How does ghci choose names for type variables? [duplicate]

Question

I made this function:

compose []     = id
compose (x:xs) = x  . (compose xs)

And when I asked for the type:

:t compose
compose :: [b -> b] -> b -> b

Why does it give compose :: [b -> b] -> b -> b and not compose :: [a -> a] -> a -> a if a comes first in alphabetic order?

Saying that, I will add this other example:

badImplementationOfCompose []     = id
badImplementationOfCompose (x:xs) =  (badImplementationOfCompose xs)

:t badImplementationOfCompose
badImplementationOfCompose :: [a1] -> a2 -> a2

It might give some hints...

Answer 1

I would guess it has to do with the type of . which is

(.) :: (b -> c) -> (a -> b) -> a -> c

and it just starts replacing from there when inferring the type.

a has to be equal to b and b has to be equal to c. So in short my guess is that it tries to keep type variable naming in line with the type variable names in used sub-functions if possible.