Here are the definitions pre-loaded for working on assignment 3:
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; booleans
let true = \x y. x in
let false = \x y. y 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
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; a list of numbers to experiment on
let mylist = make_list 1 (make_list 2 (make_list 3 empty)) in
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; church numerals
let iszero = \n. n (\x. false) true in
let succ = \n s z. s (n s z) 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
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; a fixed-point combinator for defining recursive functions
let Y = \f. (\h. f (h h)) (\h. f (h h)) in
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let length = Y (\length l. isempty l 0 (succ (length (tail l)))) in
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; synonyms
let makePair = make_pair in
let nil = empty in
let makeList = make_list in
let isZero = iszero in
let mult = mul in
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length (tail mylist)
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<input id="PARSE" value="Normalize" type="button">
<input id="ETA" type="checkbox">do eta-reductions too