[Haskell-cafe] interesting type families problem

[Miguel Mitrofanov]

On 8 Sep 2010, at 20:01, Gábor Lehel wrote:

> I'm bad at expositions so I'll just lead with the code:
> 
> {-# LANGUAGE EmptyDataDecls, TypeFamilies #-}
> 
> data True  :: *
> data False :: *
> 
> class TypeValue a where
>    type ValueTypeOf a :: *
>    value :: ValueTypeOf a
> 
> instance TypeValue True where
>    type ValueTypeOf True = Bool
>    value = True
> 
> instance TypeValue False where
>    type ValueTypeOf False = Bool
>    value = False
> 
> main = print (value :: ValueTypeOf True)
> 
> (In case this is initially confusing, there are entirely distinct
> type-level and value-level True and False involved which merely share
> a name. The idea is to take type-level 'values' and reflect them down
> to the corresponding value-level, er, values.)
> 
> Which results in the following error message:
> 
>    Couldn't match expected type `Bool'
>           against inferred type `ValueTypeOf a'
>      NB: `ValueTypeOf' is a type function, and may not be injective
>    In the first argument of `print', namely
>        `(value :: ValueTypeOf True)'
>    In the expression: print (value :: ValueTypeOf True)
>    In the definition of `main':
>        main = print (value :: ValueTypeOf True)
> 
> 
> This is strange and vaguely amusing to me. I get that type functions
> are not injective, but I can't figure out how it applies to this
> situation. Obviously if I had written `print (value :: Bool)` it would
> rightly complain that there could be any number of instances which map
> to Bool, and how in the world should it know which one I meant.

Well, it's the same thing, actually. Since "ValueTypeOf True" is "Bool",
"value :: ValueTypeOf True" is exactly the same as "value :: Bool".

> But it
> seems like in this case the compiler knows everything it needs to
> know. And it even manages to deduce, from the exact same expression
> (`print` isn't giving it any extra information), that it's
> simultaneously a Bool and not necessarily a Bool.
> 
> Is this "supposed" to work? If not, why not?
> 
> 
> -- 
> Work is punishment for failing to procrastinate effectively.
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