The WrappedArrow class allows using profunctors classes with types that only implement base arrows instances. However since profunctors depends on base, the expectation is that anything that is a Strong Category should also be an Arrow, etc, else you can't use arrow syntax!
Hence I've added the following instances:
ArrowPlus p => ArrowPlus (WrappedArrow p) -- there was ArrowZero, but not ArrowPlus for some reason
Star
MonadFix f => Costrong (Star f) -- derived from Kleisli
Monad f => Arrow (Star f) -- derived from its strength
MonadPlus f => ArrowZero (Star f) -- using Alternative (we have a Monad superclass constraint anyway, hence MonadPlus)
MonadPlus f => ArrowPlus (Star f) -- using MonadPlus
Monad f => ArrowChoice (Star f) -- derived from its choice
Monad f => ArrowApply (Star f) -- derived from Kleisli
MonadFix f => ArrowLoop (Star f) -- derived from the aforementioned costrength
Costar
Comonad f => Category (Costar f) -- derived from Cokleisli
CofreeTraversing
Category p => Category (CofreeTraversing p) -- things of the form forall x. p (x ⊗ a) (x ⊗ b) (end comonads) naturally form a category
(Category p, Profunctor p) => Arrow (CofreeTraversing p) -- derived from its strength
(ArrowLoop p, Profunctor p) => ArrowLoop (Coyoneda p) -- derived from its costrength
Rift
(Strong p, Costrong q) => Costrong (Rift p q) -- checks out
(Choice p, Cochoice q) => Cochoice (Rift p q) -- checks out
Ran
(Strong p, Costrong q) => Costrong (Ran p q) -- same as Rift
(Choice p, Cochoice q) => Cochoice (Ran p q) -- same as Rift
Codensity
(Strong p, Costrong p) => Costrong (Codensity p) -- derived from Ran p p
(Choice p, Cochoice p) => Cochoice (Codensity p) -- derived from Ran p p
Day
(Profunctor p, Strong q) => Strong (Day p q) -- this one could alternatively be defined using p's strength, but I figured it should target the same argument as does ProfunctorMonad, also swapped is right there.
(Choice p, Choice q) => Choice (Day p q)
Things like Category (Pastro p) require Strong p at which point Pastro p <-> p and if you want an arrow you can just extract, so I've decided to not bother with that. Likewise with Category (FreeTraversing p).
We know that:
Arrow=Strong+Category,ArrowChoice=Choice+Strong+CategoryArrowLoop=Costrong+Strong+CategoryThe
WrappedArrowclass allows usingprofunctorsclasses with types that only implementbasearrows instances. However sinceprofunctorsdepends onbase, the expectation is that anything that is a Strong Category should also be an Arrow, etc, else you can't use arrow syntax!Hence I've added the following instances:
ArrowPlus p => ArrowPlus (WrappedArrow p)-- there wasArrowZero, but notArrowPlusfor some reasonStarMonadFix f => Costrong (Star f)-- derived fromKleisliMonad f => Arrow (Star f)-- derived from its strengthMonadPlus f => ArrowZero (Star f)-- usingAlternative(we have aMonadsuperclass constraint anyway, henceMonadPlus)MonadPlus f => ArrowPlus (Star f)-- usingMonadPlusMonad f => ArrowChoice (Star f)-- derived from its choiceMonad f => ArrowApply (Star f)-- derived fromKleisliMonadFix f => ArrowLoop (Star f)-- derived from the aforementioned costrengthCostarComonad f => Category (Costar f)-- derived fromCokleisliCofreeTraversingCategory p => Category (CofreeTraversing p)-- things of the formforall x. p (x ⊗ a) (x ⊗ b)(end comonads) naturally form a category(Category p, Profunctor p) => Arrow (CofreeTraversing p)-- derived from its strength(ArrowZero p, Profunctor p) => ArrowZero (CofreeTraversing p)-- natural for "end comonads"(ArrowPlus p, Profunctor p) => ArrowPlus (CofreeTraversing p)-- natural for "end comonads" (the arrows are always in parallel)(Category p, Profunctor p) => ArrowChoice (CofreeTraversing p)-- derived from its choiceTambaraSumStrong p => Strong (TambaraSum p)-- looks asymmetric, but shouldn't be, given lawfulStrong pCostrong p => Costrong (TambaraSum p)-- same benign asymmetryArrow p => Arrow (TambaraSum p)-- derived from aforementioned strengthArrow p => ArrowChoice (TambaraSum p)-- derived from aforementioned choiceArrowZero p => ArrowZero (TambaraSum p)-- natural for "end comonads"ArrowPlus p => ArrowPlus (TambaraSum p)-- natural for "end comonads"PastroSumStrong p => Strong (PastroSum p)-- checks outYoneda-- degenerates whenProfunctor p, hence much like its other instances we just extract and proreturn(Arrow p, Profunctor p) => Arrow (Yoneda p)-- derived from its strength(ArrowZero p, Profunctor p) => ArrowZero (Yoneda p)(ArrowPlus p, Profunctor p) => ArrowPlus (Yoneda p)(ArrowChoice p, Profunctor p) => ArrowChoice (Yoneda p)-- derived from its choice(ArrowApply p, Profunctor p) => ArrowApply (Yoneda p)(ArrowLoop p, Profunctor p) => ArrowLoop (Yoneda p)-- derived from its costrengthCoyoneda-- likewise we just return and proextract(Arrow p, Profunctor p) => Arrow (Coyoneda p)-- derived from its strength(ArrowZero p, Profunctor p) => ArrowZero (Coyoneda p)(ArrowPlus p, Profunctor p) => ArrowPlus (Coyoneda p)(ArrowChoice p, Profunctor p) => ArrowChoice (Coyoneda p)-- derived from its choice(ArrowApply p, Profunctor p) => ArrowApply (Coyoneda p)(ArrowLoop p, Profunctor p) => ArrowLoop (Coyoneda p)-- derived from its costrengthRift(Strong p, Costrong q) => Costrong (Rift p q)-- checks out(Choice p, Cochoice q) => Cochoice (Rift p q)-- checks outRan(Strong p, Costrong q) => Costrong (Ran p q)-- same asRift(Choice p, Cochoice q) => Cochoice (Ran p q)-- same asRiftCodensity(Strong p, Costrong p) => Costrong (Codensity p)-- derived fromRan p p(Choice p, Cochoice p) => Cochoice (Codensity p)-- derived fromRan p pDay(Profunctor p, Strong q) => Strong (Day p q)-- this one could alternatively be defined usingp's strength, but I figured it should target the same argument as doesProfunctorMonad, alsoswappedis right there.(Choice p, Choice q) => Choice (Day p q)Things like
Category (Pastro p)requireStrong pat which pointPastro p <-> pand if you want an arrow you can just extract, so I've decided to not bother with that. Likewise withCategory (FreeTraversing p).