X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment_3_evaluator.mdwn;h=d7dc94ffff2b014706de6f6a1714c5adb7c53ad4;hp=c4032ee37c7f1ec456a09f7ed5a88093f932bd64;hb=658a3e2cf942421756632c2ee80084a06739a4eb;hpb=29f15e8e027b34b893874598824bdbff45096c78 diff --git a/assignment_3_evaluator.mdwn b/assignment_3_evaluator.mdwn index c4032ee3..d7dc94ff 100644 --- a/assignment_3_evaluator.mdwn +++ b/assignment_3_evaluator.mdwn @@ -22,6 +22,7 @@ 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 @@ -29,8 +30,8 @@ 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 @@ -60,11 +61,9 @@ let tc = (make\_list t1 (make\_list t23 empty)) 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 ; hint: -fold add mylist 0 +fold mylist add 0