change IntegerInterval representation similar to the one of #7

src/Data/IntegerInterval/Internal.hs

@@ -1,5 +1,5 @@
 {-# OPTIONS_GHC -Wall #-}
-{-# LANGUAGE CPP, DeriveDataTypeable #-}
+{-# LANGUAGE CPP, DeriveDataTypeable, DeriveGeneric, LambdaCase #-}
 {-# LANGUAGE Safe #-}
 #if __GLASGOW_HASKELL__ >= 708
 {-# LANGUAGE RoleAnnotations #-}
@@ -17,12 +17,19 @@ import Control.DeepSeq
 import Data.Data
 import Data.ExtendedReal
 import Data.Hashable
+import GHC.Generics (Generic)
 
 infix 5 <=..<=
 
 -- | The intervals (/i.e./ connected and convex subsets) over integers (__Z__).
-data IntegerInterval = Interval !(Extended Integer) !(Extended Integer)
-  deriving (Eq, Typeable)
+data IntegerInterval
+  = Whole
+  | Empty
+  | Point !Integer
+  | LessOrEqual !Integer
+  | GreaterOrEqual !Integer
+  | Closed !Integer !Integer
+  deriving (Eq, Generic, Typeable)
 
 -- | Lower endpoint (/i.e./ greatest lower bound)  of the interval.
 --
@@ -32,7 +39,13 @@ data IntegerInterval = Interval !(Extended Integer) !(Extended Integer)
 --
 -- * 'lowerBound' of an interval may or may not be a member of the interval.
 lowerBound :: IntegerInterval -> Extended Integer
-lowerBound (Interval lb _) = lb
+lowerBound = \case
+  Whole            -> NegInf
+  Empty            -> PosInf
+  Point r          -> Finite r
+  LessOrEqual _    -> NegInf
+  GreaterOrEqual r -> Finite r
+  Closed p _       -> Finite p
 
 -- | Upper endpoint (/i.e./ least upper bound) of the interval.
 --
@@ -42,7 +55,13 @@ lowerBound (Interval lb _) = lb
 --
 -- * 'upperBound' of an interval is a member of the interval.
 upperBound :: IntegerInterval -> Extended Integer
-upperBound (Interval _ ub) = ub
+upperBound = \case
+  Whole            -> PosInf
+  Empty            -> NegInf
+  Point r          -> Finite r
+  LessOrEqual r    -> Finite r
+  GreaterOrEqual _ -> PosInf
+  Closed _ p       -> Finite p  
 
 -- This instance preserves data abstraction at the cost of inefficiency.
 -- We provide limited reflection services for the sake of data abstraction.
@@ -61,11 +80,9 @@ intervalConstr = mkConstr intervalDataType "<=..<=" [] Infix
 intervalDataType :: DataType
 intervalDataType = mkDataType "Data.IntegerInterval.Internal.IntegerInterval" [intervalConstr]
 
-instance NFData IntegerInterval where
-  rnf (Interval lb ub) = rnf lb `seq` rnf ub
+instance NFData IntegerInterval
 
-instance Hashable IntegerInterval where
-  hashWithSalt s (Interval lb ub) = s `hashWithSalt` lb `hashWithSalt` ub
+instance Hashable IntegerInterval
 
 -- | closed interval [@l@,@u@]
 (<=..<=)
@@ -74,10 +91,16 @@ instance Hashable IntegerInterval where
   -> IntegerInterval
 (<=..<=) PosInf _ = empty
 (<=..<=) _ NegInf = empty
-(<=..<=) lb ub
-  | lb <= ub  = Interval lb ub
-  | otherwise = empty
+(<=..<=) NegInf PosInf = Whole
+(<=..<=) NegInf (Finite ub) = LessOrEqual ub
+(<=..<=) (Finite lb) PosInf = GreaterOrEqual lb
+(<=..<=) (Finite lb) (Finite ub) =
+  case compare lb ub of
+    EQ -> Point lb
+    LT -> Closed lb ub
+    GT -> Empty
+{-# INLINE (<=..<=) #-}
 
 -- | empty (contradicting) interval
 empty :: IntegerInterval
-empty = Interval PosInf NegInf
+empty = Empty