jsbin.com/yumog/4/edit

  // Exercise 1
// ==========
// Use _.add(x,y) and map(f,x) to make a function that increments a value inside a functor
console.log("--------Start exercise 1--------")

var ex1 = undefined


assertDeepEqual(Identity(3), ex1(Identity(2)))
console.log("exercise 1...ok!")

We want to add 1 inside ​Identity​. 

  var ex1 = map(_.add(1), Identity(3))

We need to map so that we can add 1 to the value inside Identity(3)

_.add is just the add function from lodash or ramda...

But we want to be able to increment any functor that comes in.

  var ex1 = map(_.add(1))

This is the solution. map is curried because it takes more than one argument (and we're only giving it one). So, later we can call ex1(Identity(2)) and it will be able to work with value inside Identity(2). Furthermore, _.add(1) is also a curried function, waiting to be run when it recieves the second argument (Identity(2)).

Remember two notes before, where we defined map with curry. Not the .map method, but the map() function!

  // from before...
var map = _.curry(function (f, obj) {
  return obj.map(f)
})

Identity is just a neutral functor, to be used for the exercises. It has no added behaviour, just to let you get used to using containers.

Another example to make it more clear:

  map(function (x) {return x.toUpperCase()}, Identity("firehose"))
// Identity(FIREHOSE)

So ​x​ became "firehose" in the ​map​. 

  map(function (x) {return x.reverse()}, Identity([6,5,4,3]))
// Identity([3,4,5,6])

Emphasises that ​map​ is not the ​map​ that iterates over lists. It runs a function over an element of a data structure. 

As a reply to a question, we don't need to deal with ​this​ with functional programming.

Why and when to use Identity?

It lets you lift values into the functional world. It's a neutral functor, when you need a functor and don't want any side effects.