let Y = \f. (\h. f (h h)) (\h. f (h h)) in let isZero = \n. n (\x. false) true in let succ = \n s z. s (n s z) in let mult = \m n s. m (n s) in let length = Y (\length l. isNil l 0 (succ (length (tail l)))) in let pred = \n. isZero n 0 (length (tail (n (\p. makeList meh p) nil))) in let leq = \m n. isZero(n pred m) in let eq = \m n. and (leq m n)(leq n m) in ; let t1 = (make_list 1 empty) in let t2 = (make_list 2 empty) in let t3 = (make_list 3 empty) in let t12 = (make_list t1 (make_list t2 empty)) in let t23 = (make_list t2 (make_list t3 empty)) in let ta = (make_list t1 t23) in let tb = (make_list t12 t3) in let tc = (make_list t1 (make_list t23 empty)) in ; ;sum-leaves t1 ~~> 1 ;sum-leaves t2 ~~> 2 ;sum-leaves t3 ~~> 3 ;sum-leaves t12 ~~> 3 ;sum-leaves t23 ~~> 5 ;sum-leaves ta ~~> 6 ;sum-leaves tb ~~> 6 ; length (tail mylist) do eta-reductions too You may not see it because you have JavaScript turned off. Uffff!
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