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Language	Haskell2010

Math.Graph.GraphMonoid

Contents

Orphan instances

Synopsis

data GraphElem v e
- = Vertex v
- | Edge e
data ReversibleGraphProp v e
- = VertexProp v
- | EdgeProp e
- | LoopProp e
- | OneLaneLoopProp e
- | BandProp e
mapGraphElem :: (v -> v') -> (e -> e') -> GraphElem v e -> GraphElem v' e'
eitherGraphElem :: (v -> w) -> (e -> w) -> GraphElem v e -> w
class (Category arr, Eq (arr a a), Monoid (arr a a)) => GraphMonoid arr a where
- gdom :: arr a a
- gcod :: arr a a
class GraphMonoid arr a => ReversibleGraphMonoid arr a where
- gnot :: arr a a
data Three b c where
- TId :: Three a a
- TDom :: Three a a
- TCod :: Three a a
three_action :: (g -> g) -> (g -> g) -> (g -> g) -> Three Bool Bool -> Endo g
three_action_arr :: ArrowChoice arr => arr g g -> arr g g -> arr g g -> Three Bool Bool -> arr g g
mappend_three :: Three b c -> Three a b -> Three a c
data Four a b where
- FId :: Four a a
- FDom :: Four a a
- FCod :: Four a a
- FNot :: Four a a
data Restricted (g :: * -> Constraint) a b where
- Restricted :: g a => a -> Restricted g a a
three_to_four :: Three a b -> Four a b
four_action_arr :: ArrowChoice arr => arr g g -> arr g g -> arr g g -> arr g g -> Four Bool Bool -> arr g g
four_action :: (g -> g) -> (g -> g) -> (g -> g) -> (g -> g) -> Four Bool Bool -> Endo g
sortPair :: Ord a => (a, a) -> (a, a)
mappend_four :: Four b c -> Four a b -> Four a c
vertexEndo :: m -> Endo a
optEndo :: Eq a => [(a, a)] -> Bool -> Endo a
edge :: a -> (a, a) -> Three Bool Bool -> a
edgeE :: e -> (v, v) -> Three Bool Bool -> GraphElem v e
bidirectionalEdge :: (f a, f a) -> (f a, f a) -> Four Bool Bool -> f a
bidirectionalEdgeE :: (e, e) -> (v, v) -> Four Bool Bool -> GraphElem v e
edgesFromMapArr :: (Ord a, ArrowChoice arr, FailureArrow arr String) => Map a (a, a) -> Three Bool Bool -> arr a a
edgesFromMapEndo :: Ord a => Map a (a, a) -> Three Bool Bool -> Endo a
edgesFromMapEndoE :: (Ord e, Ord v) => Map e (v, v) -> Three Bool Bool -> Endo (GraphElem v e)
loopEndo :: Ord a => [(a, a)] -> Three Bool Bool -> Endo a
loopEndoE :: (Ord v, Ord e) => [(v, e)] -> Three Bool Bool -> Endo (GraphElem v e)
reversibleOneLaneLoopEndoE :: (Ord v, Ord e) => [(v, e)] -> Four Bool Bool -> Endo (GraphElem v e)
reversibleLoopEndoE :: (Ord v, Ord e) => [(v, e, e)] -> Four Bool Bool -> Endo (GraphElem v e)
edgesArr :: (Eq a, ArrowChoice arr, FailureArrow arr String) => [(a, (a, a))] -> Three Bool Bool -> arr a a
edgesEndoE :: (Ord v, Ord e) => [(e, (v, v))] -> Three Bool Bool -> Endo (GraphElem v e)
edgesEndo :: Ord a => [(a, (a, a))] -> Three Bool Bool -> Endo a
edgesEndo' :: Eq a => [(a, (a, a))] -> Three Bool Bool -> Endo a
reversibleEdgesEndoE :: (Ord v, Ord e) => [((e, e), (v, v))] -> Four Bool Bool -> Endo (GraphElem v e)
reversibleEdgesEndo :: Ord a => [((a, a), (a, a))] -> Four Bool Bool -> Endo a
edgePairEndo :: (m -> Endo a) -> (n -> Endo b) -> (m, n) -> Endo (a, b)
mapEndo :: (a :==: b) -> Endo a :==: Endo b

Documentation

data GraphElem v e Source #

Constructors

Vertex v
Edge e

Instances

Instances details

(Data v, Data e) => Data (GraphElem v e) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> GraphElem v e -> c (GraphElem v e) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (GraphElem v e) # toConstr :: GraphElem v e -> Constr # dataTypeOf :: GraphElem v e -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (GraphElem v e)) # dataCast2 :: Typeable t => (forall d e0. (Data d, Data e0) => c (t d e0)) -> Maybe (c (GraphElem v e)) # gmapT :: (forall b. Data b => b -> b) -> GraphElem v e -> GraphElem v e # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> GraphElem v e -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> GraphElem v e -> r # gmapQ :: (forall d. Data d => d -> u) -> GraphElem v e -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> GraphElem v e -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> GraphElem v e -> m (GraphElem v e) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> GraphElem v e -> m (GraphElem v e) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> GraphElem v e -> m (GraphElem v e) #
(Read v, Read e) => Read (GraphElem v e) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods readsPrec :: Int -> ReadS (GraphElem v e) # readList :: ReadS [GraphElem v e] # readPrec :: ReadPrec (GraphElem v e) # readListPrec :: ReadPrec [GraphElem v e] #
(Show v, Show e) => Show (GraphElem v e) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods showsPrec :: Int -> GraphElem v e -> ShowS # show :: GraphElem v e -> String # showList :: [GraphElem v e] -> ShowS #
(PpShow v, PpShow e) => PpShow (GraphElem v e) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods pp :: GraphElem v e -> Doc Source #
(Eq v, Eq e) => Eq (GraphElem v e) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods (==) :: GraphElem v e -> GraphElem v e -> Bool # (/=) :: GraphElem v e -> GraphElem v e -> Bool #
(Ord v, Ord e) => Ord (GraphElem v e) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods compare :: GraphElem v e -> GraphElem v e -> Ordering # (<) :: GraphElem v e -> GraphElem v e -> Bool # (<=) :: GraphElem v e -> GraphElem v e -> Bool # (>) :: GraphElem v e -> GraphElem v e -> Bool # (>=) :: GraphElem v e -> GraphElem v e -> Bool # max :: GraphElem v e -> GraphElem v e -> GraphElem v e # min :: GraphElem v e -> GraphElem v e -> GraphElem v e #
(Ord v, Ord e) => DigraphFactory (Graph (Three :: Type -> Type -> Type) (GraphElem v e)) v e Source #
Instance details Defined in Math.Graph.Digraph Methods vertexGraph :: v -> Graph Three (GraphElem v e) Source # edgeGraph :: e -> v -> v -> Graph Three (GraphElem v e) Source # verticesFromSetGraph :: Set v -> Graph Three (GraphElem v e) Source # verticesGraph :: [v] -> Graph Three (GraphElem v e) Source # completeGraph :: [v] -> (v -> v -> e) -> Graph Three (GraphElem v e) Source # edgeGraphFromMap :: Map e (v, v) -> Graph Three (GraphElem v e) Source # edgesGraph :: [(e, (v, v))] -> Graph Three (GraphElem v e) Source # loopGraph :: [(v, e)] -> Graph Three (GraphElem v e) Source #
(Ord v, Ord e) => ReversibleGraphFactory (Graph (Four :: Type -> Type -> Type) (GraphElem v e)) v e Source #
Instance details Defined in Math.Graph.Digraph Methods reversibleVertexGraph :: v -> Graph Four (GraphElem v e) Source # reversibleVerticesGraph :: [v] -> Graph Four (GraphElem v e) Source # reversibleVerticesFromSetGraph :: Set v -> Graph Four (GraphElem v e) Source # reversibleEdgeGraph :: e -> e -> v -> v -> Graph Four (GraphElem v e) Source # reversibleCompleteGraph :: [v] -> (v -> v -> (e, e)) -> Graph Four (GraphElem v e) Source # reversibleEdgesGraph :: [((e, e), (v, v))] -> Graph Four (GraphElem v e) Source # reversibleLoopGraph :: [(v, e, e)] -> Graph Four (GraphElem v e) Source #

data ReversibleGraphProp v e Source #

Constructors

VertexProp v
EdgeProp e
LoopProp e
OneLaneLoopProp e
BandProp e

mapGraphElem :: (v -> v') -> (e -> e') -> GraphElem v e -> GraphElem v' e' Source #

eitherGraphElem :: (v -> w) -> (e -> w) -> GraphElem v e -> w Source #

class (Category arr, Eq (arr a a), Monoid (arr a a)) => GraphMonoid arr a where Source #

Methods

gdom :: arr a a Source #

gcod :: arr a a Source #

Instances

Instances details

GraphMonoid (Four :: Type -> Type -> Type) Bool Source #
Instance details Defined in Math.Graph.GraphMonoid Methods gdom :: Four Bool Bool Source # gcod :: Four Bool Bool Source #
GraphMonoid (Three :: Type -> Type -> Type) Bool Source #
Instance details Defined in Math.Graph.GraphMonoid Methods gdom :: Three Bool Bool Source # gcod :: Three Bool Bool Source #

class GraphMonoid arr a => ReversibleGraphMonoid arr a where Source #

Methods

gnot :: arr a a Source #

Instances

Instances details

ReversibleGraphMonoid (Four :: Type -> Type -> Type) Bool Source #
Instance details Defined in Math.Graph.GraphMonoid Methods gnot :: Four Bool Bool Source #

data Three b c where Source #

Constructors

TId :: Three a a
TDom :: Three a a
TCod :: Three a a

Instances

Instances details

Arrow arr => MonoidArrow (arr :: Type -> Type -> Type) (Three Bool Bool) Bool Source #
Instance details Defined in Math.Graph.GraphMonoid Methods monoidA :: Three Bool Bool -> arr Bool Bool Source #
Category (Three :: k -> k -> Type) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods id :: forall (a :: k0). Three a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). Three b c -> Three a b -> Three a c #
GraphMonoid (Three :: Type -> Type -> Type) Bool Source #
Instance details Defined in Math.Graph.GraphMonoid Methods gdom :: Three Bool Bool Source # gcod :: Three Bool Bool Source #
(Ord a, PpShow a) => Show (Graph (Three :: Type -> Type -> Type) a) Source #
Instance details Defined in Math.Graph.Show Methods showsPrec :: Int -> Graph Three a -> ShowS # show :: Graph Three a -> String # showList :: [Graph Three a] -> ShowS #
(Binary a, Ord a) => Binary (Graph (Three :: Type -> Type -> Type) a) Source #
Instance details Defined in Math.Graph.Show Methods put :: Graph Three a -> Put # get :: Get (Graph Three a) # putList :: [Graph Three a] -> Put #
(Ord a, PpShow a) => PpShow (Graph (Three :: Type -> Type -> Type) a) Source #
Instance details Defined in Math.Graph.Show Methods pp :: Graph Three a -> Doc Source #
(Ord v, Ord e) => DigraphFactory (Graph (Three :: Type -> Type -> Type) (GraphElem v e)) v e Source #
Instance details Defined in Math.Graph.Digraph Methods vertexGraph :: v -> Graph Three (GraphElem v e) Source # edgeGraph :: e -> v -> v -> Graph Three (GraphElem v e) Source # verticesFromSetGraph :: Set v -> Graph Three (GraphElem v e) Source # verticesGraph :: [v] -> Graph Three (GraphElem v e) Source # completeGraph :: [v] -> (v -> v -> e) -> Graph Three (GraphElem v e) Source # edgeGraphFromMap :: Map e (v, v) -> Graph Three (GraphElem v e) Source # edgesGraph :: [(e, (v, v))] -> Graph Three (GraphElem v e) Source # loopGraph :: [(v, e)] -> Graph Three (GraphElem v e) Source #
Data a => Data (Three a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Three a a -> c (Three a a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Three a a) # toConstr :: Three a a -> Constr # dataTypeOf :: Three a a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Three a a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Three a a)) # gmapT :: (forall b. Data b => b -> b) -> Three a a -> Three a a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Three a a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Three a a -> r # gmapQ :: (forall d. Data d => d -> u) -> Three a a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Three a a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Three a a -> m (Three a a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Three a a -> m (Three a a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Three a a -> m (Three a a) #
Monoid (Three a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods mempty :: Three a a # mappend :: Three a a -> Three a a -> Three a a # mconcat :: [Three a a] -> Three a a #
Semigroup (Three a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods (<>) :: Three a a -> Three a a -> Three a a # sconcat :: NonEmpty (Three a a) -> Three a a # stimes :: Integral b => b -> Three a a -> Three a a #
Show (Three a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods showsPrec :: Int -> Three a a -> ShowS # show :: Three a a -> String # showList :: [Three a a] -> ShowS #
Group (Three Bool Bool) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods ginvert :: Three Bool Bool -> Three Bool Bool Source #
PpShow (Three a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods pp :: Three a a -> Doc Source #
Universe (Three a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods all_elements :: [Three a a] Source #
Eq (Three a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods (==) :: Three a a -> Three a a -> Bool # (/=) :: Three a a -> Three a a -> Bool #
Ord (Three a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods compare :: Three a a -> Three a a -> Ordering # (<) :: Three a a -> Three a a -> Bool # (<=) :: Three a a -> Three a a -> Bool # (>) :: Three a a -> Three a a -> Bool # (>=) :: Three a a -> Three a a -> Bool # max :: Three a a -> Three a a -> Three a a # min :: Three a a -> Three a a -> Three a a #

three_action :: (g -> g) -> (g -> g) -> (g -> g) -> Three Bool Bool -> Endo g Source #

intent is that g =~= F Bool, where F : 2^{op} -> Set. But opposite categories are difficult to represent.

three_action_arr :: ArrowChoice arr => arr g g -> arr g g -> arr g g -> Three Bool Bool -> arr g g Source #

intent is that g =~= F Bool, where F : 2^{op} -> Set. But opposite categories are difficult to represent.

mappend_three :: Three b c -> Three a b -> Three a c Source #

data Four a b where Source #

Constructors

FId :: Four a a
FDom :: Four a a
FCod :: Four a a
FNot :: Four a a

Instances

Instances details

Category (Four :: k -> k -> Type) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods id :: forall (a :: k0). Four a a # (.) :: forall (b :: k0) (c :: k0) (a :: k0). Four b c -> Four a b -> Four a c #
GraphMonoid (Four :: Type -> Type -> Type) Bool Source #
Instance details Defined in Math.Graph.GraphMonoid Methods gdom :: Four Bool Bool Source # gcod :: Four Bool Bool Source #
ReversibleGraphMonoid (Four :: Type -> Type -> Type) Bool Source #
Instance details Defined in Math.Graph.GraphMonoid Methods gnot :: Four Bool Bool Source #
MonoidArrow (->) (Four Bool Bool) Bool Source #
Instance details Defined in Math.Graph.GraphMonoid Methods monoidA :: Four Bool Bool -> Bool -> Bool Source #
(Ord a, PpShow a) => Show (Graph (Four :: Type -> Type -> Type) a) Source #
Instance details Defined in Math.Graph.Show Methods showsPrec :: Int -> Graph Four a -> ShowS # show :: Graph Four a -> String # showList :: [Graph Four a] -> ShowS #
(Ord a, PpShow a) => PpShow (Graph (Four :: Type -> Type -> Type) a) Source #
Instance details Defined in Math.Graph.Show Methods pp :: Graph Four a -> Doc Source #
(Ord v, Ord e) => ReversibleGraphFactory (Graph (Four :: Type -> Type -> Type) (GraphElem v e)) v e Source #
Instance details Defined in Math.Graph.Digraph Methods reversibleVertexGraph :: v -> Graph Four (GraphElem v e) Source # reversibleVerticesGraph :: [v] -> Graph Four (GraphElem v e) Source # reversibleVerticesFromSetGraph :: Set v -> Graph Four (GraphElem v e) Source # reversibleEdgeGraph :: e -> e -> v -> v -> Graph Four (GraphElem v e) Source # reversibleCompleteGraph :: [v] -> (v -> v -> (e, e)) -> Graph Four (GraphElem v e) Source # reversibleEdgesGraph :: [((e, e), (v, v))] -> Graph Four (GraphElem v e) Source # reversibleLoopGraph :: [(v, e, e)] -> Graph Four (GraphElem v e) Source #
(Data a, Typeable a) => Data (Four a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Four a a -> c (Four a a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Four a a) # toConstr :: Four a a -> Constr # dataTypeOf :: Four a a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Four a a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Four a a)) # gmapT :: (forall b. Data b => b -> b) -> Four a a -> Four a a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Four a a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Four a a -> r # gmapQ :: (forall d. Data d => d -> u) -> Four a a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Four a a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Four a a -> m (Four a a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Four a a -> m (Four a a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Four a a -> m (Four a a) #
Monoid (Four Bool Bool) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods mempty :: Four Bool Bool # mappend :: Four Bool Bool -> Four Bool Bool -> Four Bool Bool # mconcat :: [Four Bool Bool] -> Four Bool Bool #
Semigroup (Four Bool Bool) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods (<>) :: Four Bool Bool -> Four Bool Bool -> Four Bool Bool # sconcat :: NonEmpty (Four Bool Bool) -> Four Bool Bool # stimes :: Integral b => b -> Four Bool Bool -> Four Bool Bool #
Show (Four a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods showsPrec :: Int -> Four a a -> ShowS # show :: Four a a -> String # showList :: [Four a a] -> ShowS #
Group (Four Bool Bool) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods ginvert :: Four Bool Bool -> Four Bool Bool Source #
PpShow (Four a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods pp :: Four a a -> Doc Source #
Universe (Four a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods all_elements :: [Four a a] Source #
Eq (Four a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods (==) :: Four a a -> Four a a -> Bool # (/=) :: Four a a -> Four a a -> Bool #
Ord (Four a a) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods compare :: Four a a -> Four a a -> Ordering # (<) :: Four a a -> Four a a -> Bool # (<=) :: Four a a -> Four a a -> Bool # (>) :: Four a a -> Four a a -> Bool # (>=) :: Four a a -> Four a a -> Bool # max :: Four a a -> Four a a -> Four a a # min :: Four a a -> Four a a -> Four a a #

data Restricted (g :: * -> Constraint) a b where Source #

Constructors

Restricted :: g a => a -> Restricted g a a

three_to_four :: Three a b -> Four a b Source #

four_action_arr :: ArrowChoice arr => arr g g -> arr g g -> arr g g -> arr g g -> Four Bool Bool -> arr g g Source #

intent is that g =~= F2, where F : 2^{op} -> Set. But opposite categories are difficult to represent.

four_action :: (g -> g) -> (g -> g) -> (g -> g) -> (g -> g) -> Four Bool Bool -> Endo g Source #

intent is that g =~= F2, where F : 2^{op} -> Set. But opposite categories are difficult to represent.

sortPair :: Ord a => (a, a) -> (a, a) Source #

mappend_four :: Four b c -> Four a b -> Four a c Source #

vertexEndo :: m -> Endo a Source #

optEndo :: Eq a => [(a, a)] -> Bool -> Endo a Source #

edge :: a -> (a, a) -> Three Bool Bool -> a Source #

edgeE :: e -> (v, v) -> Three Bool Bool -> GraphElem v e Source #

bidirectionalEdge :: (f a, f a) -> (f a, f a) -> Four Bool Bool -> f a Source #

bidirectionalEdgeE :: (e, e) -> (v, v) -> Four Bool Bool -> GraphElem v e Source #

edgesFromMapArr :: (Ord a, ArrowChoice arr, FailureArrow arr String) => Map a (a, a) -> Three Bool Bool -> arr a a Source #

edgesFromMapEndo :: Ord a => Map a (a, a) -> Three Bool Bool -> Endo a Source #

edgesFromMapEndoE :: (Ord e, Ord v) => Map e (v, v) -> Three Bool Bool -> Endo (GraphElem v e) Source #

loopEndo :: Ord a => [(a, a)] -> Three Bool Bool -> Endo a Source #

from list of (v_i,e_i), the loopEndo contains edges e_i : v_i -> v_i

loopEndoE :: (Ord v, Ord e) => [(v, e)] -> Three Bool Bool -> Endo (GraphElem v e) Source #

reversibleOneLaneLoopEndoE :: (Ord v, Ord e) => [(v, e)] -> Four Bool Bool -> Endo (GraphElem v e) Source #

reversibleLoopEndoE :: (Ord v, Ord e) => [(v, e, e)] -> Four Bool Bool -> Endo (GraphElem v e) Source #

edgesArr :: (Eq a, ArrowChoice arr, FailureArrow arr String) => [(a, (a, a))] -> Three Bool Bool -> arr a a Source #

edgesEndoE :: (Ord v, Ord e) => [(e, (v, v))] -> Three Bool Bool -> Endo (GraphElem v e) Source #

edgesEndo :: Ord a => [(a, (a, a))] -> Three Bool Bool -> Endo a Source #

edgesEndo' :: Eq a => [(a, (a, a))] -> Three Bool Bool -> Endo a Source #

reversibleEdgesEndoE :: (Ord v, Ord e) => [((e, e), (v, v))] -> Four Bool Bool -> Endo (GraphElem v e) Source #

reversibleEdgesEndo :: Ord a => [((a, a), (a, a))] -> Four Bool Bool -> Endo a Source #

edgePairEndo :: (m -> Endo a) -> (n -> Endo b) -> (m, n) -> Endo (a, b) Source #

mapEndo :: (a :==: b) -> Endo a :==: Endo b Source #

This is closest that the endomorphism is to a functor.

Orphan instances

FunctorArrow Endo (:==:) (:==:) Source #
Instance details Methods amap :: forall (c :: k) (d :: k). (c :==: d) -> Endo c :==: Endo d Source #
Eq (Endo Bool) Source #
Instance details Methods (==) :: Endo Bool -> Endo Bool -> Bool # (/=) :: Endo Bool -> Endo Bool -> Bool #
Eq (Bool -> Bool) Source #
Instance details Methods (==) :: (Bool -> Bool) -> (Bool -> Bool) -> Bool # (/=) :: (Bool -> Bool) -> (Bool -> Bool) -> Bool #