1 Here are the definitions pre-loaded for working on assignment 3:
3 <textarea id="INPUT" style="border: 2px solid black; color: black; font-family: monospace; height: 3in; overflow: auto; padding: 0.5em; width: 100%;">
7 let and = \l r. l (r true false) false in
8 let or = \l r. l true r in
10 let make\_pair = \f s g. g f s in
11 let get\_fst = true in
12 let get\_snd = false in
13 let empty = make\_pair true junk in
14 let isempty = \x. x get\_fst in
15 let make\_list = \h t. make\_pair false (make\_pair h t) in
16 let head = \l. isempty l err (l get\_snd get\_fst) in
17 let tail = \l. isempty l err (l get\_snd get\_snd) in
19 ; a list of numbers to experiment on
20 let mylist = make\_list 1 (make\_list 2 (make\_list 3 empty)) in
23 let iszero = \n. n (\x. false) true in
24 let succ = \n s z. s (n s z) in
25 let add = \l r. l succ r in
26 let mul = \m n s. m (n s) in
27 let pred = (\shift n. n shift (make\_pair 0 0) get\_snd) (\p. p (\x y. make\_pair (succ x) x)) in
28 let leq = \m n. iszero(n pred m) in
29 let eq = \m n. and (leq m n)(leq n m) in
31 ; a fixed-point combinator for defining recursive functions
32 let Y = \f. (\h. f (h h)) (\h. f (h h)) in
33 let length = Y (\length l. isempty l 0 (succ (length (tail l)))) in
34 let fold = Y (\f l g z. isempty l z (g (head l)(f (tail l) g z))) in
37 let makePair = make\_pair in
41 let isNil = isempty in
42 let makeList = make\_list in
43 let isZero = iszero in
46 let t1 = (make\_list 1 empty) in
47 let t2 = (make\_list 2 empty) in
48 let t3 = (make\_list 3 empty) in
49 let t12 = (make\_list t1 (make\_list t2 empty)) in
50 let t23 = (make\_list t2 (make\_list t3 empty)) in
51 let ta = (make\_list t1 t23) in
52 let tb = (make\_list t12 (make\_list t3 empty)) in
53 let tc = (make\_list t1 (make\_list t23 empty)) in
55 ;sum-leaves t1 ; ~~> 1
56 ;sum-leaves t2 ; ~~> 2
57 ;sum-leaves t3 ; ~~> 3
58 ;sum-leaves t12 ; ~~> 3
59 ;sum-leaves t23 ; ~~> 5
60 ;sum-leaves ta ; ~~> 6
61 ;sum-leaves tb ; ~~> 6
62 ;sum-leaves tc ; ~~> 6
64 ; updated: added add, and fold for v1 lists; and defn of tb fixed
69 <input id="PARSE" value="Normalize" type="button">
70 <input id="ETA" type="checkbox">do eta-reductions too
71 <noscript><p>You may not see it because you have JavaScript turned off. Uffff!</p></noscript>
72 <script src="/code/lambda.js"></script>
73 <script src="/code/tokens.js"></script>
74 <script src="/code/parse.js"></script>
75 <script src="/code/json2.js"></script>
79 /*jslint evil: true */
81 /*members create, error, message, name, prototype, stringify, toSource,
85 /*global JSON, make_parse, parse, source, tree */
87 // Make a new object that inherits members from an existing object.
89 if (typeof Object.create !== 'function') {
90 Object.create = function (o) {
97 // Transform a token object into an exception object and throw it.
99 Object.prototype.error = function (message, t) {
101 t.name = "SyntaxError";
108 var parse = make_parse();
110 function go(source) {
111 var string, tree, expr, eta;
113 tree = parse(source);
114 // string = JSON.stringify(tree, ['key', 'name', 'message', 'value', 'arity', 'first', 'second', 'third', 'fourth'], 4);
115 expr = tree.handler();
116 // string = JSON.stringify(expr, ['key', 'name', 'message', 'value', 'arity', 'first', 'second', 'tag', 'variable', 'left', 'right', 'bound', 'body' ], 4);
117 // string = expr.to_string() + "\n\n~~>\n\n";
119 eta = document.getElementById('ETA').checked;
120 string = string + reduce(expr, eta, false).to_string();
122 string = JSON.stringify(e, ['name', 'message', 'from', 'to', 'key',
123 'value', 'arity', 'first', 'second', 'third', 'fourth'], 4);
125 document.getElementById('OUTPUT').innerHTML = string
126 .replace(/&/g, '&')
127 .replace(/[<]/g, '<');
130 document.getElementById('PARSE').onclick = function (e) {
131 go(document.getElementById('INPUT').value);