X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=arithmetic.mdwn;h=62e72bf262a9abab4eac5c06d6c4be3fe081b464;hp=e948f0b48123694b7b1c1f328ff91520a374f4bd;hb=6ce866dea74b5bbf12c2360b553a58bce45bdf27;hpb=bbc4b46b396a1a5e8db1f0ca97eda1bf806ef59d

diff --git a/arithmetic.mdwn b/arithmetic.mdwn
index e948f0b4..62e72bf2 100644
--- a/arithmetic.mdwn
+++ b/arithmetic.mdwn
@@ -22,39 +22,57 @@ Here are a bunch of pre-tested operations for the untyped lambda calculus. In so
 	let make_triple = \x y z f. f x y z  in
 
 
+	; Church numerals: basic operations
+
+	let zero = \s z. z  in ; aka false
+	let one = \s z. s z  in ; aka I
+	let succ = \n s z. s (n s z)  in
+	; for any Church numeral n > zero : n (K y) z ~~> y
+	let iszero = \n. n (\x. false) true  in
+
+
 	; version 3 lists
 
 	let empty = \f z. z  in
 	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) zero  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
 	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
+	; 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
 
 	let empty = make_pair true junk  in
 	let make_list = \h t. make_pair false (make_pair h t)  in
 	let isempty = \lst. lst get_1st  in
-	let head = \lst. isempty lst error (lst get_2nd get_1st)  in
+	let head = \lst. isempty lst err (lst get_2nd get_1st)  in
 	let tail_empty = empty  in
 	let tail = \lst. isempty lst tail_empty (lst get_2nd get_2nd)  in
 	
 
+	; more math with Church numerals
 
-	; Church numerals: easy operations
-
-	let zero = \s z. z  in ; aka false
-	let one = \s z. s z  in ; aka I
-	let succ = \n s z. s (n s z)  in
-	; for any Church numeral n > zero : n (K y) z ~~> y
-	let iszero = \n. n (\x. false) true  in
 	let add = \m n. m succ n  in ; or
 	let add = \m n s z. m s (n s z)  in
 	let mul = \m n. m (\z. add n z) zero  in ; or
@@ -195,10 +213,10 @@ 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
@@ -215,7 +233,7 @@ 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
 
 
 <!--
@@ -236,3 +254,23 @@ 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
+
+-->