Safe Haskell	None
Language	GHC2024

Proarrow.Tools.Laws

Contents

Orphan instances

Documentation

data family Var (cs :: [Kind -> Constraint]) (a :: Symbol) (b :: Symbol) Source Comments #

Instances

Instances details

Show (Var '[Monoidal, SymMonoidal] a b) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal Methods showsPrec :: Int -> Var '[Monoidal, SymMonoidal] a b -> ShowS Comments # show :: Var '[Monoidal, SymMonoidal] a b -> String Comments # showList :: [Var '[Monoidal, SymMonoidal] a b] -> ShowS Comments #
Show (Var '[Monoidal] a b) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal Methods showsPrec :: Int -> Var '[Monoidal] a b -> ShowS Comments # show :: Var '[Monoidal] a b -> String Comments # showList :: [Var '[Monoidal] a b] -> ShowS Comments #
Show (Var '[HasBinaryCoproducts] a b) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods showsPrec :: Int -> Var '[HasBinaryCoproducts] a b -> ShowS Comments # show :: Var '[HasBinaryCoproducts] a b -> String Comments # showList :: [Var '[HasBinaryCoproducts] a b] -> ShowS Comments #
Show (Var '[HasBinaryProducts] a b) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods showsPrec :: Int -> Var '[HasBinaryProducts] a b -> ShowS Comments # show :: Var '[HasBinaryProducts] a b -> String Comments # showList :: [Var '[HasBinaryProducts] a b] -> ShowS Comments #
Show (Var '[HasInitialObject] a b) Source Comments #
Instance details Defined in Proarrow.Object.Initial Methods showsPrec :: Int -> Var '[HasInitialObject] a b -> ShowS Comments # show :: Var '[HasInitialObject] a b -> String Comments # showList :: [Var '[HasInitialObject] a b] -> ShowS Comments #
Show (Var '[HasTerminalObject] a b) Source Comments #
Instance details Defined in Proarrow.Object.Terminal Methods showsPrec :: Int -> Var '[HasTerminalObject] a b -> ShowS Comments # show :: Var '[HasTerminalObject] a b -> String Comments # showList :: [Var '[HasTerminalObject] a b] -> ShowS Comments #
data Var '[Monoidal, SymMonoidal] a b Source Comments #
Instance details Defined in Proarrow.Category.Monoidal data Var '[Monoidal, SymMonoidal] a b
data Var '[Monoidal] a b Source Comments #
Instance details Defined in Proarrow.Category.Monoidal data Var '[Monoidal] a b where F :: Var '[Monoidal] "A" "B" G :: Var '[Monoidal] "B" "C" H :: Var '[Monoidal] "C" "D"
data Var '[HasBinaryCoproducts] a b Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct data Var '[HasBinaryCoproducts] a b where F :: Var '[HasBinaryCoproducts] "A" "C" G :: Var '[HasBinaryCoproducts] "B" "C" H :: Var '[HasBinaryCoproducts] "C" "Z"
data Var '[HasBinaryProducts] a b Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct data Var '[HasBinaryProducts] a b where F :: Var '[HasBinaryProducts] "A" "B" G :: Var '[HasBinaryProducts] "A" "C" H :: Var '[HasBinaryProducts] "Z" "A"
data Var '[HasInitialObject] a b Source Comments #
Instance details Defined in Proarrow.Object.Initial data Var '[HasInitialObject] a b where F :: Var '[HasInitialObject] "A" "B"
data Var '[HasTerminalObject] a b Source Comments #
Instance details Defined in Proarrow.Object.Terminal data Var '[HasTerminalObject] a b where F :: Var '[HasTerminalObject] "A" "B"

class Laws (cs :: [Kind -> Constraint]) where Source Comments #

Associated Types

type EqTypes (cs :: [Kind -> Constraint]) :: [FREE cs (Var cs)] Source Comments #

Methods

laws :: [AssertEq cs] Source Comments #

Instances

Instances details

Laws '[Monoidal, SymMonoidal] Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal

Associated Types

type EqTypes '[Monoidal, SymMonoidal]

Instance details

Defined in Proarrow.Category.Monoidal

Methods

laws :: [AssertEq '[Monoidal, SymMonoidal]] Source Comments #

Laws '[Monoidal] Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal

Associated Types

type EqTypes '[Monoidal]

Instance details

Defined in Proarrow.Category.Monoidal

Methods

laws :: [AssertEq '[Monoidal]] Source Comments #

Laws '[HasBinaryCoproducts] Source Comments #

Instance details

Defined in Proarrow.Object.BinaryCoproduct

Associated Types

type EqTypes '[HasBinaryCoproducts]

Instance details

Defined in Proarrow.Object.BinaryCoproduct

type EqTypes '[HasBinaryCoproducts] = '['EMB "A" :: FREE '[HasBinaryCoproducts] (Var '[HasBinaryCoproducts]), 'EMB "B" :: FREE '[HasBinaryCoproducts] (Var '[HasBinaryCoproducts]), 'EMB "C" :: FREE '[HasBinaryCoproducts] (Var '[HasBinaryCoproducts]), 'EMB "Z" :: FREE '[HasBinaryCoproducts] (Var '[HasBinaryCoproducts]), ('EMB "A" :: FREE '[HasBinaryCoproducts] (Var '[HasBinaryCoproducts])) + ('EMB "B" :: FREE '[HasBinaryCoproducts] (Var '[HasBinaryCoproducts]))]

Methods

laws :: [AssertEq '[HasBinaryCoproducts]] Source Comments #

Laws '[HasBinaryProducts] Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

type EqTypes '[HasBinaryProducts]

Instance details

Defined in Proarrow.Object.BinaryProduct

type EqTypes '[HasBinaryProducts] = '['EMB "A" :: FREE '[HasBinaryProducts] (Var '[HasBinaryProducts]), 'EMB "B" :: FREE '[HasBinaryProducts] (Var '[HasBinaryProducts]), 'EMB "C" :: FREE '[HasBinaryProducts] (Var '[HasBinaryProducts]), 'EMB "Z" :: FREE '[HasBinaryProducts] (Var '[HasBinaryProducts]), ('EMB "B" :: FREE '[HasBinaryProducts] (Var '[HasBinaryProducts])) *! ('EMB "C" :: FREE '[HasBinaryProducts] (Var '[HasBinaryProducts]))]

Methods

laws :: [AssertEq '[HasBinaryProducts]] Source Comments #

Laws '[HasInitialObject] Source Comments #

Instance details

Defined in Proarrow.Object.Initial

Associated Types

type EqTypes '[HasInitialObject]
Instance details Defined in Proarrow.Object.Initial type EqTypes '[HasInitialObject] = '['EMB "B" :: FREE '[HasInitialObject] (Var '[HasInitialObject]), InitF :: FREE '[HasInitialObject] (Var '[HasInitialObject])]

Methods

laws :: [AssertEq '[HasInitialObject]] Source Comments #

Laws '[HasTerminalObject] Source Comments #

Instance details

Defined in Proarrow.Object.Terminal

Associated Types

type EqTypes '[HasTerminalObject]
Instance details Defined in Proarrow.Object.Terminal type EqTypes '[HasTerminalObject] = '['EMB "A" :: FREE '[HasTerminalObject] (Var '[HasTerminalObject]), TermF :: FREE '[HasTerminalObject] (Var '[HasTerminalObject])]

Methods

laws :: [AssertEq '[HasTerminalObject]] Source Comments #

data AssertEq (cs :: [Kind -> Constraint]) where Source Comments #

Constructors

(:=:) :: forall {cs :: [Kind -> Constraint]} (a :: FREE cs (Var cs)) (b :: FREE cs (Var cs)). (Elem a (EqTypes cs), Elem b (EqTypes cs)) => Free a b -> Free a b -> AssertEq cs infix 0

Instances

Instances details

Show2 (Var cs) => Show (AssertEq cs) Source Comments #
Instance details Defined in Proarrow.Tools.Laws Methods showsPrec :: Int -> AssertEq cs -> ShowS Comments # show :: AssertEq cs -> String Comments # showList :: [AssertEq cs] -> ShowS Comments #

data Place (as :: [k]) (a :: k) where Source Comments #

Constructors

Here :: forall {k} (a :: k) (as1 :: [k]). Place (a ': as1) a
There :: forall {k} (a :: k) (as1 :: [k]) (a1 :: k). Elem a as1 => Place (a1 ': as1) a

class Elem (c :: a) (cs :: [a]) where Source Comments #

Methods

place :: Place cs c Source Comments #

Instances

Instances details

Elem (c :: a) (c ': cs :: [a]) Source Comments #
Instance details Defined in Proarrow.Tools.Laws Methods place :: Place (c ': cs) c Source Comments #
Elem c cs => Elem (c :: a) (d ': cs :: [a]) Source Comments #
Instance details Defined in Proarrow.Tools.Laws Methods place :: Place (d ': cs) c Source Comments #

data Sym (a :: Symbol) (b :: Symbol) where Source Comments #

Constructors

Sym :: forall (a :: Symbol) (b :: Symbol). (KnownSymbol a, KnownSymbol b) => (a :~: b) -> Sym a b

Instances

Instances details

Promonad Sym Source Comments #
Instance details Defined in Proarrow.Tools.Laws Methods id :: forall (a :: Symbol). Ob a => Sym a a Source Comments # (.) :: forall (b :: Symbol) (c :: Symbol) (a :: Symbol). Sym b c -> Sym a b -> Sym a c Source Comments #
Profunctor Sym Source Comments #
Instance details Defined in Proarrow.Tools.Laws Methods dimap :: forall (c :: Symbol) (a :: Symbol) (b :: Symbol) (d :: Symbol). (c ~> a) -> (b ~> d) -> Sym a b -> Sym c d Source Comments # (\\) :: forall (a :: Symbol) (b :: Symbol) r. ((Ob a, Ob b) => r) -> Sym a b -> r Source Comments #

iso :: forall {cs :: [Kind -> Constraint]} (a :: FREE cs (Var cs)) (b :: FREE cs (Var cs)). (Elem a (EqTypes cs), Elem b (EqTypes cs), All cs (FREE cs (Var cs)), Typeable cs) => Free a b -> Free b a -> [AssertEq cs] Source Comments #

Orphan instances

CategoryOf Symbol Source Comments #

Instance details

Associated Types

type (~>)
Instance details Defined in Proarrow.Tools.Laws type (~>) = Sym
type Ob (a :: Symbol)
Instance details Defined in Proarrow.Tools.Laws type Ob (a :: Symbol) = KnownSymbol a