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 add = \l r. l succ r 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 let fold = Y (\f l g z. isempty l z (g (head l)(f (tail l) g z))) 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 (make_list t3 empty)) 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 ;sum-leaves tc ; ~~> 6 ; ; updated: added add, and fold for v1 lists; and defn of tb fixed ; hint: fold mylist add 0

do eta-reductions too