IntervalAlgebra

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

1. Intervallic provides an interface to the data structure of an Interval, defining how an Interval a is constructed.
2. IntervalAlgebraic provides an interface to the IntervalRelations, the workhorse of Allen's temporal logic.
3. IntervalCombinable provides an interface to methods of combining multiple 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 Intervals

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.

Classes

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

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)

Safely parse a pair of as to create an Interval a.

unsafeInterval :: a -> a -> Interval a

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

Access the ends of an Interval a .

end :: Interval a -> a

Access the ends of an Interval a .

Instances

Intervallic Int

Defined in IntervalAlgebra

Methods

parseInterval :: Int -> Int -> Either String (Interval Int)

unsafeInterval :: Int -> Int -> Interval Int

begin :: Interval Int -> Int

end :: Interval Int -> Int

Intervallic Integer

Defined in IntervalAlgebra

Methods

parseInterval :: Integer -> Integer -> Either String (Interval Integer)

unsafeInterval :: Integer -> Integer -> Interval Integer

begin :: Interval Integer -> Integer

end :: Interval Integer -> Integer

Intervallic Day

Defined in IntervalAlgebra

Methods

parseInterval :: Day -> Day -> Either String (Interval Day)

unsafeInterval :: Day -> Day -> Interval Day

begin :: Interval Day -> Day

end :: Interval Day -> Day

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

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

Compare two intervals to determine their IntervalRelation.

equals :: ComparativePredicateOf (Interval a)

Does x equal y?

meets :: ComparativePredicateOf (Interval a)

Does x meet y? Is y metBy x?

metBy :: ComparativePredicateOf (Interval a)

Does x meet y? Is y metBy x?

before :: ComparativePredicateOf (Interval a)

Is x before y? Is x after y?

after :: ComparativePredicateOf (Interval a)

Is x before y? Is x after y?

overlaps :: ComparativePredicateOf (Interval a)

Does x overlap y? Is x overlapped by y?

overlappedBy :: ComparativePredicateOf (Interval a)

Does x overlap y? Is x overlapped by y?

starts :: ComparativePredicateOf (Interval a)

Does x start y? Is x started by y?

startedBy :: ComparativePredicateOf (Interval a)

Does x start y? Is x started by y?

finishes :: ComparativePredicateOf (Interval a)

Does x finish y? Is x finished by y?

finishedBy :: ComparativePredicateOf (Interval a)

Does x finish y? Is x finished by y?

during :: ComparativePredicateOf (Interval a)

Is x during y? Does x contain y?

contains :: ComparativePredicateOf (Interval a)

Is x during y? Does x contain y?

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

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)

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

in' :: ComparativePredicateOf (Interval a)

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

Instances

IntervalAlgebraic Int

Defined in IntervalAlgebra

Methods

relate :: Interval Int -> Interval Int -> IntervalRelation

equals :: ComparativePredicateOf (Interval Int)

meets :: ComparativePredicateOf (Interval Int)

metBy :: ComparativePredicateOf (Interval Int)

before :: ComparativePredicateOf (Interval Int)

after :: ComparativePredicateOf (Interval Int)

overlaps :: ComparativePredicateOf (Interval Int)

overlappedBy :: ComparativePredicateOf (Interval Int)

starts :: ComparativePredicateOf (Interval Int)

startedBy :: ComparativePredicateOf (Interval Int)

finishes :: ComparativePredicateOf (Interval Int)

finishedBy :: ComparativePredicateOf (Interval Int)

during :: ComparativePredicateOf (Interval Int)

contains :: ComparativePredicateOf (Interval Int)

composeRelations :: [ComparativePredicateOf (Interval Int)] -> ComparativePredicateOf (Interval Int)

disjoint :: ComparativePredicateOf (Interval Int)

in' :: ComparativePredicateOf (Interval Int)

IntervalAlgebraic Integer

Defined in IntervalAlgebra

Methods

relate :: Interval Integer -> Interval Integer -> IntervalRelation

equals :: ComparativePredicateOf (Interval Integer)

meets :: ComparativePredicateOf (Interval Integer)

metBy :: ComparativePredicateOf (Interval Integer)

before :: ComparativePredicateOf (Interval Integer)

after :: ComparativePredicateOf (Interval Integer)

overlaps :: ComparativePredicateOf (Interval Integer)

overlappedBy :: ComparativePredicateOf (Interval Integer)

starts :: ComparativePredicateOf (Interval Integer)

startedBy :: ComparativePredicateOf (Interval Integer)

finishes :: ComparativePredicateOf (Interval Integer)

finishedBy :: ComparativePredicateOf (Interval Integer)

during :: ComparativePredicateOf (Interval Integer)

contains :: ComparativePredicateOf (Interval Integer)

composeRelations :: [ComparativePredicateOf (Interval Integer)] -> ComparativePredicateOf (Interval Integer)

disjoint :: ComparativePredicateOf (Interval Integer)

in' :: ComparativePredicateOf (Interval Integer)

IntervalAlgebraic Day

Defined in IntervalAlgebra

Methods

relate :: Interval Day -> Interval Day -> IntervalRelation

equals :: ComparativePredicateOf (Interval Day)

meets :: ComparativePredicateOf (Interval Day)

metBy :: ComparativePredicateOf (Interval Day)

before :: ComparativePredicateOf (Interval Day)

after :: ComparativePredicateOf (Interval Day)

overlaps :: ComparativePredicateOf (Interval Day)

overlappedBy :: ComparativePredicateOf (Interval Day)

starts :: ComparativePredicateOf (Interval Day)

startedBy :: ComparativePredicateOf (Interval Day)

finishes :: ComparativePredicateOf (Interval Day)

finishedBy :: ComparativePredicateOf (Interval Day)

during :: ComparativePredicateOf (Interval Day)

contains :: ComparativePredicateOf (Interval Day)

composeRelations :: [ComparativePredicateOf (Interval Day)] -> ComparativePredicateOf (Interval Day)

disjoint :: ComparativePredicateOf (Interval Day)

in' :: ComparativePredicateOf (Interval Day)

class IntervalAlgebraic a => IntervalCombinable a where

The IntervalCombinable typeclass provides methods combining multiple Intervals.

Minimal complete definition

Nothing

Methods

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

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

Instances

IntervalCombinable Int

Defined in IntervalAlgebra

Methods

(.+.) :: Interval Int -> Interval Int -> Maybe (Interval Int)

IntervalCombinable Integer

Defined in IntervalAlgebra

Methods

(.+.) :: Interval Integer -> Interval Integer -> Maybe (Interval Integer)

IntervalCombinable Day

Defined in IntervalAlgebra

Methods

(.+.) :: Interval Day -> Interval Day -> Maybe (Interval Day)

Data Types

newtype Interval a

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.

Constructors

Interval (a, a)

Instances

Eq a => Eq (Interval a)

Defined in IntervalAlgebra

Methods

(==) :: Interval a -> Interval a -> Bool

(/=) :: Interval a -> Interval a -> Bool

Intervallic a => Ord (Interval a)

Imposes a total ordering on Interval a based on first ordering the begins then the ends.

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)

Defined in IntervalAlgebra

Methods

showsPrec :: Int -> Interval a -> ShowS

show :: Interval a -> String

showList :: [Interval a] -> ShowS

data IntervalRelation

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

Read IntervalRelation

Defined in IntervalAlgebra

Methods

readsPrec :: Int -> ReadS IntervalRelation

readList :: ReadS [IntervalRelation]

readPrec :: ReadPrec IntervalRelation

readListPrec :: ReadPrec [IntervalRelation]

Show IntervalRelation

Defined in IntervalAlgebra

Methods

showsPrec :: Int -> IntervalRelation -> ShowS

show :: IntervalRelation -> String

showList :: [IntervalRelation] -> ShowS

type ComparativePredicateOf a = a -> a -> Bool

Defines a predicate of two objects of type a.