Safe Haskell  SafeInferred 

Bounded integer ranges
 data Range a = Range {
 lowerBound :: a
 upperBound :: a
 type BoundedInt a = (BoundedSuper a, BoundedSuper (UnsignedRep a))
 class (Ord a, Num a, Bounded a, Integral a, Bits a) => BoundedSuper a
 finiteBitSize :: Bits b => b > Int
 type family UnsignedRep a
 unsigned :: (Integral a, Integral (UnsignedRep a)) => a > UnsignedRep a
 handleSign :: forall a b. BoundedInt a => (Range a > b) > (Range a > b) > Range a > b
 showBound :: (Show a, BoundedInt a) => a > String
 showRange :: (Show a, BoundedInt a) => Range a > String
 mapMonotonic :: (a > b) > Range a > Range b
 mapMonotonic2 :: (a > b > c) > Range a > Range b > Range c
 emptyRange :: BoundedInt a => Range a
 fullRange :: BoundedInt a => Range a
 range :: Ord a => a > a > Range a
 singletonRange :: a > Range a
 naturalRange :: BoundedInt a => Range a
 positiveRange :: BoundedInt a => Range a
 negativeRange :: forall a. BoundedInt a => Range a
 rangeSize :: BoundedInt a => Range a > a
 isEmpty :: BoundedInt a => Range a > Bool
 isFull :: BoundedInt a => Range a > Bool
 isSingleton :: BoundedInt a => Range a > Bool
 isSubRangeOf :: BoundedInt a => Range a > Range a > Bool
 isNatural :: BoundedInt a => Range a > Bool
 isPositive :: BoundedInt a => Range a > Bool
 isNegative :: BoundedInt a => Range a > Bool
 inRange :: BoundedInt a => a > Range a > Bool
 rangeOp :: BoundedInt a => (Range a > Range a) > Range a > Range a
 rangeOp2 :: BoundedInt a => (Range a > Range a > Range a) > Range a > Range a > Range a
 rangeUnion :: BoundedInt a => Range a > Range a > Range a
 rangeIntersection :: BoundedInt a => Range a > Range a > Range a
 disjoint :: BoundedInt a => Range a > Range a > Bool
 rangeByRange :: BoundedInt a => Range a > Range a > Range a
 rangeGap :: BoundedInt a => Range a > Range a > Range a
 rangeLess :: BoundedInt a => Range a > Range a > Bool
 rangeLessEq :: BoundedInt a => Range a > Range a > Bool
 rangeAbs :: BoundedInt a => Range a > Range a
 rangeSignum :: BoundedInt a => Range a > Range a
 rangeSignumSigned :: BoundedInt a => Range a > Range a
 rangeSignumUnsigned :: BoundedInt a => Range a > Range a
 rangeNeg :: BoundedInt a => Range a > Range a
 rangeNegUnsigned :: BoundedInt a => Range a > Range a
 rangeNegSigned :: BoundedInt a => Range a > Range a
 rangeAdd :: BoundedInt a => Range a > Range a > Range a
 rangeAddUnsigned :: BoundedInt a => Range a > Range a > Range a
 rangeAddSigned :: BoundedInt a => Range a > Range a > Range a
 rangeSub :: BoundedInt a => Range a > Range a > Range a
 rangeSubUnsigned :: BoundedInt a => Range a > Range a > Range a
 rangeSubSigned :: BoundedInt a => Range a > Range a > Range a
 subSat :: BoundedInt a => a > a > a
 rangeSubSat :: BoundedInt a => Range a > Range a > Range a
 rangeMul :: BoundedInt a => Range a > Range a > Range a
 rangeMulSigned :: forall a. BoundedInt a => Range a > Range a > Range a
 rangeMulUnsigned :: forall a. BoundedInt a => Range a > Range a > Range a
 bits :: forall b. BoundedInt b => b > Int
 rangeExp :: BoundedInt a => Range a > Range a > Range a
 rangeExpUnsigned :: BoundedInt a => Range a > Range a > Range a
 rangeExpSigned :: BoundedInt a => Range a > Range a > Range a
 maxPlus :: BoundedInt a => a > a > a
 minOrUnsigned :: BoundedInt a => a > a > a > a > a
 minOr :: BoundedSuper a => a > a > a > a > a
 maxOrUnsigned :: BoundedInt a => a > a > a > a > a
 maxOr :: BoundedSuper a => a > a > a > a > a
 minAndUnsigned :: BoundedInt a => a > a > a > a > a
 maxAndUnsigned :: BoundedInt a => a > a > a > a > a
 minXorUnsigned :: BoundedInt a => a > a > a > a > a
 maxXorUnsigned :: BoundedInt a => a > a > a > a > a
 minOrSigned :: BoundedInt a => a > a > a > a > a
 maxOrSigned :: BoundedInt a => a > a > a > a > a
 minAndSigned :: BoundedInt a => a > a > a > a > a
 maxAndSigned :: BoundedInt a => a > a > a > a > a
 rangeOr :: forall a. BoundedInt a => Range a > Range a > Range a
 rangeOrUnsignedAccurate :: BoundedInt a => Range a > Range a > Range a
 rangeOrSignedAccurate :: BoundedInt a => Range a > Range a > Range a
 rangeAnd :: forall a. BoundedInt a => Range a > Range a > Range a
 rangeAndUnsignedAccurate :: BoundedInt a => Range a > Range a > Range a
 rangeAndSignedAccurate :: BoundedInt a => Range a > Range a > Range a
 rangeXor :: forall a. BoundedInt a => Range a > Range a > Range a
 rangeXorUnsignedAccurate :: BoundedInt a => Range a > Range a > Range a
 rangeShiftLU :: (BoundedInt a, BoundedInt b) => Range a > Range b > Range a
 rangeShiftLUUnsigned :: (BoundedInt a, Integral b) => Range a > Range b > Range a
 rangeShiftRU :: (BoundedInt a, BoundedInt b) => Range a > Range b > Range a
 rangeShiftRUUnsigned :: (BoundedInt a, BoundedInt b) => Range a > Range b > Range a
 correctShiftRU :: (Num a, Bits a, BoundedInt b) => a > b > a
 rangeComplement :: (Bits a, BoundedInt a) => Range a > Range a
 rangeMax :: BoundedInt a => Range a > Range a > Range a
 rangeMin :: BoundedInt a => Range a > Range a > Range a
 rangeMod :: BoundedInt a => Range a > Range a > Range a
 rangeRem :: BoundedInt a => Range a > Range a > Range a
 predAbs :: (Bounded a, Eq a, Num a, Enum a) => a > a
 rangeDiv :: BoundedInt a => Range a > Range a > Range a
 rangeDivU :: BoundedInt a => Range a > Range a > Range a
 rangeQuot :: BoundedInt a => Range a > Range a > Range a
 rangeQuotU :: BoundedInt a => Range a > Range a > Range a
 rangeLessAbs :: BoundedInt a => Range a > Range a > Bool
 absRangeLessAbs :: BoundedInt a => Range a > Range a > Bool
 liftR :: (BoundedInt b, BoundedInt c, BoundedInt d) => (forall a. BoundedInt a => Range a) > (Range b, Range c, Range d)
 binopR :: (BoundedInt a, BoundedInt b, BoundedInt c) => (forall d. BoundedInt d => Range d > Range d > Range d) > (Range a, Range b, Range c) > (Range a, Range b, Range c) > (Range a, Range b, Range c)
 mapR :: (BoundedInt a, BoundedInt b, BoundedInt c) => (forall d. BoundedInt d => Range d > Range d) > (Range a, Range b, Range c) > (Range a, Range b, Range c)
 approx :: (BoundedInt a, BoundedInt b, BoundedInt c, BoundedInt d) => (Range a, Range b, Range c) > Range d
Definition
A bounded range of values of type a
Range  

Eq a => Eq (Range a)  
BoundedInt a => Num (Range a)  Implements 
BoundedInt a => Ord (Range a)  
Show a => Show (Range a)  
BoundedInt a => Lattice (Range a)  
(BoundedInt a, BoundedInt b, BoundedInt c) => Num (Range a, Range b, Range c) 
type BoundedInt a = (BoundedSuper a, BoundedSuper (UnsignedRep a))Source
Convenience alias for bounded integers
class (Ord a, Num a, Bounded a, Integral a, Bits a) => BoundedSuper a Source
Super class to BoundedInt
finiteBitSize :: Bits b => b > IntSource
type family UnsignedRep a Source
Type famliy to determine the bit representation of a type
unsigned :: (Integral a, Integral (UnsignedRep a)) => a > UnsignedRep aSource
Convert an Integral
to its unsigned representation while preserving
bit width
handleSign :: forall a b. BoundedInt a => (Range a > b) > (Range a > b) > Range a > bSource
A convenience function for defining range propagation.
handleSign propU propS
chooses propU
for unsigned types and
propS
for signed types.
showBound :: (Show a, BoundedInt a) => a > StringSource
Shows a bound.
mapMonotonic :: (a > b) > Range a > Range bSource
Requires a monotonic function
mapMonotonic2 :: (a > b > c) > Range a > Range b > Range cSource
Requires a monotonic function
Lattice operations
emptyRange :: BoundedInt a => Range aSource
The range containing no elements
fullRange :: BoundedInt a => Range aSource
The range containing all elements of a type
singletonRange :: a > Range aSource
The range containing one element
naturalRange :: BoundedInt a => Range aSource
The range from 0
to the maximum element
positiveRange :: BoundedInt a => Range aSource
The range from 1
to the maximum element
negativeRange :: forall a. BoundedInt a => Range aSource
The range from the smallest negative element to 1
.
Undefined for unsigned types
rangeSize :: BoundedInt a => Range a > aSource
The size of a range. Beware that the size may not always be representable
for signed types. For instance
rangeSize (range minBound maxBound) :: Int
gives a nonsense answer.
isEmpty :: BoundedInt a => Range a > BoolSource
Checks if the range is empty
isFull :: BoundedInt a => Range a > BoolSource
Checks if the range contains all values of the type
isSingleton :: BoundedInt a => Range a > BoolSource
Checks is the range contains exactly one element
isSubRangeOf :: BoundedInt a => Range a > Range a > BoolSource
r1 `isSubRangeOf` r2
checks is all the elements in r1
are included
in r2
isNatural :: BoundedInt a => Range a > BoolSource
Checks whether a range is a subrange of the natural numbers.
isPositive :: BoundedInt a => Range a > BoolSource
Checks whether a range is a subrange of the positive numbers.
isNegative :: BoundedInt a => Range a > BoolSource
Checks whether a range is a subrange of the negative numbers.
inRange :: BoundedInt a => a > Range a > BoolSource
a `inRange` r
checks is a
is an element of the range r
.
rangeOp :: BoundedInt a => (Range a > Range a) > Range a > Range aSource
A convenience function for defining range propagation. If the input range is empty then the result is also empty.
rangeOp2 :: BoundedInt a => (Range a > Range a > Range a) > Range a > Range a > Range aSource
See rangeOp
.
rangeUnion :: BoundedInt a => Range a > Range a > Range aSource
Union on ranges.
rangeIntersection :: BoundedInt a => Range a > Range a > Range aSource
Intersection on ranges.
disjoint :: BoundedInt a => Range a > Range a > BoolSource
disjoint r1 r2
returns true when r1
and r2
have no elements in
common.
rangeByRange :: BoundedInt a => Range a > Range a > Range aSource
rangeByRange ra rb
: Computes the range of the following set
{x  a < ra, b < rb, x < Range a b}
rangeGap :: BoundedInt a => Range a > Range a > Range aSource
rangeGap r1 r2
returns a range of all the elements between r1
and
r2
including the boundary elements. If r1
and r2
have elements in
common the result is an empty range.
rangeLess :: BoundedInt a => Range a > Range a > BoolSource
r1 `rangeLess` r2:
Checks if all elements of r1
are less than all elements of r2
.
rangeLessEq :: BoundedInt a => Range a > Range a > BoolSource
r1 `rangeLessEq` r2:
Checks if all elements of r1
are less than or equal to all elements of
r2
.
Propagation
rangeAbs :: BoundedInt a => Range a > Range aSource
Propagates range information through abs
.
rangeSignum :: BoundedInt a => Range a > Range aSource
Propagates range information through signum
.
rangeSignumSigned :: BoundedInt a => Range a > Range aSource
Signed case for rangeSignum
.
rangeSignumUnsigned :: BoundedInt a => Range a > Range aSource
Unsigned case for rangeSignum
.
rangeNeg :: BoundedInt a => Range a > Range aSource
Propagates range information through negation.
rangeNegUnsigned :: BoundedInt a => Range a > Range aSource
Unsigned case for rangeNeg
.
rangeNegSigned :: BoundedInt a => Range a > Range aSource
Signed case for rangeNeg
.
rangeAdd :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through addition.
rangeAddUnsigned :: BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeAdd
.
rangeAddSigned :: BoundedInt a => Range a > Range a > Range aSource
Signed case for rangeAdd
.
rangeSub :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through subtraction.
rangeSubUnsigned :: BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeSub
.
rangeSubSigned :: BoundedInt a => Range a > Range a > Range aSource
subSat :: BoundedInt a => a > a > aSource
Saturating unsigned subtraction
rangeSubSat :: BoundedInt a => Range a > Range a > Range aSource
Range propagation for subSat
rangeMul :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through multiplication
rangeMulSigned :: forall a. BoundedInt a => Range a > Range a > Range aSource
Signed case for rangeMul
.
rangeMulUnsigned :: forall a. BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeMul
.
bits :: forall b. BoundedInt b => b > IntSource
Returns the position of the highest bit set to 1. Counting starts at 1.
rangeExp :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through exponentiation.
rangeExpUnsigned :: BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeExp
.
rangeExpSigned :: BoundedInt a => Range a > Range a > Range aSource
Sigend case for rangeExp
maxPlus :: BoundedInt a => a > a > aSource
a `maxPlus` b
adds a
and b
but if the addition overflows then
maxBound
is returned.
minOrUnsigned :: BoundedInt a => a > a > a > a > aSource
Accurate lower bound for ..
on unsigned numbers.
minOr :: BoundedSuper a => a > a > a > a > aSource
maxOrUnsigned :: BoundedInt a => a > a > a > a > aSource
Accurate upper bound for ..
on unsigned numbers.
maxOr :: BoundedSuper a => a > a > a > a > aSource
minAndUnsigned :: BoundedInt a => a > a > a > a > aSource
Accurate lower bound for .&.
on unsigned numbers
maxAndUnsigned :: BoundedInt a => a > a > a > a > aSource
Accurate upper bound for .&.
on unsigned numbers
minXorUnsigned :: BoundedInt a => a > a > a > a > aSource
Accurate lower bound for xor
on unsigned numbers
maxXorUnsigned :: BoundedInt a => a > a > a > a > aSource
Accurate upper bound for xor
on unsigned numbers
minOrSigned :: BoundedInt a => a > a > a > a > aSource
maxOrSigned :: BoundedInt a => a > a > a > a > aSource
minAndSigned :: BoundedInt a => a > a > a > a > aSource
maxAndSigned :: BoundedInt a => a > a > a > a > aSource
rangeOr :: forall a. BoundedInt a => Range a > Range a > Range aSource
Propagates range information through ..
.
rangeOrUnsignedAccurate :: BoundedInt a => Range a > Range a > Range aSource
Accurate range propagation through ..
for unsigned types.
rangeOrSignedAccurate :: BoundedInt a => Range a > Range a > Range aSource
rangeAnd :: forall a. BoundedInt a => Range a > Range a > Range aSource
Propagating range information through .&.
.
rangeAndUnsignedAccurate :: BoundedInt a => Range a > Range a > Range aSource
Accurate range propagation through .&.
for unsigned types
rangeAndSignedAccurate :: BoundedInt a => Range a > Range a > Range aSource
rangeXor :: forall a. BoundedInt a => Range a > Range a > Range aSource
Propagating range information through xor
.
rangeXorUnsignedAccurate :: BoundedInt a => Range a > Range a > Range aSource
Accurate range propagation through xor
for unsigned types
rangeShiftLU :: (BoundedInt a, BoundedInt b) => Range a > Range b > Range aSource
 Propagating range information through shiftLU
.
rangeShiftLUUnsigned :: (BoundedInt a, Integral b) => Range a > Range b > Range aSource
Unsigned case for rangeShiftLU
.
rangeShiftRU :: (BoundedInt a, BoundedInt b) => Range a > Range b > Range aSource
Propagating range information through shiftRU
.
rangeShiftRUUnsigned :: (BoundedInt a, BoundedInt b) => Range a > Range b > Range aSource
Unsigned case for rangeShiftRU
.
correctShiftRU :: (Num a, Bits a, BoundedInt b) => a > b > aSource
This is a replacement fror Haskell's shiftR. If we carelessly use Haskell's variant then we will get left shifts for very large shift values.
rangeComplement :: (Bits a, BoundedInt a) => Range a > Range aSource
Propagating range information through complement
rangeMax :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through max
.
rangeDiv :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through div
rangeQuot :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through quot
.
rangeQuotU :: BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeQuot
.
rangeLessAbs :: BoundedInt a => Range a > Range a > BoolSource
Writing d `rangeLess` abs r
doesn't mean what you think it does because
r
may contain minBound which doesn't have a positive representation.
Instead, this function should be used.
absRangeLessAbs :: BoundedInt a => Range a > Range a > BoolSource
Similar to rangeLessAbs
but replaces the expression
abs d `rangeLess` abs r
instead.
Products of ranges
liftR :: (BoundedInt b, BoundedInt c, BoundedInt d) => (forall a. BoundedInt a => Range a) > (Range b, Range c, Range d)Source
binopR :: (BoundedInt a, BoundedInt b, BoundedInt c) => (forall d. BoundedInt d => Range d > Range d > Range d) > (Range a, Range b, Range c) > (Range a, Range b, Range c) > (Range a, Range b, Range c)Source
mapR :: (BoundedInt a, BoundedInt b, BoundedInt c) => (forall d. BoundedInt d => Range d > Range d) > (Range a, Range b, Range c) > (Range a, Range b, Range c)Source
approx :: (BoundedInt a, BoundedInt b, BoundedInt c, BoundedInt d) => (Range a, Range b, Range c) > Range dSource