Safe Haskell	None
Language	GHC2021

Data.InternalQuiver.Path

Contents

Path

Synopsis

data Path v e where
- pattern Path :: v -> [e] -> v -> Path v e
- pattern EmptyPath :: v -> Path v e
- pattern NonEmptyPath :: e -> [e] -> Path v e
path :: (Eq v, IQuiver v e) => v -> [e] -> v -> Maybe (Path v e)
emptyPath :: v -> Path v e
singlePath :: IQuiver v e => e -> Path v e
composePath :: Eq v => Path v e -> Path v e -> Maybe (Path v e)
mapPath :: (IQuiver v' e', Eq v') => (v -> v') -> (e -> e') -> Path v e -> Maybe (Path v' e')
concatPath :: Path v (Path v e) -> Path v e
errPath :: (HasCallStack, Eq v, Show v, IQuiver v e) => v -> [e] -> v -> Path v e
errComposePath :: (HasCallStack, Show v, Eq v) => Path v e -> Path v e -> Path v e
errMapPath :: (HasCallStack, IQuiver v' e', Eq v') => (v -> v') -> (e -> e') -> Path v e -> Path v' e'
injectLeftPath :: Path v e -> Path (Either v w) (Either e f)
injectRightPath :: Path w f -> Path (Either v w) (Either e f)
separateSumPath :: Path (Either v w) (Either e f) -> Either (Path v e) (Path w f)
fstPath :: Path (v, w) (e, f) -> Path v e
sndPath :: Path (v, w) (e, f) -> Path w f
unsafePath :: v -> [e] -> v -> Path v e

Path

data Path v e where Source #

Bundled Patterns

pattern Path :: v -> [e] -> v -> Path v e
pattern EmptyPath :: v -> Path v e
pattern NonEmptyPath :: e -> [e] -> Path v e

Instances

Instances details

Show2 Path Source #
Instance details Defined in Data.InternalQuiver.Path Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Path a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Path a b] -> ShowS #
Eq ob => ICategory ob (Path ob mor) Source #	`Path` is the free category
Instance details Defined in Data.InternalCategory Methods foldPath :: Path ob (Path ob mor) -> Path ob mor Source # identity :: ob -> Path ob mor Source # compose :: Path ob mor -> Path ob mor -> Maybe (Path ob mor) Source #
IQuiver v (Path v e) Source #
Instance details Defined in Data.InternalQuiver.Path Methods src :: Path v e -> v Source # tgt :: Path v e -> v Source #
Show v => Show1 (Path v) Source #
Instance details Defined in Data.InternalQuiver.Path Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Path v a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Path v a] -> ShowS #
(Show v, Show e) => Show (Path v e) Source #
Instance details Defined in Data.InternalQuiver.Path Methods showsPrec :: Int -> Path v e -> ShowS # show :: Path v e -> String # showList :: [Path v e] -> ShowS #
(Eq e, Eq v) => Eq (Path v e) Source #
Instance details Defined in Data.InternalQuiver.Path Methods (==) :: Path v e -> Path v e -> Bool # (/=) :: Path v e -> Path v e -> Bool #
(Ord e, Ord v) => Ord (Path v e) Source #
Instance details Defined in Data.InternalQuiver.Path Methods compare :: Path v e -> Path v e -> Ordering # (<) :: Path v e -> Path v e -> Bool # (<=) :: Path v e -> Path v e -> Bool # (>) :: Path v e -> Path v e -> Bool # (>=) :: Path v e -> Path v e -> Bool # max :: Path v e -> Path v e -> Path v e # min :: Path v e -> Path v e -> Path v e #

Constructing path

path :: (Eq v, IQuiver v e) => v -> [e] -> v -> Maybe (Path v e) Source #

emptyPath :: v -> Path v e Source #

singlePath :: IQuiver v e => e -> Path v e Source #

composePath :: Eq v => Path v e -> Path v e -> Maybe (Path v e) Source #

mapPath :: (IQuiver v' e', Eq v') => (v -> v') -> (e -> e') -> Path v e -> Maybe (Path v' e') Source #

concatPath :: Path v (Path v e) -> Path v e Source #

Partial construction functions

errPath :: (HasCallStack, Eq v, Show v, IQuiver v e) => v -> [e] -> v -> Path v e Source #

errComposePath :: (HasCallStack, Show v, Eq v) => Path v e -> Path v e -> Path v e Source #

errMapPath :: (HasCallStack, IQuiver v' e', Eq v') => (v -> v') -> (e -> e') -> Path v e -> Path v' e' Source #

Sum and Product of paths

injectLeftPath :: Path v e -> Path (Either v w) (Either e f) Source #

injectRightPath :: Path w f -> Path (Either v w) (Either e f) Source #

separateSumPath :: Path (Either v w) (Either e f) -> Either (Path v e) (Path w f) Source #

fstPath :: Path (v, w) (e, f) -> Path v e Source #

sndPath :: Path (v, w) (e, f) -> Path w f Source #

Unsafe

unsafePath :: v -> [e] -> v -> Path v e Source #