Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	None
Language	Haskell2010

OAlg.Data.Validable

Contents

Validable
XStandard
Extensional Equality

Description

validable values x, which can be validated via validate (valid x).

Synopsis

class Validable a where
- valid :: a -> Statement
rnfValid :: NFData x => x -> Statement
class Validable (Dual1 d x) => ValidableDual1 (d :: Type -> Type) x
class Validable1 (p :: Type -> Type) where
- valid1 :: p x -> Statement
class Validable2 (h :: Type -> Type -> Type) where
- valid2 :: h x y -> Statement
class XStandard x where
- xStandard :: X x
relXStandard :: (Validable x, XStandard x) => p x -> Statement
data XStd
xStd :: (Morphism m, Transformable (ObjectClass m) XStd) => m x y -> X x
xStdStruct :: Struct XStd x -> X x
class XStandard (Dual1 d x) => XStandardDual1 (d :: Type -> Type) x
type EqualExt = Sub EqE (->)
data EqE
equalExt :: (Morphism c, Applicative1 c t, TransformableG t (ObjectClass c) EqE) => c x y -> EqualExt (t x) (t y)

Validable

class Validable a where Source #

validation of a value of a.

Methods

valid :: a -> Statement Source #

Instances

Instances details

Validable N Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: N -> Statement Source #
Validable Q Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Q -> Statement Source #
Validable Z Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Z -> Statement Source #
Validable Valid Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Valid -> Statement Source #
Validable Symbol Source #
Instance details Defined in OAlg.Data.Symbol Methods valid :: Symbol -> Statement Source #
Validable Variant Source #
Instance details Defined in OAlg.Data.Variant Methods valid :: Variant -> Statement Source #
Validable EntEmpty Source #
Instance details Defined in OAlg.Entity.Definition Methods valid :: EntEmpty -> Statement Source #
Validable N' Source #
Instance details Defined in OAlg.Entity.Natural Methods valid :: N' -> Statement Source #
Validable SomeNatural Source #
Instance details Defined in OAlg.Entity.Natural Methods valid :: SomeNatural -> Statement Source #
Validable W' Source #
Instance details Defined in OAlg.Entity.Natural Methods valid :: W' -> Statement Source #
Validable Integer Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Integer -> Statement Source #
Validable () Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: () -> Statement Source #
Validable Bool Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Bool -> Statement Source #
Validable Char Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Char -> Statement Source #
Validable Int Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Int -> Statement Source #
Validable (Ratio Integer) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Ratio Integer -> Statement Source #
Validable2 m => Validable (SomeMorphism m) Source #
Instance details Defined in OAlg.Category.Unify Methods valid :: SomeMorphism m -> Statement Source #
Validable (SomeObjectClass m) Source #
Instance details Defined in OAlg.Category.Unify Methods valid :: SomeObjectClass m -> Statement Source #
(Oriented a, XStandardPoint a) => Validable (XSomeFreeSliceFromLiftable a) Source #
Instance details Defined in OAlg.Data.FinitelyPresentable Methods valid :: XSomeFreeSliceFromLiftable a -> Statement Source #
Validable x => Validable (Id x) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Id x -> Statement Source #
Validable x => Validable (Closure x) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Closure x -> Statement Source #
Validable a => Validable (X a) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: X a -> Statement Source #
Oriented a => Validable (SomeDiagram a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods valid :: SomeDiagram a -> Statement Source #
Validable a => Validable (SomeFinList a) Source #
Instance details Defined in OAlg.Entity.FinList Methods valid :: SomeFinList a -> Statement Source #
(Additive x, FibredOriented x) => Validable (Matrix x) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods valid :: Matrix x -> Statement Source #
Galoisian x => Validable (GL2 x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods valid :: GL2 x -> Statement Source #
Oriented x => Validable (GLT x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods valid :: GLT x -> Statement Source #
Validable (Transformation x) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods valid :: Transformation x -> Statement Source #
Oriented x => Validable (ColTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation Methods valid :: ColTrafo x -> Statement Source #
Distributive k => Validable (DiagonalForm k) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation Methods valid :: DiagonalForm k -> Statement Source #
Number k => Validable (DiagonalFormStrictPositive k) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation Methods valid :: DiagonalFormStrictPositive k -> Statement Source #
Oriented x => Validable (RowTrafo x) Source #
Instance details Defined in OAlg.Entity.Matrix.Transformation Methods valid :: RowTrafo x -> Statement Source #
Semiring r => Validable (Vector r) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector Methods valid :: Vector r -> Statement Source #
Validable (W n) Source #
Instance details Defined in OAlg.Entity.Natural Methods valid :: W n -> Statement Source #
(Show x, Validable x, Eq x, Typeable x) => Validable (ProductSymbol x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol Methods valid :: ProductSymbol x -> Statement Source #
(Show i, Ord i, Validable i) => Validable (Cycle i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation Methods valid :: Cycle i -> Statement Source #
(Show i, Validable i, Typeable i, Ord i) => Validable (Permutation i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation Methods valid :: Permutation i -> Statement Source #
(Entity i, Ord i) => Validable (PermutationForm i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation Methods valid :: PermutationForm i -> Statement Source #
(Validable x, Ord x, Show x) => Validable (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods valid :: Set x -> Statement Source #
Validable (SomeFree c) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods valid :: SomeFree c -> Statement Source #
Distributive x => Validable (SomeConsecutiveZeroHom x) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero Methods valid :: SomeConsecutiveZeroHom x -> Statement Source #
Distributive x => Validable (ZeroPoint x) Source #
Instance details Defined in OAlg.Limes.Exact.ZeroPoint Methods valid :: ZeroPoint x -> Statement Source #
Fibred a => Validable (Adbl2 a) Source #
Instance details Defined in OAlg.Structure.Additive.Proposition Methods valid :: Adbl2 a -> Statement Source #
Fibred a => Validable (Adbl3 a) Source #
Instance details Defined in OAlg.Structure.Additive.Proposition Methods valid :: Adbl3 a -> Statement Source #
Additive a => Validable (XAbl a) Source #
Instance details Defined in OAlg.Structure.Additive.Proposition Methods valid :: XAbl a -> Statement Source #
Additive a => Validable (XAdd a) Source #
Instance details Defined in OAlg.Structure.Additive.Proposition Methods valid :: XAdd a -> Statement Source #
Algebraic a => Validable (XAlg a) Source #
Instance details Defined in OAlg.Structure.Algebraic.Proposition Methods valid :: XAlg a -> Statement Source #
Fibred f => Validable (Sheaf f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition Methods valid :: Sheaf f -> Statement Source #
Validable x => Validable (R x) Source #
Instance details Defined in OAlg.Structure.Fibred.Root Methods valid :: R x -> Statement Source #
ValidableRoot x => Validable (Rt x) Source #
Instance details Defined in OAlg.Structure.Fibred.Root Methods valid :: Rt x -> Statement Source #
Multiplicative c => Validable (Inv c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods valid :: Inv c -> Statement Source #
Oriented q => Validable (Endo q) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods valid :: Endo q -> Statement Source #
Oriented c => Validable (Mltp2 c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods valid :: Mltp2 c -> Statement Source #
Oriented c => Validable (Mltp3 c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods valid :: Mltp3 c -> Statement Source #
Oriented c => Validable (XMlt c) Source #
Instance details Defined in OAlg.Structure.Multiplicative.Proposition Methods valid :: XMlt c -> Statement Source #
Validable x => Validable (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite Methods valid :: Op x -> Statement Source #
Validable p => Validable (Orientation p) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation Methods valid :: Orientation p -> Statement Source #
Oriented q => Validable (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods valid :: Path q -> Statement Source #
ValidablePoint x => Validable (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods valid :: Pnt x -> Statement Source #
Validable x => Validable (U x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods valid :: U x -> Statement Source #
Oriented q => Validable (XOrtOrientation q) Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods valid :: XOrtOrientation q -> Statement Source #
Vectorial v => Validable (VectorSheaf v) Source #
Instance details Defined in OAlg.Structure.Vectorial.Definition Methods valid :: VectorSheaf v -> Statement Source #
Vectorial v => Validable (XVec v) Source #
Instance details Defined in OAlg.Structure.Vectorial.Proposition Methods valid :: XVec v -> Statement Source #
Validable a => Validable (Maybe a) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Maybe a -> Statement Source #
Validable a => Validable [a] Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: [a] -> Statement Source #
(Validable a, Validable b) => Validable (Either a b) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Either a b -> Statement Source #
Validable (Proxy x) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Proxy x -> Statement Source #
(Validable (d x), ValidableDual1 d x) => Validable (SDualBi d x) Source #
Instance details Defined in OAlg.Category.SDuality Methods valid :: SDualBi d x -> Statement Source #
Validable (EntEmpty2 x y) Source #
Instance details Defined in OAlg.Entity.Definition Methods valid :: EntEmpty2 x y -> Statement Source #
Validable (Quiver n m) Source #
Instance details Defined in OAlg.Entity.Diagram.Quiver Methods valid :: Quiver n m -> Statement Source #
Validable a => Validable (FinList n a) Source #
Instance details Defined in OAlg.Entity.FinList Methods valid :: FinList n a -> Statement Source #
Oriented x => Validable (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods valid :: Dim x p -> Statement Source #
(Show x, Show i, Validable x, Validable i, Eq x, Typeable x, Typeable i, Ord i) => Validable (Col i x) Source #
Instance details Defined in OAlg.Entity.Matrix.Entries Methods valid :: Col i x -> Statement Source #
(Show x, Show j, Validable x, Validable j, Eq x, Typeable x, Typeable j, Ord j) => Validable (Row j x) Source #
Instance details Defined in OAlg.Entity.Matrix.Entries Methods valid :: Row j x -> Statement Source #
Validable (GLApp x y) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods valid :: GLApp x y -> Statement Source #
Validable (TrApp x y) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods valid :: TrApp x y -> Statement Source #
(Oriented a, Integral r) => Validable (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods valid :: Product r a -> Statement Source #
(Oriented a, Number r) => Validable (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods valid :: ProductForm r a -> Statement Source #
(Validable a, Validable r) => Validable (Word r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods valid :: Word r a -> Statement Source #
(Entity x, Entity i, Ord i) => Validable (Graph i x) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods valid :: Graph i x -> Statement Source #
(Ord i, Ord j, XStandard i, Show i) => Validable (Monotone i j) Source #
Instance details Defined in OAlg.Entity.Sequence.PSequence Methods valid :: Monotone i j -> Statement Source #
(Entity x, Entity i, Ord i) => Validable (PSequence i x) Source #
Instance details Defined in OAlg.Entity.Sequence.PSequence Methods valid :: PSequence i x -> Statement Source #
(Entity x, Entity i, Ord i) => Validable (PTree i x) Source #
Instance details Defined in OAlg.Entity.Sequence.PSequence Methods valid :: PTree i x -> Statement Source #
Validable (Free k c) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods valid :: Free k c -> Statement Source #
Validable (SomeFreeSlice s c) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods valid :: SomeFreeSlice s c -> Statement Source #
(Validable r, Validable a) => Validable (LinearCombination r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition Methods valid :: LinearCombination r a -> Statement Source #
(Distributive r, Total r, Commutative r, Fibred a) => Validable (Sum r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition Methods valid :: Sum r a -> Statement Source #
(Fibred a, Semiring r, Commutative r) => Validable (SumForm r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition Methods valid :: SumForm r a -> Statement Source #
(Distributive r, Total r, Commutative r, Show a, Eq a, Validable a, Typeable a) => Validable (SumSymbol r a) Source #
Instance details Defined in OAlg.Entity.Sum.SumSymbol Methods valid :: SumSymbol r a -> Statement Source #
Validable (Struct s x) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Struct s x -> Statement Source #
Distributive d => Validable (DstRootSide s d) Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods valid :: DstRootSide s d -> Statement Source #
Distributive d => Validable (DstSide s d) Source #
Instance details Defined in OAlg.Structure.Distributive.Proposition Methods valid :: DstSide s d -> Statement Source #
Validable r => Validable (Digits b r) Source #
Instance details Defined in OAlg.Structure.Number.Definition Methods valid :: Digits b r -> Statement Source #
Oriented q => Validable (XOrtSite s q) Source #
Instance details Defined in OAlg.Structure.Oriented.X Methods valid :: XOrtSite s q -> Statement Source #
(Validable a, Validable b) => Validable (a, b) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: (a, b) -> Statement Source #
(XStandard x, Validable y) => Validable (x -> y) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: (x -> y) -> Statement Source #
(HomMultiplicative h, Entity2 h, XStandardPoint d, XStandard d, XStandardPoint c, XStandard c) => Validable (Adjunction h d c) Source #
Instance details Defined in OAlg.Adjunction.Definition Methods valid :: Adjunction h d c -> Statement Source #
(Category c, EqExt c) => Validable (Inv2 c x y) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Inv2 c x y -> Statement Source #
Validable2 (Path m) => Validable (Path m x y) Source #
Instance details Defined in OAlg.Category.Path Methods valid :: Path m x y -> Statement Source #
(Validable (a x), Validable (b x)) => Validable (Either1 a b x) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Either1 a b x -> Statement Source #
(Distributive a, XStandardEligibleConeCokernel N1 a, XStandardEligibleConeFactorCokernel N1 a, XStandardEligibleConeKernel N1 a, XStandardEligibleConeFactorKernel N1 a, XStandardSomeFreeSliceFromLiftable a) => Validable (FinitePresentation 'To Free a) Source #
Instance details Defined in OAlg.Data.FinitelyPresentable Methods valid :: FinitePresentation 'To Free a -> Statement Source #
(Show x, Show i, Show j, Validable x, Validable i, Validable j, Eq x, Typeable x, Typeable i, Typeable j, Ord i, Ord j) => Validable (Entries i j x) Source #
Instance details Defined in OAlg.Entity.Matrix.Entries Methods valid :: Entries i j x -> Statement Source #
Semiring r => Validable (HomSymbol r x y) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector Methods valid :: HomSymbol r x y -> Statement Source #
(Validable d, Entity i, Ord i, Entity x) => Validable (FSequenceForm d i x) Source #
Instance details Defined in OAlg.Entity.Sequence.FSequence Methods valid :: FSequenceForm d i x -> Statement Source #
Sliced i x => Validable (Slice s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods valid :: Slice s i x -> Statement Source #
(Multiplicative x, Sliced i x) => Validable (SliceFactor s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods valid :: SliceFactor s i x -> Statement Source #
Validable (SliceFactorDrop s x y) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods valid :: SliceFactorDrop s x y -> Statement Source #
(Distributive c, Sliced i c, XStandardEligibleConeKernel n c, XStandardEligibleConeFactorKernel n c, Typeable n) => Validable (KernelSliceFromSomeFreeTip n i c) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods valid :: KernelSliceFromSomeFreeTip n i c -> Statement Source #
(Multiplicative x, XStandardOrtOrientation x) => Validable (Liftable s i x) Source #
Instance details Defined in OAlg.Entity.Slice.Liftable Methods valid :: Liftable s i x -> Statement Source #
Validable (HomEmpty s x y) Source #
Instance details Defined in OAlg.Hom.Definition Methods valid :: HomEmpty s x y -> Statement Source #
Distributive x => Validable (ConsecutiveZero t n x) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero Methods valid :: ConsecutiveZero t n x -> Statement Source #
(Distributive x, Typeable t, Typeable n) => Validable (ConsecutiveZeroHom t n x) Source #
Instance details Defined in OAlg.Limes.Exact.ConsecutiveZero Methods valid :: ConsecutiveZeroHom t n x -> Statement Source #
Distributive x => Validable (ConsecutiveZeroFree t n x) Source #
Instance details Defined in OAlg.Limes.Exact.Free Methods valid :: ConsecutiveZeroFree t n x -> Statement Source #
Validable (Struct2 m x y) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: Struct2 m x y -> Statement Source #
(Validable a, Validable b, Validable c) => Validable (a, b, c) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: (a, b, c) -> Statement Source #
Oriented a => Validable (Diagram t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods valid :: Diagram t n m a -> Statement Source #
Multiplicative a => Validable (DiagramTrafo t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation Methods valid :: DiagramTrafo t n m a -> Statement Source #
Validable (Representable r h x y) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector Methods valid :: Representable r h x y -> Statement Source #
(Entity d, Entity i, Entity x, Ord i) => Validable (FSequence s d i x) Source #
Instance details Defined in OAlg.Entity.Sequence.FSequence Methods valid :: FSequence s d i x -> Statement Source #
Oriented a => Validable (DiagramFree t n m a) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods valid :: DiagramFree t n m a -> Statement Source #
(Diagrammatic d, Oriented x) => Validable (FactorChain d 'From n x) Source #
Instance details Defined in OAlg.Limes.Cone.FactorChain Methods valid :: FactorChain d 'From n x -> Statement Source #
(Diagrammatic d, Oriented x) => Validable (FactorChain d 'To n x) Source #
Instance details Defined in OAlg.Limes.Cone.FactorChain Methods valid :: FactorChain d 'To n x -> Statement Source #
(Validable a, Validable b, Validable c, Validable d) => Validable (a, b, c, d) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: (a, b, c, d) -> Statement Source #
Validable (d t n m x) => Validable (DiagramG d t n m x) Source #
Instance details Defined in OAlg.Entity.Diagram.Diagrammatic Methods valid :: DiagramG d t n m x -> Statement Source #
Validable (SliceDiagram i t n m x) Source #
Instance details Defined in OAlg.Entity.Slice.Adjunction Methods valid :: SliceDiagram i t n m x -> Statement Source #
Oriented x => Validable (DiagramSlicedCenter i t n m x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods valid :: DiagramSlicedCenter i t n m x -> Statement Source #
(Morphism h, Validable2 h) => Validable (HomDisj s o h x y) Source #
Instance details Defined in OAlg.Hom.Definition Methods valid :: HomDisj s o h x y -> Statement Source #
(Validable a, Validable b, Validable c, Validable d, Validable e) => Validable (a, b, c, d, e) Source #
Instance details Defined in OAlg.Data.Validable Methods valid :: (a, b, c, d, e) -> Statement Source #
(Morphism h, Validable2 h) => Validable (SHom r s o h x y) Source #
Instance details Defined in OAlg.Category.SDuality Methods valid :: SHom r s o h x y -> Statement Source #
(Disjunctive2 h, Validable (h x y)) => Validable (Variant2 v h x y) Source #
Instance details Defined in OAlg.Data.Variant Methods valid :: Variant2 v h x y -> Statement Source #
(Distributive x, XStandardEligibleConeKernel N1 x, XStandardEligibleConeFactorKernel N1 x, XStandardEligibleConeCokernel N1 x, XStandardEligibleConeFactorCokernel N1 x) => Validable (VarianceG t Cone Cone Diagram n x) Source #
Instance details Defined in OAlg.Limes.Exact.Deviation Methods valid :: VarianceG t Cone Cone Diagram n x -> Statement Source #
(Distributive x, XStandardEligibleConeKernel N1 x, XStandardEligibleConeFactorKernel N1 x, XStandardEligibleConeCokernel N1 x, XStandardEligibleConeFactorCokernel N1 x, Typeable t, Typeable n) => Validable (VarianceGHom t Cone Cone Diagram n x) Source #
Instance details Defined in OAlg.Limes.Exact.Deviation Methods valid :: VarianceGHom t Cone Cone Diagram n x -> Statement Source #
(Oriented x, XStandardEligibleCone s p t n m x, XStandardEligibleConeFactor s p t n m x, Typeable t, Typeable n, Typeable m) => Validable (LimesSlicedTip i s p t n m x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods valid :: LimesSlicedTip i s p t n m x -> Statement Source #
(Show (d ('Parallel 'LeftToRight) n m x), Show (d ('Parallel 'LeftToRight) n m (Op x)), Validable (d ('Parallel 'LeftToRight) n m x), Validable (d ('Parallel 'LeftToRight) n m (Op x)), Distributive x, SlicedFree x, XStandardOrtOrientation x, NaturalDiagrammaticFree s d n m, n ~ N2, m ~ N1) => Validable (ConeLiftable s p d t n m x) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods valid :: ConeLiftable s p d t n m x -> Statement Source #
(Diagrammatic d, Validable (d t n m a)) => Validable (Cone s p d t n m a) Source #
Instance details Defined in OAlg.Limes.Cone.Definition Methods valid :: Cone s p d t n m a -> Statement Source #
(Diagrammatic d, Validable (d t n ('S m) x)) => Validable (ConeZeroHead s p d t n ('S m) x) Source #
Instance details Defined in OAlg.Limes.Cone.ZeroHead.Core Methods valid :: ConeZeroHead s p d t n ('S m) x -> Statement Source #
(Conic c, Show (c s p d t n m x), Validable (c s p d t n m x)) => Validable (ConicFreeTip c s p d t n m x) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods valid :: ConicFreeTip c s p d t n m x -> Statement Source #
(Distributive x, Sliced i x, XStandardOrtOrientation x) => Validable (LiftableCone i s p d t n m x) Source #
Instance details Defined in OAlg.Entity.Slice.Liftable Methods valid :: LiftableCone i s p d t n m x -> Statement Source #
(Conic c, Diagrammatic d, XStandardEligibleConeG c s p d t n m x, XStandardEligibleConeFactorG c s p d t n m x, Show (c s p d t n m x), Validable (c s p d t n m x), Entity (d t n m x), Entity x) => Validable (LimesG c s p d t n m x) Source #
Instance details Defined in OAlg.Limes.Definition.Proposition Methods valid :: LimesG c s p d t n m x -> Statement Source #
(Conic c, Diagrammatic d, XStandardEligibleConeG c s p d t n m x, XStandardEligibleConeFactorG c s p d t n m x, XStandard (d t n m x), Show (c s p d t n m x), Validable (c s p d t n m x), Entity (d t n m x), Entity x) => Validable (LimitsG c s p d t n m x) Source #
Instance details Defined in OAlg.Limes.Limits.Proposition Methods valid :: LimitsG c s p d t n m x -> Statement Source #

rnfValid :: NFData x => x -> Statement Source #

validation of being reducible to normal form.

class Validable (Dual1 d x) => ValidableDual1 (d :: Type -> Type) x Source #

helper class to avoid undecidable instances.

Instances

Instances details

Oriented a => ValidableDual1 (Diagram t n m) a Source #
Instance details Defined in OAlg.Entity.Diagram.Definition

class Validable1 (p :: Type -> Type) where Source #

validation of a value of p x.

Minimal complete definition

Nothing

Methods

valid1 :: p x -> Statement Source #

default valid1 :: Validable (p x) => p x -> Statement Source #

Instances

Instances details

Validable1 (Proxy :: Type -> Type) Source #
Instance details Defined in OAlg.Data.Validable Methods valid1 :: Proxy x -> Statement Source #
Validable1 (Free k) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods valid1 :: Free k x -> Statement Source #
Validable1 (Struct s) Source #
Instance details Defined in OAlg.Data.Validable Methods valid1 :: Struct s x -> Statement Source #

class Validable2 (h :: Type -> Type -> Type) where Source #

validation of a value of h x y.

Minimal complete definition

Nothing

Methods

valid2 :: h x y -> Statement Source #

default valid2 :: Validable (h x y) => h x y -> Statement Source #

Instances

Instances details

Validable2 EntEmpty2 Source #
Instance details Defined in OAlg.Entity.Definition Methods valid2 :: EntEmpty2 x y -> Statement Source #
Validable2 GLApp Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods valid2 :: GLApp x y -> Statement Source #
Validable2 TrApp Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods valid2 :: TrApp x y -> Statement Source #
(Category c, EqExt c) => Validable2 (Inv2 c) Source #
Instance details Defined in OAlg.Data.Validable Methods valid2 :: Inv2 c x y -> Statement Source #
Validable2 h => Validable2 (Op2 h) Source #
Instance details Defined in OAlg.Data.Validable Methods valid2 :: Op2 h x y -> Statement Source #
(Morphism m, Validable2 m) => Validable2 (Path m) Source #
Instance details Defined in OAlg.Category.Path Methods valid2 :: Path m x y -> Statement Source #
Semiring r => Validable2 (HomSymbol r) Source #
Instance details Defined in OAlg.Entity.Matrix.Vector Methods valid2 :: HomSymbol r x y -> Statement Source #
Validable2 (SliceFactorDrop s) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods valid2 :: SliceFactorDrop s x y -> Statement Source #
Validable2 (HomEmpty s) Source #
Instance details Defined in OAlg.Hom.Definition Methods valid2 :: HomEmpty s x y -> Statement Source #
Validable2 (Struct2 m) Source #
Instance details Defined in OAlg.Data.Validable Methods valid2 :: Struct2 m x y -> Statement Source #
(Validable2 f, Validable2 g) => Validable2 (Either2 f g) Source #
Instance details Defined in OAlg.Data.Validable Methods valid2 :: Either2 f g x y -> Statement Source #
(Morphism h, Validable2 h) => Validable2 (HomDisj s o h) Source #
Instance details Defined in OAlg.Hom.Definition Methods valid2 :: HomDisj s o h x y -> Statement Source #
(Morphism h, Validable2 h) => Validable2 (SHom r s o h) Source #
Instance details Defined in OAlg.Category.SDuality Methods valid2 :: SHom r s o h x y -> Statement Source #
Validable2 h => Validable2 (SMorphism r s o h) Source #
Instance details Defined in OAlg.Category.SDuality Methods valid2 :: SMorphism r s o h x y -> Statement Source #

XStandard

class XStandard x where Source #

standard random variable for x.

Property For all x in the range of xStandard holds: valid x.

Methods

xStandard :: X x Source #

Instances

Instances details

XStandard N Source #
Instance details Defined in OAlg.Data.Validable Methods xStandard :: X N Source #
XStandard Q Source #
Instance details Defined in OAlg.Data.Validable Methods xStandard :: X Q Source #
XStandard Z Source #
Instance details Defined in OAlg.Data.Validable Methods xStandard :: X Z Source #
XStandard Symbol Source #
Instance details Defined in OAlg.Data.Symbol Methods xStandard :: X Symbol Source #
XStandard Integer Source #
Instance details Defined in OAlg.Data.Validable Methods xStandard :: X Integer Source #
XStandard () Source #
Instance details Defined in OAlg.Data.Validable Methods xStandard :: X () Source #
XStandard Int Source #
Instance details Defined in OAlg.Data.Validable Methods xStandard :: X Int Source #
XStandard x => XStandard (Id x) Source #
Instance details Defined in OAlg.Data.Validable Methods xStandard :: X (Id x) Source #
XStandard (Matrix Z) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition Methods xStandard :: X (Matrix Z) Source #
XStandard x => XStandard (Op x) Source #
Instance details Defined in OAlg.Structure.Oriented.Opposite Methods xStandard :: X (Op x) Source #
XStandard p => XStandard (Orientation p) Source #
Instance details Defined in OAlg.Structure.Oriented.Orientation Methods xStandard :: X (Orientation p) Source #
XStandardPoint x => XStandard (Pnt x) Source #
Instance details Defined in OAlg.Structure.Oriented.Point Methods xStandard :: X (Pnt x) Source #
(XStandard (d x), XStandardDual1 d x) => XStandard (SDualBi d x) Source #
Instance details Defined in OAlg.Category.SDuality Methods xStandard :: X (SDualBi d x) Source #
(Oriented x, () ~ Point x) => XStandard (Dim x ()) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods xStandard :: X (Dim x ()) Source #
(Multiplicative x, Sliced i x, XStandardOrtSite 'From x) => XStandard (Slice 'From i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods xStandard :: X (Slice 'From i x) Source #
(Multiplicative x, Sliced i x, XStandardOrtSite 'To x) => XStandard (Slice 'To i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods xStandard :: X (Slice 'To i x) Source #
(Multiplicative x, Sliced i x, XStandardOrtSite 'From x) => XStandard (SliceFactor 'From i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods xStandard :: X (SliceFactor 'From i x) Source #
(Multiplicative x, Sliced i x, XStandardOrtSite 'To x) => XStandard (SliceFactor 'To i x) Source #
Instance details Defined in OAlg.Entity.Slice.Definition Methods xStandard :: X (SliceFactor 'To i x) Source #
(Oriented a, XStandardOrtSite t a, Attestable m, n ~ (m + 1)) => XStandard (Diagram ('Chain t) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods xStandard :: X (Diagram ('Chain t) n m a) Source #
(Oriented a, m ~ N0, XStandardPoint a, Attestable n) => XStandard (Diagram 'Discrete n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods xStandard :: X (Diagram 'Discrete n m a) Source #
(Oriented a, n ~ N0, m ~ N0) => XStandard (Diagram 'Empty n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods xStandard :: X (Diagram 'Empty n m a) Source #
(Oriented a, n ~ N2, XStandardOrtOrientation a, Attestable m) => XStandard (Diagram ('Parallel 'LeftToRight) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods xStandard :: X (Diagram ('Parallel 'LeftToRight) n m a) Source #
(Oriented a, n ~ N2, XStandardOrtOrientation a, Attestable m) => XStandard (Diagram ('Parallel 'RightToLeft) n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods xStandard :: X (Diagram ('Parallel 'RightToLeft) n m a) Source #
(Oriented a, XStandardOrtSite 'From a, Attestable m) => XStandard (Diagram ('Star 'From) ('S m) m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods xStandard :: X (Diagram ('Star 'From) ('S m) m a) Source #
(Oriented a, XStandardOrtSite 'To a, Attestable m) => XStandard (Diagram ('Star 'To) ('S m) m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods xStandard :: X (Diagram ('Star 'To) ('S m) m a) Source #
(Entity p, t ~ 'Parallel 'RightToLeft, n ~ N2, Diagrammatic d, XStandard p, XStandard (d t n m (Orientation p))) => XStandard (Cone Dst 'Injective d t n m (Orientation p)) Source #
Instance details Defined in OAlg.Limes.Cone.Definition Methods xStandard :: X (Cone Dst 'Injective d t n m (Orientation p)) Source #
(Entity p, t ~ 'Parallel 'LeftToRight, n ~ N2, Diagrammatic d, XStandard p, XStandard (d t n m (Orientation p))) => XStandard (Cone Dst 'Projective d t n m (Orientation p)) Source #
Instance details Defined in OAlg.Limes.Cone.Definition Methods xStandard :: X (Cone Dst 'Projective d t n m (Orientation p)) Source #
(Entity p, Diagrammatic d, XStandard p, XStandard (d t n m (Orientation p))) => XStandard (Cone Mlt 'Injective d t n m (Orientation p)) Source #
Instance details Defined in OAlg.Limes.Cone.Definition Methods xStandard :: X (Cone Mlt 'Injective d t n m (Orientation p)) Source #
(Entity p, Diagrammatic d, XStandard p, XStandard (d t n m (Orientation p))) => XStandard (Cone Mlt 'Projective d t n m (Orientation p)) Source #
Instance details Defined in OAlg.Limes.Cone.Definition Methods xStandard :: X (Cone Mlt 'Projective d t n m (Orientation p)) Source #

relXStandard :: (Validable x, XStandard x) => p x -> Statement Source #

validity of the standard random variable associated to x (p x just serves as proxy and will not be evaluated).

data XStd Source #

type representing the class of XStandard structures.

Instances

Instances details

Transformable OrtX XStd Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tau :: Struct OrtX x -> Struct XStd x Source #
type Structure XStd x Source #
Instance details Defined in OAlg.Data.Validable type Structure XStd x = XStandard x

xStd :: (Morphism m, Transformable (ObjectClass m) XStd) => m x y -> X x Source #

the associated standard random variable for the domain.

xStdStruct :: Struct XStd x -> X x Source #

the associated standard random variable.

class XStandard (Dual1 d x) => XStandardDual1 (d :: Type -> Type) x Source #

helper class to avoid undecidable instances.

Instances

Instances details

(Oriented x, XStandardOrtSite 'To x, XStandardOrtSite 'From x, Attestable m, n ~ (m + 1)) => XStandardDual1 (SDualBi (Diagram ('Chain 'From) n m)) x Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
(Oriented x, XStandardOrtSite 'To x, XStandardOrtSite 'From x, Attestable m, n ~ (m + 1)) => XStandardDual1 (SDualBi (Diagram ('Chain 'To) n m)) x Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
(Oriented x, XStandardOrtSite 'To x, Attestable m, n ~ (m + 1)) => XStandardDual1 (Diagram ('Chain 'From) n m) x Source #
Instance details Defined in OAlg.Entity.Diagram.Definition
(Oriented x, XStandardOrtSite 'From x, Attestable m, n ~ (m + 1)) => XStandardDual1 (Diagram ('Chain 'To) n m) x Source #
Instance details Defined in OAlg.Entity.Diagram.Definition

Extensional Equality

type EqualExt = Sub EqE (->) Source #

category of extensional equality.

data EqE Source #

type representing extensional equality.

Instances

Instances details

EqExt EqualExt Source #
Instance details Defined in OAlg.Data.Validable Methods (.=.) :: EqualExt x y -> EqualExt x y -> Statement Source #
TransformableType EqE Source #
Instance details Defined in OAlg.Data.Validable
Transformable EqE Type Source #
Instance details Defined in OAlg.Data.Validable Methods tau :: Struct EqE x -> Struct Type x Source #
TransformableG Id OrtX EqE Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tauG :: Struct OrtX x -> Struct EqE (Id x) Source #
TransformableG Pnt OrtX EqE Source #
Instance details Defined in OAlg.Structure.Oriented.Definition Methods tauG :: Struct OrtX x -> Struct EqE (Pnt x) Source #
(Attestable m, n ~ (m + 1)) => TransformableG (SDualBi (Diagram ('Chain 'From) n m)) OrtSiteX EqE Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods tauG :: Struct OrtSiteX x -> Struct EqE (SDualBi (Diagram ('Chain 'From) n m) x) Source #
(Attestable m, n ~ (m + 1)) => TransformableG (SDualBi (Diagram ('Chain 'To) n m)) OrtSiteX EqE Source #
Instance details Defined in OAlg.Entity.Diagram.Definition Methods tauG :: Struct OrtSiteX x -> Struct EqE (SDualBi (Diagram ('Chain 'To) n m) x) Source #
type Structure EqE x Source #
Instance details Defined in OAlg.Data.Validable type Structure EqE x = (Show x, Eq x, XStandard x)

equalExt :: (Morphism c, Applicative1 c t, TransformableG t (ObjectClass c) EqE) => c x y -> EqualExt (t x) (t y) Source #

embedding amapG of a Applicative1 to EqualExt.