Interval Pattern

class paspailleur.bip.IntervalPattern(value: PatternValueType)

A class representing an interval as a pattern.

This class allows for the creation and manipulation of patterns that represent intervals, including operations such as intersection, union, and difference.

Attributes

PatternValueType:

The type of the pattern’s value, which is a tuple of bounds.

BoundsUniverse: list[float]

A list representing the universe of bounds for the interval.

Properties

lower_bound

Return the lower bound of the interval.

is_lower_bound_closed

Check if the lower bound is closed.

upper_bound

Return the upper bound of the interval.

is_upper_bound_closed

Check if the upper bound is closed.

atomic_patterns

Return the set of all less precise patterns that cannot be obtained by intersection of other patterns.

min_pattern

Return the minimal possible pattern for the interval pattern.

max_pattern

Return the maximal possible pattern for the interval pattern.

maximal_atoms

Return the maximal atomic patterns for the interval pattern.

Notes

The IntervalPattern can be defined by a string representation of the interval, or by an pair of two numbers, or by just one number.

Examples

>>> p1 = IntervalPattern( ((5, True), (10, False)) )  # The explicit way to define half-open interval [5, 10)
>>> p2 = IntervalPattern( "[5, 10)" )  # A more readable way to define interval [5, 10)
>>> print(p1 == p2)
True

>>> p3 = IntervalPattern( ((1, True), (1, True)) )  # The explicit way to define closed interval [1, 1]
>>> p4 = IntervalPattern( "[1, 1]" )
>>> p5 = IntervalPattern( [1, 1]  )
>>> p6 = IntervalPattern( 1 )
>>> print(p3 == p4, p3 == p5, p3 == p6)
True, True, True

>>> p7 = IntervalPattern( "[1, ∞]" )
>>> p8 = IntervalPattern( ">=1" )
>>> print(p7 == p8)
True

PatternValueType

alias of tuple[tuple[float, bool], tuple[float, bool]]

property lower_bound: float

Return the lower bound of the interval.

Returns:

bound – The lower bound of the interval.

Return type:

float

Examples

>>> IntervalPattern( "[1, 5)" ).lower_bound
1.0

property is_lower_bound_closed: bool

Check if the lower bound is closed.

Returns:

closed – True if the lower bound is closed, False otherwise.

Return type:

bool

Examples

>>> IntervalPattern( "[1, 5)" ).is_lower_bound_closed
True

property upper_bound: float

Return the upper bound of the interval.

Returns:

bound – The upper bound of the interval.

Return type:

float

Examples

>>> IIntervalPattern( "[1, 5)" ).upper_bound
5.0

property is_upper_bound_closed: bool

Check if the upper bound is closed.

Returns:

closed – True if the upper bound is closed, False otherwise.

Return type:

bool

Examples

>>> IntervalPattern( "[1, 5)" ).is_upper_bound_closed
False

classmethod parse_string_description(value: str) → tuple[tuple[float, bool], tuple[float, bool]]

Parse a string description into an interval pattern value.

Parameters:

value (str) – The string description of the interval pattern.

Returns:

parsed – The parsed interval pattern value.

Return type:

PatternValueType

Examples

>>> IntervalPattern.parse_string_description('[1, 5)')
((1.0, True), (5.0, False))

classmethod preprocess_value(value) → tuple[tuple[float, bool], tuple[float, bool]]

Preprocess the value before storing it in the interval pattern.

Parameters:

value – The value to preprocess.

Returns:

value – The preprocessed value as a tuple of bounds.

Return type:

PatternValueType

Examples

>>> IntervalPattern.preprocess_value((1, 5))
((1.0, True), (5.0, True))

atomise(atoms_configuration: Literal['min', 'max'] = 'min') → set[Self]

Split the pattern into atomic patterns, i.e. the set of one-sided intervals

Parameters:

atoms_configuration (Literal['min', 'max']) – If equals to ‘min’, return up to 2 atomic patterns each representing a bound of the original interval. If equals to ‘max’, return _all_ less precise one-sided intervals, where the bounds are defined by BoundUniverse class attribute.

Returns:

atomic_patterns – The set of atomic patterns, i.e. the set of unsplittable patterns whose join equals to the pattern.

Return type:

set[Self]

Notes

Speaking in terms of Ordered Set Theory: We say that every pattern can be represented as the join of a subset of atomic patterns, that are join-irreducible elements of the lattice of all patterns.

Considering the set of atomic patterns as a partially ordered set (where the order follows the order on patterns), every pattern can be represented by an _antichain_ of atomic patterns (when atoms_configuration = ‘min’), and by an order ideal of atomic patterns (when atoms_configuration = ‘max’).

property atomic_patterns: set[Self]

Return the set of all less precise patterns that cannot be obtained by intersection of other patterns.

For an IntervalPattern an atomic pattern is a half-bounded interval.

Returns:

atoms – A set of atomic patterns derived from the interval.

Return type:

set[Self]

Examples

>>> IntervalPattern( "[1, 5]" )atomic_patterns
{IntervalPattern("[-∞, ∞]"), IntervalPattern(">=1"), IntervalPattern("<=5") }

property atomisable: bool

Check if the pattern can be atomized. IntervalPattern can only be atomised when BoundsUniverse is defined

Returns:

flag – True if the pattern can be atomized, False otherwise.

Return type:

bool

Examples

>>> p = Pattern("example")
>>> p.atomisable
True

classmethod get_min_pattern() → Self

Return the minimal possible pattern for the interval pattern, i.e. interval [-inf, +inf]

Returns:

min – The minimal interval pattern, which is defined as [-inf, inf].

Return type:

Self

Examples

>>> IntervalPattern.get_min_pattern()
IntervalPattern('[-inf, +inf]')

classmethod get_max_pattern() → Self

Return the maximal possible pattern for the interval pattern, i.e. the empty interval.

Empty interval is the maximal pattern, because it does not cover any other interval. So it describes no objects.

Returns:

max – The maximal interval pattern, which is represented as ‘ø’.

Return type:

Self

Examples

>>> IntervalPattern.get_max_pattern()
IntervalPattern('ø')

property maximal_atoms: set[Self] | None

Return the maximal atomic patterns for the interval pattern.

Returns:

max_atoms – A set of maximal atomic patterns or None if undefined.

Return type:

Optional[set[Self]]

Examples

>>> IntervalPattern().maximal_atoms
{...}