| Copyright | (c) NoviSci Inc 2020 |
|---|---|
| License | BSD3 |
| Maintainer | bsaul@novisci.com |
| Stability | experimental |
| Safe Haskell | None |
| Language | Haskell2010 |
IntervalAlgebra
Description
The IntervalAlgebra module provides data types and related classes for the
interval-based temporal logic described in Allen (1983)
and axiomatized in Allen and Hayes (1987).
A good primer on Allen's algebra can be found here.
Design
The module is built around four typeclasses designed to separate concerns of
constructing, relating, and combining types that contain Interval
IntervallicIntervalIntervalAlgebraicIntervalRelationsIntervalCombinableIntervalsIntervalSizeable
An advantage of nested typeclass design is that developers can define an
Intervala with just the amount of structure that they need.
Total Ordering of Intervals
The modules makes the (opinionated) choice of a total ordering for IntervallicIntervalbegins
then the ends.
Development
This module is under development and the API may change in the future.
Synopsis
- class Ord a => Intervallic i a where
- getInterval :: i a -> Interval a
- setInterval :: i a -> Interval a -> i a
- begin, end :: i a -> a
- class (Eq (i a), Intervallic i a) => IntervalAlgebraic i a where
- relate :: i a -> i a -> IntervalRelation (i a)
- predicate' :: IntervalRelation (i a) -> ComparativePredicateOf (i a)
- predicates :: Set (IntervalRelation (i a)) -> [ComparativePredicateOf (i a)]
- predicate :: Set (IntervalRelation (i a)) -> ComparativePredicateOf (i a)
- toSet :: [IntervalRelation (i a)] -> Set (IntervalRelation (i a))
- compose :: IntervalRelation (i a) -> IntervalRelation (i a) -> Set (IntervalRelation (i a))
- complement :: Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a))
- intersection :: Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a))
- union :: Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a))
- converse :: Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a))
- equals :: ComparativePredicateOf (i a)
- meets, metBy :: ComparativePredicateOf (i a)
- before, after :: ComparativePredicateOf (i a)
- overlaps, overlappedBy :: ComparativePredicateOf (i a)
- starts, startedBy :: ComparativePredicateOf (i a)
- precedes, precededBy :: ComparativePredicateOf (i a)
- finishes, finishedBy :: ComparativePredicateOf (i a)
- during, contains :: ComparativePredicateOf (i a)
- unionPredicates :: [ComparativePredicateOf (i a)] -> ComparativePredicateOf (i a)
- (<|>) :: ComparativePredicateOf (i a) -> ComparativePredicateOf (i a) -> ComparativePredicateOf (i a)
- disjointRelations :: Set (IntervalRelation (i a))
- withinRelations :: Set (IntervalRelation (i a))
- disjoint :: ComparativePredicateOf (i a)
- notDisjoint :: ComparativePredicateOf (i a)
- concur :: ComparativePredicateOf (i a)
- within :: ComparativePredicateOf (i a)
- enclose :: ComparativePredicateOf (i a)
- enclosedBy :: ComparativePredicateOf (i a)
- class (IntervalAlgebraic Interval a, Show a) => IntervalCombinable a where
- class (Show a, Ord a, Num b, Ord b) => IntervalSizeable a b | a -> b where
- moment :: b
- moment' :: Intervallic i a => i a -> b
- duration :: Intervallic i a => i a -> b
- add :: b -> a -> a
- diff :: a -> a -> b
- data Interval a
- parseInterval :: (Show a, Ord a) => a -> a -> Either String (Interval a)
- unsafeInterval :: a -> a -> Interval a
- data IntervalRelation a
- type ComparativePredicateOf a = a -> a -> Bool
- expand :: (IntervalSizeable a b, Intervallic i a) => b -> b -> i a -> i a
- expandl :: (IntervalSizeable a b, Intervallic i a) => b -> i a -> i a
- expandr :: (IntervalSizeable a b, Intervallic i a) => b -> i a -> i a
- beginerval :: IntervalSizeable a b => b -> a -> Interval a
- enderval :: IntervalSizeable a b => b -> a -> Interval a
- extenterval :: IntervalAlgebraic i a => i a -> i a -> Interval a
Classes
class Ord a => Intervallic i a where Source #
The IntervallicInterval content
of a data structure. It also includes functions for getting the beginend
Minimal complete definition
Methods
getInterval :: i a -> Interval a Source #
Get the interval from an i a
setInterval :: i a -> Interval a -> i a Source #
Set the interval in an i a
Access the ends of an i a .
Access the ends of an i a .
Instances
| (Ord a, Show a) => Intervallic Interval a Source # | |
| Ord a => Intervallic (PairedInterval b) a Source # | |
Defined in IntervalAlgebra.PairedInterval Methods getInterval :: PairedInterval b a -> Interval a Source # setInterval :: PairedInterval b a -> Interval a -> PairedInterval b a Source # begin :: PairedInterval b a -> a Source # end :: PairedInterval b a -> a Source # | |
class (Eq (i a), Intervallic i a) => IntervalAlgebraic i a where Source #
The IntervalAlgebraic'Interval a', plus other useful
utilities such as disjointwithinunionPredicates
Minimal complete definition
Nothing
Methods
relate :: i a -> i a -> IntervalRelation (i a) Source #
Compare two i a to determine their IntervalRelation.
predicate' :: IntervalRelation (i a) -> ComparativePredicateOf (i a) Source #
Maps an IntervalRelation to its corresponding predicate function.
predicates :: Set (IntervalRelation (i a)) -> [ComparativePredicateOf (i a)] Source #
Given a set of IntervalRelations return a list of predicate functions
corresponding to each relation.
predicate :: Set (IntervalRelation (i a)) -> ComparativePredicateOf (i a) Source #
Forms a predicate function from the union of a set of IntervalRelations.
toSet :: [IntervalRelation (i a)] -> Set (IntervalRelation (i a)) Source #
Shortcut to creating a 'Set IntervalRelation' from a list.
compose :: IntervalRelation (i a) -> IntervalRelation (i a) -> Set (IntervalRelation (i a)) Source #
Compose two interval relations according to the rules of the algebra. The rules are enumerated according to this table.
complement :: Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a)) Source #
Finds the complement of a 'Set IntervalRelation'.
intersection :: Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a)) Source #
Find the intersection of two Sets of IntervalRelations.
union :: Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a)) Source #
Find the union of two Sets of IntervalRelations.
converse :: Set (IntervalRelation (i a)) -> Set (IntervalRelation (i a)) Source #
Find the converse of a 'Set IntervalRelation'.
equals :: ComparativePredicateOf (i a) Source #
Does x equal y?
meets :: ComparativePredicateOf (i a) Source #
Does x meet y? Is y metBy x?
metBy :: ComparativePredicateOf (i a) Source #
Does x meet y? Is y metBy x?
before :: ComparativePredicateOf (i a) Source #
Is x before y? Is x after y?
after :: ComparativePredicateOf (i a) Source #
Is x before y? Is x after y?
overlaps :: ComparativePredicateOf (i a) Source #
Does x overlap y? Is x overlapped by y?
overlappedBy :: ComparativePredicateOf (i a) Source #
Does x overlap y? Is x overlapped by y?
starts :: ComparativePredicateOf (i a) Source #
Does x start y? Is x started by y?
startedBy :: ComparativePredicateOf (i a) Source #
Does x start y? Is x started by y?
precedes :: ComparativePredicateOf (i a) Source #
precededBy :: ComparativePredicateOf (i a) Source #
finishes :: ComparativePredicateOf (i a) Source #
Does x finish y? Is x finished by y?
finishedBy :: ComparativePredicateOf (i a) Source #
Does x finish y? Is x finished by y?
during :: ComparativePredicateOf (i a) Source #
Is x during y? Does x contain y?
contains :: ComparativePredicateOf (i a) Source #
Is x during y? Does x contain y?
unionPredicates :: [ComparativePredicateOf (i a)] -> ComparativePredicateOf (i a) Source #
Compose a list of interval relations with _or_ to create a new
ComparativePredicateOf i aunionPredicates [before, meets] creates a predicate function determining
if one interval is either before or meets another interval.
(<|>) :: ComparativePredicateOf (i a) -> ComparativePredicateOf (i a) -> ComparativePredicateOf (i a) Source #
Operator for composing the union of two predicates
disjointRelations :: Set (IntervalRelation (i a)) Source #
withinRelations :: Set (IntervalRelation (i a)) Source #
disjoint :: ComparativePredicateOf (i a) Source #
notDisjoint :: ComparativePredicateOf (i a) Source #
Are x and y not disjoint; i.e. do they share any support?
concur :: ComparativePredicateOf (i a) Source #
A synonym for notDisjoint.
within :: ComparativePredicateOf (i a) Source #
enclose :: ComparativePredicateOf (i a) Source #
Does x enclose y? That is, is y within x?
enclosedBy :: ComparativePredicateOf (i a) Source #
Synonym for within.
Instances
class (IntervalAlgebraic Interval a, Show a) => IntervalCombinable a where Source #
The IntervalCombinableIntervals
Minimal complete definition
Nothing
Methods
(.+.) :: Interval a -> Interval a -> Maybe (Interval a) Source #
(><) :: Interval a -> Interval a -> Maybe (Interval a) Source #
If x is before y, then form a new Just Interval a from the
interval in the "gap" between x and y from the end of x to the
begin of y. Otherwise, Nothing.
(<+>) :: (Semigroup (f (Interval a)), Applicative f) => Interval a -> Interval a -> f (Interval a) Source #
If x is before y, return f x appended to f y. Otherwise,
return extenterval of x and y (wrapped in f). This is useful for
(left) folding over an *ordered* container of Intervals and combining
intervals when x is *not* before y.
intersect :: Interval a -> Interval a -> Maybe (Interval a) Source #
Forms a Just new interval from the intersection of two intervals,
provided the intervals are not disjoint.
Instances
class (Show a, Ord a, Num b, Ord b) => IntervalSizeable a b | a -> b where Source #
The IntervalSizeable typeclass provides functions to determine the size of an
Intervallic type and to resize an 'Interval a'.
Methods
The smallest duration for an 'Interval a'.
moment' :: Intervallic i a => i a -> b Source #
Gives back a moment based on the input's type.
duration :: Intervallic i a => i a -> b Source #
Determine the duration of an 'i a'.
Shifts an a. Most often, the b will be the same type as a.
But for example, if a is Day then b could be Int.
Takes the difference between two a to return a b.
Types
An Interval aas \( (x, y) \text{ where } x < y\). The
IntervallicparseIntervalLeftunsafeInterval as constructor for creating an
interval that may not be valid.
Instances
parseInterval :: (Show a, Ord a) => a -> a -> Either String (Interval a) Source #
Safely parse a pair of as to create an Interval a
unsafeInterval :: a -> a -> Interval a Source #
Create a new Interval a
data IntervalRelation a Source #
The IntervalRelation type enumerates the thirteen possible ways that two
Interval a
Meets, Metby
x `meets` y y `metBy` x
x: |-----| y: |-----|
Before, After
x `before` y y `after` x
x: |-----| y: |-----|
Overlaps, OverlappedBy
x `overlaps` y y `overlappedBy` x
x: |-----| y: |-----|
Starts, StartedBy
x `starts` y y `startedBy` x
x: |---| y: |-----|
Finishes, FinishedBy
x `finishes` y y `finishedBy` x
x: |---| y: |-----|
During, Contains
x `during` y y `contains` x
x: |-| y: |-----|
Equal
x `equal` y y `equal` x
x: |-----| y: |-----|
Constructors
| Meets | |
| MetBy | |
| Before | |
| After | |
| Overlaps | |
| OverlappedBy | |
| Starts | |
| StartedBy | |
| Finishes | |
| FinishedBy | |
| During | |
| Contains | |
| Equals |
Instances
type ComparativePredicateOf a = a -> a -> Bool Source #
Defines a predicate of two objects of type a.
Functions for creating new intervals from existing
expand :: (IntervalSizeable a b, Intervallic i a) => b -> b -> i a -> i a Source #
Resize an 'i a' to by expanding to "left" by l and to the
"right" by r. In the case that l or r are less than a moment
the respective endpoints are unchanged.
expandl :: (IntervalSizeable a b, Intervallic i a) => b -> i a -> i a Source #
Expands an 'i a' to left by i.
expandr :: (IntervalSizeable a b, Intervallic i a) => b -> i a -> i a Source #
Expands an 'i a' to right by i.
beginerval :: IntervalSizeable a b => b -> a -> Interval a Source #
enderval :: IntervalSizeable a b => b -> a -> Interval a Source #
extenterval :: IntervalAlgebraic i a => i a -> i a -> Interval a Source #
Creates a new Interval spanning the extent x and y.