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 (ParseErrorInterval "0<=1")

A synonym for parseInterval

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)

A synonym for beginerval

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)

A synonym for enderval

Safely creates an Interval from a pair of endpoints. IMPORTANT: This function uses beginerval, thus if the second element of the pair is <= the first element, the duration will be an Interval of moment duration.

>>> safeInterval (4, 5 ::Int)
(4, 5)
>>> safeInterval (4, 3 :: Int)
(4, 5)

A synonym for safeInterval

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.

>>> iv2to4 = safeInterval (2::Int, 4::Int)
>>> iv2to4' = expand 0 0 iv2to4
>>> iv1to5 = expand 1 1 iv2to4

>>> iv2to4
(2, 4)

>>> iv2to4'
(2, 4)

>>> iv1to5
(1, 5)

>>> pretty $ standardExampleDiagram [(iv2to4, "iv2to4"), (iv1to5, "iv1to5")] []
  --  <- [iv2to4]
 ---- <- [iv1to5]
=====

Expands an i a to the "left".

>>> iv2to4 = (safeInterval (2::Int, 4::Int))
>>> iv0to4 = expandl 2 iv2to4

>>> iv2to4
(2, 4)

>>> iv0to4
(0, 4)

>>> pretty $ standardExampleDiagram [(iv2to4, "iv2to4"), (iv0to4, "iv0to4")] []
  -- <- [iv2to4]
---- <- [iv0to4]
====

Expands an i a to the "right".

>>> iv2to4 = (safeInterval (2::Int, 4::Int))
>>> iv2to6 = expandr 2 iv2to4

>>> iv2to4
(2, 4)

>>> iv2to6
(2, 6)

>>> pretty $ standardExampleDiagram [(iv2to4, "iv2to4"), (iv2to6, "iv2to6")] []
  --   <- [iv2to4]
  ---- <- [iv2to6]
======

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?

Example data with corresponding diagram:

>>> x = bi 5 0
>>> y = bi 5 5
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
-----      <- [x]
     ----- <- [y]
==========

Examples:

>>> x `meets` y
True

>>> x `metBy` y
False

>>> y `meets` x
False

>>> y `metBy` x
True

Does x meets y? Is x metBy y?

Example data with corresponding diagram:

>>> x = bi 5 0
>>> y = bi 5 5
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
-----      <- [x]
     ----- <- [y]
==========

Examples:

>>> x `meets` y
True

>>> x `metBy` y
False

>>> y `meets` x
False

>>> y `metBy` x
True

Is x before y? Does x precedes y? Is x after y? Is x precededBy y?

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 4 6
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---        <- [x]
      ---- <- [y]
==========

Examples:

>>> x `before` y
True
>>> x `precedes` y
True

>>> x `after`y
False
>>> x `precededBy` y
False

>>> y `before` x
False
>>> y `precedes` x
False

>>> y `after` x
True
>>> y `precededBy` x
True

Is x before y? Does x precedes y? Is x after y? Is x precededBy y?

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 4 6
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---        <- [x]
      ---- <- [y]
==========

Examples:

>>> x `before` y
True
>>> x `precedes` y
True

>>> x `after`y
False
>>> x `precededBy` y
False

>>> y `before` x
False
>>> y `precedes` x
False

>>> y `after` x
True
>>> y `precededBy` x
True

Does x overlaps y? Is x overlappedBy y?

Example data with corresponding diagram:

>>> x = bi 6 0
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
------     <- [x]
    ------ <- [y]
==========

Examples:

>>> x `overlaps` y
True

>>> x `overlappedBy` y
False

>>> y `overlaps` x
False

>>> y `overlappedBy` x
True

Does x overlaps y? Is x overlappedBy y?

Example data with corresponding diagram:

>>> x = bi 6 0
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
------     <- [x]
    ------ <- [y]
==========

Examples:

>>> x `overlaps` y
True

>>> x `overlappedBy` y
False

>>> y `overlaps` x
False

>>> y `overlappedBy` x
True

Does x finishes y? Is x finishedBy y?

Example data with corresponding diagram:

>>> x = bi 3 7
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
       --- <- [x]
    ------ <- [y]
==========

Examples:

>>> x `finishes` y
True

>>> x `finishedBy` y
False

>>> y `finishes` x
False

>>> y `finishedBy` x
True

Does x finishes y? Is x finishedBy y?

Example data with corresponding diagram:

>>> x = bi 3 7
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
       --- <- [x]
    ------ <- [y]
==========

Examples:

>>> x `finishes` y
True

>>> x `finishedBy` y
False

>>> y `finishes` x
False

>>> y `finishedBy` x
True

Is x during y? Does x contains y?

Example data with corresponding diagram:

>>> x = bi 3 5
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
     ---   <- [x]
    ------ <- [y]
==========

Examples:

>>> x `during` y
True

>>> x `contains` y
False

>>> y `during` x
False

>>> y `contains` x
True

Is x during y? Does x contains y?

Example data with corresponding diagram:

>>> x = bi 3 5
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
     ---   <- [x]
    ------ <- [y]
==========

Examples:

>>> x `during` y
True

>>> x `contains` y
False

>>> y `during` x
False

>>> y `contains` x
True

Does x starts y? Is x startedBy y?

Example data with corresponding diagram:

>>> x = bi 3 4
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ---    <- [x]
    ------ <- [y]
==========

Examples:

>>> x `starts` y
True

>>> x `startedBy` y
False

>>> y `starts` x
False

>>> y `startedBy` x
True

Does x starts y? Is x startedBy y?

Example data with corresponding diagram:

>>> x = bi 3 4
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ---    <- [x]
    ------ <- [y]
==========

Examples:

>>> x `starts` y
True

>>> x `startedBy` y
False

>>> y `starts` x
False

>>> y `startedBy` x
True

Does x equals y?

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
    ------ <- [y]
==========

Examples:

>>> x `equals` y
True

>>> y `equals` x
True

Is x before y? Does x precedes y? Is x after y? Is x precededBy y?

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 4 6
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---        <- [x]
      ---- <- [y]
==========

Examples:

>>> x `before` y
True
>>> x `precedes` y
True

>>> x `after`y
False
>>> x `precededBy` y
False

>>> y `before` x
False
>>> y `precedes` x
False

>>> y `after` x
True
>>> y `precededBy` x
True

Is x before y? Does x precedes y? Is x after y? Is x precededBy y?

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 4 6
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---        <- [x]
      ---- <- [y]
==========

Examples:

>>> x `before` y
True
>>> x `precedes` y
True

>>> x `after`y
False
>>> x `precededBy` y
False

>>> y `before` x
False
>>> y `precedes` x
False

>>> y `after` x
True
>>> y `precededBy` x
True

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

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 3 5
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---      <- [x]
     --- <- [y]
========

Examples:

>>> x `disjoint` y
True

>>> y `disjoint` x
True

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 3 3
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---    <- [x]
   --- <- [y]
======

Examples:

>>> x `disjoint` y
True

>>> y `disjoint` x
True

Example data with corresponding diagram:

>>> x = bi 6 0
>>> y = bi 3 3
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
------ <- [x]
   --- <- [y]
======

Examples:

>>> x `disjoint` y
False

>>> y `disjoint` x
False

Does x concur with y? Is x notDisjoint with y?); This is the complement of disjoint.

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 3 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---     <- [x]
    --- <- [y]
=======

Examples:

>>> x `notDisjoint` y
False
>>> y `concur` x
False

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 3 3
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---    <- [x]
   --- <- [y]
======

Examples:

>>> x `notDisjoint` y
False
>>> y `concur` x
False

Example data with corresponding diagram:

>>> x = bi 6 0
>>> y = bi 3 3
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
------ <- [x]
   --- <- [y]
======

Examples:

>>> x `notDisjoint` y
True
>>> y `concur` x
True

Does x concur with y? Is x notDisjoint with y?); This is the complement of disjoint.

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 3 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---     <- [x]
    --- <- [y]
=======

Examples:

>>> x `notDisjoint` y
False
>>> y `concur` x
False

Example data with corresponding diagram:

>>> x = bi 3 0
>>> y = bi 3 3
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
---    <- [x]
   --- <- [y]
======

Examples:

>>> x `notDisjoint` y
False
>>> y `concur` x
False

Example data with corresponding diagram:

>>> x = bi 6 0
>>> y = bi 3 3
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
------ <- [x]
   --- <- [y]
======

Examples:

>>> x `notDisjoint` y
True
>>> y `concur` x
True

Is x within (enclosedBy) y? That is, during, starts, finishes, or equals?

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
    ------ <- [y]
==========

Examples:

>>> x `within` y
True

>>> y `enclosedBy` x
True

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 5 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
    -----  <- [y]
==========

Examples:

>>> x `within` y
False

>>> y `enclosedBy` x
True

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 4 5
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
     ----  <- [y]
==========

Examples:

>>> x `within` y
False
>>> y `enclosedBy` x
True

Example data with corresponding diagram:

>>> x = bi 2 7
>>> y = bi 1 5
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
       -- <- [x]
     -    <- [y]
=========

Examples:

>>> x `within` y
False

>>> y `enclosedBy` x
False

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

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
    ------ <- [y]
==========

Examples:

>>> x `encloses` y
True

>>> y `encloses` x
True

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 5 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
    -----  <- [y]
==========

Examples:

>>> x `encloses` y
True

>>> y `encloses` x
False

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 4 5
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
     ----  <- [y]
==========

Examples:

>>> x `encloses` y
True

>>> y `encloses` x
False

Example data with corresponding diagram:

>>> x = bi 2 7
>>> y = bi 1 5
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
       -- <- [x]
     -    <- [y]
=========

Examples:

>>> x `encloses` y
False

>>> y `encloses` x
False

Is x within (enclosedBy) y? That is, during, starts, finishes, or equals?

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 6 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
    ------ <- [y]
==========

Examples:

>>> x `within` y
True

>>> y `enclosedBy` x
True

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 5 4
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
    -----  <- [y]
==========

Examples:

>>> x `within` y
False

>>> y `enclosedBy` x
True

Example data with corresponding diagram:

>>> x = bi 6 4
>>> y = bi 4 5
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
    ------ <- [x]
     ----  <- [y]
==========

Examples:

>>> x `within` y
False
>>> y `enclosedBy` x
True

Example data with corresponding diagram:

>>> x = bi 2 7
>>> y = bi 1 5
>>> pretty $ standardExampleDiagram [(x, "x"), (y, "y")] []
       -- <- [x]
     -    <- [y]
=========

Examples:

>>> x `within` y
False

>>> y `enclosedBy` x
False

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.

Example data with corresponding diagram:

>>> a = bi 3 2 :: Interval Int
>>> a
(2, 5)
>>> x = bi 3 7 :: Interval Int
>>> x
(7, 10)
>>> y = bi 4 9 :: Interval Int
>>> y
(9, 13)
>>> pretty $ standardExampleDiagram [(a, "a"), (x, "x"), (y, "y")] []
  ---         <- [a]
       ---    <- [x]
         ---- <- [y]
=============

Examples:

>>> x' = shiftFromBegin a x
>>> x'
(5, 8)
>>> y' = shiftFromBegin a y
>>> y'
(7, 11)
>>> pretty $ standardExampleDiagram [(x', "x'"), (y', "y'")] []
     ---    <- [x']
       ---- <- [y']
===========

Modifies the endpoints of second argument's interval by taking the difference from the first's input's end.

Example data with corresponding diagram:

>>> a = bi 3 2 :: Interval Int
>>> a
(2, 5)
>>> x = bi 3 7 :: Interval Int
>>> x
(7, 10)
>>> y = bi 4 9 :: Interval Int
>>> y
(9, 13)
>>> pretty $ standardExampleDiagram [(a, "a"), (x, "x"), (y, "y")] []
  ---         <- [a]
       ---    <- [x]
         ---- <- [y]
=============

Examples:

>>> x' = shiftFromEnd a x
>>> x'
(2, 5)
>>> y' = shiftFromEnd a y
>>> y'
(4, 8)
>>> pretty $ standardExampleDiagram [(x', "x'"), (y', "y'")] []
  ---    <- [x']
    ---- <- [y']
========

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

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

Converts an i Int to an i a via toEnum. This assumes the provided toEnum method is strictly monotone increasing: For a types that are Ord, then for Int values x, y it holds that x < y implies toEnum x < toEnum y.

Converts an i a to an i Int via fromEnum. This assumes the provided fromEnum method is strictly monotone increasing: For a types that are Ord with values x, y, then x < y implies fromEnum x < fromEnum y, so long as the latter is well-defined.

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'.