OAlg.Entity.Sequence.PSequence

partially defined sequences of items in x with a totally ordered index type i.

Sequence

newtype PSequence i x

partially defined sequences (x0,i0),(x1,i1).. of index items in x with a totally ordered index type i.

Property Let PSequence xis be in PSequence i x then holds: i < j for all ..(_,i):(_,j).. in xis.

Examples

>>> PSequence [('a',3),('b',7),('c',12)] :: PSequence N Char
PSequence [('a',3),('b',7),('c',12)]

and

>>> validate (valid (PSequence [('a',3),('b',7),('c',12)] :: PSequence N Char))
Valid

but

>>> validate (valid (PSequence [('a',3),('b',15),('c',12)] :: PSequence N Char))
Invalid

as Char is a totally ordered type it can serve as index type

>>> validate (valid (PSequence [(12,'c'),(3,'e'),(8,'x')] :: PSequence Char Z))
Valid

and they admit a total right operation <* of Permutation i

>>> (PSequence [(12,'c'),(3,'e'),(8,'x')] :: PSequence Char Z) <* pmtSwap 'e' 'x'
PSequence [(12,'c'),(8,'e'),(3,'x')]

Note As we keep the constructor public, it is crucial for there further use to ensure that they are valid!

Constructors

PSequence [(x, i)]

Instances

Foldable (PSequence i)

Defined in OAlg.Entity.Sequence.PSequence

Methods

fold :: Monoid m => PSequence i m -> m

foldMap :: Monoid m => (a -> m) -> PSequence i a -> m

foldMap' :: Monoid m => (a -> m) -> PSequence i a -> m

foldr :: (a -> b -> b) -> b -> PSequence i a -> b

foldr' :: (a -> b -> b) -> b -> PSequence i a -> b

foldl :: (b -> a -> b) -> b -> PSequence i a -> b

foldl' :: (b -> a -> b) -> b -> PSequence i a -> b

foldr1 :: (a -> a -> a) -> PSequence i a -> a

foldl1 :: (a -> a -> a) -> PSequence i a -> a

toList :: PSequence i a -> [a]

null :: PSequence i a -> Bool

length :: PSequence i a -> Int

elem :: Eq a => a -> PSequence i a -> Bool

maximum :: Ord a => PSequence i a -> a

minimum :: Ord a => PSequence i a -> a

sum :: Num a => PSequence i a -> a

product :: Num a => PSequence i a -> a

Functor (PSequence i)

Defined in OAlg.Entity.Sequence.PSequence

Methods

fmap :: (a -> b) -> PSequence i a -> PSequence i b

(<$) :: a -> PSequence i b -> PSequence i a

(Entity x, Entity i, Ord i) => ConstructableSequence (PSequence i) i x

Defined in OAlg.Entity.Sequence.PSequence

Methods

sequence :: (i -> Maybe x) -> Set i -> PSequence i x

(<&) :: PSequence i x -> Set i -> PSequence i x

Ord i => Sequence (PSequence i) i x

Defined in OAlg.Entity.Sequence.PSequence

Methods

graph :: p i -> PSequence i x -> Graph i x

list :: p i -> PSequence i x -> [(x, i)]

(??) :: PSequence i x -> i -> Maybe x

(Entity x, Entity i, Ord i) => PermutableSequence (PSequence i) i x

Defined in OAlg.Entity.Sequence.Permutation

Methods

permuteBy :: p i -> (w -> w -> Ordering) -> (x -> w) -> PSequence i x -> (PSequence i x, Permutation i)

Embeddable [x] (PSequence N x)

Defined in OAlg.Entity.Sequence.PSequence

Methods

inj :: [x] -> PSequence N x

Projectible [x] (PSequence N x)

Defined in OAlg.Entity.Sequence.PSequence

Methods

prj :: PSequence N x -> [x]

Ord i => Opr (Permutation i) (PSequence i x)

Defined in OAlg.Entity.Sequence.Permutation

Methods

(<*) :: PSequence i x -> Permutation i -> PSequence i x

(Entity i, Ord i, Entity x) => TotalOpr (Permutation i) (PSequence i x)

Defined in OAlg.Entity.Sequence.Permutation

(Show x, Show i) => Show (PSequence i x)

Defined in OAlg.Entity.Sequence.PSequence

Methods

showsPrec :: Int -> PSequence i x -> ShowS

show :: PSequence i x -> String

showList :: [PSequence i x] -> ShowS

(Eq x, Eq i) => Eq (PSequence i x)

Defined in OAlg.Entity.Sequence.PSequence

Methods

(==) :: PSequence i x -> PSequence i x -> Bool

(/=) :: PSequence i x -> PSequence i x -> Bool

(Ord x, Ord i) => Ord (PSequence i x)

Defined in OAlg.Entity.Sequence.PSequence

Methods

compare :: PSequence i x -> PSequence i x -> Ordering

(<) :: PSequence i x -> PSequence i x -> Bool

(<=) :: PSequence i x -> PSequence i x -> Bool

(>) :: PSequence i x -> PSequence i x -> Bool

(>=) :: PSequence i x -> PSequence i x -> Bool

max :: PSequence i x -> PSequence i x -> PSequence i x

min :: PSequence i x -> PSequence i x -> PSequence i x

LengthN (PSequence i x)

Defined in OAlg.Entity.Sequence.PSequence

Methods

lengthN :: PSequence i x -> N

(Entity x, Entity i, Ord i) => Validable (PSequence i x)

Defined in OAlg.Entity.Sequence.PSequence

Methods

valid :: PSequence i x -> Statement

(Entity x, Entity i, Ord i) => Entity (PSequence i x)

Defined in OAlg.Entity.Sequence.PSequence

iProxy :: s i x -> Proxy i

proxy of the second type valiable i.

psqSpan :: Ord i => PSequence i x -> Span i

the span.

psqEmpty :: PSequence i x

the empty partially defined sequence.

psqIsEmpty :: PSequence i x -> Bool

checks of being empty.

psqxs :: PSequence i x -> [(x, i)]

the underlying list of indexed values.

psequence :: Ord i => (x -> x -> x) -> [(x, i)] -> PSequence i x

the partial sequenc given by a aggregation function an a list of value index pairs, which will be sorted and accordingly aggregated by thegiven aggregation function.

psqHead :: PSequence i x -> (x, i)

the head of a partial sequence.

psqTail :: PSequence i x -> PSequence i x

the tail.

psqMap :: (x -> y) -> PSequence i x -> PSequence i y

maps the entries, where the indices are preserved.

psqMapShift :: Number i => i -> ((x, i) -> y) -> PSequence i x -> PSequence i y

maps and shifts a partial sequence.

psqFilter :: (x -> Bool) -> PSequence i x -> PSequence i x

filters the partially defiend sequence accordingly the given predicate.

psqSplitWhile :: ((x, i) -> Bool) -> PSequence i x -> (PSequence i x, PSequence i x)

splits the sequence as long as the given predicate holds.

psqInterlace :: Ord i => (x -> y -> z) -> (x -> z) -> (y -> z) -> PSequence i x -> PSequence i y -> PSequence i z

interlaces the tow partially defined sequences according to the given mappings.

psqCompose :: (Ord i, Ord j) => PSequence i x -> PSequence j i -> PSequence j x

composition of the two partially defined sequences.

Property Let f be in PSequence i x and g be in PSequence j i then f `psqCompose` g is given by join . fmap ((??) f) . (??) g.

psqAppend :: PSequence i x -> PSequence i x -> PSequence i x

appends the second partially defined sequence to the first.

Property Let zs = psqAppend xs ys where ..(x,l) = xs and (y,f).. = ys then holds:

If

l < f

Then

zs is valid.

psqShear :: Ord i => (Maybe a -> Maybe a -> Maybe a, i) -> (Maybe a -> Maybe a -> Maybe a, i) -> PSequence i a -> PSequence i a

shears the two entries at the given position and leafs the others untouched.

Property Let x' = psqShear (sk,k) (sl,l) x, then holds

If

k < l

Then

1. x' k == sk (x k) (x l) and x' l == sl (x k) (x l).
2. x' i == x i for all i /= k, l.

psqSwap :: Ord i => i -> i -> PSequence i a -> PSequence i a

swaps the the k-th and the l-th entry.

Property Let x' = psqSwap k l x, then holds:

If

k < l

Then

1. x' k == x l and x' l == x k.
2. x' i == x i for all i /= k, l.

X

xPSequence :: Ord i => N -> N -> X x -> X i -> X (PSequence i x)

xPSequence n m random variable of partially defined sequences with maximal length min n m.