Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

OAlg.Data.Opposite

Contents

Op
Op2

Description

predicate for the opposite.

Synopsis

newtype Op x = Op x
fromOp :: Op x -> x
fromOpOp :: Op (Op x) -> x
newtype Op2 h x y = Op2 (h y x)

Op

newtype Op x Source #

Predicate for the opposite of a type x.

Constructors

Op x

Instances

Instances details

Transformable1 Op Dst Source #
Instance details Defined in OAlg.Structure.Distributive.Definition Methods tau1 :: Struct Dst x -> Struct Dst (Op x) Source #
Transformable1 Op Mlt Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods tau1 :: Struct Mlt x -> Struct Mlt (Op x) Source #
Transformable1 Op Ort Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau1 :: Struct Ort x -> Struct Ort (Op x) Source #
Sliced i c => Sliced i (Op c) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods slicePoint :: i (Op c) -> Point (Op c) Source #
Transformable1 Op (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau1 :: Struct (Alg k) x -> Struct (Alg k) (Op x) Source #
XStandardOrtSite 'From a => XStandardOrtSite 'To (Op a) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods xStandardOrtSite :: XOrtSite 'To (Op a) Source #
Read x => Read (Op x) Source #
Instance details Defined in OAlg.Data.Opposite Methods readsPrec :: Int -> ReadS (Op x) # readList :: ReadS [Op x] # readPrec :: ReadPrec (Op x) # readListPrec :: ReadPrec [Op x] #
Show x => Show (Op x) Source #
Instance details Defined in OAlg.Data.Opposite Methods showsPrec :: Int -> Op x -> ShowS # show :: Op x -> String # showList :: [Op x] -> ShowS #
Eq x => Eq (Op x) Source #
Instance details Defined in OAlg.Data.Opposite Methods (==) :: Op x -> Op x -> Bool # (/=) :: Op x -> Op x -> Bool #
Validable x => Validable (Op x) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Op x -> Statement Source #
Entity x => Entity (Op x) Source #
Instance details Defined in OAlg.Entity.Definition
(Abelian a, FibredOriented a) => Abelian (Op a) Source #
Instance details Defined in OAlg.Structure.Additive.Definition Methods negate :: Op a -> Op a Source # (-) :: Op a -> Op a -> Op a Source # ztimes :: Z -> Op a -> Op a Source #
(Additive a, FibredOriented a) => Additive (Op a) Source #
Instance details Defined in OAlg.Structure.Additive.Definition Methods zero :: Root (Op a) -> Op a Source # (+) :: Op a -> Op a -> Op a Source # ntimes :: N -> Op a -> Op a Source #
Algebraic a => Algebraic (Op a) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Distributive d => Distributive (Op d) Source #
Instance details Defined in OAlg.Structure.Distributive.Definition
FibredOriented f => Fibred (Op f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition Associated Types type Root (Op f) Source # Methods root :: Op f -> Root (Op f) Source #
FibredOriented f => FibredOriented (Op f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition
Cayleyan c => Cayleyan (Op c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
Commutative c => Commutative (Op c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition
Invertible c => Invertible (Op c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods tryToInvert :: Op c -> Solver (Op c) Source # invert :: Op c -> Op c Source # isInvertible :: Op c -> Bool Source # zpower :: Op c -> Z -> Op c Source #
Multiplicative c => Multiplicative (Op c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods one :: Point (Op c) -> Op c Source # (*) :: Op c -> Op c -> Op c Source # npower :: Op c -> N -> Op c Source #
EntityPoint x => EntityPoint (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition
Oriented q => Oriented (Op q) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Associated Types type Point (Op q) Source # Methods orientation :: Op q -> Orientation (Point (Op q)) Source # start :: Op q -> Point (Op q) Source # end :: Op q -> Point (Op q) Source #
Total x => Total (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition
(Vectorial v, FibredOriented v) => Vectorial (Op v) Source #
Instance details Defined in OAlg.Structure.Vectorial.Definition Associated Types type Scalar (Op v) Source # Methods (!) :: Scalar (Op v) -> Op v -> Op v Source #
type Root (Op f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition type Root (Op f) = Orientation (Point f)
type Point (Op q) Source #
Instance details Defined in OAlg.Structure.Oriented.Definition type Point (Op q) = Point q
type Scalar (Op v) Source #
Instance details Defined in OAlg.Structure.Vectorial.Definition type Scalar (Op v) = Scalar v

fromOp :: Op x -> x Source #

from Op x.

fromOpOp :: Op (Op x) -> x Source #

from Op (Op x).

Op2

newtype Op2 h x y Source #

Predicat for the opposite of a two parametrized type h where the two parameters x and y are switched

Constructors

Op2 (h y x)

Instances

Instances details

Category c => Category (Op2 c) Source #
Instance details Defined in OAlg.Category.Definition Methods cOne :: Struct (ObjectClass (Op2 c)) x -> Op2 c x x Source # (.) :: Op2 c y z -> Op2 c x y -> Op2 c x z Source #
Cayleyan2 c => Cayleyan2 (Op2 c) Source #
Instance details Defined in OAlg.Category.Definition Methods invert2 :: Op2 c x y -> Op2 c y x Source #
EmbeddableMorphismTyp m => EmbeddableMorphismTyp (Op2 m) Source #
Instance details Defined in OAlg.Category.Definition
Morphism h => Morphism (Op2 h) Source #
Instance details Defined in OAlg.Category.Definition Associated Types type ObjectClass (Op2 h) Source # Methods homomorphous :: Op2 h x y -> Homomorphous (ObjectClass (Op2 h)) x y Source # domain :: Op2 h x y -> Struct (ObjectClass (Op2 h)) x Source # range :: Op2 h x y -> Struct (ObjectClass (Op2 h)) y Source #
Eq2 h => Eq2 (Op2 h) Source #
Instance details Defined in OAlg.Data.Opposite Methods eq2 :: Op2 h x y -> Op2 h x y -> Bool Source #
Show2 h => Show2 (Op2 h) Source #
Instance details Defined in OAlg.Data.Opposite Methods show2 :: Op2 h a b -> String Source #
Validable2 h => Validable2 (Op2 h) Source #
Instance details Defined in OAlg.Data.Validable Methods valid2 :: Op2 h x y -> Statement Source #
EmbeddableMorphism m t => EmbeddableMorphism (Op2 m) t Source #
Instance details Defined in OAlg.Category.Definition
type ObjectClass (Op2 h) Source #
Instance details Defined in OAlg.Category.Definition type ObjectClass (Op2 h) = ObjectClass h