Mathematical concepts such as monads, functors, monoids, and semigroups
are expressed in Haskell as typeclasses. Therefore, in order to exploit
relations such as “every monad is a functor”, and “every monoid is
a semigroup”, we need to be able to also express relations between
typeclasses.

Currently, the only way to do so is using superclasses. However,
superclasses can be problematic due to their closed nature. Adding a
superclass implies modifying the subclass’ definition, which is either
impossible if one does not own such code, or painful as it requires
cascading changes and the introduction of boilerplate throughout the
codebase.

In this article, we introduce class morphisms, a way to relate
classes in an open fashion, without changing class definitions. We
show how class morphisms improve the expressivity, conciseness, and
maintainability of code. Further, we show how to implement them while
maintaining canonicity and coherence, two key properties of the Haskell
type system. Extending a typechecker with class morphisms amounts to
adding an elaboration phase and is an unintrusive change. We back this
claim with a prototype extension of GHC.