What does it mean that 'lift is pretty much the same as map'?

Question

Leonardo Borges has written an excellent post called "Functional Composition With Monads, Kleislis and Functors".

In it he comments:

Mark pointed out to me that lift is pretty much the same as map but with the arguments reversed.

This means that this:

val f = Functor[Option].lift(parts) compose make

can be refactored to:

val g = make(_:Int).map(parts)

My question is,What does it mean that 'lift is pretty much the same as map?'

I'd even rather say that `map` is just a flipped `lift`. Scala is the only language I know of that uses that order of arguments: Consider Python's `map`, Haskell's `fmap`, Lisp's `mapcar`... they're all in `lift`'s order. That probably comes from Scala's tendency to infix notation. — phipsgabler, Jun 23 '14 at 09:04

score 3 · Accepted Answer · answered Jun 23 '14 at 06:09

From scalaz functor code:

def map[A, B](fa: F[A])(f: A => B): F[B]

def lift[A, B](f: A => B): F[A] => F[B] = map(_)(f)

NOTE: lift is just defined in terms of map (reversing the arguments)

Mostly when people start with Functional programming they are introduced to map as mapping a function over a sequence of things, but map in general is a more abstract concept related to functor.

What does it mean that 'lift is pretty much the same as map'?

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