Subcategories induced by class constraints

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The subcategories package

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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.

[^1]: Strictly speaking, CFoldable, a constrained counterpart of Foldable, doesn’t require a functoriality as with the original Foldable.


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, they can have different representations; indeed, doesn’t require a to be Ord-instance and therefore the implementation of cmap discards the dictionary for Ord a to call


Changelog for subcategories

  • Supports GHC 9.6

  • Supports GHC >= 9.2.
  • As base >= 4.16 removes Data.Semigroup.Option, this package drops instance for Option accordingly for GHC >= 9.2. It seems that PVP demands us to bump the major version.

  • Support GHC >= 9.0

  • Initial Release