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/src/Data/IntegerInterval/Internal.hs

{-# OPTIONS_GHC -Wall #-}
{-# LANGUAGE CPP, DeriveDataTypeable, LambdaCase #-}
{-# LANGUAGE Safe #-}
#if __GLASGOW_HASKELL__ >= 708
{-# LANGUAGE RoleAnnotations #-}
#endif

module Data.IntegerInterval.Internal
  ( IntegerInterval
  , lowerBound
  , upperBound
  , (<=..<=)
  , empty
  ) where

import Control.DeepSeq
import Data.Data
import Data.ExtendedReal
import Data.Hashable

infix 5 <=..<=

-- | The intervals (/i.e./ connected and convex subsets) over integers (__Z__).
data IntegerInterval
  = Whole
  | Empty
  | Point !Integer
  | LessOrEqual !Integer
  | GreaterOrEqual !Integer
  | BothClosed !Integer !Integer
  deriving (Eq, Typeable)

-- | Lower endpoint (/i.e./ greatest lower bound)  of the interval.
--
-- * 'lowerBound' of the empty interval is 'PosInf'.
--
-- * 'lowerBound' of a left unbounded interval is 'NegInf'.
--
-- * 'lowerBound' of an interval may or may not be a member of the interval.
lowerBound :: IntegerInterval -> Extended Integer
lowerBound = \case
  Whole            -> NegInf
  Empty            -> PosInf
  Point r          -> Finite r
  LessOrEqual _    -> NegInf
  GreaterOrEqual r -> Finite r
  BothClosed p _   -> Finite p

-- | Upper endpoint (/i.e./ least upper bound) of the interval.
--
-- * 'upperBound' of the empty interval is 'NegInf'.
--
-- * 'upperBound' of a right unbounded interval is 'PosInf'.
--
-- * 'upperBound' of an interval is a member of the interval.
upperBound :: IntegerInterval -> Extended Integer
upperBound = \case
  Whole            -> PosInf
  Empty            -> NegInf
  Point r          -> Finite r
  LessOrEqual r    -> Finite r
  GreaterOrEqual _ -> PosInf
  BothClosed _ p   -> Finite p

-- This instance preserves data abstraction at the cost of inefficiency.
-- We provide limited reflection services for the sake of data abstraction.

instance Data IntegerInterval where
  gfoldl k z x   = z (<=..<=) `k` lowerBound x `k` upperBound x
  toConstr _     = intervalConstr
  gunfold k z c  = case constrIndex c of
    1 -> k (k (z (<=..<=)))
    _ -> error "gunfold"
  dataTypeOf _   = intervalDataType

intervalConstr :: Constr
intervalConstr = mkConstr intervalDataType "<=..<=" [] Infix

intervalDataType :: DataType
intervalDataType = mkDataType "Data.IntegerInterval.Internal.IntegerInterval" [intervalConstr]

instance NFData IntegerInterval where
  rnf = \case
    Whole            -> ()
    Empty            -> ()
    Point r          -> rnf r
    LessOrEqual r    -> rnf r
    GreaterOrEqual r -> rnf r
    BothClosed p q   -> rnf p `seq` rnf q

instance Hashable IntegerInterval where
  hashWithSalt s = \case
    Whole            -> s `hashWithSalt`  (1 :: Int)
    Empty            -> s `hashWithSalt`  (2 :: Int)
    Point r          -> s `hashWithSalt`  (3 :: Int) `hashWithSalt` r
    LessOrEqual r    -> s `hashWithSalt`  (4 :: Int) `hashWithSalt` r
    GreaterOrEqual r -> s `hashWithSalt`  (5 :: Int) `hashWithSalt` r
    BothClosed p q   -> s `hashWithSalt`  (6 :: Int) `hashWithSalt` p `hashWithSalt` q

-- | closed interval [@l@,@u@]
(<=..<=)
  :: Extended Integer -- ^ lower bound @l@
  -> Extended Integer -- ^ upper bound @u@
  -> IntegerInterval
(<=..<=) PosInf _ = empty
(<=..<=) _ NegInf = 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 -> BothClosed lb ub
    GT -> Empty
{-# INLINE (<=..<=) #-}

-- | empty (contradicting) interval
empty :: IntegerInterval
empty = Empty

1	{-# OPTIONS_GHC -Wall #-}
2	{-# LANGUAGE CPP, DeriveDataTypeable, LambdaCase #-}
3	{-# LANGUAGE Safe #-}
4	#if __GLASGOW_HASKELL__ >= 708
5	{-# LANGUAGE RoleAnnotations #-}
6	#endif
7
8	module Data.IntegerInterval.Internal
9	( IntegerInterval
10	, lowerBound
11	, upperBound
12	, (<=..<=)
13	, empty
14	) where
15
16	import Control.DeepSeq
17	import Data.Data
18	import Data.ExtendedReal
19	import Data.Hashable
20
21	infix 5 <=..<=
22
23	-- \| The intervals (/i.e./ connected and convex subsets) over integers (__Z__).
24	data IntegerInterval
25	= Whole
26	\| Empty
27	\| Point !Integer
28	\| LessOrEqual !Integer
29	\| GreaterOrEqual !Integer
30	\| BothClosed !Integer !Integer
31	deriving (Eq, Typeable)	1✔
32
33	-- \| Lower endpoint (/i.e./ greatest lower bound) of the interval.
34	--
35	-- * 'lowerBound' of the empty interval is 'PosInf'.
36	--
37	-- * 'lowerBound' of a left unbounded interval is 'NegInf'.
38	--
39	-- * 'lowerBound' of an interval may or may not be a member of the interval.
40	lowerBound :: IntegerInterval -> Extended Integer
41	lowerBound = \case	1✔
42	Whole -> NegInf	1✔
43	Empty -> PosInf	1✔
44	Point r -> Finite r	1✔
45	LessOrEqual _ -> NegInf	1✔
46	GreaterOrEqual r -> Finite r	1✔
47	BothClosed p _ -> Finite p	1✔
48
49	-- \| Upper endpoint (/i.e./ least upper bound) of the interval.
50	--
51	-- * 'upperBound' of the empty interval is 'NegInf'.
52	--
53	-- * 'upperBound' of a right unbounded interval is 'PosInf'.
54	--
55	-- * 'upperBound' of an interval is a member of the interval.
56	upperBound :: IntegerInterval -> Extended Integer
57	upperBound = \case	1✔
58	Whole -> PosInf	1✔
59	Empty -> NegInf	1✔
60	Point r -> Finite r	1✔
61	LessOrEqual r -> Finite r	1✔
62	GreaterOrEqual _ -> PosInf	1✔
63	BothClosed _ p -> Finite p	1✔
64
65	-- This instance preserves data abstraction at the cost of inefficiency.
66	-- We provide limited reflection services for the sake of data abstraction.
67
68	instance Data IntegerInterval where
69	gfoldl k z x = z (<=..<=) `k` lowerBound x `k` upperBound x	1✔
70	toConstr _ = intervalConstr	×
71	gunfold k z c = case constrIndex c of	×
72	1 -> k (k (z (<=..<=)))	×
73	_ -> error "gunfold"	×
74	dataTypeOf _ = intervalDataType	×
75
76	intervalConstr :: Constr
77	intervalConstr = mkConstr intervalDataType "<=..<=" [] Infix	×
78
79	intervalDataType :: DataType
80	intervalDataType = mkDataType "Data.IntegerInterval.Internal.IntegerInterval" [intervalConstr]	×
81
82	instance NFData IntegerInterval where
83	rnf = \case	1✔
84	Whole -> ()	1✔
85	Empty -> ()	1✔
86	Point r -> rnf r	×
87	LessOrEqual r -> rnf r	1✔
88	GreaterOrEqual r -> rnf r	1✔
89	BothClosed p q -> rnf p `seq` rnf q	1✔
90
91	instance Hashable IntegerInterval where
92	hashWithSalt s = \case	1✔
93	Whole -> s `hashWithSalt` (1 :: Int)	1✔
94	Empty -> s `hashWithSalt` (2 :: Int)	1✔
95	Point r -> s `hashWithSalt` (3 :: Int) `hashWithSalt` r	×
96	LessOrEqual r -> s `hashWithSalt` (4 :: Int) `hashWithSalt` r	1✔
97	GreaterOrEqual r -> s `hashWithSalt` (5 :: Int) `hashWithSalt` r	1✔
98	BothClosed p q -> s `hashWithSalt` (6 :: Int) `hashWithSalt` p `hashWithSalt` q	1✔
99
100	-- \| closed interval [@l@,@u@]
101	(<=..<=)
102	:: Extended Integer -- ^ lower bound @l@
103	-> Extended Integer -- ^ upper bound @u@
104	-> IntegerInterval
105	(<=..<=) PosInf _ = empty	1✔
106	(<=..<=) _ NegInf = empty	1✔
107	(<=..<=) NegInf PosInf = Whole	1✔
108	(<=..<=) NegInf (Finite ub) = LessOrEqual ub	1✔
109	(<=..<=) (Finite lb) PosInf = GreaterOrEqual lb	1✔
110	(<=..<=) (Finite lb) (Finite ub) =
111	case compare lb ub of	1✔
112	EQ -> Point lb	1✔
113	LT -> BothClosed lb ub	1✔
114	GT -> Empty	1✔
115	{-# INLINE (<=..<=) #-}
116
117	-- \| empty (contradicting) interval
118	empty :: IntegerInterval
119	empty = Empty	1✔

msakai / data-interval / 23

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