X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=arithmetic.mdwn;h=289b28438916da6ca8a35ff9d23b34e772e43177;hp=62e72bf262a9abab4eac5c06d6c4be3fe081b464;hb=e1860468dc97e6249ecd19e96a2e7fffe9430d0e;hpb=49c3a5fc92288886f467bd231ae13818fbabf75c

diff --git a/arithmetic.mdwn b/arithmetic.mdwn
index 62e72bf2..289b2843 100644
--- a/arithmetic.mdwn
+++ b/arithmetic.mdwn
@@ -1,5 +1,17 @@
 Here are a bunch of pre-tested operations for the untyped lambda calculus. In some cases multiple versions are offered.
 
+Some of these are drawn from:
+
+*	[[!wikipedia Lambda calculus]]
+*	[[!wikipedia Church encoding]]
+*	Oleg's [Basic Lambda Calculus Terms](http://okmij.org/ftp/Computation/lambda-calc.html#basic)
+
+and all sorts of other places. Others of them are our own handiwork.
+
+
+**Spoilers!** Below you'll find implementations of map and filter for v3 lists, and several implementations of leq for Church numerals. Those were all requested in Assignment 2; so if you haven't done that yet, you should try to figure them out on your own. (You can find implementations of these all over the internet, if you look for them, so these are no great secret. In fact, we'll be delighted if you're interested enough in the problem to try to think through alternative implementations.)
+
+
 	; booleans
 	let true = \y n. y  in ; aka K
 	let false = \y n. n  in ; aka K I
@@ -46,8 +58,13 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
 	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 list2 to list1 with: list1 make_list list2
-	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
@@ -223,6 +240,10 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
 	let length = Y (\self lst. isempty lst 0 (succ (self (tail lst))))  in
 
 
+	true
+
+<!--
+
 	; numhelper 0 f z ~~> z
 	; when n > 0: numhelper n f z ~~> f (pred n)
 	; compare Bunder/Urbanek pred
@@ -234,7 +255,7 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
 
 
 	fact Theta 3  ; returns 6
-
+-->
 
 <!--
 	; my original efficient comparisons
@@ -271,6 +292,7 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
 
 		negate_int = \int. sign_case int (church_to_negint (abs int)) zero (church_to_int (abs int))
 
-	for more, see http://okmij.org/ftp/Computation/lambda-arithm-neg.scm
+	for more, see http://okmij.org/ftp/Computation/lambda-calc.html#neg
+
 
 -->