### Data.SetBy is the higher-order version of Data.Set

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 definition module Data.SetBy /** * An efficient implementation of sets. * * This version is the same as Data.Set, except that the overloaded API is replaced * with a higher-order function API. * * For all documentation, please consult Data.Set. * * The `morally equivalent` function from Data.Set is added in the comment. * * When using the functions in Data.SetBy, make sure to use the same higher-order * function parameter for the same data structure to ensure internal integrity. * This higher-order function represents the < ordering on your set elements and * should have the usual ordering properties: * * - if a < b and b < c then a < c * - if a < b then not (b < a) * - if not (a < b) and not (b < a) then a and b are considered to 'equal' * */ from StdOverloaded import class ==, class < (..) from StdClass import class Ord (..), <=, > from StdList import foldl, map from Data.Maybe import :: Maybe from StdBool import not, && from Data.GenLexOrd import :: LexOrd import qualified Data.Foldable from Data.Foldable import class Foldable :: SetBy a = TipBy | BinBy !Int !a !(SetBy a) !(SetBy a) instance == (SetBy a) | == a /** * True iff first set is `smaller` than second set, according to * first argument (assuming the two sets are ordered with the * same first function argument). * * Morally equivalent function: instance < (Set a) | < a */ isOrderedBy :: !(a a -> Bool) !(SetBy a) !(SetBy a) -> Bool /** * EQ iff the two sets have the same number of elements, occurring in the * same order. * LT iff the first set is the common prefix of the second set or the common * prefix is followed in the first set with an element that is considered * than the corresponding element in the second set. * GT iff the second set is the common prefix of the first set or the common * prefix is followed in the second set with an element that is considered * greater than the corresponding element in the first set. * The comparison of elements is done with the first function argument. * * Morally equivalent function: derive gLexOrd Set */ lexOrdBy :: !(a a -> Bool) !(SetBy a) !(SetBy a) -> LexOrd instance Foldable SetBy /** * True iff this is the empty set. * @type (SetBy a) -> Bool * @property equivalence with size 0: A.s :: SetBy a: * size s == 0 <==> null s * @property equivalence with newSet: A.s :: SetBy a: * s == newSetBy <==> null s */ null s :== case s of TipBy -> True (BinBy sz _ _ _) -> False /** * The number of elements in the set. * @type (SetBy a) -> Int * @property correctness: A.s :: SetBy a: * size s =.= length (toList s) */ size s :== case s of TipBy -> 0 (BinBy sz _ _ _) -> sz /** * Is the element in the set? * * Morally equivalent function: Data.Set.member x s = Data.SetBy.memberBy (<) x s */ memberBy :: !(a a -> Bool) !a !(SetBy a) -> Bool /** * Checks if an element is not in the set. */ notMemberBy comp x t :== not (memberBy comp x t) /** * Is t1 a subset of t2? * * Morally equivalent function: Data.Set.isSubsetOf s1 s2 = Data.SetBy.isSubsetOfBy (<) s1 s2 */ isSubsetOfBy comp t1 t2 :== (size t1 <= size t2) && (isSubsetOfXBy comp t1 t2) isSubsetOfXBy :: !(a a -> Bool) !(SetBy a) !(SetBy a) -> Bool /** * Is t1 a proper subset of t2? * * Morally equivalent function: Data.Set.isProperSubsetOf s1 s2 = Data.SetBy.isProperSubsetOfBy (<) s1 s2 */ isProperSubsetOfBy comp s1 s2 :== (size s1 < size s2) && (isSubsetOfBy comp s1 s2) /** * The empty set. * @complexity O(1) * @property is null: * null newSetBy */ newSetBy :: SetBy a /** * Create a singleton set. * @complexity O(1) */ singletonBy :: !u:a -> w:(SetBy u:a), [w <= u] /** * Insert an element in a set. If the set already contains an element equal to * the given value, it is replaced with the new value. * * Morally equivalent function: Data.Set.insert x s = Data.SetBy.insertBy (<) x s */ insertBy :: !(a a -> Bool) !a !.(SetBy a) -> SetBy a /** * Delete an element from a set. * * Morally equivalent function: Data.Set.delete x s = Data.SetBy (<) x s */ deleteBy :: !(a a -> Bool) !a !.(SetBy a) -> SetBy a /** * The minimal element of a set. * * Morally equivalent function: Data.Set.findMin */ findMin :: !(SetBy a) -> a /** * The maximal element of a set. * * Morally equivalent function: Data.Set.findMax */ findMax :: !(SetBy a) -> a /** * Delete the minimal element. * * Morally equivalent function: Data.Set.deleteMin */ deleteMin :: !.(SetBy a) -> SetBy a /** * Delete the maximal element. * * Morally equivalent function: Data.Set.deleteMax */ deleteMax :: !.(SetBy a) -> SetBy a /** * deleteFindMin set = (findMin set, deleteMin set) */ deleteFindMin :: !.(SetBy a) -> (!a, !SetBy a) /** * deleteFindMax set = (findMax set, deleteMax set) */ deleteFindMax :: !.(SetBy a) -> (!a, !SetBy a) /** * Retrieves the minimal key of the set, and the set stripped of that element, * or 'Nothing' if passed an empty set. */ minView :: !.(SetBy a) -> .(Maybe (!a, !SetBy a)) /** * Retrieves the maximal key of the set, and the set stripped of that element, * or 'Nothing' if passed an empty set. */ maxView :: !.(SetBy a) -> .(Maybe (!a, !SetBy a)) /** * The union of two sets, preferring the first set when equal elements are * encountered. * * Morally equivalent function: Data.Set.union s1 s2 = Data.SetBy.unionBy (<) s1 s2 */ unionBy :: !(a a -> Bool) !u:(SetBy a) !u:(SetBy a) -> SetBy a /** * The union of a list of sets. * * Morally equivalent function: Data.Set.unions ts = Data.SetBy.unionsBy (<) ts */ unionsBy ts :== foldl unionBy newSetBy ts /** * Difference of two sets. * * Morally equivalent function: Data.Set.difference s1 s2 = Data.SetBy.differenceBy (<) s1 s2 */ differenceBy :: !(a a -> Bool) !(SetBy a) !(SetBy a) -> SetBy a /** * The intersection of two sets. * Elements of the result come from the first set. * * Morally equivalent function: Data.Set.intersection s1 s2 = Data.SetBy.intersectionBy (<) s1 s2 */ intersectionBy :: !(a a -> Bool) !(SetBy a) !(SetBy a) -> SetBy a /** * The intersection of a list of sets. * Elements of the result come from the first set * * Morally equivalent function: Data.Set.intersections ts = Data.SetBy.intersectionsBy (<) ts */ intersectionsBy :: !(a a -> Bool) ![SetBy a] -> SetBy a /** * Filter all elements that satisfy the predicate. * * Morally equivalent function: Data.Set.filter */ filter :: !(a -> Bool) !(SetBy a) -> SetBy a /** * Partition the set into two sets, one with all elements that satisfy the * predicate and one with all elements that don't satisfy the predicate. * * Morally equivalent function: Data.Set.partition */ partition :: !(a -> Bool) !(SetBy a) -> (!SetBy a, !SetBy a) /** * Split a set in elements less and elements greater than a certain pivot. * * Morally equivalent function: Data.Set.split x s = Data.SetBy.splitBy (<) x s */ splitBy :: !(a a -> Bool) !a !(SetBy a) -> (!SetBy a, !SetBy a) /** * Performs a 'split' but also returns whether the pivot element was found in * the original set. * * Morally equivalent function: Data.Set.splitMember x s = Data.SetBy.splitMemberBy (<) x s */ splitMemberBy :: !(a a -> Bool) !a !(SetBy a) -> (!SetBy a, !Bool, !SetBy a) /** * Convert the set to an ascending list of elements. */ toList s :== toAscList s /** * Same as toList. */ toAscList t :== 'Data.Foldable'.foldr` (\a as -> [a:as]) [] t /** * Create a set from a list of elements. * * Morally equivalent function: Data.Set.fromList xs = Data.SetBy.fromListBy (<) xs */ fromListBy :: !(a a -> Bool) ![a] -> SetBy a /** * Map a function to all elements in a set. * * Morally equivalent function: Data.Set.mapSet f s = Data.SetBy.mapSetBy (<) f s */ mapSetBy comp_b f s :== fromListBy comp_b (map f (toList s)) /** * Map a set without converting it to and from a list. * * Morally equivalent function: Data.Set.mapSetMonotonic */ mapSetByMonotonic :: !(a -> b) !(SetBy a) -> SetBy b
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