[Haskell-cafe] How to spot Monads, Applicatives ...

[Tom Ellis]

On Sat, Jun 18, 2016 at 10:31:54AM +0200, martin wrote:
> Suppose I came to the conclusion that "s->(s,a)" is useful to model
> stateful computations.  Next I want want to make it a Functor.  This
> raises two questions:
> 
> (1) Why do I want to do this in the first place?

"s -> (s, a)" simply *is* functorial in 'a'.  There's no "want" about that
part.  From that point on it's just a minor question of whether you want to
write out a Functor instance so you can conveniently use that fact as part
of the programs you write.

> (2) What keeps me from trying "instance Functor (MyState a)" instead of
> "instance Functor (MyState s)?  Is trying it the wrong way and failing the
> only way to make that choice?  I suppose there must be some reasoning
> which is closer to the problem. 

You mean 'instead of "instance Functor (State s)"'.  The answer is that 's'
appears on the left hand side of the arrow in "s -> (s, a)" so there's no
way the 's' type parameter can be functorial.

Tom