Dict c a is evidence that there exists an instance of c a.

It is essentially equivalent to Dict (c a) from the constraints package, but because of its kind, it allows us to define things like Dict Show.

Turn a constrained-function into an unconstrained one that uses the packed instance dictionary instead.

Instances of this class provide means to talk about constraints, both at compile-time, using AllB, and at run-time, in the form of Dict, via baddDicts.

A manual definition would look like this:

data T f = A (f Int) (f String) | B (f Bool) (f Int)

instance ConstraintsB T where
  type AllB c T = (c Int, c String, c Bool)

  baddDicts t = case t of
    A x y -> A (Pair Dict x) (Pair Dict y)
    B z w -> B (Pair Dict z) (Pair Dict w)

Now if we given a T f, we need to use the Show instance of their fields, we can use:

baddDicts :: AllB Show b => b f -> b (Dict Show Product b)

There is a default implementation of ConstraintsB for Generic types, so in practice one will simply do:

derive instance Generic (T f)
instance ConstraintsB T

Every type b that is an instance of both ProductB and ConstraintsB can be made an instance of ProductBC as well.

Intuitively, in addition to buniq from ProductB, one can define buniqC that takes into account constraints:

buniq :: (forall a . f a) -> b f
buniqC :: AllB c b => (forall a . c a => f a) -> b f

For technical reasons, buniqC is not currently provided as a method of this class and is instead defined in terms bdicts, which is similar to baddDicts but can produce the instance dictionaries out-of-the-blue. bdicts could also be defined in terms of buniqC, so they are essentially equivalent.

bdicts :: forall c b . AllB c b => b (Dict c)
bdicts = buniqC (Dict @c)

There is a default implementation for Generic types, so instances can derived automatically.

Like bmap but a constraint is allowed to be required on each element of b

E.g. If all fields of b are Showable then you could store each shown value in it's slot using Const:

showFields :: (AllB Show b, ConstraintsB b) => b Identity -> b (Const String)
showFields = bmapC @Show showField
  where
    showField :: forall a. Show a => Identity a -> Const String a
    showField (Identity a) = Const (show a)

Like btraverse but with a constraint on the elements of b.

Similar to AllB but will put the functor argument f between the constraint c and the type a. For example:

  AllB  Show   Barbie ~ (Show    String,  Show    Int)
  AllBF Show f Barbie ~ (Show (f String), Show (f Int))
  

ClassF has one universal instance that makes ClassF c f a equivalent to c (f a). However, we have

'ClassF c f :: k -> Constraint

This is useful since it allows to define constraint-constructors like ClassF Monoid Maybe

Like ClassF but for binary relations.