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| Data.Relation.SetOfPairs | | Portability | portable | | Stability | experimental | | Maintainer | joost.visser@di.uminho.pt |
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| Description |
| An implementation of relations as sets of pairs.
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| Synopsis |
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| type Rel a b = Set (a, b) | | | emptyRel :: Rel a b | | | mkRel :: (Ord a, Ord b) => [(a, b)] -> Rel a b | | | identityRel :: Ord a => Set a -> Rel a a | | | totalRel :: Ord a => Set a -> Rel a a | | | chainRel :: (Enum n, Num n, Ord n) => n -> Rel n n | | | dom :: Ord a => Rel a b -> Set a | | | rng :: Ord b => Rel a b -> Set b | | | ent :: Ord a => Rel a a -> Set a | | | pairs :: (Ord a, Ord b) => Rel a b -> [(a, b)] | | | inv :: (Ord a, Ord b) => Rel a b -> Rel b a | | | comp :: (Ord a, Eq b, Ord c) => Rel b c -> Rel a b -> Rel a c | | | reflClose :: Ord a => Rel a a -> Rel a a | | | symmClose :: Ord a => Rel a a -> Rel a a | | | transClose :: Ord a => Rel a a -> Rel a a | | | reflTransClose :: Ord a => Rel a a -> Rel a a | | | equiv :: Ord b => Rel b b -> Rel b b | | | project :: (Ord a, Ord b) => Set a -> Rel a b -> Rel a b | | | projectBackward :: (Ord a, Ord b) => Set b -> Rel a b -> Rel a b | | | slice :: Ord a => Set a -> Rel a a -> Rel a a | | | sliceUntil :: Ord a => Set a -> Set a -> Rel a a -> Rel a a | | | sliceBackward :: Ord a => Set a -> Rel a a -> Rel a a | | | chop :: Ord a => Set a -> Set a -> Rel a a -> Rel a a |
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| Representation |
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| type Rel a b = Set (a, b) |
| Type of relations |
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| Building relations |
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| emptyRel :: Rel a b |
| Build an empty relation. |
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| mkRel :: (Ord a, Ord b) => [(a, b)] -> Rel a b |
| Build a relation from a list of pairs. |
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| identityRel :: Ord a => Set a -> Rel a a |
| Build identity relation, which contains an edge from each node to itself. |
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| totalRel :: Ord a => Set a -> Rel a a |
| Build total relation, which contains an edge from each node to
each other node and to itself. |
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| chainRel :: (Enum n, Num n, Ord n) => n -> Rel n n |
| Build a chain relation of given number of numerals. |
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| Basic operations |
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| dom :: Ord a => Rel a b -> Set a |
| Obtain the domain of a relation |
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| rng :: Ord b => Rel a b -> Set b |
| Obtain the range of a relation |
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| ent :: Ord a => Rel a a -> Set a |
| Obtain all entities in a relation (union of domain and range) |
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| pairs :: (Ord a, Ord b) => Rel a b -> [(a, b)] |
| Convert relation to a list of pairs. |
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| inv :: (Ord a, Ord b) => Rel a b -> Rel b a |
| Take the inverse of a relation |
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| comp :: (Ord a, Eq b, Ord c) => Rel b c -> Rel a b -> Rel a c |
| Compose two relations |
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| Closures |
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| reflClose :: Ord a => Rel a a -> Rel a a |
| Compute the reflective closure |
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| symmClose :: Ord a => Rel a a -> Rel a a |
| Compute the symmetric closure |
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| transClose :: Ord a => Rel a a -> Rel a a |
| Compute the transitive closure |
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| reflTransClose :: Ord a => Rel a a -> Rel a a |
| Compute the reflexive, transitive closure |
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| equiv :: Ord b => Rel b b -> Rel b b |
| Compute the reflexive, transitive, symmetric closure, i.e. the
induced equivalence relation. |
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| Selections (project, slice, chop) |
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| project :: (Ord a, Ord b) => Set a -> Rel a b -> Rel a b |
| Projection of set through relation |
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| projectBackward :: (Ord a, Ord b) => Set b -> Rel a b -> Rel a b |
| Projection of set backward through relation |
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| slice :: Ord a => Set a -> Rel a a -> Rel a a |
| Compute forward slice starting from seeds. |
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| sliceUntil :: Ord a => Set a -> Set a -> Rel a a -> Rel a a |
| Compute forward slice starting from seeds, stopping at stoppers. |
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| sliceBackward :: Ord a => Set a -> Rel a a -> Rel a a |
| Compute backward slice starting from seeds. |
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| chop :: Ord a => Set a -> Set a -> Rel a a -> Rel a a |
| Compute chop between seeds and sinks. |
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| Produced by Haddock version 0.6 |
