Create Data.Profunctor.Representable

Data/Profunctor/Cayley.idr

@@ -9,6 +9,8 @@ import Data.Profunctor.Sieve
 %default total
 
 
+-- NOTE: This may be better as a type synonym instead of a new type?
+
 public export
 record Cayley {0 k1,k2,k3 : Type} f (p : k1 -> k2 -> k3) a b where
   constructor MkCayley

Data/Profunctor/Representable.idr

@@ -0,0 +1,49 @@
+module Data.Profunctor.Representable
+
+import Control.Monad.Identity
+import Data.Morphisms
+import Data.Profunctor
+import Data.Profunctor.Costrong
+import Data.Profunctor.Sieve
+
+%default total
+
+
+public export
+interface (Sieve p f, Strong p) => Representable p f | p where
+  tabulate : (a -> f b) -> p a b
+
+
+export
+Representable Morphism Identity where
+  tabulate f = Mor (runIdentity . f)
+
+export
+[Function] Representable (\a,b => a -> b) Identity
+    using Sieve.Function Strong.Function where
+  tabulate = (runIdentity .)
+
+export
+Functor f => Representable (Kleislimorphism f) f where
+  tabulate = Kleisli
+
+export
+Functor f => Representable (Star f) f where
+  tabulate = MkStar
+
+
+export
+tabulated : (Representable q f, Representable r g) => forall p. Profunctor p =>
+              p (q a b) (r a' b') -> p (a -> f b) (a' -> g b')
+tabulated = dimap tabulate sieve
+
+
+public export
+interface (Cosieve p f, Costrong p) => Corepresentable p f | p where
+  cotabulate : (f a -> b) -> p a b
+
+
+export
+cotabulated : (Corepresentable q f, Corepresentable r g) => forall p. Profunctor p =>
+              p (q a b) (r a' b') -> p (f a -> b) (g a' -> b')
+cotabulated = dimap cotabulate cosieve