Remove Ord from Bounded

Author: garyb

docs/Prelude.md

@@ -17,6 +17,7 @@ instance numUnit :: Num Unit
 instance eqUnit :: Eq Unit
 instance ordUnit :: Ord Unit
 instance boundedUnit :: Bounded Unit
+instance boundedOrdUnit :: BoundedOrd Unit
 instance booleanAlgebraUnit :: BooleanAlgebra Unit
 instance showUnit :: Show Unit
 ```
@@ -713,6 +714,7 @@ instance semigroupOrdering :: Semigroup Ordering
 instance eqOrdering :: Eq Ordering
 instance ordOrdering :: Ord Ordering
 instance boundedOrdering :: Bounded Ordering
+instance boundedOrdOrdering :: BoundedOrd Ordering
 instance showOrdering :: Show Ordering
 ```
 
@@ -785,7 +787,7 @@ Test whether one value is _non-strictly greater than_ another.
 #### `Bounded`
 
 ``` purescript
-class (Ord a) <= Bounded a where
+class Bounded a where
   top :: a
   bottom :: a
 ```
@@ -796,14 +798,18 @@ instance boundedBoolean :: Bounded Boolean
 instance boundedUnit :: Bounded Unit
 instance boundedOrdering :: Bounded Ordering
 instance boundedInt :: Bounded Int
+instance boundedFn :: (Bounded b) => Bounded (a -> b)
 ```
 
-The `Bounded` type class represents types that are finite partially
-ordered sets.
+The `Bounded` type class represents types that are finite.
 
-Instances should satisfy the following law in addition to the `Ord` laws:
+Although there are no "internal" laws for `Bounded`, every value of `a`
+should be considered less than or equal to `top` by some means, and greater
+than or equal to `bottom`.
 
-- Ordering: `bottom <= a <= top`
+The lack of explicit `Ord` constraint allows flexibility in the use of
+`Bounded` so it can apply to total and partially ordered sets, boolean
+algebras, etc.
 
 #### `BooleanAlgebra`
 
@@ -818,6 +824,7 @@ class (Bounded a) <= BooleanAlgebra a where
 ``` purescript
 instance booleanAlgebraBoolean :: BooleanAlgebra Boolean
 instance booleanAlgebraUnit :: BooleanAlgebra Unit
+instance booleanAlgebraFn :: (BooleanAlgebra b) => BooleanAlgebra (a -> b)
 ```
 
 The `BooleanAlgebra` type class represents types that behave like boolean

src/Prelude.purs

@@ -699,13 +699,16 @@ unsafeCompare = unsafeCompareImpl LT EQ GT
 
 foreign import unsafeCompareImpl :: forall a. Ordering -> Ordering -> Ordering -> a -> a -> Ordering
 
--- | The `Bounded` type class represents types that are finite partially
--- | ordered sets.
+-- | The `Bounded` type class represents types that are finite.
 -- |
--- | Instances should satisfy the following law in addition to the `Ord` laws:
+-- | Although there are no "internal" laws for `Bounded`, every value of `a`
+-- | should be considered less than or equal to `top` by some means, and greater
+-- | than or equal to `bottom`.
 -- |
--- | - Ordering: `bottom <= a <= top`
-class (Ord a) <= Bounded a where
+-- | The lack of explicit `Ord` constraint allows flexibility in the use of
+-- | `Bounded` so it can apply to total and partially ordered sets, boolean
+-- | algebras, etc.
+class Bounded a where
   top :: a
   bottom :: a
 
@@ -725,6 +728,22 @@ instance boundedInt :: Bounded Int where
   top = 2147483647
   bottom = -2147483648
 
+instance boundedFn :: (Bounded b) => Bounded (a -> b) where
+  top _ = top
+  bottom _ = bottom
+
+-- | The `BoundedOrd` type class represents totally ordered finite data types.
+-- |
+-- | Instances should satisfy the following law in addition to the `Ord` laws:
+-- |
+-- | - Ordering: `bottom <= a <= top`
+class (Bounded a, Ord a) <= BoundedOrd a
+
+instance boundedOrdBoolean :: BoundedOrd Boolean where
+instance boundedOrdUnit :: BoundedOrd Unit where
+instance boundedOrdOrdering :: BoundedOrd Ordering where
+instance boundedOrdInt :: BoundedOrd Int where
+
 -- | The `BooleanAlgebra` type class represents types that behave like boolean
 -- | values.
 -- |
@@ -769,6 +788,11 @@ instance booleanAlgebraUnit :: BooleanAlgebra Unit where
   disj _ _ = unit
   not _ = unit
 
+instance booleanAlgebraFn :: (BooleanAlgebra b) => BooleanAlgebra (a -> b) where
+  conj fx fy a = fx a `conj` fy a
+  disj fx fy a = fx a `disj` fy a
+  not fx a = not (fx a)
+
 infixr 2 ||
 infixr 3 &&