var flatten = function(arrays) {
  return arrays.reduce( function(p,n){
    return p.concat(n);
  });
};

var invert = function(arr) {
  return arr.map(function(x, i, a) {
    return a[a.length - (i+1)];
  });
};

var bind = Function.prototype.call.bind(Function.prototype.bind);
var call = bind(Function.prototype.call, Function.prototype.call);
var apply = bind(Function.prototype.call, Function.prototype.apply);

var checkTypes = function( typeSafeties ) {
  arrayOf(func)(arr(typeSafeties));
  var argLength = typeSafeties.length;
  return function(args) {
    arr(args);
    if (args.length != argLength) {
      throw new TypeError('Expected '+ argLength + ' arguments');
    }
    var results = [];
    for (var i=0; i<argLength; i++) {
      results[i] = typeSafeties[i](args[i]);
    }
    return results;
  };
};

var homoMorph = function( /* arg1, arg2, ..., argN, output */ ) {
  var before = checkTypes(arrayOf(func)(Array.prototype.slice.call(arguments, 0, arguments.length-1)));
  var after = func(arguments[arguments.length-1])
  return function(middle) {
    return function(args) {
      return after(middle.apply(this, before([].slice.apply(arguments))));
    };
  };
};

Function.prototype.compose = function(prevFunc) {
  var nextFunc = this;
  return function() {
    return nextFunc.call(this,prevFunc.apply(this,arguments));
  };
};

Function.prototype.sequence  = function(prevFunc) {
  var nextFunc = this;
  return function() {
    return prevFunc.call(this,nextFunc.apply(this,arguments));
  };
};

Function.prototype.curry = function (numArgs) {
  var func = this;
  numArgs = numArgs || func.length;
  // recursively acquire the arguments
  function subCurry(prev) {
    return function (arg) {
      var args = prev.concat(arg);
      if (args.length < numArgs) {
        // recursive case: we still need more args
        return subCurry(args);
      }
      else {
        // base case: apply the function
        return func.apply(this, args);
      }
    };
  };
  return subCurry([]);
};

// map :: (a -> b) -> [a] -> [b]
var map = function(f, a) {
  return arr(a).map(func(f));
}

// strmap :: (str -> str) -> str -> str
var strmap = function(f, s) {
  return str(s).split('').map(func(f)).join('');
}

// fcompose :: (a -> b)* -> (a -> b)
var fcompose = function() {
  var funcs = arrayOf(func)(arguments);
  return function() {
    var argsOfFuncs = arguments;
    for (var i = funcs.length; i > 0; i -= 1) {
      argsOfFuncs  = [funcs[i].apply(this, args)];
    }
    return args[0];
  };
};

var lens = function(get, set) {
  var f = function (a) {return get(a)};
  f.get = function (a) {return get(a)}; 
  f.set = set;
  f.mod = function (f, a) {return set(a, f(get(a)))};
  return f;
};

// usage:
var first = lens(
  function (a) { return arr(a)[0]; }, // get
  function (a, b) { return [b].concat(arr(a).slice(1)); } // set
);

var Maybe = function(){}; 
Maybe.prototype.orElse = function(y) {
  if (this instanceof Just) {
    return this.x;
  }
  else {
    return y;
  }
};

var None = function(){}; 
None.prototype = Object.create(Maybe.prototype);
None.prototype.toString = function(){return 'None';};
var none = function(){return new None()};
// and the Just instance, a wrapper for an object with a value
var Just = function(x){return this.x = x;};
Just.prototype = Object.create(Maybe.prototype);
Just.prototype.toString = function(){return "Just "+this.x;};
var just = function(x) {return new Just(x)};
var maybe = function(m){
  if (m instanceof None) {
    return m;
  }
  else if (m instanceof Just) {
    return just(m.x);
  }
  else {
    throw new TypeError("Error: Just or None expected, " + m.toString() + " given."); 
  }
};

var maybeOf = function(f){
  return function(m) {
    if (m instanceof None) {
      return m;
    }
    else if (m instanceof Just) {
      return just(f(m.x));
    }
    else {
      throw new TypeError("Error: Just or None expected, " + m.toString() + " given."); 
    }
  };
};

Object.prototype.plusMixin = function(mixin) {
  var newObj = this;
  newObj.prototype = Object.create(this.prototype);
  newObj.prototype.constructor = newObj;
  for (var prop in mixin) {
    if (mixin.hasOwnProperty(prop)) {
      newObj.prototype[prop] = mixin[prop];
    }
  }
  return newObj;
};

function bindFirstArg(func, a) {
  return function(b) {
    return func(a, b);
  };
};

Function.prototype.partialApply = function(){
  var func = this; 
  var args = Array.prototype.slice.call(arguments);
  return function(){
    return func.apply(this, args.concat(
      Array.prototype.slice.call(arguments)
    ));
  };
};

Function.prototype.partialApplyRight = function(){
  var func = this; 
  var args = Array.prototype.slice.call(arguments);
  return function(){
    return func.apply(
      this,
      Array.protype.slice.call(arguments, 0)
    .concat(args));
  };
};

var trampoline = function(f) {
  while (f && f instanceof Function) {
    f = f.apply(f.context, f.args);
  }
  return f;
};

var thunk = function (fn) {
  return function() {
    var args = Array.prototype.slice.apply(arguments);
    return function() { return fn.apply(this, args); };
  };
};

var typeOf = function(type) {
  return function(x) {
    if (typeof x === type) {
      return x;
    }
    else {
      throw new TypeError("Error: "+type+" expected, "+typeof x+" given.");
    }
  };
};

var str = typeOf('string'),
  num = typeOf('number'),
  func = typeOf('function'),
  bool = typeOf('boolean');

var objectTypeOf = function(name) {
  return function(o) {
    if (Object.prototype.toString.call(o) === "[object "+name+"]") {
      return o;
    }
    else {
      throw new TypeError("Error: '+name+' expected, something else given."); 
    }
  };
};
var obj = objectTypeOf('Object');
var arr = objectTypeOf('Array');
var date = objectTypeOf('Date');
var div = objectTypeOf('HTMLDivElement');

// arrayOf :: (a -> b) -> ([a] -> [b])
var arrayOf = function(f) {
  return function(a) {
    return map(func(f), arr(a));
  }
};

var Y = function(F) {
  return (function (f) {
    return f(f);
  }(function (f) {
    return F(function (x) {
      return f(f)(x);
    });
  }));
};

// Memoizing Y-Combinator:
var Ymem = function(F, cache) {
  if (!cache) {
    cache = {} ; // Create a new cache.
  }
  return function(arg) {
    if (cache[arg]) {
      // Answer in cache
      return cache[arg] ;
    }
    // else compute the answer
    var answer = (F(function(n){
      return (Ymem(F,cache))(n);
    }))(arg); // Compute the answer.
    cache[arg] = answer; // Cache the answer.
    return answer;
  };
};