[Haskell-cafe] Type Family Relations

[Thomas DuBuisson]

Cafe,
I am wondering if there is a way to enforce compile time checking of
an axiom relating two separate type families.

Mandatory contrived example:

> type family AddressOf h
> type family HeaderOf a
>
> -- I'm looking for something to the effect of:
> type axiom HeaderOf (AddressOf x) ~ x
>
> -- Valid:
> type instance AddressOf IPv4Header = IPv4
> type instance HeaderOf IPv4 = IPv4Header
>
> -- Invalid
> type instance AddressOf AppHeader = AppAddress
> type instance HeaderOf AppAddress = [AppHeader]

So this is  a universally enforced type equivalence.  The stipulation
could be arbitrarily complex, checked at compile time, and must hold
for all instances of either type family.

Am I making this too hard?  Is there already a solution I'm missing?

Cheers,
Tom