change structure & add laws for enums

README.md

@@ -2,15 +2,35 @@
 
 ## Module Data.Enum
 
+### Types
+
+    newtype Cardinality a where
+      Cardinality :: Number -> Cardinality a
+
+
 ### Type Classes
 
-    class Enum a where
-      toEnum :: Prim.Number -> Maybe a
-      fromEnum :: a -> Prim.Number
+    class (Ord a) <= Enum a where
+      cardinality :: Cardinality a
+      firstEnum :: a
+      lastEnum :: a
+      succ :: a -> Maybe a
+      pred :: a -> Maybe a
+
+
+### Type Class Instances
+
+    instance enumBoolean :: Enum Boolean
+
+    instance enumMaybe :: (Enum a) => Enum (Maybe a)
+
+    instance enumTuple :: (Enum a, Enum b) => Enum (Tuple a b)
 
 
 ### Values
 
-    pred :: forall a. (Enum a) => a -> Maybe a
+    fromEnum :: forall a. (Enum a) => a -> Number
+
+    runCardinality :: forall a. Cardinality a -> Number
 
-    succ :: forall a. (Enum a) => a -> Maybe a
+    toEnum :: forall a. (Enum a) => Number -> Maybe a

bower.json

@@ -18,6 +18,7 @@
     "package.json"
   ],
   "dependencies": {
-    "purescript-maybe": "*"
+    "purescript-maybe":  "*",
+    "purescript-tuples": "*"
   }
 }

src/Data/Enum.purs

@@ -1,13 +1,91 @@
-module Data.Enum where
+module Data.Enum 
+  ( Enum
+  , Cardinality(..)
+  , fromEnum
+  , runCardinality
+  , toEnum
+  ) where
 
-import Data.Maybe
+  import Data.Maybe
+  import Data.Tuple
+  import Data.Maybe.Unsafe
 
-class Enum a where
-  toEnum :: Number -> Maybe a
-  fromEnum :: a -> Number
+  newtype Cardinality a = Cardinality Number 
 
-succ :: forall a. (Enum a) => a -> Maybe a
-succ x = toEnum (fromEnum x + 1)
+  runCardinality :: forall a. Cardinality a -> Number
+  runCardinality (Cardinality a) = a
 
-pred :: forall a. (Enum a) => a -> Maybe a
-pred x = toEnum (fromEnum x - 1)
+  -- | Type class for enumerations. This should not be considered a part of a
+  -- | numeric hierarchy, ala Haskell. Rather, this is a type class for small,
+  -- | ordered sum types with statically-determined cardinality and the ability 
+  -- | to easily compute successor and predecessor elements. e.g. DayOfWeek, etc.
+  -- |
+  -- | Laws:
+  -- |   succ firstEnum >>= succ >>= succ ... succ [cardinality times] == lastEnum
+  -- |   pred lastEnum  >>= pred >>= pred ... pred [cardinality times] == firstEnum
+  -- |
+  -- |   Just $ e1 `compare` e2 == fromEnum e1 `compare` fromEnum e2
+  -- |
+  -- |   for all a > firstEnum: pred a >>= succ == Just a
+  -- |   for all a < lastEnum:  succ a >>= pred == Just a
+  class (Ord a) <= Enum a where
+    cardinality :: Cardinality a
+
+    firstEnum :: a
+
+    lastEnum :: a
+
+    succ :: a -> Maybe a
+
+    pred :: a -> Maybe a
+
+  toEnum :: forall a. (Enum a) => Number -> Maybe a
+  toEnum n | n < 0 = Nothing
+  toEnum 0         = Just firstEnum
+  toEnum n         = toEnum (n - 1) >>= succ
+
+  fromEnum :: forall a. (Enum a) => a -> Number
+  fromEnum e = maybe 0 ((+) 1 <<< fromEnum) (pred e)
+
+  maybeCardinality :: forall a. (Enum a) => Cardinality a -> Cardinality (Maybe a)
+  maybeCardinality c = Cardinality $ 1 + (runCardinality c)
+
+  instance enumMaybe :: (Enum a) => Enum (Maybe a) where
+    cardinality = maybeCardinality cardinality
+
+    firstEnum = Nothing
+
+    lastEnum = Just $ lastEnum
+
+    succ Nothing = Just $ firstEnum
+    succ (Just a) = Just <$> succ a
+
+    pred Nothing = Nothing
+    pred (Just a) = Just <$> pred a
+
+  instance enumBoolean :: Enum Boolean where
+    cardinality = Cardinality 2
+
+    firstEnum = false
+
+    lastEnum = true
+
+    succ false = Just true
+    succ _     = Nothing
+
+    pred true  = Just false
+    pred _     = Nothing
+
+  instance enumTuple :: (Enum a, Enum b) => Enum (Tuple a b) where
+    cardinality = tupleCardinality cardinality cardinality
+
+    firstEnum = Tuple firstEnum firstEnum
+
+    lastEnum = Tuple lastEnum lastEnum
+
+    succ (Tuple a b) = maybe (flip Tuple firstEnum <$> succ a) (Just <<< Tuple a) (succ b)
+
+    pred (Tuple a b) = maybe (flip Tuple firstEnum <$> pred a) (Just <<< Tuple a) (pred b)
+
+  tupleCardinality :: forall a b. (Enum a, Enum b) => Cardinality a -> Cardinality b -> Cardinality (Tuple a b)
+  tupleCardinality l r = Cardinality $ (runCardinality l) * (runCardinality r)