Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	None
Language	Haskell2010

OAlg.Entity.Sequence.Graph

Contents

Graph
- Lattice
Conversions

Description

graphs of entities in x.

Synopsis

newtype Graph i x = Graph [(i, x)]
gphLength :: Graph i x -> N
gphxs :: Graph i x -> [(i, x)]
gphSqc :: (i -> Maybe x) -> Set i -> Graph i x
gphLookup :: Ord i => Graph i x -> i -> Maybe x
gphTakeN :: N -> Graph i x -> Graph i x
gphSetFilter :: (b -> Bool) -> Graph a (Set b) -> Graph a (Set b)
gphUnion :: (Ord a, Ord b) => Graph a (Set b) -> Graph a (Set b) -> Graph a (Set b)
gphIntersection :: (Ord a, Ord b) => Graph a (Set b) -> Graph a (Set b) -> Graph a (Set b)
gphDifference :: (Ord a, Ord b) => Graph a (Set b) -> Graph a (Set b) -> Graph a (Set b)
isSubGraph :: (Ord a, Ord b) => Graph a (Set b) -> Graph a (Set b) -> Bool
gphset :: Graph a (Set b) -> Set (a, b)
setgph :: Eq a => Set (a, b) -> Graph a (Set b)

Graph

newtype Graph i x Source #

mapping from an ordered index type i to a Entity type x.

Property Let g = Graph ixs be in Graph i x for a ordered Entity type i and Entity type x, then holds:

For all ..(i,_):(j,_).. in ixs holds: i < j.
lengthN g == lengthN ixs.

Constructors

Graph [(i, x)]

Instances

Instances details

Functor (Graph i) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods fmap :: (a -> b) -> Graph i a -> Graph i b # (<$) :: a -> Graph i b -> Graph i a #
Filterable (Graph i) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods filter :: (x -> Bool) -> Graph i x -> Graph i x Source #
(Entity x, Entity i, Ord i) => ConstructableSequence (Graph i) i x Source #
Instance details Defined in OAlg.Entity.Sequence.Definition Methods sequence :: (i -> Maybe x) -> Set i -> Graph i x Source # (<&) :: Graph i x -> Set i -> Graph i x Source #
Ord i => Sequence (Graph i) i x Source #
Instance details Defined in OAlg.Entity.Sequence.Definition Methods graph :: p i -> Graph i x -> Graph i x Source # list :: p i -> Graph i x -> [(x, i)] Source # (??) :: Graph i x -> i -> Maybe x Source #
(Show i, Show x) => Show (Graph i x) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods showsPrec :: Int -> Graph i x -> ShowS # show :: Graph i x -> String # showList :: [Graph i x] -> ShowS #
(Eq i, Eq x) => Eq (Graph i x) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods (==) :: Graph i x -> Graph i x -> Bool # (/=) :: Graph i x -> Graph i x -> Bool #
(Ord i, Ord x) => Ord (Graph i x) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods compare :: Graph i x -> Graph i x -> Ordering # (<) :: Graph i x -> Graph i x -> Bool # (<=) :: Graph i x -> Graph i x -> Bool # (>) :: Graph i x -> Graph i x -> Bool # (>=) :: Graph i x -> Graph i x -> Bool # max :: Graph i x -> Graph i x -> Graph i x # min :: Graph i x -> Graph i x -> Graph i x #
(Ord a, Ord b) => Erasable (Graph a (Set b)) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods (//) :: Graph a (Set b) -> Graph a (Set b) -> Graph a (Set b) Source #
(Ord a, Ord b) => Logical (Graph a (Set b)) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods (\|\|) :: Graph a (Set b) -> Graph a (Set b) -> Graph a (Set b) Source # (&&) :: Graph a (Set b) -> Graph a (Set b) -> Graph a (Set b) Source #
LengthN (Graph i x) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods lengthN :: Graph i x -> N Source #
(Entity x, Entity i, Ord i) => Validable (Graph i x) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods valid :: Graph i x -> Statement Source #
(Ord a, Ord b) => Lattice (Graph a (Set b)) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph
(Ord a, Ord b) => Empty (Graph a (Set b)) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods empty :: Graph a (Set b) Source # isEmpty :: Graph a (Set b) -> Bool Source #
(Ord a, Ord b) => PartiallyOrdered (Graph a (Set b)) Source #
Instance details Defined in OAlg.Entity.Sequence.Graph Methods (<<=) :: Graph a (Set b) -> Graph a (Set b) -> Bool Source #

gphLength :: Graph i x -> N Source #

the length of a graph.

gphxs :: Graph i x -> [(i, x)] Source #

the underlying associations.

gphSqc :: (i -> Maybe x) -> Set i -> Graph i x Source #

the induced graph given by a set of indices and a mapping.

gphLookup :: Ord i => Graph i x -> i -> Maybe x Source #

looks up the mapping of an index.

gphTakeN :: N -> Graph i x -> Graph i x Source #

takes the first n elements.

gphSetFilter :: (b -> Bool) -> Graph a (Set b) -> Graph a (Set b) Source #

filtering elements of the associated sets.

Lattice

gphUnion :: (Ord a, Ord b) => Graph a (Set b) -> Graph a (Set b) -> Graph a (Set b) Source #

the union of two graphs on sets.

gphIntersection :: (Ord a, Ord b) => Graph a (Set b) -> Graph a (Set b) -> Graph a (Set b) Source #

the intersection of two graphs on sets.

gphDifference :: (Ord a, Ord b) => Graph a (Set b) -> Graph a (Set b) -> Graph a (Set b) Source #

the difference of two graphs on sets.

isSubGraph :: (Ord a, Ord b) => Graph a (Set b) -> Graph a (Set b) -> Bool Source #

testing of being a sub graph.

Conversions

gphset :: Graph a (Set b) -> Set (a, b) Source #

converts a graph of sets to a set of pairs. The inverse is given by setgph.

Note

This works also with infinite graphs of sets.
It is not true that setgph and gphset are inverse in the strict sense, but almost, i.e. only in one restricts the graph to not empty associations. For example Graph [(1,Set []) :: Graph N (Set Char) and Graph [] :: Graph N (Set Char) both are mapped under gphset to Set [] :: Set (N,Char).

setgph :: Eq a => Set (a, b) -> Graph a (Set b) Source #

converts a set of pairs to a graph of sets. The inverse is given by gphset.

Note This works also with infinite sets of pairs..