--- /dev/null
+This lambda evaluator will allow you to write lambda terms and evaluate (that is, normalize) them, and inspect the results.
+(This won't work in Racket, because Racket doesn't even try to represent the internal structure of a function in a human-readable way.)
+
+*Lambda terms*: lambda terms are written with a backslash, thus: `((\x (\y x)) z)`.
+
+If you click "Normalize", the system will try to produce a normal-form lambda expression that your original term reduces to (~~>). So `((\x (\y x)) z)` reduces to `(\y z)`.
+
+*Let*: in order to make building a more elaborate set of terms easier, it is possible to define values using `let`.
+In this toy system, `let`s should only be used at the beginning of a file. If we have, for intance,
+
+ let true = (\x (\y x)) in
+ let false = (\x (\y y)) in
+ ((true yes) no)
+
+the result is `yes`.
+
+*Comments*: anything following a semicolon to the end of the line is ignored.
+Blank lines are fine.
+
+*Abbreviations*: In an earlier version, you couldn't use abbreviations. `\x y. y x x` had to be written `(\x (\y ((y x) x)))`. We've upgraded the parser though, so now it should be able to understand any lambda term that you can.
+
+*Constants*: The combinators `S`, `K`, `I`, `C`, `B`, `W`, `T`, `M` (aka <code>ω</code>) and `L` are pre-defined to their standard values. Also, integers will automatically be converted to Church numerals. (`0` is `\s z. z`, `1` is `\s z. s z`, and so on.)
+
+*Variables*: Variables must start with a letter and can continue with any sequence of letters, numbers, `_`, `-`, or `/`. They may optionally end with `?` or `!`. When the evaluator does alpha-conversion, it may change `x` into `x'` or `x''` and so on. But you should not attempt to use primed variable names yourself.
+
+
+<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 false in
+(
+ (and true true yes no)
+ (and true false yes no)
+ (and false true yes no)
+ (and false false yes no)
+)
+</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, '&')
+ .replace(/[<]/g, '<');
+ }
+
+ document.getElementById('PARSE').onclick = function (e) {
+ go(document.getElementById('INPUT').value);
+ };
+}());
+
+</script>
+
+
+
+Under the hood
+---------------
+
+The interpreter is written in JavaScript and runs inside your browser.
+So if you decide to reduce a term that does not terminate (such as `((\x (x x)) (\x (x x)))`), it will be your
+browser that stops responding, not the wiki server.
+
+The main code is [here](http://lambda.jimpryor.net/code/lambda.js). Suggestions for improvements welcome.
+
+The code is based on:
+
+* Chris Barker's JavaScript lambda calculator
+* [Oleg Kiselyov's Haskell lambda calculator](http://okmij.org/ftp/Computation/lambda-calc.html#lambda-calculator-haskell).
+* The top-down JavaScript lexer and parser at <http://javascript.crockford.com/tdop/index.html>.
+
+Improvements we hope to add:
+
+* detecting some common cases of non-normalizing terms (the problem of determining in general whether a term will normalize is undecidable)
+* returning results in combinator form (the evaluator already accepts combinators as input)
+* displaying reductions one step at a time
+* specifying the reduction order and depth
+* allow other binders such as ∀ and ∃ (though these won't be interpreted as doing anything other than binding variables)
+
+<a name="other_evaluators"></a>
+Other Lambda Evaluators/Calculutors
+-----------------------------------
+
+* [Peter Sestoft's Lambda Calculus Reducer](http://www.itu.dk/people/sestoft/lamreduce/index.html): Very nice! Allows you to select different evaluation strategies, and shows stepwise reductions.
+* [Chris Barker's Lambda Tutorial](http://homepages.nyu.edu/~cb125/Lambda)
+* [Penn Lambda Calculator](http://www.ling.upenn.edu/lambda/): Pedagogical software developed by Lucas Champollion, Josh Tauberer and Maribel Romero. Linguistically oriented. Requires installing Java (Mac users will probably already have it installed).
+* [Mike Thyer's Lambda Animator](http://thyer.name/lambda-animator/): Graphical tool for experimenting with different reduction strategies. Also requires installing Java, and Graphviz.
+* [Matt Might's Lambda Evaluator](http://matt.might.net/articles/implementing-a-programming-language/) in Scheme (R5RS and Racket).
+
+See also:
+
+* [Jason Jorendorff's Try Scheme](http://tryscheme.sourceforge.net/about.html): Runs a miniature Scheme interpreter in Javascript, in your browser.
+