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 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
</textarea>

<input id="PARSE" value="Normalize" type="button">
<input id="ETA" type="checkbox">do eta-reductions too
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<script src="/code/lambda.js"></script>
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<script src="/code/parse.js"></script>
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<pre id="OUTPUT">
</pre>
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			string = string + reduce(expr, eta, false).to_string();
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