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Synopsis | ||||||||||||

Ranged Set Type | ||||||||||||

data RSet v | ||||||||||||

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rSetRanges :: RSet v -> [Range v] | ||||||||||||

Ranged Set construction functions and their Preconditions | ||||||||||||

makeRangedSet :: DiscreteOrdered v => [Range v] -> RSet v | ||||||||||||

Create a new Ranged Set from a list of ranges. The list may contain ranges that overlap or are not in ascending order. | ||||||||||||

unsafeRangedSet :: DiscreteOrdered v => [Range v] -> RSet v | ||||||||||||

Create a new Ranged Set from a list of ranges. validRangeList ranges
must return True. This precondition is not checked.
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validRangeList :: DiscreteOrdered v => [Range v] -> Bool | ||||||||||||

Determine if the ranges in the list are both in order and non-overlapping. If so then they are suitable input for the unsafeRangedSet function. | ||||||||||||

normaliseRangeList :: DiscreteOrdered v => [Range v] -> [Range v] | ||||||||||||

Rearrange and merge the ranges in the list so that they are in order and non-overlapping. | ||||||||||||

rSingleton :: DiscreteOrdered v => v -> RSet v | ||||||||||||

Create a Ranged Set from a single element. | ||||||||||||

Predicates | ||||||||||||

rSetIsEmpty :: DiscreteOrdered v => RSet v -> Bool | ||||||||||||

True if the set has no members. | ||||||||||||

(-?-) :: DiscreteOrdered v => RSet v -> v -> Bool | ||||||||||||

rSetHas :: DiscreteOrdered v => RSet v -> v -> Bool | ||||||||||||

True if the value is within the ranged set. Infix precedence is left 5. | ||||||||||||

(-<=-) :: DiscreteOrdered v => RSet v -> RSet v -> Bool | ||||||||||||

rSetIsSubset :: DiscreteOrdered v => RSet v -> RSet v -> Bool | ||||||||||||

True if the first argument is a subset of the second argument, or is equal. Infix precedence is left 5. | ||||||||||||

(-<-) :: DiscreteOrdered v => RSet v -> RSet v -> Bool | ||||||||||||

rSetIsSubsetStrict :: DiscreteOrdered v => RSet v -> RSet v -> Bool | ||||||||||||

True if the first argument is a strict subset of the second argument. Infix precedence is left 5. | ||||||||||||

Set Operations | ||||||||||||

(-\/-) :: DiscreteOrdered v => RSet v -> RSet v -> RSet v | ||||||||||||

rSetUnion :: DiscreteOrdered v => RSet v -> RSet v -> RSet v | ||||||||||||

Set union for ranged sets. Infix precedence is left 6. | ||||||||||||

(-/\-) :: DiscreteOrdered v => RSet v -> RSet v -> RSet v | ||||||||||||

rSetIntersection :: DiscreteOrdered v => RSet v -> RSet v -> RSet v | ||||||||||||

Set intersection for ranged sets. Infix precedence is left 7. | ||||||||||||

(-!-) :: DiscreteOrdered v => RSet v -> RSet v -> RSet v | ||||||||||||

rSetDifference :: DiscreteOrdered v => RSet v -> RSet v -> RSet v | ||||||||||||

Set difference. Infix precedence is left 6. | ||||||||||||

rSetNegation :: DiscreteOrdered a => RSet a -> RSet a | ||||||||||||

Set negation. | ||||||||||||

Useful Sets | ||||||||||||

rSetEmpty :: DiscreteOrdered a => RSet a | ||||||||||||

The empty set. | ||||||||||||

rSetFull :: DiscreteOrdered a => RSet a | ||||||||||||

The set that contains everything. | ||||||||||||

rSetUnfold | ||||||||||||

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QuickCheck Properties | ||||||||||||

Construction | ||||||||||||

A normalised range list is valid for unsafeRangedSet prop_validNormalised ls = validRangeList $ normaliseRangeList ls where types = ls :: [Range Double] Iff a value is in a range list then it is in a ranged set constructed from that list. prop_has ls v = (ls `rangeListHas` v) == rangedSet ls -?- v | ||||||||||||

Basic Operations | ||||||||||||

Iff a value is in either of two ranged sets then it is in the union of those two sets. prop_union rs1 rs2 v = (rs1 -?- v || rs2 -?- v) == ((rs1 -\/- rs2) -?- v) Iff a value is in both of two ranged sets then it is in the intersection of those two sets. prop_intersection rs1 rs2 v = (rs1 -?- v && rs2 -?- v) == ((rs1 -/\- rs2) -?- v) Iff a value is in ranged set 1 and not in ranged set 2 then it is in the difference of the two. prop_difference rs1 rs2 v = (rs1 -?- v && not (rs2 -?- v)) == ((rs1 -!- rs2) -?- v) Iff a value is not in a ranged set then it is in its negation. prop_negation rs v = rs -?- v == not (rSetNegation rs -?- v) A set that contains a value is not empty prop_not_empty rs v = (rs -?- v) ==> not (rSetIsEmpty rs) | ||||||||||||

Some Identities and Inequalities | ||||||||||||

The empty set has no members. prop_empty v = not (rSetEmpty -?- v) The full set has every member. prop_full v = rSetFull -?- v The intersection of a set with its negation is empty. prop_empty_intersection rs = rSetIsEmpty (rs -/\- rSetNegation rs) The union of a set with its negation is full. prop_full_union rs v = rSetIsFull (rs -\/- rSetNegation rs) The union of two sets is the non-strict superset of both. prop_union_superset rs1 rs2 = rs1 -<=- u && rs2 -<=- u where u = rs1 -\/- rs2 The intersection of two sets is the non-strict subset of both. prop_intersection_subset rs1 rs2 = i -<=- rs1 && i -<=- rs2 where i = rs1 -/\- rs2 The difference of two sets intersected with the subtractand is empty. prop_diff_intersect rs1 rs2 = rSetIsEmpty ((rs1 -!- rs2) -/\- rs2) A set is the non-strict subset of itself. prop_subset rs = rs -<=- rs A set is not the strict subset of itself. prop_strict_subset rs = not (rs -<- rs) If rs1 - rs2 is not empty then the union of rs1 and rs2 will be a strict superset of rs2. prop_union_strict_superset rs1 rs2 = (not $ rSetIsEmpty (rs1 -!- rs2)) ==> (rs2 -<- (rs1 -\/- rs2)) Intersection commutes prop_intersection_commutes rs1 rs2 = (rs1 -/\- rs2) == (rs2 -/\- rs1) Union commutes prop_union_commutes rs1 rs2 = (rs1 -\/- rs2) == (rs2 -\/- rs1) Intersection associates prop_intersection_associates rs1 rs2 rs3 = ((rs1 -/\- rs2) -/\- rs3) == (rs1 -/\- (rs2 -/\- rs3)) Union associates prop_union_associates rs1 rs2 rs3 = ((rs1 -\/- rs2) -\/- rs3) == (rs1 -\/- (rs2 -\/- rs3)) De Morgan's Law for Intersection prop_de_morgan_intersection rs1 rs2 = rSetNegation (rs1 -/\- rs2) == (rSetNegation rs1 -\/- rSetNegation rs2) De Morgan's Law for Union prop_de_morgan_union rs1 rs2 = rSetNegation (rs1 -\/- rs2) == (rSetNegation rs1 -/\- rSetNegation rs2) | ||||||||||||

Produced by Haddock version 0.8 |