F# type inferencing

Question

I'm working with fsharp type inferencing and I'm trying to understand how they work. Why is it that

List.filter List.head

is type bool list list -> bool list list?

Answer 1

List.filter has the type (just enter List.filter;; in FSI):

> List.filter;;
val it : (('a -> bool) -> 'a list -> 'a list)

so it takes a 'a -> bool and results in a 'a list -> 'a list

Now you feed it with

> List.head;;
val it : ('b list -> 'b)

(it's another 'a really so I renamed it) and now you have:

'a -> bool ~ 'b list -> 'b

you can unify this and see:

• 'b ~ bool (from the right-hand-sides of ->)
• 'a ~ 'b list ~ bool list (from the left-hand-side)

but this all together and you get the answer F#`s type-inference gives you:

'a list -> 'a list 
~ ('b list) list -> ('b list) list 
~ (bool list) list -> (bool list) list
~ bool list list -> bool list list