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

OAlg.Entity.Sequence.Set

Contents

Set
Operations
Lookup
X
Propositions

Description

sets of ordered entities.

Synopsis

newtype Set x = Set [x]
set :: Ord x => [x] -> Set x
setSpan :: Set x -> Span x
setxs :: Set x -> [x]
setSqc :: Ord x => (i -> Maybe x) -> Set i -> Set x
setMap :: Ord y => (x -> y) -> Set x -> Set y
isSubSet :: Ord x => Set x -> Set x -> Bool
setPower :: Set x -> Set (N, Set (Set x))
setFilter :: (x -> Bool) -> Set x -> Set x
setTakeN :: N -> Set x -> Set x
setEmpty :: Set x
setIsEmpty :: Set x -> Bool
setUnion :: Ord x => Set x -> Set x -> Set x
setIntersection :: Ord x => Set x -> Set x -> Set x
setDifference :: Ord x => Set x -> Set x -> Set x
setIndex :: Ord x => Set x -> x -> Maybe N
xSet :: Ord x => N -> X x -> X (Set x)
prpSetUnion :: (Ord x, Show x) => X (Set x) -> Statement

Set

newtype Set x Source #

set of ordered entities in x.

Property Let s = Set xs be in Set x for a ordered Entity type x, then holds:

For all ..x:y.. in xs holds: x < y.
lengthN s == lengthN xs.

Note The canonical ordering Ord and the subset ordering PartiallyOrdered are not equivalent.

Constructors

Set [x]

Instances

Instances details

Foldable Set Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # toList :: Set a -> [a] # null :: Set a -> Bool # length :: Set a -> Int # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # minimum :: Ord a => Set a -> a # sum :: Num a => Set a -> a # product :: Num a => Set a -> a #
Filterable Set Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods filter :: (x -> Bool) -> Set x -> Set x Source #
(Integral r, Enum r, Entity x, Ord x) => ConstructableSequence Set r x Source #
Instance details Defined in OAlg.Entity.Sequence.Definition Methods sequence :: (r -> Maybe x) -> Set r -> Set x Source # (<&) :: Set x -> Set r -> Set x Source #
(Integral r, Enum r) => Sequence Set r x Source #
Instance details Defined in OAlg.Entity.Sequence.Definition Methods graph :: p r -> Set x -> Graph r x Source # list :: p r -> Set x -> [(x, r)] Source # (??) :: Set x -> r -> Maybe x Source #
ApplicativeG Set (Map EntOrd) (->) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods amapG :: Map EntOrd x y -> Set x -> Set y Source #
ApplicativeG Set (Map Ord') (->) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods amapG :: Map Ord' x y -> Set x -> Set y Source #
FunctorialG Set (Map EntOrd) (->) Source #
Instance details Defined in OAlg.Entity.Sequence.Set
FunctorialG Set (Map Ord') (->) Source #
Instance details Defined in OAlg.Entity.Sequence.Set
Show x => Show (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods showsPrec :: Int -> Set x -> ShowS # show :: Set x -> String # showList :: [Set x] -> ShowS #
Eq x => Eq (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods (==) :: Set x -> Set x -> Bool # (/=) :: Set x -> Set x -> Bool #
Ord x => Ord (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods compare :: Set x -> Set x -> Ordering # (<) :: Set x -> Set x -> Bool # (<=) :: Set x -> Set x -> Bool # (>) :: Set x -> Set x -> Bool # (>=) :: Set x -> Set x -> Bool # max :: Set x -> Set x -> Set x # min :: Set x -> Set x -> Set x #
Ord x => Erasable (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods (//) :: Set x -> Set x -> Set x Source #
Ord x => Logical (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods (\|\|) :: Set x -> Set x -> Set x Source # (&&) :: Set x -> Set x -> Set x Source #
LengthN (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods lengthN :: Set x -> N Source #
(Validable x, Ord x, Show x) => Validable (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods valid :: Set x -> Statement Source #
Ord x => Lattice (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set
Ord x => Empty (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods empty :: Set x Source # isEmpty :: Set x -> Bool Source #
Ord x => PartiallyOrdered (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods (<<=) :: Set x -> Set x -> Bool Source #
(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 #
(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 #

set :: Ord x => [x] -> Set x Source #

makes a set from the given list.

setSpan :: Set x -> Span x Source #

the span of a set.

setxs :: Set x -> [x] Source #

the elements of a set.

setSqc :: Ord x => (i -> Maybe x) -> Set i -> Set x Source #

mapping a set.

setMap :: Ord y => (x -> y) -> Set x -> Set y Source #

mapping of sets.

Note This works only for finite sets!

isSubSet :: Ord x => Set x -> Set x -> Bool Source #

checks for being a sub set.

setPower :: Set x -> Set (N, Set (Set x)) Source #

the power set of a given set, grouped by there length.

setFilter :: (x -> Bool) -> Set x -> Set x Source #

filtering a set according to a given predicate.

setTakeN :: N -> Set x -> Set x Source #

takes the first n elements.

Operations

setEmpty :: Set x Source #

the empty set.

setIsEmpty :: Set x -> Bool Source #

checking for the empty set.

setUnion :: Ord x => Set x -> Set x -> Set x Source #

the union of two sets.

setIntersection :: Ord x => Set x -> Set x -> Set x Source #

intersection of two sets.

setDifference :: Ord x => Set x -> Set x -> Set x Source #

difference of two sets.

Lookup

setIndex :: Ord x => Set x -> x -> Maybe N Source #

the index of an element, where the elements of the given set are indexed from 0.

Examples

>>> setIndex (Set ['a'..'x']) 'c'
Just 2

X

xSet :: Ord x => N -> X x -> X (Set x) Source #

random variable of sets with a maximal length of the given length.

Propositions

prpSetUnion :: (Ord x, Show x) => X (Set x) -> Statement Source #

validity for the union operator of sets.