Here are the definitions pre-loaded for working on assignment 3:
-<textarea id="INPUT" style="border: 2px solid black; color: black; font-family: monospace; height: 3in; overflow: auto; padding: 0.5em; width: 100%;">
-let true = \x y. x in
-let false = \x y. y in
-let and = \l r. l (r true false) false in
-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
-let mylist = makeList 1 (makeList 2 (makeList 3 nil)) in
-let Y = \f. (\h. f (h h)) (\h. f (h h)) in
-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 pred = \n. isZero n 0 (length (tail (n (\p. makeList meh p) nil))) in
-let leq = \m n. isZero(n pred m) in
-let eq = \m n. and (leq m n)(leq n m) in
-;
-length (tail mylist)
+<textarea id="INPUT" style="border: 2px solid black; color: black; font-family:
+monospace; height: 3in; overflow: auto; padding: 0.5em; width: 100%;">
+
+ ; 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 fst = true in
+ let snd = false in
+ let empty = make_pair true junk in
+ let isempty = \x. x fst in
+ let make_list = \h t. make_pair false (make_pair h t) in
+ let head = \l. isempty l err (l snd fst) in
+ let tail = \l. isempty l err (l snd 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 mul = \m n s. m (n s) in
+ let pred = \n. iszero n 0 (length (tail (n (\p. make_list junk p) empty))) 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
+
+ ; synonyms
+ let makePair = make_pair in
+ let nil = empty in
+ let isNil = isempty in
+ let makeList = make_list in
+ let isZero = iszero in
+ let mult = mul in
+
+ length (tail mylist)
+
</textarea>
<input id="PARSE" value="Normalize" type="button">
<input id="ETA" type="checkbox">do eta-reductions too