-#Writing recursive functions on version 1 style lists#
-
-Recall that version 1 style lists are constructed like this (see
-[[lists and numbers]]):
-
- ; booleans
- let true = \x y. x in
- let false = \x y. y in
- let and = \l r. l (r true false) false in
-
- let make_pair = \f s g. g f s in
- let get_fst = true in
- let get_snd = false in
- let empty = make_pair true junk in
- let isempty = \x. x get_fst in
- let make_list = \h t. make_pair false (make_pair h t) in
- let head = \l. isempty l err (l get_snd get_fst) in
- let tail = \l. isempty l err (l get_snd get_snd) in
-
- ; a list of numbers to experiment on
- let mylist = make_list 1 (make_list 2 (make_list 3 empty)) in
-
- ; church numerals
- let iszero = \n. n (\x. false) true in
- let succ = \n s z. s (n s z) in
- let add = \l r. l succ r in
- let mul = \m n s. m (n s) in
- let pred = (\shift n. n shift (make\_pair 0 0) get\_snd) (\p. p (\x y. make\_pair (succ x) x)) in
- let leq = \m n. iszero(n pred m) in
- let eq = \m n. and (leq m n)(leq n m) in
-
- ; a fixed-point combinator for defining recursive functions
- let Y = \f. (\h. f (h h)) (\h. f (h h)) in
- let length = Y (\length l. isempty l 0 (succ (length (tail l)))) in
- let fold = Y (\f l g z. isempty l z (g (head l)(f (tail l) g z))) in
-
- eq 2 2 yes no
+##Writing recursive functions on version 1 style lists##
+
+Recall that version 1 style lists are constructed like this:
+
+<pre>
+; booleans
+let true = \x y. x in
+let false = \x y. y in
+let and = \l r. l (r true false) false in
+
+; version 1 lists
+let makePair = \f s g. g f s in
+let fst = true in
+let snd = false in
+let nil = makePair true meh in
+let isNil = \x. x fst in
+let makeList = \h t. makePair false (makePair h t) in
+let head = \l. isNil l err (l snd fst) in
+let tail = \l. isNil l err (l snd snd) in
+
+; a list of numbers to experiment on
+let mylist = makeList 1 (makeList 2 (makeList 3 nil)) in
+
+; a fixed-point combinator for defining recursive functions
+let Y = \f. (\h. f (h h)) (\h. f (h h)) in
+
+; church numerals
+let isZero = \n. n (\x. false) true in
+let succ = \n s z. s (n s z) in
+let mult = \m n s. m (n s) in
+let length = Y (\length l. isNil l 0 (succ (length (tail l)))) in
+let predecessor = \n. length (tail (n (\p. makeList meh p) nil)) in
+let leq = ; (leq m n) will be true iff m is less than or equal to n
+ Y (\leq m n. isZero m true (isZero n false (leq (predecessor m)(predecessor n)))) in
+let eq = \m n. and (leq m n)(leq n m) in
+
+eq 3 3
+</pre>