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
+ let zip = \left right. left (\h sofar. sofar (\x y. isempty y
+ sofar
+ (make_pair (make_list () x) (tail y))
+ )
+ (make_pair empty (map right (\h u v. u v h)))
+ )
+ (\x y. reverse x) 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
)) 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
- fact Z 3 ; returns 6
+ fact Theta 3 ; returns 6
<!--
; 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
+
+-->