Implement Mu, Nu, type class instances

Author: jonsterling

src/Data/Eq1.purs

@@ -0,0 +1,6 @@
+module Data.Eq1 where
+
+import Prelude
+
+class Eq1 f where
+  eq1 :: forall a. (Eq a) => f a -> f a -> Boolean

src/Data/Functor/Mu.purs

@@ -5,6 +5,10 @@ module Data.Functor.Mu
   ) where
 
 import Prelude
+import Data.TacitString as TS
+
+import Data.Eq1
+import Data.Ord1
 
 -- | `Mu f` is the least fixed point of a functor `f`, when it exists.
 data Mu f = In (f (Mu f))
@@ -14,3 +18,18 @@ roll = In
 
 unroll :: forall f. Mu f -> f (Mu f)
 unroll (In x) = x
+
+-- | To implement `Eq`, we require `f` to have higher-kinded equality.
+instance eqMu :: (Eq1 f) => Eq (Mu f) where
+  eq (In x) (In y) = eq1 x y
+
+-- | To implement `Ord`, we require `f` to have higher-kinded comparison.
+instance ordMu :: (Eq1 f, Ord1 f) => Ord (Mu f) where
+  compare (In x) (In y) = compare1 x y
+
+-- | `Show` is compositional, so we only `f` to be able to show a single layer of structure.
+-- Therefore, there is no need for `Show1`; we use `TacitString` in order to prevent
+-- extra quotes from appearing.
+instance showMu :: (Show (f TS.TacitString), Functor f) => Show (Mu f) where
+  show (In x) = show $ x <#> (show >>> TS.hush)
+

src/Data/Ord1.purs

@@ -0,0 +1,6 @@
+module Data.Ord1 where
+
+import Prelude
+
+class Ord1 f where
+  compare1 :: forall a. (Ord a) => f a -> f a -> Ordering

src/Data/TacitString.purs

@@ -0,0 +1,13 @@
+module Data.TacitString
+  ( TacitString()
+  , hush
+  ) where
+
+import Prelude
+
+newtype TacitString = TacitString String
+instance showTacitString :: Show TacitString where
+  show (TacitString str) = str
+
+hush :: String -> TacitString
+hush = TacitString