Cabal-2.0.1.0: A framework for packaging Haskell software

Copyright | (c) Edward Z. Yang 2016
License | BSD3
Maintainer | cabal-dev@haskell.org
Stability | experimental
Portability | portable
Safe Haskell | None
Language | Haskell2010

Distribution.Compat.Graph

Contents

- Graph type
- Query
- Construction
- Combine
- Graph algorithms
- Conversions
  - Maps
  - Lists
  - Sets
  - Graphs
- Node type

Description

A data type representing directed graphs, backed by Data.Graph. It is strict in the node type.

This is an alternative interface to Data.Graph. In this interface, nodes (identified by the `IsNode` type class) are associated with a key and record the keys of their neighbors. This interface is more convenient than `Graph`, which requires vertices to be explicitly handled by integer indexes.

The current implementation has somewhat peculiar performance characteristics. The asymptotics of all map-like operations mirror their counterparts in Data.Map. However, to perform a graph operation, we first must build the Data.Graph representation, an operation that takes O(V + E log V). However, this operation can be amortized across all queries on that particular graph.

Some nodes may be broken, i.e., refer to neighbors which are not stored in the graph. In our graph algorithms, we transparently ignore such edges; however, you can easily query for the broken vertices of a graph using `broken` (and should, e.g., to ensure that a closure of a graph is well-formed.) It's possible to take a closed subset of a broken graph and get a well-formed graph.

Synopsis

- data Graph a
- class Ord (Key a) => IsNode a where
  - type Key a :: *
- null :: Graph a -> Bool
- size :: Graph a -> Int
- member :: IsNode a => Key a -> Graph a -> Bool
- lookup :: IsNode a => Key a -> Graph a -> Maybe a
- empty :: IsNode a => Graph a
- insert :: IsNode a => a -> Graph a -> Graph a
- deleteKey :: IsNode a => Key a -> Graph a -> Graph a
- deleteLookup :: IsNode a => Key a -> Graph a -> (Maybe a, Graph a)
- unionLeft :: IsNode a => Graph a -> Graph a -> Graph a
- unionRight :: IsNode a => Graph a -> Graph a -> Graph a
- stronglyConnComp :: Graph a -> [SCC a]
- data SCC vertex :: * -> *
  - = AcyclicSCC vertex
  - | CyclicSCC [vertex]
- cycles :: Graph a -> [[a]]
- broken :: Graph a -> [(a, [Key a])]
- neighbors :: Graph a -> Key a -> Maybe [a]
- revNeighbors :: Graph a -> Key a -> Maybe [a]
- closure :: Graph a -> [Key a] -> Maybe [a]
- revClosure :: Graph a -> [Key a] -> Maybe [a]
- topSort :: Graph a -> [a]
- revTopSort :: Graph a -> [a]
- toMap :: Graph a -> Map (Key a) a
- fromDistinctList :: (IsNode a, Show (Key a)) => [a] -> Graph a
- toList :: Graph a -> [a]
- keys :: Graph a -> [Key a]
- keysSet :: Graph a -> Set (Key a)
- toGraph :: Graph a -> (Graph, Vertex -> a, Key a -> Maybe Vertex)
- data Node k a = N a k [k]
- nodeValue :: Node k a -> a

# Graph type

data Graph a #

A graph of nodes `a`. The nodes are expected to have instance of class `IsNode`.

Instances

Foldable Graph # |

Methods

fold :: Monoid m => Graph m -> m Source #

foldMap :: Monoid m => (a -> m) -> Graph a -> m Source #

foldr :: (a -> b -> b) -> b -> Graph a -> b Source #

foldr' :: (a -> b -> b) -> b -> Graph a -> b Source #

foldl :: (b -> a -> b) -> b -> Graph a -> b Source #

foldl' :: (b -> a -> b) -> b -> Graph a -> b Source #

foldr1 :: (a -> a -> a) -> Graph a -> a Source #

foldl1 :: (a -> a -> a) -> Graph a -> a Source #

toList :: Graph a -> [a] Source #

null :: Graph a -> Bool Source #

length :: Graph a -> Int Source #

elem :: Eq a => a -> Graph a -> Bool Source #

maximum :: Ord a => Graph a -> a Source #

minimum :: Ord a => Graph a -> a Source #

sum :: Num a => Graph a -> a Source #

product :: Num a => Graph a -> a Source #

(Eq (Key a), Eq a) => Eq (Graph a) # |
Methods (==) :: Graph a -> Graph a -> Bool # (/=) :: Graph a -> Graph a -> Bool #
(IsNode a, Read a, Show (Key a)) => Read (Graph a) # |
Methods readsPrec :: Int -> ReadS (Graph a) Source # readList :: ReadS [Graph a] Source # readPrec :: ReadPrec (Graph a) Source # readListPrec :: ReadPrec [Graph a] Source #
Show a => Show (Graph a) # |
Methods showsPrec :: Int -> Graph a -> ShowS Source # show :: Graph a -> String Source # showList :: [Graph a] -> ShowS Source #
(NFData a, NFData (Key a)) => NFData (Graph a) # |
Methods rnf :: Graph a -> () Source #
(IsNode a, Binary a, Show (Key a)) => Binary (Graph a) # |
Methods put :: Graph a -> Put Source # get :: Get (Graph a) Source # putList :: [Graph a] -> Put Source #

class Ord (Key a) => IsNode a where #

The `IsNode` class is used for datatypes which represent directed graph nodes. A node of type `a` is associated with some unique key of type ``Key` a`; given a node we can determine its key (`nodeKey`) and the keys of its neighbors (`nodeNeighbors`).

Minimal complete definition

nodeKey, nodeNeighbors

Associated Types

type Key a :: * #

Methods

nodeKey :: a -> Key a #

nodeNeighbors :: a -> [Key a] #

Instances

IsNode InstalledPackageInfo # |
Associated Types type Key InstalledPackageInfo :: * # Methods nodeKey :: InstalledPackageInfo -> Key InstalledPackageInfo # nodeNeighbors :: InstalledPackageInfo -> [Key InstalledPackageInfo] #
IsNode ComponentLocalBuildInfo # |
Associated Types type Key ComponentLocalBuildInfo :: * # Methods nodeKey :: ComponentLocalBuildInfo -> Key ComponentLocalBuildInfo # nodeNeighbors :: ComponentLocalBuildInfo -> [Key ComponentLocalBuildInfo] #
IsNode TargetInfo # |
Associated Types type Key TargetInfo :: * # Methods nodeKey :: TargetInfo -> Key TargetInfo # nodeNeighbors :: TargetInfo -> [Key TargetInfo] #
(IsNode a, IsNode b, (~) * (Key a) (Key b)) => IsNode (Either a b) # |
Associated Types type Key (Either a b) :: * # Methods nodeKey :: Either a b -> Key (Either a b) # nodeNeighbors :: Either a b -> [Key (Either a b)] #
Ord k => IsNode (Node k a) # |
Associated Types type Key (Node k a) :: * # Methods nodeKey :: Node k a -> Key (Node k a) # nodeNeighbors :: Node k a -> [Key (Node k a)] #

# Query

null :: Graph a -> Bool #

O(1). Is the graph empty?

size :: Graph a -> Int #

O(1). The number of nodes in the graph.

member :: IsNode a => Key a -> Graph a -> Bool #

O(log V). Check if the key is in the graph.

lookup :: IsNode a => Key a -> Graph a -> Maybe a #

O(log V). Lookup the node at a key in the graph.

# Construction

empty :: IsNode a => Graph a #

O(1). The empty graph.

insert :: IsNode a => a -> Graph a -> Graph a #

O(log V). Insert a node into a graph.

deleteKey :: IsNode a => Key a -> Graph a -> Graph a #

O(log V). Delete the node at a key from the graph.

deleteLookup :: IsNode a => Key a -> Graph a -> (Maybe a, Graph a) #

O(log V). Lookup and delete. This function returns the deleted value if it existed.

# Combine

unionLeft :: IsNode a => Graph a -> Graph a -> Graph a #

O(V + V'). Left-biased union, preferring entries from the first map when conflicts occur.

unionRight :: IsNode a => Graph a -> Graph a -> Graph a #

O(V + V'). Right-biased union, preferring entries from the second map when conflicts occur. ``nodeKey` x = `nodeKey` (f x)`.

# Graph algorithms

stronglyConnComp :: Graph a -> [SCC a] #

Ω(V + E). Compute the strongly connected components of a graph. Requires amortized construction of graph.

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

Functor SCC |
Methods fmap :: (a -> b) -> SCC a -> SCC b Source # (<$) :: a -> SCC b -> SCC a Source #
Foldable SCC |

Methods

fold :: Monoid m => SCC m -> 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 |
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 |
Methods liftEq :: (a -> b -> Bool) -> SCC a -> SCC b -> Bool Source #
Read1 SCC |
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 |
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) |
Methods (==) :: SCC vertex -> SCC vertex -> Bool # (/=) :: SCC vertex -> SCC vertex -> Bool #
Data vertex => Data (SCC vertex) |

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 :: (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) |
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) |
Methods showsPrec :: Int -> SCC vertex -> ShowS Source # show :: SCC vertex -> String Source # showList :: [SCC vertex] -> ShowS Source #
Generic (SCC vertex) |
Associated Types type Rep (SCC vertex) :: * -> * Source # Methods from :: SCC vertex -> Rep (SCC vertex) x Source # to :: Rep (SCC vertex) x -> SCC vertex Source #
NFData a => NFData (SCC a) |
Methods rnf :: SCC a -> () Source #
Generic1 * SCC |
Associated Types type Rep1 SCC (f :: SCC -> *) :: k -> * Source # Methods from1 :: f a -> Rep1 SCC f a Source # to1 :: Rep1 SCC f a -> f a Source #
type Rep (SCC vertex) |
type Rep (SCC vertex) = D1 * (MetaData "SCC" "Data.Graph" "containers-0.5.10.2" False) ((:+:) * (C1 * (MetaCons "AcyclicSCC" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * vertex))) (C1 * (MetaCons "CyclicSCC" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * [vertex]))))
type Rep1 * SCC |
type Rep1 * SCC = D1 * (MetaData "SCC" "Data.Graph" "containers-0.5.10.2" False) ((:+:) * (C1 * (MetaCons "AcyclicSCC" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) (C1 * (MetaCons "CyclicSCC" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * []))))

cycles :: Graph a -> [[a]] #

Ω(V + E). Compute the cycles of a graph. Requires amortized construction of graph.

broken :: Graph a -> [(a, [Key a])] #

O(1). Return a list of nodes paired with their broken neighbors (i.e., neighbor keys which are not in the graph). Requires amortized construction of graph.

neighbors :: Graph a -> Key a -> Maybe [a] #

Lookup the immediate neighbors from a key in the graph. Requires amortized construction of graph.

revNeighbors :: Graph a -> Key a -> Maybe [a] #

Lookup the immediate reverse neighbors from a key in the graph. Requires amortized construction of graph.

closure :: Graph a -> [Key a] -> Maybe [a] #

Compute the subgraph which is the closure of some set of keys. Returns `Nothing` if one (or more) keys are not present in the graph. Requires amortized construction of graph.

revClosure :: Graph a -> [Key a] -> Maybe [a] #

Compute the reverse closure of a graph from some set of keys. Returns `Nothing` if one (or more) keys are not present in the graph. Requires amortized construction of graph.

topSort :: Graph a -> [a] #

Topologically sort the nodes of a graph. Requires amortized construction of graph.

revTopSort :: Graph a -> [a] #

Reverse topologically sort the nodes of a graph. Requires amortized construction of graph.

# Conversions

## Maps

toMap :: Graph a -> Map (Key a) a #

O(1). Convert a graph into a map from keys to nodes. The resulting map `m` is guaranteed to have the property that ``all` ((k,n) -> k == `nodeKey` n) (`toList` m)`.

## Lists

fromDistinctList :: (IsNode a, Show (Key a)) => [a] -> Graph a #

O(V log V). Convert a list of nodes (with distinct keys) into a graph.

toList :: Graph a -> [a] #

O(V). Convert a graph into a list of nodes.

keys :: Graph a -> [Key a] #

O(V). Convert a graph into a list of keys.

## Sets

keysSet :: Graph a -> Set (Key a) #

O(V). Convert a graph into a set of keys.

## Graphs

toGraph :: Graph a -> (Graph, Vertex -> a, Key a -> Maybe Vertex) #

O(1). Convert a graph into a `Graph`. Requires amortized construction of graph.

# Node type

data Node k a #

A simple, trivial data type which admits an `IsNode` instance.

Constructors

N a k [k] |

Instances

Functor (Node k) # |
Methods fmap :: (a -> b) -> Node k a -> Node k b Source # (<$) :: a -> Node k b -> Node k a Source #
(Eq k, Eq a) => Eq (Node k a) # |
Methods (==) :: Node k a -> Node k a -> Bool # (/=) :: Node k a -> Node k a -> Bool #
(Show k, Show a) => Show (Node k a) # |
Methods showsPrec :: Int -> Node k a -> ShowS Source # show :: Node k a -> String Source # showList :: [Node k a] -> ShowS Source #
Ord k => IsNode (Node k a) # |
Associated Types type Key (Node k a) :: * # Methods nodeKey :: Node k a -> Key (Node k a) # nodeNeighbors :: Node k a -> [Key (Node k a)] #
type Key (Node k a) # |
type Key (Node k a) = k

nodeValue :: Node k a -> a #

Get the value from a `Node`.