[Haskell] functional dependency violation?

[Mark Brown]

Hi,

On 20-May-2005, Conal Elliott <conal at conal.net> wrote:
> The program below fails to compile under ghc 6.4, giving the following
> error message:
> 
>     c:/conal/Eros/Haskell/PTest.hs:13:0:
>         Illegal instance declaration for `Path (PCompose po pi) a a'
> whole whole''
>             (the instance types do not agree with the functional
> dependencies of the class)
>         In the instance declaration for `Path (PCompose po pi) a a'
> whole whole''
>     Failed, modules loaded: none.
> 
> I'm stumped.  Can anyone explain how this instance violates the
> functional dependencies?

The problem is that whole' can't be determined from po, pi, a, a' and
whole, therefore the first functional dependency is not met.  The
two constraints on the instance and the two functional dependencies on
the class induce the following four dependencies between the type
variables in the instance:

	pi a a' mid -> mid'
	pi mid mid' -> a a'
	po mid mid' whole -> whole'
	po whole whole' -> mid mid'

None of these rules can fire given po, pi, a, a' and whole, which means
that no other variables are determined from them.

Cheers,
Mark.