Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
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
setEmpty :: Set x
setUnion :: 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.

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 #
(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 #
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 #
LengthN (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods lengthN :: Set x -> N Source #
Ord x => POrd (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set Methods (<<=) :: Set x -> Set x -> Bool 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 #
(Entity x, Ord x) => Entity (Set x) Source #
Instance details Defined in OAlg.Entity.Sequence.Set

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.

Operations

setEmpty :: Set x Source #

the empty set.

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

the union 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 maximal the given length.

Propositions

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

validity for the union operator of sets.