Here are the definitions pre-loaded for working on assignment 3: ; booleans let true = \x y. x in let false = \x y. y in let and = \l r. l (r true false) false in let or = \l r. l true r in ; let make\_pair = \f s g. g f s in let get\_fst = true in let get\_snd = false in let empty = make\_pair true junk in let isempty = \x. x get\_fst in let make\_list = \h t. make\_pair false (make\_pair h t) in let head = \l. isempty l err (l get\_snd get\_fst) in let tail = \l. isempty l err (l get\_snd get\_snd) in ; ; a list of numbers to experiment on let mylist = make\_list 1 (make\_list 2 (make\_list 3 empty)) in ; ; church numerals let iszero = \n. n (\x. false) true in let succ = \n s z. s (n s z) in let mul = \m n s. m (n s) in let pred = (\shift n. n shift (make\_pair 0 0) get\_snd) (\p. p (\x y. make\_pair (succ x) x)) in let leq = \m n. iszero(n pred m) in let eq = \m n. and (leq m n)(leq n m) in ; ; a fixed-point combinator for defining recursive functions let Y = \f. (\h. f (h h)) (\h. f (h h)) in ; let length = Y (\length l. isempty l 0 (succ (length (tail l)))) in ; ; synonyms let makePair = make\_pair in let fst = get\_fst in let snd = get\_snd in let nil = empty in let isNil = isempty in let makeList = make\_list in let isZero = iszero in let mult = mul 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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