├── .gitignore
├── .travis.yml
├── README.md
├── lambda.js
├── lambda.min.js
├── package.json
└── test
    ├── helper.js
    ├── index.html
    └── test.js


/.gitignore:
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 1 | lib-cov
 2 | *.seed
 3 | *.log
 4 | *.csv
 5 | *.dat
 6 | *.out
 7 | *.pid
 8 | *.gz
 9 | 
10 | pids
11 | logs
12 | results
13 | 
14 | npm-debug.log
15 | 


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/.travis.yml:
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1 | language: node_js
2 | node_js:
3 |   - "node"
4 |   - "iojs"
5 | 


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/README.md:
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  1 | [![build status](https://secure.travis-ci.org/dankogai/js-lambda.png)](http://travis-ci.org/dankogai/js-lambda)
  2 | 
  3 | js-lambda
  4 | =========
  5 | 
  6 | DSL for, but not limited to, the lambda calculus.
  7 | 
  8 | USAGE
  9 | -----
 10 | 
 11 | ### In Browser
 12 | 
 13 | ````html
 14 | <script src="lambda.js" charset="UTF-8"></script>
 15 | ````
 16 | 
 17 | ### node.js
 18 | 
 19 | ````javascript
 20 | var lambda = require('./lambda.js').lambda,
 21 | λ = lambda;
 22 | ````
 23 | 
 24 | SYNOPSIS
 25 | --------
 26 | 
 27 | ````javascript
 28 | lambda("x:x")(42) === 42;
 29 | λ("x:x")(42) === 42;                        // λ = lambda
 30 | λ("n:n<=1?n:n*_0(n-1)")(10) === 3628800;    // _0 for recursion
 31 | λ("x,y:Math.sqrt(x*x+y*y)")(3,4) === 5;     // multiple arguments, 
 32 | λ("x:λ(y:Math.sqrt(x*x+y*y))")(3)(4) === 5; // λ can be nested
 33 | ````
 34 | ````javascript
 35 | // church numerals
 36 | var cn2num = λ("f:f(λ(n:n+1))(0)"),
 37 | succ = λ("n:λ(f:λ(x:f(n(f)(x))))"),
 38 | zero = λ("f:λ(x:x)"),
 39 | one = succ(zero),
 40 | add = λ("m:λ(n:m("+succ+")(n))"),
 41 | two = add(one)(one),
 42 | mul = λ("m:λ(n:m("+add+"(n))("+zero+"))"),
 43 | four = mul(two)(two),
 44 | pow = λ("b:λ(e:e(b))"),
 45 | sixteen = pow(two)(four);
 46 | cn2num(sixteen) === 16;
 47 | ````
 48 | 
 49 | DESCRIPTION
 50 | -----------
 51 | 
 52 | This script exports `lambda()` and its alias `λ()`.  As seen in the synopsis, it is a DSL compiler that returns a function.
 53 | 
 54 | ### the lambda notation
 55 | 
 56 | As seen in [SYNOPSYS](#synopsis), 
 57 | 
 58 | `lambda(`*arg0,arg1,...argn*:*expression*`)`
 59 | 
 60 | Turns into:
 61 | 
 62 | `function(`*arg0, arg1, ...argn*`){return ` *expression* `}`
 63 | 
 64 | ### nesting and recursion
 65 | 
 66 | As seen in [SYNOPSYS](#synopsis), the lambda can be nested.
 67 | 
 68 | ````javascript
 69 | λ('x:λ(y:Math.sqrt(x*x+y*y))');
 70 | ````
 71 | 
 72 | Turns into:
 73 | 
 74 | ````javascript
 75 | function _0(x){return function _1(y){return Math.sqrt(x*x+y*y)}}
 76 | ````
 77 | 
 78 | As seen above, the function is named accordingly to [De Bruijin index]. `_`*n* is the nth level function.
 79 | 
 80 | [De Bruijin index]: http://en.wikipedia.org/wiki/De_Bruijn_index
 81 | 
 82 | Use the name to implement self-recursion.  The strict mode has deprived us of beloved `arguments.callee` but with lambda.js, it is as short as `_0`.
 83 | 
 84 | ````javascript
 85 | // function fact(n){ return n <= 1 ? n : n * fact(n-1) }
 86 | λ("n:n<=1?n:n*_0(n-1)");
 87 | ````
 88 | 
 89 | ### limitation
 90 | 
 91 | To use lexical functions, you have to "interpolate".
 92 | 
 93 | ````javascript
 94 | var succ = λ("n:λ(f:λ(x:f(n(f)(x))))"),
 95 | add = λ("m:λ(n:m("+succ+")(n))");	// λ("m:λ(n:m(succ)(n))") does not work
 96 | ````
 97 | 
 98 | This is because `lambda()` needs to `eval()` to compile the function but lexicals are out of its scope.
 99 | 
100 | ### memoization
101 | 
102 | By default, the compiled function is [memoized].  Suppose you have:
103 | 
104 | [memoized]: http://en.wikipedia.org/wiki/Memoization
105 | 
106 | ````javascript
107 | function rms(ary) {
108 |     return Math.sqrt(ary.reduce(λ("t,x:t+x*x"), 0))
109 | }
110 | ````
111 | 
112 | And you use `rms` over and over, the same function is used throughout the session.  If that is not what you want, you can suppress it by passing truish value to the second argument:
113 | 
114 | ````javascript
115 | var uncached = lambda("a,b,c:...", true);
116 | ````
117 | 
118 | And if you wish, you can inspect cached functions via `lambda.memo`.
119 | 
120 | 
121 | SEE ALSO
122 | --------
123 | 
124 | + http://docs.python.org/2/tutorial/controlflow.html#lambda-forms
125 | + http://www.ruby-doc.org/core-2.0/Kernel.html#method-i-lambda
126 | + http://wiki.ecmascript.org/doku.php?id=harmony:arrow_function_syntax
127 | 


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/lambda.js:
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 1 | /*
 2 |  * $Id: lambda.js,v 0.2 2013/04/04 16:19:55 dankogai Exp dankogai $
 3 |  *
 4 |  * lambda.js
 5 |  *
 6 |  *  (c) 2013 Dan Kogai
 7 |  *
 8 |  *  Licensed under the MIT license.
 9 |  *  http://www.opensource.org/licenses/mit-license
10 |  *
11 |  */
12 | (function(ctx) {
13 |     'use strict';
14 |     var parse = function(src, lv) {
15 |         var body = '', idx, m, i, d, l;
16 |         while (m = src.match(/^([\s\S]*?)(lambda|λ)\(/)) {
17 |             body += m[1];
18 |             src = src.substr(m[0].length-1);
19 |             for (i = d = 1, l = src.length; i < l; ++i) {
20 |                 if      (src.charAt(i) === '(') d++;
21 |                 else if (src.charAt(i) === ')') d--;
22 |                 if (!d) break;
23 |             };
24 |             if (i === l) throw new SyntaxError('() mismatch');
25 |             var t = src.substr(1,i-1);
26 |             body += lambda(t, true, lv+1);
27 |             src = src.substr(i+1);
28 |         }
29 |         return body + src;
30 |     };
31 |     function lambda(src, nomemo, lv) {
32 |         if (!nomemo && src in lambda.memo) return lambda.memo[src];
33 |         if (!lv) lv = 0;
34 |         var parts = src.match(/^([^:]*):([\s\S]+)/),
35 |         head = parts[1],
36 |         body = parse(parts[2], lv);
37 |         var fun = eval(
38 |             '(function _' + (lv) + '('+head+'){return '+body+'})'
39 |         );
40 |         if (!nomemo) lambda.memo[src] = fun;
41 |         return fun;
42 |     };
43 |     lambda.memo = {};
44 |     ctx.λ = ctx.lambda = lambda;
45 | })(this);
46 | 


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/lambda.min.js:
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1 | (function(ctx){"use strict";var parse=function(src,lv){var body="",idx,m,i,d,l;while(m=src.match(/^([\s\S]*?)(lambda|λ)\(/)){body+=m[1];src=src.substr(m[0].length-1);for(i=d=1,l=src.length;i<l;++i){if(src.charAt(i)==="(")d++;else if(src.charAt(i)===")")d--;if(!d)break}if(i===l)throw new SyntaxError("() mismatch");var t=src.substr(1,i-1);body+=lambda(t,true,lv+1);src=src.substr(i+1)}return body+src};function lambda(src,nomemo,lv){if(!nomemo&&src in lambda.memo)return lambda.memo[src];if(!lv)lv=0;var parts=src.match(/^([^:]*):([\s\S]+)/),head=parts[1],body=parse(parts[2],lv);var fun=eval("(function _"+lv+"("+head+"){return "+body+"})");if(!nomemo)lambda.memo[src]=fun;return fun}lambda.memo={};ctx.λ=ctx.lambda=lambda})(this);


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/package.json:
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 1 | {
 2 |   "name": "js-lambda",
 3 |   "version": "0.0.2",
 4 |   "description": "DSL for lambda calculus",
 5 |   "main": "lambda.js",
 6 |   "directories": {
 7 |     "test": "test"
 8 |   },
 9 |   "scripts": {
10 |     "test": "mocha"
11 |   },
12 |   "devDependencies": {
13 |       "mocha" : "*"
14 |   },
15 |   "repository": {
16 |     "type": "git",
17 |     "url": "git://github.com/dankogai/js-lambda.git"
18 |   },
19 |   "keywords": [
20 |     "lambda",
21 |     "λ",
22 |     "DSL"
23 |   ],
24 |   "author": "Dan Kogai",
25 |   "license": "BSD",
26 |   "readmeFilename": "README.md",
27 |   "gitHead": "bcd815ecb46ebfd594d8ddf9acbc1c6a7933b5e2"
28 | }
29 | 


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/test/helper.js:
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 1 | /*
 2 |  * use mocha to test me
 3 |  * http://visionmedia.github.com/mocha/
 4 |  */
 5 | var assert;
 6 | if (this['window'] !== this) {
 7 |     assert = require("assert");
 8 | }
 9 | ok = function (pred) {
10 |     return function () {
11 |         assert(pred)
12 |     }
13 | };
14 | eq = function (a, e, m) {
15 |     return function () {
16 |         assert.equal(a, e, m)
17 |     }
18 | };
19 | eq_deeply = function (a, e, m) {
20 |     return function () {
21 |         assert.equal(JSON.stringify(a), JSON.stringify(e), m)
22 |     }
23 | };
24 | 


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/test/index.html:
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 1 | <html>
 2 | <head>
 3 | <meta charset="utf-8" />
 4 | <title>Tester</title>
 5 | <link rel="stylesheet" href="https://raw.github.com/visionmedia/mocha/master/mocha.css" />
 6 | </head>
 7 | <body>
 8 | <div id="mocha"></div>
 9 | <script src="https://raw.github.com/visionmedia/mocha/master/mocha.js"></script>
10 | <script>mocha.setup('bdd');</script>
11 | <!--begin customize-->
12 | <script src="./helper.js"></script>
13 | <script src="../lambda.js"></script>
14 | <script src="./test.js"></script>
15 | <!--end customize -->
16 | <script>
17 | assert = assert || function(expr, msg) {
18 |   if (!expr) throw new Error(msg || 'failed');
19 | };      
20 | assert.equal = assert.equal || function(a, b, msg) {
21 |   if (a !== b) throw new Error(msg || ('failed : '+a+','+b));
22 | };
23 | </script>
24 | <script src="http://ajax.googleapis.com/ajax/libs/jquery/1.8/jquery.min.js"></script>
25 | <script>$(function() { mocha.run() });
26 | </script>
27 | </body>
28 | </html>
29 | 


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/test/test.js:
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 1 | /*
 2 |  * use mocha to test me
 3 |  * http://visionmedia.github.com/mocha/
 4 |  */
 5 | if (this['window'] !== this) {
 6 |     require('./helper.js');
 7 |     // not "var _"; node also aliases _ to global by default
 8 |     var lambda = require('../lambda.js').lambda,
 9 |     λ = lambda;
10 | }
11 | 
12 | (function(root){
13 |     'use strict';
14 |     describe('λ', function(){
15 |         it('λ("x:x")(42) === 42;', eq(λ("x:x")(42), 42));
16 |         it('λ("n:n<=1?n:n*_0(n-1)")(10) === 3628800;',
17 |            eq(λ("n:n<=1?n:n*_0(n-1)")(10), 3628800));
18 |         it('λ("x,y:Math.sqrt(x*x+y*y)")(3,4) === 5;', 
19 |            eq(λ("x,y:Math.sqrt(x*x+y*y)")(3,4), 5));
20 |         it('λ("x:λ(y:Math.sqrt(x*x+y*y))")(3)(4) === 5;', 
21 |            eq(λ("x:λ(y:Math.sqrt(x*x+y*y))")(3)(4), 5));
22 |     });
23 |     describe('Church numerals', function(){
24 |         var cn2num = λ("f:f(λ(n:n+1))(0)");
25 |         var succ = λ("n:λ(f:λ(x:f(n(f)(x))))"),
26 |         zero = λ("f:λ(x:x)"),
27 |         one = succ(zero);
28 |         it('cn2num(one) === 1', eq(cn2num(one), 1));
29 |         var add = λ("m:λ(n:m("+succ+")(n))"),
30 |         two = add(one)(one);
31 |         it('cn2num(two) === 2', eq(cn2num(two), 2));
32 |         var mul = λ("m:λ(n:m("+add+"(n))("+zero+"))"),
33 |         four = mul(two)(two);
34 |         it('cn2num(four) === 4', eq(cn2num(four), 4));
35 |         var pow = λ("b:λ(e:e(b))"),
36 |         sixteen = pow(two)(four);
37 |         it('cn2num(sixteen) === 16', eq(cn2num(sixteen), 16));
38 |     });
39 | })(this);
40 | 


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