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

OAlg.Entity.Sequence.FSequence

Contents

FSequence
Form
Default Value
Proposition

Description

Total sequences according to a index with finite support, i.e only finite many values are not equal to the default value.

The implementation is optimized for:

retrieving the values by an index.
values which may have a very time consuming evaluation.

Synopsis

data FSequence (s :: Behavior) d i x
data Behavior
- = Strict
- | Lazy
fsqIsEmpty :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x) => FSequence s d i x -> Bool
fsqxs :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x) => FSequence s d i x -> [(x, i)]
fsqx :: forall d i x (s :: Behavior). (DefaultValue d i x, Ord i) => FSequence s d i x -> i -> x
fsqSpan :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x, Ord i) => FSequence s d i x -> Span i
fsqMin :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x, Ord i) => FSequence s d i x -> Closure i
fsqMax :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x, Ord i) => FSequence s d i x -> Closure i
fsqD :: forall (s :: Behavior) d i x. FSequence s d i x -> d
fsqForm :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x) => FSequence s d i x -> FSequenceForm d i x
fsqMakeStrict :: (DefaultValue d i x, Eq x) => FSequenceForm d i x -> FSequence 'Strict d i x
fsqMakeLazy :: FSequenceForm d i x -> FSequence 'Lazy d i x
fsqMap :: forall d i y x (s :: Behavior). (DefaultValue d i y, Eq y) => (x -> y) -> FSequence s d i x -> FSequence s d i y
fsqMapShift :: forall e i y d x (s :: Behavior). (DefaultValue e i y, Eq y, Number i) => (d -> e) -> i -> ((x, i) -> y) -> FSequence s d i x -> FSequence s e i y
fsqMapWithIndex :: forall e j y d i x (s :: Behavior). (DefaultValue e j y, Eq y) => (d -> e) -> Monotone i j -> ((x, i) -> y) -> FSequence s d i x -> FSequence s e j y
fsqMapWithIndexStrict :: (DefaultValue e j y, Eq y) => (d -> e) -> Monotone i j -> ((x, i) -> y) -> FSequence 'Strict d i x -> FSequence 'Strict e j y
fsqMapWithIndexLazy :: (d -> e) -> Monotone i j -> ((x, i) -> y) -> FSequence 'Lazy d i x -> FSequence 'Lazy e j y
fsqFilter :: forall x (s :: Behavior) d i. (x -> Bool) -> FSequence s d i x -> FSequence s d i x
data FSequenceForm d i x = FSequenceForm d (PSequence i x)
rdcFSequenceForm :: (DefaultValue d i x, Eq x) => FSequenceForm d i x -> FSequenceForm d i x
class DefaultValue d i x where
- defaultValue :: d -> i -> x
isDefaultValue :: (DefaultValue d i x, Eq x) => d -> (x, i) -> Bool
relHomogenRoot :: forall d i x (s :: Behavior). (DefaultValue d i x, Fibred x, Show i) => FSequence s d i x -> Statement
prpFSequenceSpan :: N -> Statement
prpFSequence :: Statement

FSequence

data FSequence (s :: Behavior) d i x Source #

total sequence according to the index i with finite support, i.e only finite many values are not equal to the default value according to a given index.

It comes with to flavors which defines the behavior of creating the sequence via make:

Strict: eliminates all default values from the form to create the sequence. In this case for example the testing of equality is efficient.

Lazy: takes all the values form the form to create the sequence. In this case for example the testing of equality is less efficient.

Both flavors have equal forms.

Instances

Instances details

Foldable (FSequence s d i) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Methods

fold :: Monoid m => FSequence s d i m -> m #

foldMap :: Monoid m => (a -> m) -> FSequence s d i a -> m #

foldMap' :: Monoid m => (a -> m) -> FSequence s d i a -> m #

foldr :: (a -> b -> b) -> b -> FSequence s d i a -> b #

foldr' :: (a -> b -> b) -> b -> FSequence s d i a -> b #

foldl :: (b -> a -> b) -> b -> FSequence s d i a -> b #

foldl' :: (b -> a -> b) -> b -> FSequence s d i a -> b #

foldr1 :: (a -> a -> a) -> FSequence s d i a -> a #

foldl1 :: (a -> a -> a) -> FSequence s d i a -> a #

toList :: FSequence s d i a -> [a] #

null :: FSequence s d i a -> Bool #

length :: FSequence s d i a -> Int #

elem :: Eq a => a -> FSequence s d i a -> Bool #

maximum :: Ord a => FSequence s d i a -> a #

minimum :: Ord a => FSequence s d i a -> a #

sum :: Num a => FSequence s d i a -> a #

product :: Num a => FSequence s d i a -> a #

(DefaultValue d i x, Eq x, Show d, Show i, Show x) => Show (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Methods

showsPrec :: Int -> FSequence s d i x -> ShowS #

show :: FSequence s d i x -> String #

showList :: [FSequence s d i x] -> ShowS #

(DefaultValue d i x, Eq d, Eq i, Eq x) => Eq (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Methods

(==) :: FSequence s d i x -> FSequence s d i x -> Bool #

(/=) :: FSequence s d i x -> FSequence s d i x -> Bool #

(DefaultValue d i x, Ord d, Ord i, Ord x) => Ord (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Methods

compare :: FSequence s d i x -> FSequence s d i x -> Ordering #

(<) :: FSequence s d i x -> FSequence s d i x -> Bool #

(<=) :: FSequence s d i x -> FSequence s d i x -> Bool #

(>) :: FSequence s d i x -> FSequence s d i x -> Bool #

(>=) :: FSequence s d i x -> FSequence s d i x -> Bool #

max :: FSequence s d i x -> FSequence s d i x -> FSequence s d i x #

min :: FSequence s d i x -> FSequence s d i x -> FSequence s d i x #

(DefaultValue d i x, Eq x) => Constructable (FSequence 'Lazy d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Methods

make :: Form (FSequence 'Lazy d i x) -> FSequence 'Lazy d i x Source #

(DefaultValue d i x, Eq x) => Constructable (FSequence 'Strict d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Methods

make :: Form (FSequence 'Strict d i x) -> FSequence 'Strict d i x Source #

(DefaultValue d i x, Eq x) => Exposable (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Associated Types

type Form (FSequence s d i x)
Instance details Defined in OAlg.Entity.Sequence.FSequence type Form (FSequence s d i x) = FSequenceForm d i x

Methods

form :: FSequence s d i x -> Form (FSequence s d i x) Source #

(Entity d, Entity i, Entity x, Ord i) => Validable (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Methods

valid :: FSequence s d i x -> Statement Source #

(DefaultValue d i x, Entity d, Entity i, Entity x, Ord i, Typeable s) => Fibred (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Methods

root :: FSequence s d i x -> Root (FSequence s d i x) Source #

Eq d => EqRoot (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Show d => ShowRoot (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Typeable d => TypeableRoot (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

Validable d => ValidableRoot (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

type Form (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

type Form (FSequence s d i x) = FSequenceForm d i x

type Root (FSequence s d i x) Source #

Instance details

Defined in OAlg.Entity.Sequence.FSequence

type Root (FSequence s d i x) = d

data Behavior Source #

the evaluation behavior of a FSequence.

Constructors

Strict
Lazy

Instances

Instances details

Enum Behavior Source #
Instance details Defined in OAlg.Entity.Sequence.FSequence Methods succ :: Behavior -> Behavior # pred :: Behavior -> Behavior # toEnum :: Int -> Behavior # fromEnum :: Behavior -> Int # enumFrom :: Behavior -> [Behavior] # enumFromThen :: Behavior -> Behavior -> [Behavior] # enumFromTo :: Behavior -> Behavior -> [Behavior] # enumFromThenTo :: Behavior -> Behavior -> Behavior -> [Behavior] #
Show Behavior Source #
Instance details Defined in OAlg.Entity.Sequence.FSequence Methods showsPrec :: Int -> Behavior -> ShowS # show :: Behavior -> String # showList :: [Behavior] -> ShowS #
Eq Behavior Source #
Instance details Defined in OAlg.Entity.Sequence.FSequence Methods (==) :: Behavior -> Behavior -> Bool # (/=) :: Behavior -> Behavior -> Bool #
Ord Behavior Source #
Instance details Defined in OAlg.Entity.Sequence.FSequence Methods compare :: Behavior -> Behavior -> Ordering # (<) :: Behavior -> Behavior -> Bool # (<=) :: Behavior -> Behavior -> Bool # (>) :: Behavior -> Behavior -> Bool # (>=) :: Behavior -> Behavior -> Bool # max :: Behavior -> Behavior -> Behavior # min :: Behavior -> Behavior -> Behavior #

fsqIsEmpty :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x) => FSequence s d i x -> Bool Source #

testing the first entry of being empty.

fsqxs :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x) => FSequence s d i x -> [(x, i)] Source #

the underlying list of non-default, indexed values,

fsqx :: forall d i x (s :: Behavior). (DefaultValue d i x, Ord i) => FSequence s d i x -> i -> x Source #

retrieving a value according to a given index.

fsqSpan :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x, Ord i) => FSequence s d i x -> Span i Source #

the support, i.e the minimal and the maximal index of the FSequence.

fsqMin :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x, Ord i) => FSequence s d i x -> Closure i Source #

the minimal index.

fsqMax :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x, Ord i) => FSequence s d i x -> Closure i Source #

the maxiaml index.

fsqD :: forall (s :: Behavior) d i x. FSequence s d i x -> d Source #

the underlying definition.

fsqForm :: forall d i x (s :: Behavior). (DefaultValue d i x, Eq x) => FSequence s d i x -> FSequenceForm d i x Source #

the underlying form.

fsqMakeStrict :: (DefaultValue d i x, Eq x) => FSequenceForm d i x -> FSequence 'Strict d i x Source #

makes a FSequence with a strict behavior.

fsqMakeLazy :: FSequenceForm d i x -> FSequence 'Lazy d i x Source #

makes a FSequence with a lazy behavior.

fsqMap :: forall d i y x (s :: Behavior). (DefaultValue d i y, Eq y) => (x -> y) -> FSequence s d i x -> FSequence s d i y Source #