mirror of
https://github.com/GrammaticalFramework/gf-core.git
synced 2026-04-13 06:49:31 -06:00
131 lines
4.7 KiB
Haskell
131 lines
4.7 KiB
Haskell
----------------------------------------------------------------------
|
|
-- |
|
|
-- Module : Relation
|
|
-- Maintainer : BB
|
|
-- Stability : (stable)
|
|
-- Portability : (portable)
|
|
--
|
|
-- > CVS $Date: 2005/10/26 17:13:13 $
|
|
-- > CVS $Author: bringert $
|
|
-- > CVS $Revision: 1.1 $
|
|
--
|
|
-- A simple module for relations.
|
|
-----------------------------------------------------------------------------
|
|
|
|
module GF.Speech.Relation (Rel, mkRel, mkRel'
|
|
, allRelated , isRelatedTo
|
|
, transitiveClosure
|
|
, reflexiveClosure, reflexiveClosure_
|
|
, symmetricClosure
|
|
, symmetricSubrelation, reflexiveSubrelation
|
|
, reflexiveElements
|
|
, equivalenceClasses
|
|
, isTransitive, isReflexive, isSymmetric
|
|
, isEquivalence
|
|
, isSubRelationOf) where
|
|
|
|
import Data.List
|
|
import Data.Maybe
|
|
import Data.Map (Map)
|
|
import qualified Data.Map as Map
|
|
import Data.Set (Set)
|
|
import qualified Data.Set as Set
|
|
|
|
import GF.Data.Utilities
|
|
|
|
type Rel a = Map a (Set a)
|
|
|
|
-- | Creates a relation from a list of related pairs.
|
|
mkRel :: Ord a => [(a,a)] -> Rel a
|
|
mkRel ps = relates ps Map.empty
|
|
|
|
-- | Creates a relation from a list pairs of elements and the elements
|
|
-- related to them.
|
|
mkRel' :: Ord a => [(a,[a])] -> Rel a
|
|
mkRel' xs = Map.fromListWith Set.union [(x,Set.fromList ys) | (x,ys) <- xs]
|
|
|
|
relToList :: Rel a -> [(a,a)]
|
|
relToList r = [ (x,y) | (x,ys) <- Map.toList r, y <- Set.toList ys ]
|
|
|
|
-- | Add a pair to the relation.
|
|
relate :: Ord a => a -> a -> Rel a -> Rel a
|
|
relate x y r = Map.insertWith Set.union x (Set.singleton y) r
|
|
|
|
-- | Add a list of pairs to the relation.
|
|
relates :: Ord a => [(a,a)] -> Rel a -> Rel a
|
|
relates ps r = foldl (\r' (x,y) -> relate x y r') r ps
|
|
|
|
-- | Checks if an element is related to another.
|
|
isRelatedTo :: Ord a => Rel a -> a -> a -> Bool
|
|
isRelatedTo r x y = maybe False (y `Set.member`) (Map.lookup x r)
|
|
|
|
-- | Get the set of elements to which a given element is related.
|
|
allRelated :: Ord a => Rel a -> a -> Set a
|
|
allRelated r x = fromMaybe Set.empty (Map.lookup x r)
|
|
|
|
-- | Get all elements in the relation.
|
|
domain :: Ord a => Rel a -> Set a
|
|
domain r = foldl Set.union (Map.keysSet r) (Map.elems r)
|
|
|
|
-- | Keep only pairs for which both elements are in the given set.
|
|
intersectSetRel :: Ord a => Set a -> Rel a -> Rel a
|
|
intersectSetRel s = filterRel (\x y -> x `Set.member` s && y `Set.member` s)
|
|
|
|
transitiveClosure :: Ord a => Rel a -> Rel a
|
|
transitiveClosure r = fix (Map.map growSet) r
|
|
where growSet ys = foldl Set.union ys (map (allRelated r) $ Set.toList ys)
|
|
|
|
reflexiveClosure_ :: Ord a => [a] -- ^ The set over which the relation is defined.
|
|
-> Rel a -> Rel a
|
|
reflexiveClosure_ u r = relates [(x,x) | x <- u] r
|
|
|
|
-- | Uses 'domain'
|
|
reflexiveClosure :: Ord a => Rel a -> Rel a
|
|
reflexiveClosure r = reflexiveClosure_ (Set.toList $ domain r) r
|
|
|
|
symmetricClosure :: Ord a => Rel a -> Rel a
|
|
symmetricClosure r = relates [ (y,x) | (x,y) <- relToList r ] r
|
|
|
|
symmetricSubrelation :: Ord a => Rel a -> Rel a
|
|
symmetricSubrelation r = filterRel (flip $ isRelatedTo r) r
|
|
|
|
reflexiveSubrelation :: Ord a => Rel a -> Rel a
|
|
reflexiveSubrelation r = intersectSetRel (reflexiveElements r) r
|
|
|
|
-- | Get the set of elements which are related to themselves.
|
|
reflexiveElements :: Ord a => Rel a -> Set a
|
|
reflexiveElements r = Set.fromList [ x | (x,ys) <- Map.toList r, x `Set.member` ys ]
|
|
|
|
-- | Keep the related pairs for which the predicate is true.
|
|
filterRel :: Ord a => (a -> a -> Bool) -> Rel a -> Rel a
|
|
filterRel p = purgeEmpty . Map.mapWithKey (Set.filter . p)
|
|
|
|
-- | Remove keys that map to no elements.
|
|
purgeEmpty :: Ord a => Rel a -> Rel a
|
|
purgeEmpty r = Map.filter (not . Set.null) r
|
|
|
|
|
|
-- | Get the equivalence classes from an equivalence relation.
|
|
equivalenceClasses :: Ord a => Rel a -> [Set a]
|
|
equivalenceClasses r = equivalenceClasses_ (Map.keys r) r
|
|
where equivalenceClasses_ [] _ = []
|
|
equivalenceClasses_ (x:xs) r = ys:equivalenceClasses_ zs r
|
|
where ys = allRelated r x
|
|
zs = [x' | x' <- xs, not (x' `Set.member` ys)]
|
|
|
|
isTransitive :: Ord a => Rel a -> Bool
|
|
isTransitive r = and [z `Set.member` ys | (x,ys) <- Map.toList r,
|
|
y <- Set.toList ys, z <- Set.toList (allRelated r y)]
|
|
|
|
isReflexive :: Ord a => Rel a -> Bool
|
|
isReflexive r = all (\ (x,ys) -> x `Set.member` ys) (Map.toList r)
|
|
|
|
isSymmetric :: Ord a => Rel a -> Bool
|
|
isSymmetric r = and [isRelatedTo r y x | (x,y) <- relToList r]
|
|
|
|
isEquivalence :: Ord a => Rel a -> Bool
|
|
isEquivalence r = isReflexive r && isSymmetric r && isTransitive r
|
|
|
|
isSubRelationOf :: Ord a => Rel a -> Rel a -> Bool
|
|
isSubRelationOf r1 r2 = all (uncurry (isRelatedTo r2)) (relToList r1)
|