Arrow Theories (panproto mirror)¶
ThCategory_, ThArrow, ThArrowChoice, ThArrowApply, ThArrowLoop, ThArrowZero, ThArrowPlus, panproto-theory record-stubs for each arrow typeclass.
Panproto theories mirroring the arrow typeclass tower.
Each Hughes-style arrow typeclass corresponds to a panproto theory that declares the operations and laws the typeclass requires:
ThCategory_— composition + identity, with the three category laws.ThArrow— addsarrandfirst; the seven Hughes arrow laws.ThArrowChoice,ThArrowApply,ThArrowLoop,ThArrowZero,ThArrowPlus— the additional operations and laws of each extension.
The bridges in quivers.monadic.bridges correspond to panproto
theory morphisms ThMonad → ThArrowApply (Kleisli construction)
and back (ArrowMonad construction); the round-trip composition is
the identity on the appropriate theory image.