Copyright	(c) NoviSci Inc 2020
License	BSD3
Maintainer	bsaul@novisci.com
Stability	experimental
Safe Haskell	None
Language	Haskell2010

IntervalAlgebra

Contents

Classes
Types

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 five typeclasses designed to separate concerns of constructing, relating, and combining Intervals:

Intervallic provides an interface to the data structure of an Interval, defining how an Interval a is constructed.
IntervalAlgebraic provides an interface to the IntervalRelations, the workhorse of Allen's temporal logic.
IntervalCombinable provides an interface to methods of combining two Intervals.
IntervalSizeable provides methods for measuring and modifying the size of an interval.
IntervalFilterable provides methods for filtering Filterable collections of intervals.

An advantage of nested typeclass design is that developers can define an Interval of type a with just the amount of structure that they need.

Total Ordering of `Interval`s

The modules makes the (opinionated) choice of a total ordering for Intervallic Intervals. Namely, the ordering is based on first ordering the begins then the ends.

Development

This module is under development and the API may change in the future.

Synopsis

class (Ord a, Show a) => Intervallic a where
- parseInterval :: a -> a -> Either String (Interval a)
- unsafeInterval :: a -> a -> Interval a
- begin, end :: Interval a -> a
class (Eq a, Intervallic a) => IntervalAlgebraic a where
- relate :: Interval a -> Interval a -> IntervalRelation
- equals :: ComparativePredicateOf (Interval a)
- meets, metBy :: ComparativePredicateOf (Interval a)
- before, after :: ComparativePredicateOf (Interval a)
- overlaps, overlappedBy :: ComparativePredicateOf (Interval a)
- starts, startedBy :: ComparativePredicateOf (Interval a)
- finishes, finishedBy :: ComparativePredicateOf (Interval a)
- during, contains :: ComparativePredicateOf (Interval a)
- composeRelations :: [ComparativePredicateOf (Interval a)] -> ComparativePredicateOf (Interval a)
- disjoint :: ComparativePredicateOf (Interval a)
- in' :: ComparativePredicateOf (Interval a)
class IntervalAlgebraic a => IntervalCombinable a where
- (.+.) :: Interval a -> Interval a -> Maybe (Interval a)
- extenterval :: Interval a -> Interval a -> Interval a
- (><) :: Interval a -> Interval a -> Maybe (Interval a)
- (<+>) :: (Semigroup (f (Interval a)), Applicative f) => Interval a -> Interval a -> f (Interval a)
class (Intervallic a, Num b, Ord b) => IntervalSizeable a b | a -> b where
- duration :: Interval a -> b
- moment :: a -> b
- add :: b -> a -> a
- expand :: b -> b -> Interval a -> Interval a
- expandl :: b -> Interval a -> Interval a
- expandr :: b -> Interval a -> Interval a
class (Filterable f, IntervalAlgebraic a) => IntervalFilterable f a where
- filterMaker :: ComparativePredicateOf (Interval a) -> Interval a -> f (Interval a) -> f (Interval a)
- filterOverlaps :: Interval a -> f (Interval a) -> f (Interval a)
- filterOverlappedBy :: Interval a -> f (Interval a) -> f (Interval a)
- filterBefore :: Interval a -> f (Interval a) -> f (Interval a)
- filterAfter :: Interval a -> f (Interval a) -> f (Interval a)
- filterMeets :: Interval a -> f (Interval a) -> f (Interval a)
- filterMetBy :: Interval a -> f (Interval a) -> f (Interval a)
- filterDuring :: Interval a -> f (Interval a) -> f (Interval a)
- filterContains :: Interval a -> f (Interval a) -> f (Interval a)
data Interval a
data IntervalRelation
type ComparativePredicateOf a = a -> a -> Bool

Classes

class (Ord a, Show a) => Intervallic a where Source #

The Intervallic typeclass specifies how an Interval as is constructed. It also includes functions for getting the begin and end of an Interval a.

Minimal complete definition

Nothing

Methods

parseInterval :: 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. This function is not safe as it does not enforce that \(x < y\). Use with caution. It is meant to be helper function in early prototyping of this package. This function may be deprecated in future releases.

begin :: Interval a -> a Source #

Access the ends of an Interval a .

end :: Interval a -> a Source #

Access the ends of an Interval a .

Instances

Instances details

Intervallic Int Source #
Instance details Defined in IntervalAlgebra Methods parseInterval :: Int -> Int -> Either String (Interval Int) Source # unsafeInterval :: Int -> Int -> Interval Int Source # begin :: Interval Int -> Int Source # end :: Interval Int -> Int Source #
Intervallic Integer Source #
Instance details Defined in IntervalAlgebra Methods parseInterval :: Integer -> Integer -> Either String (Interval Integer) Source # unsafeInterval :: Integer -> Integer -> Interval Integer Source # begin :: Interval Integer -> Integer Source # end :: Interval Integer -> Integer Source #
Intervallic Day Source #
Instance details Defined in IntervalAlgebra Methods parseInterval :: Day -> Day -> Either String (Interval Day) Source # unsafeInterval :: Day -> Day -> Interval Day Source # begin :: Interval Day -> Day Source # end :: Interval Day -> Day Source #

class (Eq a, Intervallic a) => IntervalAlgebraic a where Source #

The IntervalAlgebraic typeclass specifies the functions and relational operators for interval-based temporal logic. The typeclass defines the relational operators for intervals, plus other useful utilities such as disjoint, in', and composeRelations.

Minimal complete definition

Nothing

Methods

relate :: Interval a -> Interval a -> IntervalRelation Source #

Compare two intervals to determine their IntervalRelation.

equals :: ComparativePredicateOf (Interval a) Source #

Does x equal y?

meets :: ComparativePredicateOf (Interval a) Source #

Does x meet y? Is y metBy x?

metBy :: ComparativePredicateOf (Interval a) Source #

Does x meet y? Is y metBy x?

before :: ComparativePredicateOf (Interval a) Source #

Is x before y? Is x after y?

after :: ComparativePredicateOf (Interval a) Source #

Is x before y? Is x after y?

overlaps :: ComparativePredicateOf (Interval a) Source #

Does x overlap y? Is x overlapped by y?

overlappedBy :: ComparativePredicateOf (Interval a) Source #

Does x overlap y? Is x overlapped by y?

starts :: ComparativePredicateOf (Interval a) Source #

Does x start y? Is x started by y?

startedBy :: ComparativePredicateOf (Interval a) Source #

Does x start y? Is x started by y?

finishes :: ComparativePredicateOf (Interval a) Source #

Does x finish y? Is x finished by y?

finishedBy :: ComparativePredicateOf (Interval a) Source #

Does x finish y? Is x finished by y?

during :: ComparativePredicateOf (Interval a) Source #

Is x during y? Does x contain y?

contains :: ComparativePredicateOf (Interval a) Source #

Is x during y? Does x contain y?

composeRelations :: [ComparativePredicateOf (Interval a)] -> ComparativePredicateOf (Interval a) Source #

Compose a list of interval relations with _or_ to create a new ComparativePredicateOf Interval a. For example, composeRelations [before, meets] creates a predicate function determining if one interval is either before or meets another interval.

disjoint :: ComparativePredicateOf (Interval a) Source #

Are x and y disjoint (before, after, meets, or metBy)?

in' :: ComparativePredicateOf (Interval a) Source #

Is x contained in y in any sense (during, starts, finishes or equals?

Instances

Instances details

IntervalAlgebraic Int Source #
Instance details Defined in IntervalAlgebra Methods relate :: Interval Int -> Interval Int -> IntervalRelation Source # equals :: ComparativePredicateOf (Interval Int) Source # meets :: ComparativePredicateOf (Interval Int) Source # metBy :: ComparativePredicateOf (Interval Int) Source # before :: ComparativePredicateOf (Interval Int) Source # after :: ComparativePredicateOf (Interval Int) Source # overlaps :: ComparativePredicateOf (Interval Int) Source # overlappedBy :: ComparativePredicateOf (Interval Int) Source # starts :: ComparativePredicateOf (Interval Int) Source # startedBy :: ComparativePredicateOf (Interval Int) Source # finishes :: ComparativePredicateOf (Interval Int) Source # finishedBy :: ComparativePredicateOf (Interval Int) Source # during :: ComparativePredicateOf (Interval Int) Source # contains :: ComparativePredicateOf (Interval Int) Source # composeRelations :: [ComparativePredicateOf (Interval Int)] -> ComparativePredicateOf (Interval Int) Source # disjoint :: ComparativePredicateOf (Interval Int) Source # in' :: ComparativePredicateOf (Interval Int) Source #
IntervalAlgebraic Integer Source #
Instance details Defined in IntervalAlgebra Methods relate :: Interval Integer -> Interval Integer -> IntervalRelation Source # equals :: ComparativePredicateOf (Interval Integer) Source # meets :: ComparativePredicateOf (Interval Integer) Source # metBy :: ComparativePredicateOf (Interval Integer) Source # before :: ComparativePredicateOf (Interval Integer) Source # after :: ComparativePredicateOf (Interval Integer) Source # overlaps :: ComparativePredicateOf (Interval Integer) Source # overlappedBy :: ComparativePredicateOf (Interval Integer) Source # starts :: ComparativePredicateOf (Interval Integer) Source # startedBy :: ComparativePredicateOf (Interval Integer) Source # finishes :: ComparativePredicateOf (Interval Integer) Source # finishedBy :: ComparativePredicateOf (Interval Integer) Source # during :: ComparativePredicateOf (Interval Integer) Source # contains :: ComparativePredicateOf (Interval Integer) Source # composeRelations :: [ComparativePredicateOf (Interval Integer)] -> ComparativePredicateOf (Interval Integer) Source # disjoint :: ComparativePredicateOf (Interval Integer) Source # in' :: ComparativePredicateOf (Interval Integer) Source #
IntervalAlgebraic Day Source #
Instance details Defined in IntervalAlgebra Methods relate :: Interval Day -> Interval Day -> IntervalRelation Source # equals :: ComparativePredicateOf (Interval Day) Source # meets :: ComparativePredicateOf (Interval Day) Source # metBy :: ComparativePredicateOf (Interval Day) Source # before :: ComparativePredicateOf (Interval Day) Source # after :: ComparativePredicateOf (Interval Day) Source # overlaps :: ComparativePredicateOf (Interval Day) Source # overlappedBy :: ComparativePredicateOf (Interval Day) Source # starts :: ComparativePredicateOf (Interval Day) Source # startedBy :: ComparativePredicateOf (Interval Day) Source # finishes :: ComparativePredicateOf (Interval Day) Source # finishedBy :: ComparativePredicateOf (Interval Day) Source # during :: ComparativePredicateOf (Interval Day) Source # contains :: ComparativePredicateOf (Interval Day) Source # composeRelations :: [ComparativePredicateOf (Interval Day)] -> ComparativePredicateOf (Interval Day) Source # disjoint :: ComparativePredicateOf (Interval Day) Source # in' :: ComparativePredicateOf (Interval Day) Source #

class IntervalAlgebraic a => IntervalCombinable a where Source #

The IntervalCombinable typeclass provides methods for (possibly) combining two Intervals.

Minimal complete definition

Nothing

Methods

(.+.) :: Interval a -> Interval a -> Maybe (Interval a) Source #

Maybe form a new Interval by the union of two Intervals that meets.

extenterval :: Interval a -> Interval a -> Interval a Source #

Creates a new Interval spanning the extent x and y

(><) :: 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 folding over an *ordered* container of Intervals and combining intervals when x is *not* before y.

Instances

Instances details

IntervalCombinable Int Source #
Instance details Defined in IntervalAlgebra Methods (.+.) :: Interval Int -> Interval Int -> Maybe (Interval Int) Source # extenterval :: Interval Int -> Interval Int -> Interval Int Source # (><) :: Interval Int -> Interval Int -> Maybe (Interval Int) Source # (<+>) :: (Semigroup (f (Interval Int)), Applicative f) => Interval Int -> Interval Int -> f (Interval Int) Source #
IntervalCombinable Integer Source #
Instance details Defined in IntervalAlgebra Methods (.+.) :: Interval Integer -> Interval Integer -> Maybe (Interval Integer) Source # extenterval :: Interval Integer -> Interval Integer -> Interval Integer Source # (><) :: Interval Integer -> Interval Integer -> Maybe (Interval Integer) Source # (<+>) :: (Semigroup (f (Interval Integer)), Applicative f) => Interval Integer -> Interval Integer -> f (Interval Integer) Source #
IntervalCombinable Day Source #
Instance details Defined in IntervalAlgebra Methods (.+.) :: Interval Day -> Interval Day -> Maybe (Interval Day) Source # extenterval :: Interval Day -> Interval Day -> Interval Day Source # (><) :: Interval Day -> Interval Day -> Maybe (Interval Day) Source # (<+>) :: (Semigroup (f (Interval Day)), Applicative f) => Interval Day -> Interval Day -> f (Interval Day) Source #

class (Intervallic a, Num b, Ord b) => IntervalSizeable a b | a -> b where Source #

The IntervalSizeable typeclass provides functions to determine the size of and to resize an 'Interval a'.

Minimal complete definition

duration, add

Methods

duration :: Interval a -> b Source #

Determine the duration of an 'Interval a'.

moment :: a -> b Source #

Sets the length of a moment for an 'Interval a'.

add :: b -> a -> a Source #

Shifts an a. Most often, the c will be the same type as the a. But for example, if a is Day then c would be Int.

expand :: b -> b -> Interval a -> Interval a Source #

Resize an 'Interval a' to by expanding to "left" by max l moment and to the "right" by min r moment.

expandl :: b -> Interval a -> Interval a Source #

Expands an 'Interval a' to left by i.

expandr :: b -> Interval a -> Interval a Source #

Expands an 'Interval a' to right by i.

Instances

Instances details

IntervalSizeable Int Int Source #
Instance details Defined in IntervalAlgebra Methods duration :: Interval Int -> Int Source # moment :: Int -> Int Source # add :: Int -> Int -> Int Source # expand :: Int -> Int -> Interval Int -> Interval Int Source # expandl :: Int -> Interval Int -> Interval Int Source # expandr :: Int -> Interval Int -> Interval Int Source #
IntervalSizeable Integer Integer Source #
Instance details Defined in IntervalAlgebra Methods duration :: Interval Integer -> Integer Source # moment :: Integer -> Integer Source # add :: Integer -> Integer -> Integer Source # expand :: Integer -> Integer -> Interval Integer -> Interval Integer Source # expandl :: Integer -> Interval Integer -> Interval Integer Source # expandr :: Integer -> Interval Integer -> Interval Integer Source #
IntervalSizeable Day Integer Source #
Instance details Defined in IntervalAlgebra Methods duration :: Interval Day -> Integer Source # moment :: Day -> Integer Source # add :: Integer -> Day -> Day Source # expand :: Integer -> Integer -> Interval Day -> Interval Day Source # expandl :: Integer -> Interval Day -> Interval Day Source # expandr :: Integer -> Interval Day -> Interval Day Source #

class (Filterable f, IntervalAlgebraic a) => IntervalFilterable f a where Source #

The IntervalFilterable class provides functions for filtering Filterables of Intervals based on IntervalAlgebraic relations.

Minimal complete definition

Nothing

Methods

filterMaker :: ComparativePredicateOf (Interval a) -> Interval a -> f (Interval a) -> f (Interval a) Source #

Creates a function for filtering a Filterable of Interval as based on a predicate

filterOverlaps :: Interval a -> f (Interval a) -> f (Interval a) Source #

Filter a Filterable of Interval as to those that overlaps the Interval a in the first argument.

filterOverlappedBy :: Interval a -> f (Interval a) -> f (Interval a) Source #

Filter a Filterable of Interval as to those overlappedBy the Interval a in the first argument.

filterBefore :: Interval a -> f (Interval a) -> f (Interval a) Source #

Filter a Filterable of Interval as to those before the Interval a in the first argument.

filterAfter :: Interval a -> f (Interval a) -> f (Interval a) Source #

Filter a Filterable of Interval as to those after the Interval a in the first argument.

filterMeets :: Interval a -> f (Interval a) -> f (Interval a) Source #

Filter a Filterable of Interval as to those that meets the Interval a in the first argument.

filterMetBy :: Interval a -> f (Interval a) -> f (Interval a) Source #

Filter a Filterable of Interval as to those metBy the Interval a in the first argument.

filterDuring :: Interval a -> f (Interval a) -> f (Interval a) Source #

Filter a Filterable of Interval as to those during the Interval a in the first argument.

filterContains :: Interval a -> f (Interval a) -> f (Interval a) Source #

Filter a Filterable of Interval as to those that contains the Interval a in the first argument.

Instances

Instances details

IntervalFilterable [] Int Source #
Instance details Defined in IntervalAlgebra Methods filterMaker :: ComparativePredicateOf (Interval Int) -> Interval Int -> [Interval Int] -> [Interval Int] Source # filterOverlaps :: Interval Int -> [Interval Int] -> [Interval Int] Source # filterOverlappedBy :: Interval Int -> [Interval Int] -> [Interval Int] Source # filterBefore :: Interval Int -> [Interval Int] -> [Interval Int] Source # filterAfter :: Interval Int -> [Interval Int] -> [Interval Int] Source # filterMeets :: Interval Int -> [Interval Int] -> [Interval Int] Source # filterMetBy :: Interval Int -> [Interval Int] -> [Interval Int] Source # filterDuring :: Interval Int -> [Interval Int] -> [Interval Int] Source # filterContains :: Interval Int -> [Interval Int] -> [Interval Int] Source #
IntervalFilterable [] Integer Source #
Instance details Defined in IntervalAlgebra Methods filterMaker :: ComparativePredicateOf (Interval Integer) -> Interval Integer -> [Interval Integer] -> [Interval Integer] Source # filterOverlaps :: Interval Integer -> [Interval Integer] -> [Interval Integer] Source # filterOverlappedBy :: Interval Integer -> [Interval Integer] -> [Interval Integer] Source # filterBefore :: Interval Integer -> [Interval Integer] -> [Interval Integer] Source # filterAfter :: Interval Integer -> [Interval Integer] -> [Interval Integer] Source # filterMeets :: Interval Integer -> [Interval Integer] -> [Interval Integer] Source # filterMetBy :: Interval Integer -> [Interval Integer] -> [Interval Integer] Source # filterDuring :: Interval Integer -> [Interval Integer] -> [Interval Integer] Source # filterContains :: Interval Integer -> [Interval Integer] -> [Interval Integer] Source #
IntervalFilterable [] Day Source #
Instance details Defined in IntervalAlgebra Methods filterMaker :: ComparativePredicateOf (Interval Day) -> Interval Day -> [Interval Day] -> [Interval Day] Source # filterOverlaps :: Interval Day -> [Interval Day] -> [Interval Day] Source # filterOverlappedBy :: Interval Day -> [Interval Day] -> [Interval Day] Source # filterBefore :: Interval Day -> [Interval Day] -> [Interval Day] Source # filterAfter :: Interval Day -> [Interval Day] -> [Interval Day] Source # filterMeets :: Interval Day -> [Interval Day] -> [Interval Day] Source # filterMetBy :: Interval Day -> [Interval Day] -> [Interval Day] Source # filterDuring :: Interval Day -> [Interval Day] -> [Interval Day] Source # filterContains :: Interval Day -> [Interval Day] -> [Interval Day] Source #

Types

data Interval a Source #

An Interval a is a pair of as \( (x, y) \text{ where } x < y\). The Intervallic class provides a safe parseInterval function that returns a Left error if \(y < x\) and unsafeInterval as constructor for creating an interval that may not be valid.

Instances

Instances details

Eq a => Eq (Interval a) Source #
Instance details Defined in IntervalAlgebra Methods (==) :: Interval a -> Interval a -> Bool # (/=) :: Interval a -> Interval a -> Bool #
Intervallic a => Ord (Interval a) Source #	Imposes a total ordering on `Interval a` based on first ordering the `begin`s then the `end`s.
Instance details Defined in IntervalAlgebra Methods compare :: Interval a -> Interval a -> Ordering # (<) :: Interval a -> Interval a -> Bool # (<=) :: Interval a -> Interval a -> Bool # (>) :: Interval a -> Interval a -> Bool # (>=) :: Interval a -> Interval a -> Bool # max :: Interval a -> Interval a -> Interval a # min :: Interval a -> Interval a -> Interval a #
(Intervallic a, Show a) => Show (Interval a) Source #
Instance details Defined in IntervalAlgebra Methods showsPrec :: Int -> Interval a -> ShowS # show :: Interval a -> String # showList :: [Interval a] -> ShowS #
Arbitrary (Interval Int) Source #
Instance details Defined in IntervalAlgebra.Arbitrary Methods arbitrary :: Gen (Interval Int) # shrink :: Interval Int -> [Interval Int] #
Arbitrary (Interval Day) Source #
Instance details Defined in IntervalAlgebra.Arbitrary Methods arbitrary :: Gen (Interval Day) # shrink :: Interval Day -> [Interval Day] #

data IntervalRelation Source #

The IntervalRelation type enumerates the thirteen possible ways that two Interval a objects can relate according to the interval algebra.

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: |-----|

Instances

Instances details

Read IntervalRelation Source #
Instance details Defined in IntervalAlgebra Methods readsPrec :: Int -> ReadS IntervalRelation # readList :: ReadS [IntervalRelation] # readPrec :: ReadPrec IntervalRelation # readListPrec :: ReadPrec [IntervalRelation] #
Show IntervalRelation Source #
Instance details Defined in IntervalAlgebra Methods showsPrec :: Int -> IntervalRelation -> ShowS # show :: IntervalRelation -> String # showList :: [IntervalRelation] -> ShowS #

type ComparativePredicateOf a = a -> a -> Bool Source #

Defines a predicate of two objects of type a.

Design

Total Ordering of Intervals

Development

Classes

Instances

Instances

Instances

Instances

Instances

Types

Instances

Meets, Metby

Before, After

Overlaps, OverlappedBy

Starts, StartedBy

Finishes, FinishedBy

During, Contains

Equal

Instances

Total Ordering of `Interval`s