Safe Haskell	Safe-Inferred
Language	Haskell2010

Algebra.Category.BlockMatrix

Documentation

data M s a b where Source #

Constructors

Zero :: M s a b
Diag :: s -> M s a a
(:▵) :: M s a b -> M s a c -> M s a (b ⊕ c)
(:▿) :: M s b a -> M s c a -> M s (b ⊕ c) a
EmptyL :: M s Zero a
EmptyR :: M s a Zero

Instances

Instances details

Ring s => Category (M s :: Type -> Type -> Type) Source #
Instance details Defined in Algebra.Category.BlockMatrix Associated Types type Obj (M s) :: k -> Constraint Source # Methods (.) :: forall (a :: k) (b :: k) (c :: k). (Obj (M s) a, Obj (M s) b, Obj (M s) c) => M s b c -> M s a b -> M s a c Source # id :: forall (a :: k). Obj (M s) a => M s a a Source #
Ring s => Braided ((⊕) :: Type -> Type -> Type) (Zero :: Type) (M s :: Type -> Type -> Type) Source #
Instance details Defined in Algebra.Category.BlockMatrix Methods swap :: forall (a :: k) (b :: k). (Obj (M s) a, Obj (M s) b) => M s (a ⊕ b) (b ⊕ a) Source # swap_ :: forall (a :: k) (b :: k). (Obj (M s) a, Obj (M s) b) => M s (a ⊕ b) (b ⊕ a) Source #
Ring s => Cartesian ((⊕) :: Type -> Type -> Type) (Zero :: Type) (M s :: Type -> Type -> Type) Source #
Instance details Defined in Algebra.Category.BlockMatrix Methods exl :: forall (a :: k) (b :: k). O2 (M s) a b => M s (a ⊕ b) a Source # exr :: forall (a :: k) (b :: k). O2 (M s) a b => M s (a ⊕ b) b Source # dis :: forall (a :: k). Obj (M s) a => M s a Zero Source # dup :: forall (a :: k). Obj (M s) a => M s a (a ⊕ a) Source # (▵) :: forall (a :: k) (b :: k) (c :: k). (Obj (M s) a, Obj (M s) b, Obj (M s) c) => M s a b -> M s a c -> M s a (b ⊕ c) Source #
Ring s => CoCartesian ((⊕) :: Type -> Type -> Type) (Zero :: Type) (M s :: Type -> Type -> Type) Source #
Instance details Defined in Algebra.Category.BlockMatrix Methods inl :: forall (a :: k) (b :: k). O2 (M s) a b => M s a (a ⊕ b) Source # inr :: forall (a :: k) (b :: k). O2 (M s) a b => M s b (a ⊕ b) Source # new :: forall (a :: k). Obj (M s) a => M s Zero a Source # jam :: forall (a :: k). Obj (M s) a => M s (a ⊕ a) a Source # (▿) :: forall (a :: k) (b :: k) (c :: k). (Obj (M s) a, Obj (M s) b, Obj (M s) c) => M s b a -> M s c a -> M s (b ⊕ c) a Source #
Ring s => Monoidal ((⊕) :: Type -> Type -> Type) (Zero :: Type) (M s :: Type -> Type -> Type) Source #
Instance details Defined in Algebra.Category.BlockMatrix Methods (⊗) :: forall (a :: k) (b :: k) (c :: k) (d :: k). (Obj (M s) a, Obj (M s) b, Obj (M s) c, Obj (M s) d) => M s a b -> M s c d -> M s (a ⊕ c) (b ⊕ d) Source # assoc :: forall (a :: k) (b :: k) (c :: k). (Obj (M s) a, Obj (M s) b, Obj (M s) c) => M s ((a ⊕ b) ⊕ c) (a ⊕ (b ⊕ c)) Source # assoc_ :: forall (a :: k) (b :: k) (c :: k). (Obj (M s) a, Obj (M s) b, Obj (M s) c) => M s (a ⊕ (b ⊕ c)) ((a ⊕ b) ⊕ c) Source # unitorR :: forall (a :: k). (Obj (M s) a, Obj (M s) Zero) => M s a (a ⊕ Zero) Source # unitorR_ :: forall (a :: k). (Obj (M s) a, Obj (M s) Zero) => M s (a ⊕ Zero) a Source # unitorL :: forall (a :: k). (Obj (M s) a, Obj (M s) Zero) => M s a (Zero ⊕ a) Source # unitorL_ :: forall (a :: k). (Obj (M s) a, Obj (M s) Zero) => M s (Zero ⊕ a) a Source #
Ring s => Symmetric ((⊕) :: Type -> Type -> Type) (Zero :: Type) (M s :: Type -> Type -> Type) Source #
Instance details Defined in Algebra.Category.BlockMatrix
Ring s => Scalable s (M s a b) Source #
Instance details Defined in Algebra.Category.BlockMatrix Methods (*^) :: s -> M s a b -> M s a b Source #
Show s => Show (M s a b) Source #
Instance details Defined in Algebra.Category.BlockMatrix Methods showsPrec :: Int -> M s a b -> ShowS # show :: M s a b -> String # showList :: [M s a b] -> ShowS #
Additive s => Additive (M s a b) Source #
Instance details Defined in Algebra.Category.BlockMatrix Methods (+) :: M s a b -> M s a b -> M s a b Source # zero :: M s a b Source # times :: Natural -> M s a b -> M s a b Source #
Group s => Group (M s a b) Source #
Instance details Defined in Algebra.Category.BlockMatrix Methods (-) :: M s a b -> M s a b -> M s a b Source # subtract :: M s a b -> M s a b -> M s a b Source # negate :: M s a b -> M s a b Source # mult :: Integer -> M s a b -> M s a b Source #
(Show s, Additive s, TestEqual s) => TestEqual (M s a b) Source #
Instance details Defined in Algebra.Category.BlockMatrix Methods (=.=) :: M s a b -> M s a b -> Property Source #
type Obj (M s :: Type -> Type -> Type) Source #
Instance details Defined in Algebra.Category.BlockMatrix type Obj (M s :: Type -> Type -> Type) = Trivial :: Type -> Constraint

testZero :: (Additive s, TestEqual s) => M s a b -> Property Source #

findSplit :: M s a (b ⊕ c) -> (M s a b, M s a c) Source #

findSplit' :: M s (b ⊕ c) a -> (M s b a, M s c a) Source #

transpose :: M s a b -> M s b a Source #

genMorphism :: Arbitrary s => Ring s => Repr (⊗) One (⊕) Zero a -> Repr (⊗) One (⊕) Zero b -> Gen (M s a b) Source #

prop_block_matrix :: Property Source #