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 make\_pair = \f s g. g f s in let fst = true in let snd = false in let empty = make\_pair true junk in let isempty = \x. x fst in let make\_list = \h t. make\_pair false (make\_pair h t) in let head = \l. isempty l err (l snd fst) in let tail = \l. isempty l err (l snd 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 = \n. iszero n 0 (length (tail (n (\p. make\_list junk p) empty))) 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 nil = empty in let isNil = isempty in let makeList = make\_list in let isZero = iszero in let mult = mul in ; length (tail mylist) do eta-reductions too You may not see it because you have JavaScript turned off. Uffff!
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