CODEWITHSUNDEEP
scalafunctional-programmingmonads
nsfyn55
nsfyn55

Reputation: 15363

Second Monad Law:Unit

I am reading James Iry's blog post on Monads in scala. I am in part three and I am confused about his description of the second law of monads regarding Unit. Specifically this claim:

 unit(x) flatMap f = f(x)

When I apply my mental examples which are jame's previous examples of monadic types this never seems to work out

 val x = 1
 val f = (_:Int) * 2
 f(x) == 2 //true
 List(x) flatMap f == 2 //fail
 Some(x) flatMap f == 2 //fail

As a matter of fact they don't even compile due to type issues.

To clarify I understand why these are failing. I understand the how to fix them so they compile.

My confusion is that these seem to be in conflict with the theory presented in the article. Is there a step I am missing? Are these types not really monads? Is the section entitled "Second Law of Monads:Unit" incorrect?

Upvotes: 4

Views: 745

Answers (2)

Ben
Ben

Reputation: 71590

The fact that it doesn't compile due to type issues should tell you something: f is not the kind of function that the monad law applies to!

flatMap, when seen as a monadic operation rather than a collection operation, takes a "monadic value" and a function from ordinary values to monadic values. Your f function is a function from ordinary values to ordinary values.

Passing f to flatMap doesn't break the monadic laws, it just doesn't mean anything at all. It's an invalid expression. Similarly 1 + "fork" - 1 doesn't violate the law from arithmetic that 1 + x - 1 = x; from this law we might conclude that 1 + "fork" - 1 should equal "fork", when in fact it's a compiler error. That would be a silly conclusion though; the laws are only talking about things that are type-correct.

Upvotes: 8

Jesper
Jesper

Reputation: 207006

Scala's flatMap needs a function that returns a collection, not a function that returns a single element, like your function f.

Either use map:

List(x) map f

or make your function return a collection:

val f = (x: Int) => List(x * 2)

List(x) flatMap f

Note that it will also return a collection, not a single integer (you'll get List(2), not just 2).

Upvotes: 9

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