An Interval a is a pair \( (x, y) \text{ such that } x < y\). To create intervals use the parseInterval, beginerval, or enderval functions.

The Intervallic typeclass defines how to get and set the Interval content of a data structure. It also includes functions for getting the endpoints of the Interval via begin and end.

>>> getInterval (Interval (0, 10))
(0, 10)

>>> begin (Interval (0, 10))
0

>>> end (Interval (0, 10))
10

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

>>> parseInterval 0 1
Right (0, 1)

>>> parseInterval 1 0
Left "0<1"

Safely creates an 'Interval a' using x as the begin and adding max moment dur to x as the end.

>>> beginerval (0::Int) (0::Int)
(0, 1)

>>> beginerval (1::Int) (0::Int)
(0, 1)

>>> beginerval (2::Int) (0::Int)
(0, 2)

Safely creates an 'Interval a' using x as the end and adding negate max moment dur to x as the begin.

>>> enderval (0::Int) (0::Int)
(-1, 0)

>>> enderval (1::Int) (0::Int)
(-1, 0)

>>> enderval (2::Int) (0::Int)
(-2, 0)

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.

>>> expand 0 0 (Interval (0::Int, 2::Int))
(0, 2)

>>> expand 1 1 (Interval (0::Int, 2::Int))
(-1, 3)

Expands an i a to "left".

>>> expandl 2 (Interval (0::Int, 2::Int))
(-2, 2)

Expands an i a to "right".

>>> expandr 2 (Interval (0::Int, 2::Int))
(0, 4)

The IntervalRelation type and the associated predicate functions enumerate the thirteen possible ways that two Interval objects may relate according to Allen's interval algebra. Constructors are shown with their corresponding predicate function.

Does x meets y? Is x metBy y?

Does x meets y? Is x metBy y?

Is x before y? Is x after y?

Is x before y? Is x after y?

Does x overlap y? Is x overlapped by y?

Does x overlap y? Is x overlapped by y?

Does x finish y? Is x finished by y?

Does x finish y? Is x finished by y?

Is x during y? Does x contain y?

Is x during y? Does x contain y?

Does x start y? Is x started by y?

Does x start y? Is x started by y?

Does x equal y?

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

Are x and y not disjoint (concur); i.e. do they share any support? This is the complement of disjoint.

Are x and y not disjoint (concur); i.e. do they share any support? This is the complement of disjoint.

Is x entirely *within* (enclosed by) the endpoints of y? That is, during, starts, finishes, or equals?

Does x enclose y? That is, is y within x?

Is x entirely *within* (enclosed by) the endpoints of y? That is, during, starts, finishes, or equals?

Operator for composing the union of two predicates

Compose a list of interval relations with _or_ to create a new ComparativePredicateOf1 i a. For example, unionPredicates [before, meets] creates a predicate function determining if one interval is either before or meets another interval.

Defines a predicate of two objects of type a.

Defines a predicate of two object of different types.

The Set of all IntervalRelations.

Compare two i a to determine their IntervalRelation.

>>> relate (Interval (0::Int, 1)) (Interval (1, 2))
Meets

>>> relate (Interval (1::Int, 2)) (Interval (0, 1))
MetBy

Compose two interval relations according to the rules of the algebra. The rules are enumerated according to this table.

Finds the complement of a Set IntervalRelation.

Find the union of two Sets of IntervalRelations.

Find the intersection of two Sets of IntervalRelations.

Find the converse of a Set IntervalRelation.

The IntervalCombinable typeclass provides methods for (possibly) combining two i as to form an Interval.

Creates a new Interval spanning the extent x and y.

>>> extenterval (Interval (0, 1)) (Interval (9, 10))
(0, 10)

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