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%;">
+; booleans
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 make_pair = \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 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 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 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
<noscript><p>You may not see it because you have JavaScript turned off. Uffff!</p></noscript>