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 fst = true in
-let snd = false in
+let get\_fst = true in
+let get\_snd = false in
let empty = make\_pair true junk in
-let isempty = \x. x fst 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 snd fst) in
-let tail = \l. isempty l err (l snd snd) 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 = \n. iszero n 0 (length (tail (n (\p. make\_list junk p) empty))) 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
-
-length (tail mylist)
+;
+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">