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

A type identifying interval parsing errors.

Access the endpoints of an i a .

Access the endpoints of an i a .

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?

Is x before y? Is x after y?

Is x before y? Is x after 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

Forms a predicate function from the union of a set of IntervalRelations.

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.

The set of IntervalRelation meaning two intervals are disjoint.

The set of IntervalRelation meaning one interval is within the other.

The set of IntervalRelation meaning one interval is *strictly* within the other.

Defines a predicate of two objects of type a.

Defines a predicate of two object of different types.

Creates a new Interval from the end of an i a.

Creates a new Interval from the begin of an i a.

Safely creates a new Interval with moment length with begin at x

>>> beginervalMoment (10 :: Int)
(10, 11)

Safely creates a new Interval with moment length with end at x

>>> endervalMoment (10 :: Int)
(9, 10)

Modifies the endpoints of second argument's interval by taking the difference from the first's input's begin. >>> diffFromBegin (Interval ((5::Int), 6)) (Interval (10, 15)) (5, 10)

>>> diffFromBegin (Interval ((1::Int), 2)) (Interval (3, 15))
(2, 14)

Modifies the endpoints of second argument's interval by taking the difference from the first's input's end. >>> diffFromEnd (Interval ((5::Int), 6)) (Interval (10, 15)) (4, 9)

>>> diffFromEnd (Interval ((1::Int), 2)) (Interval (3, 15))
(1, 13)

Changes the duration of an Intervallic value to a moment starting at the begin of the interval.

>>> momentize (Interval (6, 10))
(6, 7)

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 a Maybe i a, or in case of ><, a possibly different Intervallic type.

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'.