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