The subcategories package

This package provides variants of functor-like structures, with domain types are constrained. In particular, this package provides an abstraction for functorial containers, which can be expressed as a functor from a full-subcategory of Hask to Hask itself ¹.

For example:

• We can treat Set as if it is a Fuctor, Foldable, Applicative, with their domain restricted to full-subcategory Ord of Ord instances of Hask.
• For MonoFoldable or MonoTraversable types (from mono-traversable package), we provide WrapMono wrapper with zero-cost coercion. Such monos can be regarded as a functorial structure from the full subcategory consisting of just a single object, say Element mono.

Optimisation

This library is designed to keep the abstraction runtime overhead as minimum as possible.

Some notes:

• If a constrained term such as cmap or czipWith has concrete type, it must have exactly the same representation as the corresponding operation modulo (zero-cost) coercion.
  • The same still holds if the set of required constraints coincides.
  • Although the constructor of WrapMono mono a is hidden, its just a newtype-wrapper around mono; hence, constrained operators must have the same representations as the corresponding combinators in mono-traversable package.
• OTOH, for a polymorphic term, like cmap :: (Ord a, Ord b) => (a -> b) Set a -> Set b and Set.map, they can have different representations; indeed, Set.map doesn't require a to be Ord-instance and therefore the implementation of cmap discards the dictionary for Ord a to call Set.map.

Footnotes

1. Strictly speaking, CFoldable, a constrained counterpart of Foldable, doesn't require a functoriality as with the original Foldable. ↩