Functional combinators in JavaScript

u.js

var u = (function() {
  var id       = function(x)    { return x; }
  var constant = function(x)    { return function() { return x; }}

  var ap    = function(f,g)     { return function(x) { return f(x)(g(x)); }}
  var slice = function(args, n) { return Array.prototype.slice.call(args, n || 0); }
  var attr  = function(name)    { return function(object) { return object[name]; }}
  var bind  = function(ctx)     { return function(method) { return function() { return method.apply(ctx, slice(arguments)); }}}
  var call  = function(args)    { return function(func) { return func.apply(null, slice(args)); }}
  var flip  = function(func)    { return function(a) { return function(b) { return func(b)(a); }}}
  var apply = function()        { return call(slice(arguments)); }
  var compose = function(f,g)   { return function(x) { return f(g(x)); }}
  var method  = function(name)  { return ap(bind, attr(name)); }
  var invoke  = function(name)  { return compose(call(slice(arguments, 1)), method(name)); }

  var curry = function(f,n) {
    if (n === 0) return f;
    var args = []
      , last = function(x) { args.push(x); return f.apply(null, args); }
      , fold = function(g) { return function(x) { args.push(x); return g; }};
    return _.reduce(_.range(n-1), fold, last); }

  return ({id: id, constant: constant, ap: ap, slice: slice, attr: attr, bind: bind, call: call,
    flip: flip, apply: apply, compose: compose, method: method, curry: curry, invoke: invoke});
})();

var op = ({
  'add': u.curry(function(x,y) { return x + y; },  2)
, 'sub': u.curry(function(x,y) { return x - y; },  2)
, 'mul': u.curry(function(x,y) { return x * y; },  2)
, 'div': u.curry(function(x,y) { return x / y; },  2)
, 'mod': u.curry(function(x,y) { return x % y; },  2)
, 'eq':  u.curry(function(x,y) { return x === y; }, 2)
, 'ne':  u.curry(function(x,y) { return x !== y; }, 2)
, 'gt':  u.curry(function(x,y) { return x > y; },   2)
, 'lt':  u.curry(function(x,y) { return x < y; },   2)
, 'lte': u.curry(function(x,y) { return x <= y; },  2)
, 'gte': u.curry(function(x,y) { return x >= y; },  2)
, 'or':  u.curry(function(x,y) { return x || y; },  2)
, 'and': u.curry(function(x,y) { return x && y; },  2)
, 'xor': u.curry(function(x,y) { return x !== y; }, 2)
, 'not': function(x) { return !x; }
, 'typeof':     function(x) { return typeof x; }
, 'instanceof': function(x) { return function(y) { return x instanceof y; }}
});


// Where does 'x' occur in each element?
_.map(['xbc', 'dxf', 'ghx'], u.invoke('indexOf', 'x'))

// What's the remainder of each element divided by 3?
_.map([12345, 23456, 56789], u.flip(op.mod)(3))

// What's the length of each element?
_.map(['abc', 'def', 'ghi'], u.attr('length'))

// Does anyone have an 'o'?
_.any(['xbc', 'dxf', 'ghx'], u.compose(op.ne(-1), u.invoke('indexOf', 'o')))

Oh, I noticed your fix is still incomplete. This is a classic case where mutable state can really be a pain in the ass.

var xyz = curry(function(x,y,z) { return x + y + z; }, 3);
var z = xyz(1)(2);
z(3) //=> 3
z(3) //=> NaN