Merge pull request #79 from purescript/natendo

Add natural transformation synonym & operator

Author: garyb

src/Data/NaturalTransformation.purs

@@ -0,0 +1,19 @@
+module Data.NaturalTransformation where
+
+-- | A type for natural transformations.
+-- |
+-- | A natural transformation is a mapping between type constructors of kind
+-- | `* -> *` where the mapping operation has no ability to manipulate the
+-- | inner values.
+-- |
+-- | An example of this is the `fromFoldable` function provided in
+-- | `purescript-lists`, where some foldable structure containing values of
+-- | type `a` is converted into a `List a`.
+-- |
+-- | The definition of a natural transformation in category theory states that
+-- | `f` and `g` should be functors, but the `Functor` constraint is not
+-- | enforced here; that the types are of kind `* -> *` is enough for our
+-- | purposes.
+type NaturalTransformation f g = forall a. f a -> g a
+
+infixr 4 type NaturalTransformation as ~>

src/Prelude.purs

@@ -15,6 +15,7 @@ module Prelude
   , module Data.Function
   , module Data.Functor
   , module Data.HeytingAlgebra
+  , module Data.NaturalTransformation
   , module Data.Ord
   , module Data.Ordering
   , module Data.Ring
@@ -42,6 +43,7 @@ import Data.Field (class Field)
 import Data.Function (const, flip, ($), (#))
 import Data.Functor (class Functor, map, void, ($>), (<#>), (<$), (<$>))
 import Data.HeytingAlgebra (class HeytingAlgebra, conj, disj, not, (&&), (||))
+import Data.NaturalTransformation (type (~>))
 import Data.Ord (class Ord, compare, (<), (<=), (>), (>=), comparing, min, max, clamp, between)
 import Data.Ordering (Ordering(..))
 import Data.Ring (class Ring, negate, sub, (-))