Trifunctors

Data.UnifyBifunctorProfunctor

classDiagram
   FunctorLeft <|-- Bifunctor
   FunctorRight <|-- Bifunctor
   FunctorRight <|-- Profunctor
   ContravariantLeft <|-- Profunctor
   
   class FunctorLeft {
     ) lmap :: (a -> aa) -> f a b -> f aa b
   }
   class FunctorRight {
     ) rmap :: (b -> bb) -> f a b -> f a bb
   }
   class Bifunctor {
     ) bimap :: (a -> aa) -> (b -> bb) -> f a b -> f aa bb
   }
   class ContravariantLeft {
     ) lcontramap :: (aa -> a) -> f a b -> f aa b
   }
   class Profunctor {
     ) dimap :: (aa -> a) -> (b -> bb) -> p a b -> p aa bb
   }

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Explore encoding of Bifunctor and Profunctor

class (FunctorLeft f, FunctorRight f) => Bifunctor f where
  bimap :: (a -> aa) -> (b -> bb) -> f a b -> f aa bb
  bimap f g = lmap f . rmap g

class (ContravariantLeft p, FunctorRight p) => Profunctor p where
  dimap :: (aa -> a) -> (b -> bb) -> p a b -> p aa bb
  dimap f g = lcontramap f . rmap g

using 3 typeclass'es:

class FunctorRight f where
  rmap :: (b -> bb) -> f a b -> f a bb

class FunctorLeft f where
  lmap :: (a -> aa) -> f a b -> f aa b

class ContravariantLeft f where
  lcontramap :: (aa -> a) -> f a b -> f aa b

that is more modular:

• reveal that rmap in Profunctor and Bifunctor is the same thing
• split laws into into each typeclass

Data.Zifunctor

Push this idea to types with 3 type arguments. This leads to Zifunctor abstraction that can be used to describe calculations that can fail with aa or succeed with rr and require input of type e.

class (FunctorLeft f, FunctorRight f, ContravariantRight f) => Zifunctor f where
  zimap :: (ee -> e) -> (a -> aa) -> (r -> rr) -> f e a r -> f ee aa rr

Related projects

• Originally idea was encoded in Scala in lemastero/Triglav
• Encoding in Idris Idris-Trifunctors
• snoyberg//trio is more faithfull to ZIO - use data types instead of typeclasses
• n-ary-functor
• FunctorOf