Provides a wide array of (semi)groupoids and operations for working with them.
A 'Semigroupoid' is a 'Category' without the requirement of identity arrows for
every object in the category.
A 'Category' is any 'Semigroupoid' for which the Yoneda lemma holds.
When working with comonads you often have the '<*>' portion of an
'Applicative', but not the 'pure'. This was captured in Uustalu and Vene's
"Essence of Dataflow Programming" in the form of the 'ComonadZip' class in the
days before 'Applicative'. Apply provides a weaker invariant, but for the
comonads used for data flow programming (found in the streams package), this
invariant is preserved. Applicative function composition forms a semigroupoid.
Similarly many structures are nearly a comonad, but not quite, for instance
lists provide a reasonable 'extend' operation in the form of 'tails', but do
not always contain a value.
We describe the relationships between the type classes defined in this package
and those from
base (and some from
contravariant) in the diagram below.
Thick-bordered nodes correspond to type classes defined in this package;
thin-bordered ones correspond to type classes from elsewhere. Solid edges
indicate a subclass relationship that actually exists; dashed edges indicate a
subclass relationship that /should/ exist, but currently doesn't.
Relationships among type classes from this package and others>>
Apply, Bind, and Extend (not shown) give rise the Static, Kleisli and Cokleisli
This lets us remove many of the restrictions from various monad transformers as
in many cases the binding operation or '<*>' operation does not require them.
Finally, to work with these weaker structures it is beneficial to have
containers that can provide stronger guarantees about their contents, so
versions of 'Traversable' and 'Foldable' that can be folded with just a
'Semigroup' are added.