Monads in JavaScript

_helpers.js

var extend = function(a, b) {
  for (var i in b)
    a[i] = b[i];
  return a;
};

var fluent = function(f) {
  return function() {
    var clone = extend(Object.create(null), this);
    f.apply(clone, arguments);
    return clone;
  };
};

var toArray = function(x) {
  return Array.prototype.slice.call(x);
};

either.js

var Either = {
  unit: function(x) {
    return this.right(x);
  },
  bind: function(f) {
    if (this.isLeft) {
      return this.left(this.l);
    } else if (this.isRight) {
      return f.call(this, this.r);
    }
  },
  left: fluent(function(l) {
    this.l = l;
    this.isLeft = true;
    this.toString = function() {
      return "Left: " + JSON.stringify(this.l);
    };
    this.valueOf = function() {
      return this.l;
    };
  }),
  right: fluent(function(r) {
    this.r = r;
    this.isRight = true;
    this.toString = function() {
      return "Right: " + JSON.stringify(this.r);
    };
    this.valueOf = function() {
      return this.r;
    };
  })
};

var div = function(x, y) {
  if (y === 0) {
    return Either.left('division by 0');
  }
  return Either.right(x/y);
};

var result = div(4,2).bind(function(x) {
  return div(x,2).bind(function(y) {
    return this.unit(x + y);
  });
});

console.log(result.toString()); //=> Right: 3

var result = div(4,2).bind(function(x) {
  return div(x,0).bind(function(y) {
    return this.unit(x + y);
  });
});

console.log(result.toString()); //=> Left: division by 0

list.js

var List = {
  unit: fluent(function() {
    this.x = toArray(arguments);
  }),
  bind: function(f) {
    var fx = this.x.map(f.bind(this));
    var a = fx[0];
    for (var i=1; i<fx.length; i++)
      a.x = a.x.concat(fx[i].x);
    return a;
  },
  lift: function(f) {
    return function(x) {
      return List.unit(f(x));
    }
  },
  toString: function() {
    return 'List: '+ JSON.stringify(this.x);
  },
  valueOf: function() {
    return this.x;
  }
};

var add1 = function(x) {
  return x + 1;
};

// lift
var result = List.unit(1,2,3).bind(List.lift(add1));

console.log(result.toString()); //=> List: [2,3,4]

// do
var result = List.unit(1,2).bind(function(x) {
  return this.unit(3,4).bind(function(y) {
    return this.unit(x + y);
  });
});

console.log(result.toString()); //=> List: [4,5,5,6]

maybe.js

var Maybe = {
  unit: function(x) {
    return this.just(x);
  },
  bind: function(f) {
    if (this.isNothing) {
      return this.nothing();
    } else if (this.isJust) {
      return f.call(this, this.x);
    }
  },
  lift: function(f) {
    var self = this;
    return function() {
      if (~toArray(arguments).indexOf(null)) {
        return self.nothing();
      }
      return self.just(f.apply(self, arguments));
    };
  },
  nothing: fluent(function() {
    this.x = null;
    this.isNothing = true;
    this.toString = function() {
      return 'Nothing';
    };
  }),
  just: fluent(function(x) {
    this.x = x;
    this.isJust = true;
    this.toString = function() {
      return 'Just: '+ JSON.stringify(this.x);
    };
  }),
  valueOf: function() {
    return this.x;
  }
};

var by2 = function(x) {
  return x * 2;
};

var add = function(x, y) {
  return x + y;
};

var result = Maybe.unit(2).bind(Maybe.lift(by2));

console.log(result.toString()); //=> Just: 4

var addM = Maybe.lift(add);

var result = addM(1,2).bind(function(x) {
  return addM(x,3).bind(function(y) {
    return this.unit(x + y);
  });
});

console.log(result.toString()); //=> Just: 9

var result = addM(1,2).bind(function(x) {
  return addM(x,null).bind(function(y) {
    return this.unit(x + y);
  });
});

console.log(result.toString()); //=> Nothing

writer.js

var Writer = {
  unit: fluent(function(x, w) {
    this.w = w == null ? [] : [w];
    this.x = x;
  }),
  bind: function(f) {
    var w = this.w
      , fx = f.call(this, this.x);
    fx.w = w.concat(fx.w);
    return fx;
  },
  tell: fluent(function(w) {
    this.w = [w];
  }),
  toString: function() {
    return 'Writer: ('+ this.x +', '+ JSON.stringify(this.w) +')';
  },
  valueOf: function() {
    return this.x;
  }
};

var add = function(x, y) {
  return Writer.unit(x + y, 'add '+ x +' plus '+ y);
};

var result = add(1,2).bind(function(x) {
  return add(x,2).bind(function(y) {
    return this.tell('multiply '+ x +' by '+ y).bind(function() {
      return this.unit(x * y);
    });
  });
});

console.log(result.toString());
//^ Writer (15, ["add 1 plus 2", "add 3 plus 2", "multiply 3 by 5"])