Data.Sign

This module provides arithmetic over signs (i.e. {-, 0, +}) and set of signs.

For the purpose of abstract interpretation, it might be convenient to use Lattice instance. See also lattices package (http://hackage.haskell.org/package/lattices).

The Sign data type

data Sign

Signs of real numbers.

Constructors

Neg

negative

Zero

zero

Pos

positive

Instances

Bounded Sign

Defined in Data.Sign

Methods

minBound :: Sign

maxBound :: Sign

Enum Sign

Defined in Data.Sign

Methods

succ :: Sign -> Sign

pred :: Sign -> Sign

toEnum :: Int -> Sign

fromEnum :: Sign -> Int

enumFrom :: Sign -> [Sign]

enumFromThen :: Sign -> Sign -> [Sign]

enumFromTo :: Sign -> Sign -> [Sign]

enumFromThenTo :: Sign -> Sign -> Sign -> [Sign]

Eq Sign

Defined in Data.Sign

Methods

(==) :: Sign -> Sign -> Bool

(/=) :: Sign -> Sign -> Bool

Data Sign

Defined in Data.Sign

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sign -> c Sign

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Sign

toConstr :: Sign -> Constr

dataTypeOf :: Sign -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Sign)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Sign)

gmapT :: (forall b. Data b => b -> b) -> Sign -> Sign

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sign -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sign -> r

gmapQ :: (forall d. Data d => d -> u) -> Sign -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Sign -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sign -> m Sign

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sign -> m Sign

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sign -> m Sign

Ord Sign

Defined in Data.Sign

Methods

compare :: Sign -> Sign -> Ordering

(<) :: Sign -> Sign -> Bool

(<=) :: Sign -> Sign -> Bool

(>) :: Sign -> Sign -> Bool

(>=) :: Sign -> Sign -> Bool

max :: Sign -> Sign -> Sign

min :: Sign -> Sign -> Sign

Read Sign

Defined in Data.Sign

Methods

readsPrec :: Int -> ReadS Sign

readList :: ReadS [Sign]

readPrec :: ReadPrec Sign

readListPrec :: ReadPrec [Sign]

Show Sign

Defined in Data.Sign

Methods

showsPrec :: Int -> Sign -> ShowS

show :: Sign -> String

showList :: [Sign] -> ShowS

NFData Sign

Defined in Data.Sign

Methods

rnf :: Sign -> ()

Hashable Sign

Defined in Data.Sign

Methods

hashWithSalt :: Int -> Sign -> Int

hash :: Sign -> Int

Universe Sign

Defined in Data.Sign

Methods

universe :: [Sign]

Finite Sign

Defined in Data.Sign

Methods

universeF :: [Sign]

cardinality :: Tagged Sign Natural

Fractional (Set Sign)

Defined in Data.Sign

Methods

(/) :: Set Sign -> Set Sign -> Set Sign

recip :: Set Sign -> Set Sign

fromRational :: Rational -> Set Sign

Num (Set Sign)

Defined in Data.Sign

Methods

(+) :: Set Sign -> Set Sign -> Set Sign

(-) :: Set Sign -> Set Sign -> Set Sign

(*) :: Set Sign -> Set Sign -> Set Sign

negate :: Set Sign -> Set Sign

abs :: Set Sign -> Set Sign

signum :: Set Sign -> Set Sign

fromInteger :: Integer -> Set Sign

Operations over signs

negate :: Sign -> Sign

Unary negation.

abs :: Sign -> Sign

Absolute value.

mult :: Sign -> Sign -> Sign

Multiplication.

recip :: Sign -> Sign

Reciprocal fraction.

div :: Sign -> Sign -> Sign

Fractional division.

pow :: Integral x => Sign -> x -> Sign

Exponentiation s^x.

Note that we define pow Zero 0 = Pos assuming 0^0 = 1.

signOf :: Real a => a -> Sign

Sign of a number.

symbol :: Sign -> String

Mnemonic symbol of a number.

This function returns "-", "0", "+" respectively for Neg, Zero, Pos.

Operations over sets of signs

Set Sign is equipped with instances of Num and Fractional. Therefore arithmetic operations can be applied to Set Sign.

Instances of Lattice and BoundedLattice are also provided for the purpose of abstract interpretation.