Can I add constrained polymorphic methods to a signature?

[isovector]

I'd like QuickSpec to find monoid homomorphisms of the form foo (x <> y) = foo x <> foo y, but it's not clear how to give the (<>) :: Monoid m => m -> m -> m method to the signature, as it complains there is no Monoid instance for A.

[nick8325]

QuickSpec does (experimentally) support typeclass polymorphism; see https://github.com/nick8325/quickspec/blob/master/examples/tests/TypeClass.hs for an example. Internally this uses Dict from the constraints package; you can add a typeclass-polymorphic function by converting it to take an explicit Dict parameter instead, and QuickSpec will recognise the use of Dict as typeclass polymorphism and handle it specially (e.g. hiding the Dict arguments when printing out laws).

However, there is a catch: QuickSpec assumes that all polymorphic terms can be tested by defaulting them to a single type (by default Int). In this case, since there's no Monoid Int instance, you won't be able to test any term that has a Monoid m constraint. You can use defaultTo to change the type used for defaulting (e.g. [Int] would work in this case), but if you have several different typeclasses this only works if you can find one instance that fits them all.

[isovector]

To clarify what I think you mean, if I have (assume I've correctly fiddled the dicts):

signature
  [ con "<>" $ (<>) @A
  , con "mempty" $ mempty @A
  , con "Nothing" $ Nothing @Int
  ]

QS will not find the monoid laws due to the Int defaulting, but it will find the mempty = Nothing law?

[nick8325]

Yes, that's right!

[isovector]

Amazing! Thanks for the explanation. I'll see about finding somewhere to document this :)