# [Haskell-cafe] Inferring the most general type

Job Vranish job.vranish at gmail.com
Tue Jun 22 11:06:21 EDT 2010

```Esteemed fellow haskellers,

I recently ran into a very simple real life case where Haskell's rules for
inferring the types for mutually recursive definitions resulted in a type
that was less general than it could be. It took me a while to realize that
the type error I was getting wasn't actually a problem with my code. I
understand why Haskell does this (it infers the strongly connected mutually
recursive definitions monomorphically), but I think it _could_ infer the
more general type even with recursive definitions like this.

Here is a simplified example that illustrates the problem:

> import Data.Maybe

> -- The fixed point datatype
> data Y f = Y (f (Y f))

> -- silly dummy function
> maybeToInt :: Maybe a -> Int
> maybeToInt = length . maybeToList

> -- f :: Y Maybe -> Int
> f (Y x) = g maybeToInt x

> g h x = h \$ fmap f x

This is the type it wants to infer for g
g :: (Maybe Int -> Int) -> Maybe (Y Maybe) -> Int

This is the type I think it should have, note you can't force the type with
a typesig without -XRelaxedPolyRec
g :: (Functor f) => (f Int -> b) -> f (Y Maybe) -> b

If I use -XRelaxedPolyRec I can manually specify the more general type, but
then I have to convince myself that there isn't a more general type that I'm
missing.

Are there other known algorithms that yield a more general type? and if so,
what was the rational for Haskell keeping the current method?

I worked out an alternative algorithm that would give a more general type
(perhaps the most general type) but it has factorial complexity and probably
wouldn't be good for strongly connected groups with 7 or more members.

Even so, I would much rather have the inferred types always be the most
general ones and be required to add type signatures for mutually recursive
groups with 7 or more members (which probably need to be redesigned anyway)
than be always required to manually figure out the more general signatures.
What do you think?

- Job
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