I don't actually know much about GHC's type checker itself, but I think it uses a form of bidirectional type checking. A bidirectional type checker has two modes:

infer :: Term -> Type

check :: Term -> Type -> Bool

The syntax is divided into two classes. The types for one of these classes can be inferred, but the other can only be checked. Given a type checkable term, you can create a type inferable term by giving it a type annotation. That is, `infer (x :: T) = check x T`.

On Sun, Jun 7, 2020 at 4:19 PM Olaf Klinke <olf@aatal-apotheke.de> wrote:

> f 0 x = 0
> f 1 x = f 0 ()
> f n x = f (n-1) 'a'

That's very interesting, I learned something new about GHC today. I
used to believe that my Haskell compiler always type checks
declarations on its own, and after that unifies its result with the
type declaration that I provide. Polymorphic recursion yields a case
where the compiler's inference procedure is evidently not independent
of my provided type declaration. Can the above be abused to compile
programs containing false type declarations? (It seems the answer is
no, but maybe I lack the fantasy.)

Thanks,
Olaf

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