; 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
;
; 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 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 t3) 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 t23 ; ~~> 5
;sum-leaves ta ; ~~> 6
;sum-leaves tb ; ~~> 6
+;sum-leaves tc ; ~~> 6
;
-length (tail mylist)
+; updated: added add, and fold for v1 lists; and defn of tb fixed
+; hint:
+fold mylist add 0
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