Copyright	(c) Masahiro Sakai 2013
License	BSD-style
Maintainer	masahiro.sakai@gmail.com
Stability	provisional
Portability	non-portable (FlexibleInstances, DeriveDataTypeable, CPP)
Safe Haskell	Safe
Language	Haskell2010

Data.Sign

Contents

The Sign data type
Operations over signs
Operations over sets of signs

Description

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).

Synopsis

data Sign
- = Neg
- | Zero
- | Pos
negate :: Sign -> Sign
abs :: Sign -> Sign
mult :: Sign -> Sign -> Sign
recip :: Sign -> Sign
div :: Sign -> Sign -> Sign
pow :: Integral x => Sign -> x -> Sign
signOf :: Real a => a -> Sign
symbol :: Sign -> String

The Sign data type

data Sign Source #

Signs of real numbers.

Constructors

Neg	negative
Zero	zero
Pos	positive

Instances

Bounded Sign Source #
Instance details Defined in Data.Sign Methods minBound :: Sign # maxBound :: Sign #
Enum Sign Source #
Instance details 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 Source #
Instance details Defined in Data.Sign Methods (==) :: Sign -> Sign -> Bool # (/=) :: Sign -> Sign -> Bool #
Data Sign Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details Defined in Data.Sign Methods readsPrec :: Int -> ReadS Sign # readList :: ReadS [Sign] # readPrec :: ReadPrec Sign # readListPrec :: ReadPrec [Sign] #
Show Sign Source #
Instance details Defined in Data.Sign Methods showsPrec :: Int -> Sign -> ShowS # show :: Sign -> String # showList :: [Sign] -> ShowS #
NFData Sign Source #
Instance details Defined in Data.Sign Methods rnf :: Sign -> () #
Hashable Sign Source #
Instance details Defined in Data.Sign Methods hashWithSalt :: Int -> Sign -> Int # hash :: Sign -> Int #
Universe Sign Source #
Instance details Defined in Data.Sign Methods universe :: [Sign] #
Finite Sign Source #
Instance details Defined in Data.Sign Methods universeF :: [Sign] # cardinality :: Tagged Sign Natural #
Fractional (Set Sign) Source #
Instance details Defined in Data.Sign Methods (/) :: Set Sign -> Set Sign -> Set Sign # recip :: Set Sign -> Set Sign # fromRational :: Rational -> Set Sign #
Num (Set Sign) Source #
Instance details 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 #