# 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 `mono`s can be
regarded as a functorial structure from the full subcategory consisting of just a single object,
say `Element mono`.
[^1]: Strictly speaking, `CFoldable`, a constrained counterpart of `Foldable`, doesn't require a functoriality as with the original `Foldable`.
## 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`.