Safe Haskell	None
Language	Haskell98

Polarity

Synopsis

class Polarity pol where
- erased :: pol -> Bool
- compose :: pol -> pol -> pol
- neutral :: pol
- promote :: pol -> pol
- demote :: pol -> pol
- hidden :: pol
type PVarId = Int
data Pol
- = Const
- | SPos
- | Pos
- | Neg
- | Param
- | Rec
- | Default
- | PVar PVarId
mixed :: Pol
defaultPol :: Pol
showPVar :: Show a => a -> String
isPVar :: Pol -> Bool
leqPol :: Pol -> Pol -> Bool
polNeg :: Pol -> Pol
polComp :: Pol -> Pol -> Pol
invComp :: Pol -> Pol -> Pol
polAnd :: Pol -> Pol -> Pol
relPol :: Pol -> (a -> a -> Bool) -> a -> a -> Bool
relPolM :: Monad m => Pol -> (a -> a -> m ()) -> a -> a -> m ()
data Multiplicity
- = POne
- | PTwo
addMultiplicity :: Multiplicity -> Multiplicity -> Multiplicity
type VarMults = Map PVarId Multiplicity
showMults :: VarMults -> String
multsEmpty :: VarMults
multsSingle :: Int -> VarMults
data PProd = PProd {
- coeff :: Pol
- varMults :: VarMults
}
pprod :: Pol -> PProd
fromPProd :: PProd -> Maybe Pol
isSPos :: PProd -> Bool
polProd :: PProd -> PProd -> PProd
data PPoly = PPoly {
- monomials :: [PProd]
}
ppoly :: PProd -> PPoly
polSum :: PPoly -> PPoly -> PPoly
polProduct :: PPoly -> PPoly -> PPoly

Documentation

class Polarity pol where Source #

Methods

erased :: pol -> Bool Source #

compose :: pol -> pol -> pol Source #

neutral Source #

Arguments

:: pol

neutral for compose.

promote :: pol -> pol Source #

demote :: pol -> pol Source #

hidden Source #

Arguments

:: pol

corresponding to hidden quantification

Instances

Instances details

Polarity PProd Source #
Instance details Defined in Polarity Methods erased :: PProd -> Bool Source # compose :: PProd -> PProd -> PProd Source # neutral :: PProd Source # promote :: PProd -> PProd Source # demote :: PProd -> PProd Source # hidden :: PProd Source #
Polarity Pol Source #
Instance details Defined in Polarity Methods erased :: Pol -> Bool Source # compose :: Pol -> Pol -> Pol Source # neutral :: Pol Source # promote :: Pol -> Pol Source # demote :: Pol -> Pol Source # hidden :: Pol Source #
Polarity a => Polarity (Decoration a) Source #
Instance details Defined in Abstract Methods erased :: Decoration a -> Bool Source # compose :: Decoration a -> Decoration a -> Decoration a Source # neutral :: Decoration a Source # promote :: Decoration a -> Decoration a Source # demote :: Decoration a -> Decoration a Source # hidden :: Decoration a Source #

type PVarId = Int Source #

data Pol Source #

Constructors

Const
SPos
Pos
Neg
Param
Rec
Default
PVar PVarId

Instances

Instances details

LensPol Dec Source #
Instance details Defined in Abstract Methods getPol :: Dec -> Pol Source # setPol :: Pol -> Dec -> Dec Source # mapPol :: (Pol -> Pol) -> Dec -> Dec Source #
Switchable Pol Source #
Instance details Defined in Eval Methods switch :: Pol -> Pol Source #
Polarity Pol Source #
Instance details Defined in Polarity Methods erased :: Pol -> Bool Source # compose :: Pol -> Pol -> Pol Source # neutral :: Pol Source # promote :: Pol -> Pol Source # demote :: Pol -> Pol Source # hidden :: Pol Source #
SemiRing Pol Source #
Instance details Defined in Polarity Methods oplus :: Pol -> Pol -> Pol Source # otimes :: Pol -> Pol -> Pol Source # ozero :: Pol Source # oone :: Pol Source #
Show Pol Source #
Instance details Defined in Polarity Methods showsPrec :: Int -> Pol -> ShowS # show :: Pol -> String # showList :: [Pol] -> ShowS #
Eq Pol Source #
Instance details Defined in Polarity Methods (==) :: Pol -> Pol -> Bool # (/=) :: Pol -> Pol -> Bool #
Ord Pol Source #
Instance details Defined in Polarity Methods compare :: Pol -> Pol -> Ordering # (<) :: Pol -> Pol -> Bool # (<=) :: Pol -> Pol -> Bool # (>) :: Pol -> Pol -> Bool # (>=) :: Pol -> Pol -> Bool # max :: Pol -> Pol -> Pol # min :: Pol -> Pol -> Pol #

mixed :: Pol Source #

defaultPol :: Pol Source #

showPVar :: Show a => a -> String Source #

isPVar :: Pol -> Bool Source #

leqPol :: Pol -> Pol -> Bool Source #

polNeg :: Pol -> Pol Source #

polComp :: Pol -> Pol -> Pol Source #

invComp :: Pol -> Pol -> Pol Source #

polAnd :: Pol -> Pol -> Pol Source #

relPol :: Pol -> (a -> a -> Bool) -> a -> a -> Bool Source #

relPolM :: Monad m => Pol -> (a -> a -> m ()) -> a -> a -> m () Source #

data Multiplicity Source #

Constructors

POne
PTwo

Instances

Instances details

Show Multiplicity Source #
Instance details Defined in Polarity Methods showsPrec :: Int -> Multiplicity -> ShowS # show :: Multiplicity -> String # showList :: [Multiplicity] -> ShowS #
Eq Multiplicity Source #
Instance details Defined in Polarity Methods (==) :: Multiplicity -> Multiplicity -> Bool # (/=) :: Multiplicity -> Multiplicity -> Bool #
Ord Multiplicity Source #
Instance details Defined in Polarity Methods compare :: Multiplicity -> Multiplicity -> Ordering # (<) :: Multiplicity -> Multiplicity -> Bool # (<=) :: Multiplicity -> Multiplicity -> Bool # (>) :: Multiplicity -> Multiplicity -> Bool # (>=) :: Multiplicity -> Multiplicity -> Bool # max :: Multiplicity -> Multiplicity -> Multiplicity # min :: Multiplicity -> Multiplicity -> Multiplicity #

addMultiplicity :: Multiplicity -> Multiplicity -> Multiplicity Source #

type VarMults = Map PVarId Multiplicity Source #

showMults :: VarMults -> String Source #

multsEmpty :: VarMults Source #

multsSingle :: Int -> VarMults Source #

data PProd Source #

Constructors

PProd
Fields coeff :: Pol varMults :: VarMults

Instances

Instances details

Polarity PProd Source #
Instance details Defined in Polarity Methods erased :: PProd -> Bool Source # compose :: PProd -> PProd -> PProd Source # neutral :: PProd Source # promote :: PProd -> PProd Source # demote :: PProd -> PProd Source # hidden :: PProd Source #
Show PProd Source #
Instance details Defined in Polarity Methods showsPrec :: Int -> PProd -> ShowS # show :: PProd -> String # showList :: [PProd] -> ShowS #
Eq PProd Source #
Instance details Defined in Polarity Methods (==) :: PProd -> PProd -> Bool # (/=) :: PProd -> PProd -> Bool #
Ord PProd Source #
Instance details Defined in Polarity Methods compare :: PProd -> PProd -> Ordering # (<) :: PProd -> PProd -> Bool # (<=) :: PProd -> PProd -> Bool # (>) :: PProd -> PProd -> Bool # (>=) :: PProd -> PProd -> Bool # max :: PProd -> PProd -> PProd # min :: PProd -> PProd -> PProd #

pprod :: Pol -> PProd Source #

fromPProd :: PProd -> Maybe Pol Source #

fails if not a simple polarity

isSPos :: PProd -> Bool Source #

polProd :: PProd -> PProd -> PProd Source #

data PPoly Source #

Constructors

PPoly
Fields monomials :: [PProd]

Instances

Instances details

SemiRing PPoly Source #
Instance details Defined in Polarity Methods oplus :: PPoly -> PPoly -> PPoly Source # otimes :: PPoly -> PPoly -> PPoly Source # ozero :: PPoly Source # oone :: PPoly Source #
Show PPoly Source #
Instance details Defined in Polarity Methods showsPrec :: Int -> PPoly -> ShowS # show :: PPoly -> String # showList :: [PPoly] -> ShowS #
Eq PPoly Source #
Instance details Defined in Polarity Methods (==) :: PPoly -> PPoly -> Bool # (/=) :: PPoly -> PPoly -> Bool #
Ord PPoly Source #
Instance details Defined in Polarity Methods compare :: PPoly -> PPoly -> Ordering # (<) :: PPoly -> PPoly -> Bool # (<=) :: PPoly -> PPoly -> Bool # (>) :: PPoly -> PPoly -> Bool # (>=) :: PPoly -> PPoly -> Bool # max :: PPoly -> PPoly -> PPoly # min :: PPoly -> PPoly -> PPoly #

ppoly :: PProd -> PPoly Source #

polSum :: PPoly -> PPoly -> PPoly Source #

polProduct :: PPoly -> PPoly -> PPoly Source #