+
+
+ ; 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_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) 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 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
+