Data.Graph

containers-0.6.2.1: Assorted concrete container types

Copyright | (c) The University of Glasgow 2002
License | BSD-style (see the file libraries/base/LICENSE)
Maintainer | libraries@haskell.org
Portability | portable
Safe Haskell | Safe
Language | Haskell98

Data.Graph

Contents

- Graphs
  - Graph Construction
  - Graph Properties
  - Graph Transformations
  - Graph Algorithms
- Strongly Connected Components
  - Construction
  - Conversion
- Trees

Description

# Finite Graphs

The ``Graph`` type is an adjacency list representation of a finite, directed graph with vertices of type `Int`.

The ``SCC`` type represents a strongly-connected component of a graph.

## Implementation

The implementation is based on

- Structuring Depth-First Search Algorithms in Haskell, by David King and John Launchbury, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.6526

Synopsis

- type Graph = Array Vertex [Vertex]
- type Bounds = (Vertex, Vertex)
- type Edge = (Vertex, Vertex)
- type Vertex = Int
- type Table a = Array Vertex a
- graphFromEdges :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key]), key -> Maybe Vertex)
- graphFromEdges' :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key]))
- buildG :: Bounds -> [Edge] -> Graph
- vertices :: Graph -> [Vertex]
- edges :: Graph -> [Edge]
- outdegree :: Graph -> Array Vertex Int
- indegree :: Graph -> Array Vertex Int
- transposeG :: Graph -> Graph
- dfs :: Graph -> [Vertex] -> Forest Vertex
- dff :: Graph -> Forest Vertex
- topSort :: Graph -> [Vertex]
- components :: Graph -> Forest Vertex
- scc :: Graph -> Forest Vertex
- bcc :: Graph -> Forest [Vertex]
- reachable :: Graph -> Vertex -> [Vertex]
- path :: Graph -> Vertex -> Vertex -> Bool
- data SCC vertex
  - = AcyclicSCC vertex
  - | CyclicSCC [vertex]
- stronglyConnComp :: Ord key => [(node, key, [key])] -> [SCC node]
- stronglyConnCompR :: Ord key => [(node, key, [key])] -> [SCC (node, key, [key])]
- flattenSCC :: SCC vertex -> [vertex]
- flattenSCCs :: [SCC a] -> [a]
- type Forest a = [Tree a]
- data Tree a = Node a (Forest a)

# Graphs

type Graph = Array Vertex [Vertex] Source #

Adjacency list representation of a graph, mapping each vertex to its list of successors.

type Bounds = (Vertex, Vertex) Source #

The bounds of an `Array`.

type Edge = (Vertex, Vertex) Source #

An edge from the first vertex to the second.

type Vertex = Int Source #

Abstract representation of vertices.

type Table a = Array Vertex a Source #

Table indexed by a contiguous set of vertices.

Note: This is included for backwards compatibility.

## Graph Construction

graphFromEdges :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key]), key -> Maybe Vertex) Source #

Build a graph from a list of nodes uniquely identified by keys, with a list of keys of nodes this node should have edges to.

This function takes an adjacency list representing a graph with vertices of type `key` labeled by values of type `node` and produces a `Graph`-based representation of that list. The `Graph` result represents the shape of the graph, and the functions describe a) how to retrieve the label and adjacent vertices of a given vertex, and b) how to retrive a vertex given a key.

    (graph, nodeFromVertex, vertexFromKey) = graphFromEdges edgeList

- `graph :: Graph` is the raw, array based adjacency list for the graph.
- `nodeFromVertex :: Vertex -> (node, key, [key])` returns the node associated with the given 0-based `Int` vertex; see warning below.
- `vertexFromKey :: key -> Maybe Vertex` returns the `Int` vertex for the key if it exists in the graph, `Nothing` otherwise.

To safely use this API you must either extract the list of vertices directly from the graph or first call `vertexFromKey k` to check if a vertex corresponds to the key `k`. Once it is known that a vertex exists you can use `nodeFromVertex` to access the labelled node and adjacent vertices. See below for examples.

Note: The out-list may contain keys that don't correspond to nodes of the graph; they are ignored.

Warning: The `nodeFromVertex` function will cause a runtime exception if the given `Vertex` does not exist.

#### Examples

Expand

An empty graph.

    (graph, nodeFromVertex, vertexFromKey) = graphFromEdges []
    graph = array (0,-1) []

A graph where the out-list references unspecified nodes (`'c'`), these are ignored.

    (graph, _, _) = graphFromEdges [("a", 'a', ['b']), ("b", 'b', ['c'])]
    array (0,1) [(0,[1]),(1,[])]

A graph with 3 vertices: ("a") -> ("b") -> ("c")

    (graph, nodeFromVertex, vertexFromKey) = graphFromEdges [("a", 'a', ['b']), ("b", 'b', ['c']), ("c", 'c', [])]
    graph == array (0,2) [(0,[1]),(1,[2]),(2,[])]
    nodeFromVertex 0 == ("a",'a',"b")
    vertexFromKey 'a' == Just 0

Get the label for a given key.

    let getNodePart (n, _, _) = n
    (graph, nodeFromVertex, vertexFromKey) = graphFromEdges [("a", 'a', ['b']), ("b", 'b', ['c']), ("c", 'c', [])]
    getNodePart . nodeFromVertex <$> vertexFromKey 'a' == Just "A"

graphFromEdges' :: Ord key => [(node, key, [key])] -> (Graph, Vertex -> (node, key, [key])) Source #

Identical to `graphFromEdges`, except that the return value does not include the function which maps keys to vertices. This version of `graphFromEdges` is for backwards compatibility.

buildG :: Bounds -> [Edge] -> Graph Source #

Build a graph from a list of edges.

Warning: This function will cause a runtime exception if a vertex in the edge list is not within the given `Bounds`.

#### Examples

Expand

    buildG (0,-1) [] == array (0,-1) []
    buildG (0,2) [(0,1), (1,2)] == array (0,1) [(0,[1]),(1,[2])]
    buildG (0,2) [(0,1), (0,2), (1,2)] == array (0,2) [(0,[2,1]),(1,[2]),(2,[])]

## Graph Properties

vertices :: Graph -> [Vertex] Source #

Returns the list of vertices in the graph.

#### Examples

Expand

    vertices (buildG (0,-1) []) == []

    vertices (buildG (0,2) [(0,1),(1,2)]) == [0,1,2]

edges :: Graph -> [Edge] Source #

Returns the list of edges in the graph.

#### Examples

Expand

    edges (buildG (0,-1) []) == []

    edges (buildG (0,2) [(0,1),(1,2)]) == [(0,1),(1,2)]

outdegree :: Graph -> Array Vertex Int Source #

A table of the count of edges from each node.

#### Examples

Expand

    outdegree (buildG (0,-1) []) == array (0,-1) []

    outdegree (buildG (0,2) [(0,1), (1,2)]) == array (0,2) [(0,1),(1,1),(2,0)]

indegree :: Graph -> Array Vertex Int Source #

A table of the count of edges into each node.

#### Examples

Expand

    indegree (buildG (0,-1) []) == array (0,-1) []

    indegree (buildG (0,2) [(0,1), (1,2)]) == array (0,2) [(0,0),(1,1),(2,1)]

## Graph Transformations

transposeG :: Graph -> Graph Source #

The graph obtained by reversing all edges.

#### Examples

Expand

    transposeG (buildG (0,2) [(0,1), (1,2)]) == array (0,2) [(0,[]),(1,[0]),(2,[1])]

## Graph Algorithms

dfs :: Graph -> [Vertex] -> Forest Vertex Source #

A spanning forest of the part of the graph reachable from the listed vertices, obtained from a depth-first search of the graph starting at each of the listed vertices in order.

dff :: Graph -> Forest Vertex Source #

A spanning forest of the graph, obtained from a depth-first search of the graph starting from each vertex in an unspecified order.

topSort :: Graph -> [Vertex] Source #

A topological sort of the graph. The order is partially specified by the condition that a vertex i precedes j whenever j is reachable from i but not vice versa.

components :: Graph -> Forest Vertex Source #

The connected components of a graph. Two vertices are connected if there is a path between them, traversing edges in either direction.

scc :: Graph -> Forest Vertex Source #

The strongly connected components of a graph, in reverse topological order.

#### Examples

Expand

    scc (buildG (0,3) [(3,1),(1,2),(2,0),(0,1)])
      == [Node {rootLabel = 0, subForest = [Node {rootLabel = 1, subForest = [Node {rootLabel = 2, subForest = []}]}]}
         ,Node {rootLabel = 3, subForest = []}]

bcc :: Graph -> Forest [Vertex] Source #

The biconnected components of a graph. An undirected graph is biconnected if the deletion of any vertex leaves it connected.

reachable :: Graph -> Vertex -> [Vertex] Source #

Returns the list of vertices reachable from a given vertex.

#### Examples

Expand

    reachable (buildG (0,0) []) 0 == [0]

    reachable (buildG (0,2) [(0,1), (1,2)]) 0 == [0,1,2]

path :: Graph -> Vertex -> Vertex -> Bool Source #

Returns `True` if the second vertex reachable from the first.

#### Examples

Expand

    path (buildG (0,0) []) 0 0 == True

    path (buildG (0,2) [(0,1), (1,2)]) 0 2 == True

    path (buildG (0,2) [(0,1), (1,2)]) 2 0 == False

# Strongly Connected Components

data SCC vertex Source #

Strongly connected component.

Constructors

AcyclicSCC vertex | A single vertex that is not in any cycle.
CyclicSCC [vertex] | A maximal set of mutually reachable vertices.

#### Instances

Instances details

Functor SCC # | Since: containers-0.5.4
Instance details Defined in Data.Graph Methods fmap :: (a -> b) -> SCC a -> SCC b Source # (<$) :: a -> SCC b -> SCC a Source #
Foldable SCC # | Since: containers-0.5.9
Instance details Defined in Data.Graph Methods fold :: Monoid m => SCC m -> m Source # foldMap :: Monoid m => (a -> m) -> SCC a -> m Source # foldMap' :: Monoid m => (a -> m) -> SCC a -> m Source # foldr :: (a -> b -> b) -> b -> SCC a -> b Source # foldr' :: (a -> b -> b) -> b -> SCC a -> b Source # foldl :: (b -> a -> b) -> b -> SCC a -> b Source # foldl' :: (b -> a -> b) -> b -> SCC a -> b Source # foldr1 :: (a -> a -> a) -> SCC a -> a Source # foldl1 :: (a -> a -> a) -> SCC a -> a Source # toList :: SCC a -> [a] Source # null :: SCC a -> Bool Source # length :: SCC a -> Int Source # elem :: Eq a => a -> SCC a -> Bool Source # maximum :: Ord a => SCC a -> a Source # minimum :: Ord a => SCC a -> a Source # sum :: Num a => SCC a -> a Source # product :: Num a => SCC a -> a Source #
Traversable SCC # | Since: containers-0.5.9
Instance details Defined in Data.Graph Methods traverse :: Applicative f => (a -> f b) -> SCC a -> f (SCC b) Source # sequenceA :: Applicative f => SCC (f a) -> f (SCC a) Source # mapM :: Monad m => (a -> m b) -> SCC a -> m (SCC b) Source # sequence :: Monad m => SCC (m a) -> m (SCC a) Source #
Eq1 SCC # | Since: containers-0.5.9
Instance details Defined in Data.Graph Methods liftEq :: (a -> b -> Bool) -> SCC a -> SCC b -> Bool Source #
Read1 SCC # | Since: containers-0.5.9
Instance details Defined in Data.Graph Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (SCC a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [SCC a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (SCC a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [SCC a] Source #
Show1 SCC # | Since: containers-0.5.9
Instance details Defined in Data.Graph Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> SCC a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [SCC a] -> ShowS Source #
Eq vertex => Eq (SCC vertex) # | Since: containers-0.5.9
Instance details Defined in Data.Graph Methods (==) :: SCC vertex -> SCC vertex -> Bool # (/=) :: SCC vertex -> SCC vertex -> Bool #
Data vertex => Data (SCC vertex) # | Since: containers-0.5.9
Instance details Defined in Data.Graph Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> SCC vertex -> c (SCC vertex) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (SCC vertex) Source # toConstr :: SCC vertex -> Constr Source # dataTypeOf :: SCC vertex -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (SCC vertex)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (SCC vertex)) Source # gmapT :: (forall b. Data b => b -> b) -> SCC vertex -> SCC vertex Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> SCC vertex -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> SCC vertex -> r Source # gmapQ :: (forall d. Data d => d -> u) -> SCC vertex -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> SCC vertex -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> SCC vertex -> m (SCC vertex) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> SCC vertex -> m (SCC vertex) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> SCC vertex -> m (SCC vertex) Source #
Read vertex => Read (SCC vertex) # | Since: containers-0.5.9
Instance details Defined in Data.Graph Methods readsPrec :: Int -> ReadS (SCC vertex) Source # readList :: ReadS [SCC vertex] Source # readPrec :: ReadPrec (SCC vertex) Source # readListPrec :: ReadPrec [SCC vertex] Source #
Show vertex => Show (SCC vertex) # | Since: containers-0.5.9
Instance details Defined in Data.Graph Methods showsPrec :: Int -> SCC vertex -> ShowS Source # show :: SCC vertex -> String Source # showList :: [SCC vertex] -> ShowS Source #
Generic (SCC vertex) # | Since: containers-0.5.9
Instance details Defined in Data.Graph Associated Types type Rep (SCC vertex) :: Type -> Type Source # Methods from :: SCC vertex -> Rep (SCC vertex) x Source # to :: Rep (SCC vertex) x -> SCC vertex Source #
NFData a => NFData (SCC a) # |
Instance details Defined in Data.Graph Methods rnf :: SCC a -> () Source #
Generic1 SCC # | Since: containers-0.5.9
Instance details Defined in Data.Graph Associated Types type Rep1 SCC :: k -> Type Source # Methods from1 :: forall (a :: k). SCC a -> Rep1 SCC a Source # to1 :: forall (a :: k). Rep1 SCC a -> SCC a Source #
type Rep (SCC vertex) # |
Instance details Defined in Data.Graph type Rep (SCC vertex) = D1 ('MetaData "SCC" "Data.Graph" "containers-0.6.2.1" 'False) (C1 ('MetaCons "AcyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 vertex)) :+: C1 ('MetaCons "CyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [vertex])))
type Rep1 SCC # |
Instance details Defined in Data.Graph type Rep1 SCC = D1 ('MetaData "SCC" "Data.Graph" "containers-0.6.2.1" 'False) (C1 ('MetaCons "AcyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: C1 ('MetaCons "CyclicSCC" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 [])))

## Construction

stronglyConnComp Source #

Arguments

:: Ord key |
=> [(node, key, [key])] | The graph: a list of nodes uniquely identified by keys, with a list of keys of nodes this node has edges to. The out-list may contain keys that don't correspond to nodes of the graph; such edges are ignored.
-> [SCC node] |

The strongly connected components of a directed graph, reverse topologically sorted.

#### Examples

Expand

    stronglyConnComp [("a",0,[1]),("b",1,[2,3]),("c",2,[1]),("d",3,[3])]
      == [CyclicSCC ["d"],CyclicSCC ["b","c"],AcyclicSCC "a"]

stronglyConnCompR Source #

Arguments

:: Ord key |
=> [(node, key, [key])] | The graph: a list of nodes uniquely identified by keys, with a list of keys of nodes this node has edges to. The out-list may contain keys that don't correspond to nodes of the graph; such edges are ignored.
-> [SCC (node, key, [key])] | Reverse topologically sorted

The strongly connected components of a directed graph, reverse topologically sorted. The function is the same as `stronglyConnComp`, except that all the information about each node retained. This interface is used when you expect to apply `SCC` to (some of) the result of `SCC`, so you don't want to lose the dependency information.

#### Examples

Expand

    stronglyConnCompR [("a",0,[1]),("b",1,[2,3]),("c",2,[1]),("d",3,[3])]
     == [CyclicSCC [("d",3,[3])],CyclicSCC [("b",1,[2,3]),("c",2,[1])],AcyclicSCC ("a",0,[1])]

## Conversion

flattenSCC :: SCC vertex -> [vertex] Source #

The vertices of a strongly connected component.

flattenSCCs :: [SCC a] -> [a] Source #

The vertices of a list of strongly connected components.

# Trees

type Forest a = [Tree a] Source #

data Tree a Source #

Non-empty, possibly infinite, multi-way trees; also known as rose trees.

Constructors

Node a (Forest a) |

#### Instances

Instances details

Monad Tree # |
Instance details Defined in Data.Tree Methods (>>=) :: Tree a -> (a -> Tree b) -> Tree b Source # (>>) :: Tree a -> Tree b -> Tree b Source # return :: a -> Tree a Source #
Functor Tree # |
Instance details Defined in Data.Tree Methods fmap :: (a -> b) -> Tree a -> Tree b Source # (<$) :: a -> Tree b -> Tree a Source #
MonadFix Tree # | Since: containers-0.5.11
Instance details Defined in Data.Tree Methods mfix :: (a -> Tree a) -> Tree a Source #
Applicative Tree # |
Instance details Defined in Data.Tree Methods pure :: a -> Tree a Source # (<*>) :: Tree (a -> b) -> Tree a -> Tree b Source # liftA2 :: (a -> b -> c) -> Tree a -> Tree b -> Tree c Source # (*>) :: Tree a -> Tree b -> Tree b Source # (<*) :: Tree a -> Tree b -> Tree a Source #
Foldable Tree # |
Instance details Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m Source # foldMap :: Monoid m => (a -> m) -> Tree a -> m Source # foldMap' :: Monoid m => (a -> m) -> Tree a -> m Source # foldr :: (a -> b -> b) -> b -> Tree a -> b Source # foldr' :: (a -> b -> b) -> b -> Tree a -> b Source # foldl :: (b -> a -> b) -> b -> Tree a -> b Source # foldl' :: (b -> a -> b) -> b -> Tree a -> b Source # foldr1 :: (a -> a -> a) -> Tree a -> a Source # foldl1 :: (a -> a -> a) -> Tree a -> a Source # toList :: Tree a -> [a] Source # null :: Tree a -> Bool Source # length :: Tree a -> Int Source # elem :: Eq a => a -> Tree a -> Bool Source # maximum :: Ord a => Tree a -> a Source # minimum :: Ord a => Tree a -> a Source # sum :: Num a => Tree a -> a Source # product :: Num a => Tree a -> a Source #
Traversable Tree # |
Instance details Defined in Data.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b) Source # sequenceA :: Applicative f => Tree (f a) -> f (Tree a) Source # mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b) Source # sequence :: Monad m => Tree (m a) -> m (Tree a) Source #
Eq1 Tree # | Since: containers-0.5.9
Instance details Defined in Data.Tree Methods liftEq :: (a -> b -> Bool) -> Tree a -> Tree b -> Bool Source #
Ord1 Tree # | Since: containers-0.5.9
Instance details Defined in Data.Tree Methods liftCompare :: (a -> b -> Ordering) -> Tree a -> Tree b -> Ordering Source #
Read1 Tree # | Since: containers-0.5.9
Instance details Defined in Data.Tree Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Tree a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Tree a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Tree a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Tree a] Source #
Show1 Tree # | Since: containers-0.5.9
Instance details Defined in Data.Tree Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Tree a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Tree a] -> ShowS Source #
MonadZip Tree # |
Instance details Defined in Data.Tree Methods mzip :: Tree a -> Tree b -> Tree (a, b) Source # mzipWith :: (a -> b -> c) -> Tree a -> Tree b -> Tree c Source # munzip :: Tree (a, b) -> (Tree a, Tree b) Source #
Eq a => Eq (Tree a) # |
Instance details Defined in Data.Tree Methods (==) :: Tree a -> Tree a -> Bool # (/=) :: Tree a -> Tree a -> Bool #
Data a => Data (Tree a) # |
Instance details Defined in Data.Tree Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Tree a -> c (Tree a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Tree a) Source # toConstr :: Tree a -> Constr Source # dataTypeOf :: Tree a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Tree a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Tree a)) Source # gmapT :: (forall b. Data b => b -> b) -> Tree a -> Tree a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Tree a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Tree a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Tree a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Tree a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Tree a -> m (Tree a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Tree a -> m (Tree a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Tree a -> m (Tree a) Source #
Read a => Read (Tree a) # |
Instance details Defined in Data.Tree Methods readsPrec :: Int -> ReadS (Tree a) Source # readList :: ReadS [Tree a] Source # readPrec :: ReadPrec (Tree a) Source # readListPrec :: ReadPrec [Tree a] Source #
Show a => Show (Tree a) # |
Instance details Defined in Data.Tree Methods showsPrec :: Int -> Tree a -> ShowS Source # show :: Tree a -> String Source # showList :: [Tree a] -> ShowS Source #
Generic (Tree a) # | Since: containers-0.5.8
Instance details Defined in Data.Tree Associated Types type Rep (Tree a) :: Type -> Type Source # Methods from :: Tree a -> Rep (Tree a) x Source # to :: Rep (Tree a) x -> Tree a Source #
NFData a => NFData (Tree a) # |
Instance details Defined in Data.Tree Methods rnf :: Tree a -> () Source #
Generic1 Tree # | Since: containers-0.5.8
Instance details Defined in Data.Tree Associated Types type Rep1 Tree :: k -> Type Source # Methods from1 :: forall (a :: k). Tree a -> Rep1 Tree a Source # to1 :: forall (a :: k). Rep1 Tree a -> Tree a Source #
type Rep (Tree a) # |
Instance details Defined in Data.Tree type Rep (Tree a) = D1 ('MetaData "Tree" "Data.Tree" "containers-0.6.2.1" 'False) (C1 ('MetaCons "Node" 'PrefixI 'True) (S1 ('MetaSel ('Just "rootLabel") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Just "subForest") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Forest a))))
type Rep1 Tree # |
Instance details Defined in Data.Tree type Rep1 Tree = D1 ('MetaData "Tree" "Data.Tree" "containers-0.6.2.1" 'False) (C1 ('MetaCons "Node" 'PrefixI 'True) (S1 ('MetaSel ('Just "rootLabel") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1 :*: S1 ('MetaSel ('Just "subForest") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) ([] :.: Rec1 Tree)))