One can define a functor on kinds, using "data kind promotion"
data Product m = E| I m | P (Product m, Product m)
It maps a kind m
to the sum kind Product m
which has 3 types, the empty type, a type of kind m
and a type of kind (Product m, Product m)
We can define an algebra at *
for this functor with the type family
type family MHask (mp :: Product (*)) :: * where
MHask E = ()
MHask (P '(m, n)) = (MHask m, MHask n)
MHask (I m) = m
But can we define the class of algebras for this functor ?
class MK m where
--type To (Product m) :: m -- type family declaration should have form "type family To a"
type To :: Product m -> m
-- instance MonoidalK (*) where
-- -- type To = MonoidalHask -- type family ‘MonoidalHask’ should have 1 argument
-- -- type To m = MonoidalHask m -- Number of parameters must match family declaration; expected 0
-- type To = ?
CodePudding user response:
Type families have an arity, which is the number of arguments it may "pattern-match" on, and it is specified by putting those arguments to the left of ::
in its declaration.
class MK m where
type To (x :: Product m) :: m
which is practically the same as
type family To (x :: Product m) :: m