X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=arithmetic.mdwn;h=fafecafdba3036c095fe1e50d26e5bf1da6395d9;hp=cac56f206cb497b9acb87272a4e363a0a9c841bd;hb=86a7982ef67a424a823da45ad03a839f64ec56a7;hpb=e24b3eb555211cb2d9af17355b305313ba0eaf7a diff --git a/arithmetic.mdwn b/arithmetic.mdwn index cac56f20..fafecafd 100644 --- a/arithmetic.mdwn +++ b/arithmetic.mdwn @@ -37,14 +37,34 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so let make_list = \h t f z. f h (t f z) in let isempty = \lst. lst (\h sofar. false) true in let head = \lst. lst (\h sofar. h) junk in - let tail = \lst. (\shift lst. lst shift (make_pair empty junk) get_2nd) + let tail_empty = empty in + let tail = \lst. (\shift. lst shift (make_pair empty tail_empty) get_2nd) ; where shift is (\h p. p (\t y. make_pair (make_list h t) t)) in let length = \lst. lst (\h sofar. succ sofar) 0 in let map = \f lst. lst (\h sofar. make_list (f h) sofar) empty in let filter = \f lst. lst (\h sofar. f h (make_list h sofar) sofar) empty in ; or let filter = \f lst. lst (\h. f h (make_list h) I) empty in - + let singleton = \x f z. f x z in + ; append [a;b;c] [x;y;z] ~~> [a;b;c;x;y;z] + let append = \left right. left make_list right in + ; very inefficient but correct reverse + let reverse = \lst. lst (\h sofar. append sofar (singleton h)) empty in ; or + ; more efficient reverse builds a left-fold instead + ; (make_left_list a (make_left_list b (make_left_list c empty)) ~~> \f z. f c (f b (f a z)) + let reverse = (\make_left_list lst. lst make_left_list empty) (\h t f z. t f (f h z)) in + ; zip [a;b;c] [x; y; z] ~~> [(a,x);(b,y);(c,z)] + let zip = \left right. (\base build. reverse left build base (\x y. reverse x)) + ; where base is + (make_pair empty (map (\h u. u h) right)) + ; and build is + (\h sofar. sofar (\x y. isempty y + sofar + (make_pair (make_list (\u. head y (u h)) x) (tail y)) + )) in + let all = \f lst. lst (\h sofar. and sofar (f h)) true in + let any = \f lst. lst (\h sofar. or sofar (f h)) false in + ; version 1 lists @@ -201,7 +221,7 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so ; Rosenbloom's fixed point combinator let Y = \f. (\h. f (h h)) (\h. f (h h)) in ; Turing's fixed point combinator - let Z = (\u f. f (u u f)) (\u f. f (u u f)) in + let Theta = (\u f. f (u u f)) (\u f. f (u u f)) in ; length for version 1 lists @@ -218,7 +238,7 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so - fact Z 3 ; returns 6 + fact Theta 3 ; returns 6