[Haskell-cafe] type families and type signatures

Martin Sulzmann martin.sulzmann at gmail.com
Wed Apr 9 03:53:07 EDT 2008

I think it's not fair to say TFs as implemented in GHC are broken.
Fine, they are situations where the current implementation is overly 

The point is that the GHC type checker relies on automatic inference. 
Hence, there'll
always be cases where certain "reasonable" type signatures are rejected.

For example, consider the case of "undecidable" and "non-confluent" type 
class instances.

instance Foo a => Bar a    -- (1)

instance Erk a => Bar [a]  -- (2)

GHC won't accept the above type class instance (note: instances are a 
kind of type signature) because

- instance (1) is potentially non-terminating (the size of the type term 
is not decreasing)
- instance (2) overlaps with (1),  hence, it can happen that during 
context reduction we choose
  the "wrong" instance.

To conclude, any system with automatic inference will necessary reject 
certain type signatures/instances
in order to guarantee soundness, completeness and termination.

Lennart, you said
> (It's also pretty easy to fix the problem.)

What do you mean? Easy to fix the type checker, or easy to fix the 
program by inserting annotations
to guide the type checker?


Lennart Augustsson wrote:
> Let's look at this example from a higher level.
> Haskell is a language which allows you to write type signatures for 
> functions, and even encourages you to do it.
> Sometimes you even have to do it.  Any language feature that stops me 
> from writing a type signature is in my opinion broken.
> TFs as implemented in currently implemented ghc stops me from writing 
> type signatures.  They are thus, in my opinion, broken.
> A definition should either be illegal or it should be able to have a 
> signature.  I think this is a design goal.  It wasn't true in Haskell 
> 98, and it's generally agreed that this was a mistake.
> To summarize: I don't care if the definition is useless, I want to be 
> able to give it a type signature anyway.
> (It's also pretty easy to fix the problem.)
>   -- Lennart
> On Wed, Apr 9, 2008 at 7:20 AM, Martin Sulzmann 
> <martin.sulzmann at gmail.com <mailto:martin.sulzmann at gmail.com>> wrote:
>     Manuel said earlier that the source of the problem here is foo's
>     ambiguous type signature
>     (I'm switching back to the original, simplified example).
>     Type checking with ambiguous type signatures is hard because the
>     type checker has to guess
>     types and this guessing step may lead to too many (ambiguous)
>     choices. But this doesn't mean
>     that this worst case scenario always happens.
>     Consider your example again
>     type family Id a
>     type instance Id Int = Int
>     foo :: Id a -> Id a
>     foo = id
>     foo' :: Id a -> Id a
>     foo' = foo
>     The type checking problem for foo' boils down to verifying the formula
>     forall a. exists b. Id a ~ Id b
>     Of course for any a we can pick b=a to make the type equation
>     statement hold.
>     Fairly easy here but the point is that the GHC type checker
>     doesn't do any guessing
>     at all. The only option you have (at the moment, there's still
>     lots of room for improving
>     GHC's type checking process) is to provide some hints, for example
>     mimicking
>     System F style type application by introducing a type proxy
>     argument in combination
>     with lexically scoped type variables.
>     foo :: a -> Id a -> Id a
>     foo _ = id
>     foo' :: Id a -> Id a
>     foo' = foo (undefined :: a)
>     Martin
>     Ganesh Sittampalam wrote:
>         On Wed, 9 Apr 2008, Manuel M T Chakravarty wrote:
>             Sittampalam, Ganesh:
>                 No, I meant can't it derive that equality when
>                 matching (Id a) against (Id b)? As you say, it can't
>                 derive (a ~ b) at that point, but (Id a ~ Id b) is
>                 known, surely?
>             No, it is not know.  Why do you think it is?
>         Well, if the types of foo and foo' were forall a . a -> a and
>         forall b . b -> b, I would expect the type-checker to unify a
>         and b in the argument position and then discover that this
>         equality made the result position unify too. So why can't the
>         same happen but with Id a and Id b instead?
>             The problem is really with foo and its signature, not with
>             any use of foo. The function foo is (due to its type)
>             unusable.  Can't you change foo?
>         Here's a cut-down version of my real code. The type family
>         Apply is very important because it allows me to write class
>         instances for things that might be its first parameter, like
>         Id and Comp SqlExpr Maybe, without paying the syntactic
>         overhead of forcing client code to use Id/unId and
>         Comp/unComp. It also squishes nested Maybes which is important
>         to my application (since SQL doesn't have them).
>         castNum is the simplest example of a general problem - the
>         whole point is to allow clients to write code that is
>         overloaded over the first parameter to Apply using primitives
>         like castNum. I'm not really sure how I could get away from
>         the ambiguity problem, given that desire.
>         Cheers,
>         Ganesh
>         {-# LANGUAGE TypeFamilies, GADTs, UndecidableInstances,
>         NoMonomorphismRestriction #-}
>         newtype Id a = Id { unId :: a }
>         newtype Comp f g x = Comp { unComp :: f (g x) }
>         type family Apply (f :: * -> *) a
>         type instance Apply Id a = a
>         type instance Apply (Comp f g) a = Apply f (Apply g a)
>         type instance Apply SqlExpr a = SqlExpr a
>         type instance Apply Maybe Int = Maybe Int
>         type instance Apply Maybe Double = Maybe Double
>         type instance Apply Maybe (Maybe a) = Apply Maybe a
>         class DoubleToInt s where
>           castNum :: Apply s Double -> Apply s Int
>         instance DoubleToInt Id where
>           castNum = round
>         instance DoubleToInt SqlExpr where
>           castNum = SECastNum
>         data SqlExpr a where
>          SECastNum :: SqlExpr Double -> SqlExpr Int
>         castNum' :: (DoubleToInt s) => Apply s Double -> Apply s Int
>         castNum' = castNum
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