X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=arithmetic.mdwn;h=fafecafdba3036c095fe1e50d26e5bf1da6395d9;hp=beedc2874eeaa662e21006803bf59321567cbce3;hb=86a7982ef67a424a823da45ad03a839f64ec56a7;hpb=6dcf7995023877c6946a45657126ead9266dcb40

diff --git a/arithmetic.mdwn b/arithmetic.mdwn
index beedc287..fafecafd 100644
--- a/arithmetic.mdwn
+++ b/arithmetic.mdwn
@@ -45,10 +45,14 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
 	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
-
-	; append list2 to list1 with: list1 make_list list2
 	let singleton = \x f z. f x z  in
-	let reverse = \lst. lst (\h sofar. sofar make_list (singleton h)) empty  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
@@ -58,7 +62,6 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
                                                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