Safe Haskell	Safe-Inferred
Language	Haskell2010

ConCat.Chain

Description

Category of linear operation sequences

Documentation

data Chain :: (* -> * -> *) -> * -> * -> * where Source #

Constructors

Nil :: Ok k a => Chain k a a
(:<) :: Ok3 k a b c => (a `k` b) -> Chain k b c -> Chain k a c infixr 5

Instances

Instances details

AssociativePCat k => AssociativePCat (Chain k) Source #
Instance details Defined in ConCat.Chain Methods lassocP :: Ok3 (Chain k) a b c => Chain k (Prod (Chain k) a (Prod (Chain k) b c)) (Prod (Chain k) (Prod (Chain k) a b) c) Source # rassocP :: Ok3 (Chain k) a b c => Chain k (Prod (Chain k) (Prod (Chain k) a b) c) (Prod (Chain k) a (Prod (Chain k) b c)) Source #
BraidedPCat k => BraidedPCat (Chain k) Source #
Instance details Defined in ConCat.Chain Methods swapP :: Ok2 (Chain k) a b => Chain k (Prod (Chain k) a b) (Prod (Chain k) b a) Source #
Category (Chain k) Source #
Instance details Defined in ConCat.Chain Associated Types type Ok (Chain k) :: Type -> Constraint Source # Methods id :: Ok (Chain k) a => Chain k a a Source # (.) :: forall b c a. Ok3 (Chain k) a b c => Chain k b c -> Chain k a b -> Chain k a c Source #
(MonoidalPCat k, BraidedPCat k) => MonoidalPCat (Chain k) Source #
Instance details Defined in ConCat.Chain Methods (***) :: Ok4 (Chain k) a b c d => Chain k a c -> Chain k b d -> Chain k (Prod (Chain k) a b) (Prod (Chain k) c d) Source # first :: forall a a' b. Ok3 (Chain k) a b a' => Chain k a a' -> Chain k (Prod (Chain k) a b) (Prod (Chain k) a' b) Source # second :: Ok3 (Chain k) a b b' => Chain k b b' -> Chain k (Prod (Chain k) a b) (Prod (Chain k) a b') Source #
ProductCat k => ProductCat (Chain k) Source #
Instance details Defined in ConCat.Chain Methods exl :: Ok2 (Chain k) a b => Chain k (Prod (Chain k) a b) a Source # exr :: Ok2 (Chain k) a b => Chain k (Prod (Chain k) a b) b Source # dup :: Ok (Chain k) a => Chain k a (Prod (Chain k) a a) Source #
TerminalCat k => TerminalCat (Chain k) Source #
Instance details Defined in ConCat.Chain Methods it :: Ok (Chain k) a => Chain k a (Unit (Chain k)) Source #
(BraidedPCat k, MProductCat k, TerminalCat k) => UnitCat (Chain k) Source #
Instance details Defined in ConCat.Chain Methods lunit :: Ok (Chain k) a => Chain k a (Prod (Chain k) (Unit (Chain k)) a) Source # lcounit :: Ok (Chain k) a => Chain k (Prod (Chain k) (Unit (Chain k)) a) a Source # runit :: Ok (Chain k) a => Chain k a (Prod (Chain k) a (Unit (Chain k))) Source # rcounit :: Ok (Chain k) a => Chain k (Prod (Chain k) a (Unit (Chain k))) a Source #
(OkProd k, NumCat k a) => NumCat (Chain k) a Source #
Instance details Defined in ConCat.Chain Methods negateC :: Chain k a a Source # addC :: Chain k (Prod (Chain k) a a) a Source # subC :: Chain k (Prod (Chain k) a a) a Source # mulC :: Chain k (Prod (Chain k) a a) a Source # powIC :: Chain k (Prod (Chain k) a Int) a Source #
Show2 k => Show (Chain k a b) Source #
Instance details Defined in ConCat.Chain Methods showsPrec :: Int -> Chain k a b -> ShowS Source # show :: Chain k a b -> String Source # showList :: [Chain k a b] -> ShowS Source #
type Ok (Chain k) Source #
Instance details Defined in ConCat.Chain type Ok (Chain k) = Ok k

evalChain :: Category k => Chain k a b -> a `k` b Source #

pureChain :: Ok2 k a b => (a `k` b) -> Chain k a b Source #

toList :: forall k z a b. (forall u v. (u `k` v) -> z) -> Chain k a b -> [z] Source #

(++*) :: Ok3 k a b c => Chain k a b -> Chain k b c -> Chain k a c infixr 5 Source #

data Exists2 k Source #

Constructors

forall a b. Exists2 (a `k` b)

Instances

Instances details

Show2 k => Show (Exists2 k) Source #
Instance details Defined in ConCat.Chain Methods showsPrec :: Int -> Exists2 k -> ShowS Source # show :: Exists2 k -> String Source # showList :: [Exists2 k] -> ShowS Source #