Algebras is a collection type classes providing the structure for F-algebras and common operations on inductive types derived from those structures as well as a free isomorphism for converting between inductive types. Algebras values generality but not at the expense of efficency - only operations whose asymptotic complexity could not be smaller in a specific case are provided. For example the general implementation for drop of O(n) cannot ergonomically compete with the O(1) in Data.Seq.drop thus it is not provided; however, dropWhile is necessarily O(n) so we can derive it from an instance of FCoalgebra.

Algebras is suitable for use case where we care about being collection indiscriminate. For example a combinatorial parser can be implemented entirely from a FCoalgebra. Another minor benefit is that explicit implementations of list-like operations which would typically collide are now aggergated under a single interface.

F-algebras model constructors for inductive types, so for example we can define lists as an F-algebra by

instance FAlgebra [a] where
  -- The type of elements in our collection.
  type FElem [a] = (a, [a])

  -- ^ How we append an element to our collection.
  fcons (x, xs) = x : xs

instance FCoalgebra [a] where
  -- The result of a destruction.
  type FCoelem [a] = Maybe (a, [a])

  -- How we destruct an element of [a].
  funcons []       = Nothing
  funcons (x : xs) = Just (x, xs)

similar instaces exists for:

• Text
• Seq
• ByteSring
• DList
• etc...

Issue and pull requests are welcome so long as the changes adhere to the guiding princples of the project mentioned in the overview. I could be convinced of extending the library with things like drop or take if comes packaged in a way that does not sacrifice type inference, ergonomics, or efficency but I have not found any great canidates for such a thing.

If you'd like to contribute to algebras here is a current list of ways the library could be extended.

• Add notionally distinct instances for algebras using Reverse to implement snoc, last, and other functions operating at the end of lists.
• Add generics to automatically derive F-algebras and F-coalgebras if possible.