Safe Haskell	Safe-Inferred
Language	Haskell2010

ConCat.Choice

Description

Indexed sets of morphisms

Synopsis

newtype Choice con a b = Choice (OptArg con (a -> b))
onChoice :: forall con a b q. con () => (forall p. con p => (p -> a -> b) -> q) -> Choice con a b -> q
exactly :: con () => (a -> b) -> Choice con a b
chooseC :: forall con p a b. (CartCon con, con p) => Choice con p (a -> b) -> Choice con a b
choose :: forall con p a. (CartCon con, con p) => (p -> a) -> a
op1C :: forall con a b c d. CartCon con => ((a -> b) -> c -> d) -> Choice con a b -> Choice con c d
op2C :: forall con a b c d e f. CartCon con => ((a -> b) -> (c -> d) -> e -> f) -> Choice con a b -> Choice con c d -> Choice con e f
data OptArg con z
- = NoArg z
- | forall p.con p => Arg (p -> z)
onOptArg :: forall con z q. con () => (forall p. con p => (p -> z) -> q) -> OptArg con z -> q
onOptArg' :: forall con z q. con () => (z -> q) -> (forall p. con p => (p -> z) -> q) -> OptArg con z -> q
type CartCon con = (con (), OpCon (:*) (Sat con))

Documentation

newtype Choice con a b Source #

Nondeterminism category. Like a set of morphisms all of the same type, but represented as a function whose range is that set. The function's domain is existentially hidden.

Constructors

Choice (OptArg con (a -> b))

Instances

Instances details

con () => BottomCat (Choice con :: Type -> Type -> Type) (a :: Type) (b :: Type) Source #
Instance details Defined in ConCat.Choice Methods bottomC :: Choice con a b Source #
(Integral a, Num b, con ()) => FromIntegralCat (Choice con :: Type -> Type -> Type) (a :: Type) (b :: Type) Source #
Instance details Defined in ConCat.Choice Methods fromIntegralC :: Choice con a b Source # foo_FromIntegralCat :: () Source #
con () => UnknownCat (Choice con :: Type -> Type -> Type) (a :: Type) (b :: Type) Source #
Instance details Defined in ConCat.Choice Methods unknownC :: Choice con a b Source #
(RepCat (->) a r, con ()) => RepCat (Choice con :: Type -> Type -> Type) (a :: Type) (r :: Type) Source #
Instance details Defined in ConCat.Choice Methods reprC :: Choice con a r Source # abstC :: Choice con r a Source #
CartCon con => BoolCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods notC :: Choice con (BoolOf (Choice con)) (BoolOf (Choice con)) Source # andC :: Choice con (Prod (Choice con) (BoolOf (Choice con)) (BoolOf (Choice con))) (BoolOf (Choice con)) Source # orC :: Choice con (Prod (Choice con) (BoolOf (Choice con)) (BoolOf (Choice con))) (BoolOf (Choice con)) Source # xorC :: Choice con (Prod (Choice con) (BoolOf (Choice con)) (BoolOf (Choice con))) (BoolOf (Choice con)) Source #
CartCon con => BraidedPCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods swapP :: Ok2 (Choice con) a b => Choice con (Prod (Choice con) a b) (Prod (Choice con) b a) Source #
CartCon con => BraidedSCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods swapS :: Ok2 (Choice con) a b => Choice con (Coprod (Choice con) a b) (Coprod (Choice con) b a) Source #
CartCon con => Category (Choice con) Source #
Instance details Defined in ConCat.Choice Associated Types type Ok (Choice con) :: Type -> Constraint Source # Methods id :: Ok (Choice con) a => Choice con a a Source # (.) :: forall b c a. Ok3 (Choice con) a b c => Choice con b c -> Choice con a b -> Choice con a c Source #
CartCon con => ClosedCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods apply :: Ok2 (Choice con) a b => Choice con (Prod (Choice con) (Exp (Choice con) a b) a) b Source # curry :: Ok3 (Choice con) a b c => Choice con (Prod (Choice con) a b) c -> Choice con a (Exp (Choice con) b c) Source # uncurry :: Ok3 (Choice con) a b c => Choice con a (Exp (Choice con) b c) -> Choice con (Prod (Choice con) a b) c Source #
CartCon con => CoproductCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods inl :: Ok2 (Choice con) a b => Choice con a (Coprod (Choice con) a b) Source # inr :: Ok2 (Choice con) a b => Choice con b (Coprod (Choice con) a b) Source # jam :: Ok (Choice con) a => Choice con (Coprod (Choice con) a a) a Source #
CartCon con => DistribCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods distl :: Ok3 (Choice con) a u v => Choice con (Prod (Choice con) a (Coprod (Choice con) u v)) (Coprod (Choice con) (Prod (Choice con) a u) (Prod (Choice con) a v)) Source # distr :: Ok3 (Choice con) u v b => Choice con (Prod (Choice con) (Coprod (Choice con) u v) b) (Coprod (Choice con) (Prod (Choice con) u b) (Prod (Choice con) v b)) Source #
CartCon con => MonoidalPCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods (***) :: Ok4 (Choice con) a b c d => Choice con a c -> Choice con b d -> Choice con (Prod (Choice con) a b) (Prod (Choice con) c d) Source # first :: forall a a' b. Ok3 (Choice con) a b a' => Choice con a a' -> Choice con (Prod (Choice con) a b) (Prod (Choice con) a' b) Source # second :: Ok3 (Choice con) a b b' => Choice con b b' -> Choice con (Prod (Choice con) a b) (Prod (Choice con) a b') Source #
CartCon con => MonoidalSCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods (+++) :: Ok4 (Choice con) a b c d => Choice con c a -> Choice con d b -> Choice con (Coprod (Choice con) c d) (Coprod (Choice con) a b) Source # left :: forall a a' b. Oks (Choice con) '[a, b, a'] => Choice con a a' -> Choice con (Coprod (Choice con) a b) (Coprod (Choice con) a' b) Source # right :: Oks (Choice con) '[a, b, b'] => Choice con b b' -> Choice con (Coprod (Choice con) a b) (Coprod (Choice con) a b') Source #
CartCon con => ProductCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods exl :: Ok2 (Choice con) a b => Choice con (Prod (Choice con) a b) a Source # exr :: Ok2 (Choice con) a b => Choice con (Prod (Choice con) a b) b Source # dup :: Ok (Choice con) a => Choice con a (Prod (Choice con) a a) Source #
CartCon con => TerminalCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods it :: Ok (Choice con) a => Choice con a (Unit (Choice con)) Source #
CartCon con => UnitCat (Choice con) Source #
Instance details Defined in ConCat.Choice Methods lunit :: Ok (Choice con) a => Choice con a (Prod (Choice con) (Unit (Choice con)) a) Source # lcounit :: Ok (Choice con) a => Choice con (Prod (Choice con) (Unit (Choice con)) a) a Source # runit :: Ok (Choice con) a => Choice con a (Prod (Choice con) a (Unit (Choice con))) Source # rcounit :: Ok (Choice con) a => Choice con (Prod (Choice con) a (Unit (Choice con))) a Source #
CartCon con => ConstCat (Choice con) b Source #
Instance details Defined in ConCat.Choice Methods const :: Ok (Choice con) a => b -> Choice con a (ConstObj (Choice con) b) Source # unitArrow :: b -> Choice con (Unit (Choice con)) (ConstObj (Choice con) b) Source #
(Enum a, CartCon con) => EnumCat (Choice con) a Source #
Instance details Defined in ConCat.Choice Methods succC :: Choice con a a Source # predC :: Choice con a a Source #
(Eq a, CartCon con) => EqCat (Choice con) a Source #
Instance details Defined in ConCat.Choice Methods equal :: Choice con (Prod (Choice con) a a) (BoolOf (Choice con)) Source # notEqual :: Choice con (Prod (Choice con) a a) (BoolOf (Choice con)) Source #
(Floating a, con ()) => FloatingCat (Choice con) a Source #
Instance details Defined in ConCat.Choice Methods expC :: Choice con a a Source # logC :: Choice con a a Source # cosC :: Choice con a a Source # sinC :: Choice con a a Source # sqrtC :: Choice con a a Source # tanhC :: Choice con a a Source #
(Fractional a, con ()) => FractionalCat (Choice con) a Source #
Instance details Defined in ConCat.Choice Methods recipC :: Choice con a a Source # divideC :: Choice con (Prod (Choice con) a a) a Source #
(CartCon con, Functor h) => FunctorCat (Choice con) h Source #
Instance details Defined in ConCat.Choice Methods fmapC :: Ok2 (Choice con) a b => Choice con a b -> Choice con (h a) (h b) Source # unzipC :: Ok2 (Choice con) a b => Choice con (h (a :* b)) (h a :* h b) Source #
CartCon con => IfCat (Choice con) a Source #
Instance details Defined in ConCat.Choice Methods ifC :: IfT (Choice con) a Source #
(Integral a, con ()) => IntegralCat (Choice con) a Source #
Instance details Defined in ConCat.Choice Methods divC :: Choice con (Prod (Choice con) a a) a Source # modC :: Choice con (Prod (Choice con) a a) a Source #
(Ord a, CartCon con) => MinMaxCat (Choice con) a Source #
Instance details Defined in ConCat.Choice Methods minC :: Choice con (Prod (Choice con) a a) a Source # maxC :: Choice con (Prod (Choice con) a a) a Source #
(Num a, CartCon con) => NumCat (Choice con) a Source #
Instance details Defined in ConCat.Choice Methods negateC :: Choice con a a Source # addC :: Choice con (Prod (Choice con) a a) a Source # subC :: Choice con (Prod (Choice con) a a) a Source # mulC :: Choice con (Prod (Choice con) a a) a Source # powIC :: Choice con (Prod (Choice con) a Int) a Source #
OkFunctor (Choice con) h Source #
Instance details Defined in ConCat.Choice Methods okFunctor :: Ok' (Choice con) a \|- Ok' (Choice con) (h a) Source #
(Ord a, CartCon con) => OrdCat (Choice con) a Source #
Instance details Defined in ConCat.Choice Methods lessThan :: Choice con (Prod (Choice con) a a) (BoolOf (Choice con)) Source # greaterThan :: Choice con (Prod (Choice con) a a) (BoolOf (Choice con)) Source # lessThanOrEqual :: Choice con (Prod (Choice con) a a) (BoolOf (Choice con)) Source # greaterThanOrEqual :: Choice con (Prod (Choice con) a a) (BoolOf (Choice con)) Source #
(Representable f, CartCon con) => RepresentableCat (Choice con) f Source #
Instance details Defined in ConCat.Choice Methods tabulateC :: Ok (Choice con) a => Choice con (Rep f -> a) (f a) Source # indexC :: Ok (Choice con) a => Choice con (f a) (Rep f -> a) Source #
(Zip h, CartCon con) => ZipCat (Choice con) h Source #
Instance details Defined in ConCat.Choice Methods zipC :: Ok2 (Choice con) a b => Choice con (h a :* h b) (h (a :* b)) Source #
(AddCat (->) h a, CartCon con) => AddCat (Choice con) h a Source #
Instance details Defined in ConCat.Choice Methods sumAC :: Choice con (h a) a Source #
(Distributive g, Functor f, CartCon con) => DistributiveCat (Choice con) g f Source #
Instance details Defined in ConCat.Choice Methods distributeC :: Ok (Choice con) a => Choice con (f (g a)) (g (f a)) Source #
(Pointed h, CartCon con) => PointedCat (Choice con) h a Source #
Instance details Defined in ConCat.Choice Methods pointC :: Choice con a (h a) Source #
(Integral b, RealFrac a, con ()) => RealFracCat (Choice con) a b Source #
Instance details Defined in ConCat.Choice Methods floorC :: Choice con a b Source # ceilingC :: Choice con a b Source # truncateC :: Choice con a b Source #
Newtype (Choice con a b) Source #
Instance details Defined in ConCat.Choice Associated Types type O (Choice con a b) Source # Methods pack :: O (Choice con a b) -> Choice con a b Source # unpack :: Choice con a b -> O (Choice con a b) Source #
type Ok (Choice con) Source #
Instance details Defined in ConCat.Choice type Ok (Choice con) = Yes1 :: Type -> Constraint
type O (Choice con a b) Source #
Instance details Defined in ConCat.Choice type O (Choice con a b) = OptArg con (a -> b)

onChoice :: forall con a b q. con () => (forall p. con p => (p -> a -> b) -> q) -> Choice con a b -> q Source #

exactly :: con () => (a -> b) -> Choice con a b Source #

Deterministic (trivially nondeterministic) arrow

chooseC :: forall con p a b. (CartCon con, con p) => Choice con p (a -> b) -> Choice con a b Source #

Generate any value of type p.

choose :: forall con p a. (CartCon con, con p) => (p -> a) -> a Source #

Generate any value of type p.

op1C :: forall con a b c d. CartCon con => ((a -> b) -> c -> d) -> Choice con a b -> Choice con c d Source #

op2C :: forall con a b c d e f. CartCon con => ((a -> b) -> (c -> d) -> e -> f) -> Choice con a b -> Choice con c d -> Choice con e f Source #

data OptArg con z Source #

Constructors

NoArg z
forall p.con p => Arg (p -> z)

Instances

Instances details

CartCon con => Applicative (OptArg con) Source #
Instance details Defined in ConCat.Choice Methods pure :: a -> OptArg con a Source # (<>) :: OptArg con (a -> b) -> OptArg con a -> OptArg con b Source # liftA2 :: (a -> b -> c) -> OptArg con a -> OptArg con b -> OptArg con c Source # (>) :: OptArg con a -> OptArg con b -> OptArg con b Source # (<*) :: OptArg con a -> OptArg con b -> OptArg con a Source #
CartCon con => Functor (OptArg con) Source #
Instance details Defined in ConCat.Choice Methods fmap :: (a -> b) -> OptArg con a -> OptArg con b Source # (<$) :: a -> OptArg con b -> OptArg con a Source #

onOptArg :: forall con z q. con () => (forall p. con p => (p -> z) -> q) -> OptArg con z -> q Source #

onOptArg' :: forall con z q. con () => (z -> q) -> (forall p. con p => (p -> z) -> q) -> OptArg con z -> q Source #

type CartCon con = (con (), OpCon (:*) (Sat con)) Source #