X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=arithmetic.mdwn;h=d27248754b7832b7c5edadb702823f11a35c3457;hp=fc7249f6bfa8ac73fc468506d1df556ad4628909;hb=0dd9b48d6a2e74d618a99a101f0122f4d7c076fb;hpb=af844d6cdbd502a2fe9aa0756ab83a84ff66909d

diff --git a/arithmetic.mdwn b/arithmetic.mdwn
index fc7249f6..d2724875 100644
--- a/arithmetic.mdwn
+++ b/arithmetic.mdwn
@@ -39,7 +39,7 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
 	let head = \lst. lst (\h sofar. h) junk  in
 	let tail = \lst. (\shift lst. lst shift (make_pair empty junk) get_2nd)
 				; where shift is
-				(\h p. p (\t y. make_pair (make-list h t) t))  in
+				(\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
@@ -198,10 +198,10 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
 		))  in
 
 
-	; Curry's fixed point combinator
+	; 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 +218,7 @@ 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
 
 
 <!--
@@ -239,3 +239,23 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
 			; and consume is
 			(\p. p get_2nd p)  in ; or
 -->
+
+<!--
+	gcd
+	pow_mod
+
+
+	show Oleg's definition of integers:
+		church_to_int = \n sign. n
+		church_to_negint = \n sign s z. sign (n s z)
+
+		; int_to_church
+		abs = \int. int I
+
+		sign_case = \int ifpos ifzero ifneg. int (K ifneg) (K ifpos) ifzero
+
+		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
+
+-->