subcategories: Subcategories induced by class constraints

[ bsd3, data, library ] [ Propose Tags ]
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Dependencies base (>=4.7 && <5), containers, data-default, foldl, hashable, mono-traversable, pointed, primitive, reflection, semialign, template-haskell, text, these, unordered-containers, vector, vector-algorithms, vector-builder [details]
License BSD-3-Clause
Copyright 2023 (c) Hiromi ISHII
Author Hiromi ISHII
Maintainer konn.jinro _at_
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Uploaded by HiromiIshii at 2024-06-09T12:15:43Z
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Readme for subcategories-

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The subcategories package

Haskell CI Hackage Hackage-Deps

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.


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

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