semigroupoids vs laravel/framework

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.

The Laravel Framework.