Assignment 3
------------

Once again, the lambda evaluator will make working through this
assignment much faster and more secure.

*Writing recursive functions on version 1 style lists*

Recall that version 1 style lists are constructed like this:

<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 makePair = \f s g. g f s in
let nil = makePair true meh in
let makeList = \h t. makePair false (makePair h t) in
let mylist = makeList 1 (makeList 2 (makeList 3 nil)) in
let fst = true in
let snd = false in
let isNil = \x. x fst in
let head = \l. isNil l err (l snd fst) in
let tail = \l. isNil l err (l snd snd) in
let succ = \n s z. s (n s z) in
let Y = \f. (\h. f (h h)) (\h. f (h h)) in
let length = Y (\length l. isNil l 0 (succ (length (tail l)))) in

length 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>
<script src="/code/lambda.js"></script>
<script src="/code/tokens.js"></script>
<script src="/code/parse.js"></script>
<script src="/code/json2.js"></script>
<pre id="OUTPUT">
</pre>
<script>
/*jslint evil: true */

/*members create, error, message, name, prototype, stringify, toSource,
    toString, write
*/

/*global JSON, make_parse, parse, source, tree */

// Make a new object that inherits members from an existing object.

if (typeof Object.create !== 'function') {
    Object.create = function (o) {
        function F() {}
        F.prototype = o;
        return new F();
    };
}

// Transform a token object into an exception object and throw it.

Object.prototype.error = function (message, t) {
    t = t || this;
    t.name = "SyntaxError";
    t.message = message;
    throw t;
};


(function () {
    var parse = make_parse();

    function go(source) {
        var string, tree, expr, eta;
        try {
            tree = parse(source);
 //           string = JSON.stringify(tree, ['key', 'name', 'message', 'value', 'arity', 'first', 'second', 'third', 'fourth'], 4);
			expr = tree.handler();
            // string = JSON.stringify(expr, ['key', 'name', 'message', 'value', 'arity', 'first', 'second', 'tag', 'variable', 'left', 'right', 'bound', 'body' ], 4);
//			string = expr.to_string() + "\n\n~~>\n\n";
			string = '';
			eta = document.getElementById('ETA').checked;
			string = string + reduce(expr, eta, false).to_string();
        } catch (e) {
            string = JSON.stringify(e, ['name', 'message', 'from', 'to', 'key',
                    'value', 'arity', 'first', 'second', 'third', 'fourth'], 4);
        }
        document.getElementById('OUTPUT').innerHTML = string
            .replace(/&/g, '&amp;')
            .replace(/[<]/g, '&lt;');
    }

    document.getElementById('PARSE').onclick = function (e) {
        go(document.getElementById('INPUT').value);
    };
}());

</script>