js-lambda


js-lambda
=========

DSL for, but not limited to, the lambda calculus.

USAGE
-----

$3

```html

``

$3

``javascript
var lambda = require('./lambda.js').lambda,
λ = lambda;
``

SYNOPSIS
--------

``javascript
lambda("x:x")(42) === 42;
λ("x:x")(42) === 42; // λ = lambda
λ("n:n<=1?n:n*_0(n-1)")(10) === 3628800; // _0 for recursion
λ("x,y:Math.sqrt(xx+yy)")(3,4) === 5; // multiple arguments,
λ("x:λ(y:Math.sqrt(xx+yy))")(3)(4) === 5; // λ can be nested
``
``javascript
// church numerals
var cn2num = λ("f:f(λ(n:n+1))(0)"),
succ = λ("n:λ(f:λ(x:f(n(f)(x))))"),
zero = λ("f:λ(x:x)"),
one = succ(zero),
add = λ("m:λ(n:m("+succ+")(n))"),
two = add(one)(one),
mul = λ("m:λ(n:m("+add+"(n))("+zero+"))"),
four = mul(two)(two),
pow = λ("b:λ(e:e(b))"),
sixteen = pow(two)(four);
cn2num(sixteen) === 16;
``

DESCRIPTION
-----------

This script exports lambda() and its alias λ(). As seen in the synopsis, it is a DSL compiler that returns a function.

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As seen in SYNOPSYS,

lambda(arg0,arg1,...argn:expression)

Turns into:

function(arg0, arg1, ...argn){return expression }

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As seen in SYNOPSYS, the lambda can be nested.

``javascript
λ('x:λ(y:Math.sqrt(xx+yy))');
``

Turns into:

``javascript
function _0(x){return function _1(y){return Math.sqrt(xx+yy)}}
``

As seen above, the function is named accordingly to [De Bruijin index]. _n is the nth level function.

[De Bruijin index]: http://en.wikipedia.org/wiki/De_Bruijn_index

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.

``javascript
// function fact(n){ return n <= 1 ? n : n * fact(n-1) }
λ("n:n<=1?n:n*_0(n-1)");
``

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To use lexical functions, you have to "interpolate".

``javascript
var succ = λ("n:λ(f:λ(x:f(n(f)(x))))"),
add = λ("m:λ(n:m("+succ+")(n))"); // λ("m:λ(n:m(succ)(n))") does not work
``

This is because lambda() needs to eval() to compile the function but lexicals are out of its scope.

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By default, the compiled function is [memoized]. Suppose you have:

[memoized]: http://en.wikipedia.org/wiki/Memoization

``javascript
function rms(ary) {
return Math.sqrt(ary.reduce(λ("t,x:t+x*x"), 0))
}
``

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:

``javascript
var uncached = lambda("a,b,c:...", true);
``

And if you wish, you can inspect cached functions via lambda.memo`.

SEE ALSO
--------

+ http://docs.python.org/2/tutorial/controlflow.html#lambda-forms
+ http://www.ruby-doc.org/core-2.0/Kernel.html#method-i-lambda
+ https://developer.mozilla.org/en-US/docs/JavaScript/Reference/arrow_functions