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Theportion library provides data structure and operations for intervals in Python.In particular, it provides the following features:

• Support intervals of any (comparable) objects;
• Closed or open, finite or (semi-)infinite intervals;
• Interval sets (union of atomic intervals) are supported;
• Automatic simplification of intervals;
• Support comparison, transformation, intersection, union, complement, difference and containment;
• Provide test for emptiness, atomicity, overlap and adjacency;
• Discrete iterations on the values of an interval;
• Dict-like structure to map intervals to data;
• Import and export intervals to strings and to Python built-in data types;
• Heavily tested with high code coverage (regardless of what it means);
• Mainly developed by a stubborn but enthusiastic Pythonista!

• Installation
• Documentation & usage
  • Interval creation
  • Interval bounds & attributes
  • Interval operations
  • Comparison operators
  • Interval transformation
  • Discrete iteration
  • Map intervals to data
  • Import & export intervals to strings
  • Import & export intervals to Python built-in data types
  • Specialize & customize intervals
• Changelog
• Contributions
• License

You can usepip to install it, as usual:pip install portion. This will install the latest available version fromPyPI.Pre-releases are available from themaster branch onGitHub and can be installed withpip install git+https://github.com/AlexandreDecan/portion (but don't trust pre-releases!).

You can installportion and its development environment usingpip install --group dev at the root of this repository. This automatically installspytest (for the test suites) andruff (for code style).

Assuming this library is imported usingimport portion as P, intervals can be easily created using one of the following helpers:

>>>P.open(1,2)(1,2)>>>P.closed(1,2)[1,2]>>>P.openclosed(1,2)(1,2]>>>P.closedopen(1,2)[1,2)>>>P.singleton(1)[1]>>>P.empty()()

The bounds of an interval can be any arbitrary values, as long as they are comparable:

>>>P.closed(1.2,2.4)[1.2,2.4]>>>P.closed('a','z')['a','z']>>>importdatetime>>>P.closed(datetime.date(2011,3,15),datetime.date(2013,10,10))[datetime.date(2011,3,15),datetime.date(2013,10,10)]

Infinite and semi-infinite intervals are supported usingP.inf and-P.inf as upper or lower bounds.These two objects support comparison with any other object.When infinities are used as a lower or upper bound, the corresponding boundary is automatically converted to an open one.

>>>P.inf>'a',P.inf>0,P.inf>True(True,True,True)>>>P.openclosed(-P.inf,0)(-inf,0]>>>P.closed(-P.inf,P.inf)# Automatically converted to an open interval(-inf,+inf)

Intervals created with this library areInterval instances.AnInterval instance is a disjunction of atomic intervals each representing a single interval (e.g.[1,2]).Intervals can be iterated to access the underlying atomic intervals, sorted by their lower and upper bounds.

>>>list(P.open(10,11)|P.closed(0,1)|P.closed(20,21))[[0,1], (10,11), [20,21]]>>>list(P.empty())[]

Nested (sorted) intervals can also be retrieved with a position or a slice:

>>> (P.open(10,11)|P.closed(0,1)|P.closed(20,21))[0][0,1]>>> (P.open(10,11)|P.closed(0,1)|P.closed(20,21))[-2](10,11)>>> (P.open(10,11)|P.closed(0,1)|P.closed(20,21))[:2][0,1]| (10,11)

For convenience, intervals are automatically simplified:

>>>P.closed(0,2)|P.closed(2,4)[0,4]>>>P.closed(1,2)|P.closed(3,4)|P.closed(2,3)[1,4]>>>P.empty()|P.closed(0,1)[0,1]>>>P.closed(1,2)|P.closed(2,3)|P.closed(4,5)[1,3]| [4,5]

Note that, by default, simplification of discrete intervals isnot supported byportion (but it can be simulated though, see#24).For example, combining[0,1] with[2,3] willnot result in[0,3] even if there is no integer between1 and2.Refer toSpecialize & customize intervals to see how to create and use specialized discrete intervals.

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AnInterval defines the following properties:

• i.empty isTrue if and only if the interval is empty.

  >>>P.closed(0,1).emptyFalse>>>P.closed(0,0).emptyFalse>>>P.openclosed(0,0).emptyTrue>>>P.empty().emptyTrue

• i.atomic isTrue if and only if the interval is empty or is a disjunction of a single interval.

  >>>P.empty().atomicTrue>>>P.closed(0,2).atomicTrue>>> (P.closed(0,1)|P.closed(1,2)).atomicTrue>>> (P.closed(0,1)|P.closed(2,3)).atomicFalse

• i.enclosure refers to the smallest atomic interval that includes the current one.

  >>> (P.closed(0,1)|P.open(2,3)).enclosure[0,3)

The left and right boundaries, and the lower and upper bounds of an interval can be respectively accessed with itsleft,right,lower andupper attributes.Theleft andright bounds are eitherP.CLOSED orP.OPEN.By definition,P.CLOSED == ~P.OPEN and vice-versa.

>>P.CLOSED,P.OPENCLOSED,OPEN>>>x=P.closedopen(0,1)>>>x.left,x.lower,x.upper,x.right(CLOSED,0,1,OPEN)

By convention, empty intervals resolve to(P.inf, -P.inf):

>>>i=P.empty()>>>i.left,i.lower,i.upper,i.right(OPEN,+inf,-inf,OPEN)

If the interval is not atomic, thenleft andlower refer to the lower bound of its enclosure, whileright andupper refer to the upper bound of its enclosure:

>>>x=P.open(0,1)|P.closed(3,4)>>>x.left,x.lower,x.upper,x.right(OPEN,0,4,CLOSED)

One can easily check for some interval properties based on the bounds of an interval:

>>>x=P.openclosed(-P.inf,0)>>># Check that interval is left/right closed>>>x.left==P.CLOSED,x.right==P.CLOSED(False,True)>>># Check that interval is left/right bounded>>>x.lower==-P.inf,x.upper==P.inf(True,False)>>># Check for singleton>>>x.lower==x.upperFalse

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Interval instances support the following operations:

• i.intersection(other) andi & other return the intersection of two intervals.

  >>>P.closed(0,2)&P.closed(1,3)[1,2]>>>P.closed(0,4)&P.open(2,3)(2,3)>>>P.closed(0,2)&P.closed(2,3)[2]>>>P.closed(0,2)&P.closed(3,4)()

• i.union(other) andi | other return the union of two intervals.

  >>>P.closed(0,1)|P.closed(1,2)[0,2]>>>P.closed(0,1)|P.closed(2,3)[0,1]| [2,3]

• i.complement(other) and~i return the complement of the interval.

  >>>~P.closed(0,1)(-inf,0)| (1,+inf)>>>~(P.open(-P.inf,0)|P.open(1,P.inf))[0,1]>>>~P.open(-P.inf,P.inf)()

• i.difference(other) andi - other return the difference betweeni andother.

  >>>P.closed(0,2)-P.closed(1,2)[0,1)>>>P.closed(0,4)-P.closed(1,2)[0,1)| (2,4]

• i.contains(other) andother in i hold if given item is contained in the interval.It supports intervals and arbitrary comparable values.

  >>>2inP.closed(0,2)True>>>2inP.open(0,2)False>>>P.open(0,1)inP.closed(0,2)True

• i.adjacent(other) tests if the two intervals are adjacent, i.e., if they do not overlap and their union form a single atomic interval.While this definition corresponds to the usual notion of adjacency for atomic intervals, it has stronger requirements for non-atomic ones since it requires all underlying atomic intervals to be adjacent (i.e. that one interval fills the gaps between the atomic intervals of the other one).

  >>>P.closed(0,1).adjacent(P.openclosed(1,2))True>>>P.closed(0,1).adjacent(P.closed(1,2))False>>> (P.closed(0,1)|P.closed(2,3)).adjacent(P.open(1,2)|P.open(3,4))True>>> (P.closed(0,1)|P.closed(2,3)).adjacent(P.open(3,4))False>>>P.closed(0,1).adjacent(P.open(1,2)|P.open(3,4))False

• i.overlaps(other) tests if there is an overlap between two intervals.

  >>>P.closed(1,2).overlaps(P.closed(2,3))True>>>P.closed(1,2).overlaps(P.open(2,3))False

Finally, intervals are hashable as long as their bounds are hashable (and we have defined a hash value forP.inf and-P.inf).

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Equality between intervals can be checked with the classical== operator:

>>>P.closed(0,2)==P.closed(0,1)|P.closed(1,2)True>>>P.closed(0,2)==P.open(0,2)False

Moreover, intervals are comparable using>,>=,< or<=.These comparison operators have a different behaviour than the usual ones.For instance,a < b holds if all values ina are lower than the minimal value ofb (i.e.,a is entirely on the left of the lower bound ofb).

>>>P.closed(0,1)<P.closed(2,3)True>>>P.closed(0,1)<P.closed(1,2)False

Similarly,a <= b if all values ina are lower than the maximal value ofb (i.e.,a is entirely on the left of the upper bound ofb).

>>>P.closed(0,1)<=P.closed(2,3)True>>>P.closed(0,2)<=P.closed(1,3)True>>>P.closed(0,3)<=P.closed(1,2)False

If an interval needs to be compared against a single value, convert the value to a singleton interval first:

>>>P.singleton(0)<P.closed(0,10)False>>>P.singleton(0)<=P.closed(0,10)True>>>P.singleton(5)<=P.closed(0,10)True>>>P.closed(0,1)<P.singleton(2)True

Note that all these semantics differ from classical comparison operators.As a consequence, the empty interval is never<,<=,> nor>= than any other interval, and no interval is<,>,<= or>= when compared to the empty interval.

>>>e=P.empty()>>>e<eore>eore<=eore>=eFalse>>>i=P.closed(0,1)>>>e<iore<=iore>iore>=iFalse

Moreover, some non-empty intervals are also not comparable in the classical sense, as illustrated hereafter:

>>>a,b=P.closed(0,4),P.closed(1,2)>>>a<bora>bFalse>>>a<=bora>=bFalse>>>b<=aandb>=aTrue

As a general rule, ifa < b holds, thena <= b,b > a,b >= a,not (a > b),not (b < a),not (a >= b), andnot (b <= a) hold.

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Intervals are immutable but provide areplace method to create a new interval based on the current one. This method accepts four optional parametersleft,lower,upper, andright:

>>>i=P.closed(0,2)>>>i.replace(P.OPEN,-1,3,P.CLOSED)(-1,3]>>>i.replace(lower=1,right=P.OPEN)[1,2)

Functions can be passed instead of values. If a function is passed, it is called with the current corresponding value.

>>>P.closed(0,2).replace(upper=lambdax:2*x)[0,4]

The provided function won't be called on infinities, unlessignore_inf is set toFalse.

>>>i=P.closedopen(0,P.inf)>>>i.replace(upper=lambdax:10)# No change, infinity is ignored[0,+inf)>>>i.replace(upper=lambdax:10,ignore_inf=False)# Infinity is not ignored[0,10)

Whenreplace is applied on an interval that is not atomic, it is extended and/or restricted such that its enclosure satisfies the new bounds.

>>>i=P.openclosed(0,1)|P.closed(5,10)>>>i.replace(P.CLOSED,-1,8,P.OPEN)[-1,1]| [5,8)>>>i.replace(lower=4)(4,10]

To apply arbitrary transformations on the underlying atomic intervals, intervals expose anapply method that acts likemap.This method accepts a function that will be applied on each of the underlying atomic intervals to perform the desired transformation.The provided function is expected to return either anInterval, or a 4-uple(left, lower, upper, right).

>>>i=P.closed(2,3)|P.open(4,5)>>># Increment bound values>>>i.apply(lambdax: (x.left,x.lower+1,x.upper+1,x.right))[3,4]| (5,6)>>># Invert bounds>>>i.apply(lambdax: (~x.left,x.lower,x.upper,~x.right))(2,3)| [4,5]

Theapply method is very powerful when used in combination withreplace.Because the latter allows functions to be passed as parameters and ignores infinities by default, it can be conveniently used to transform (disjunction of) intervals in presence of infinities.

>>>i=P.openclosed(-P.inf,0)|P.closed(3,4)|P.closedopen(8,P.inf)>>># Increment bound values>>>i.apply(lambdax:x.replace(upper=lambdav:v+1))(-inf,1]| [3,5]| [8,+inf)>>># Intervals are still automatically simplified>>>i.apply(lambdax:x.replace(lower=lambdav:v*2))(-inf,0]| [16,+inf)>>># Invert bounds>>>i.apply(lambdax:x.replace(left=lambdav:~v,right=lambdav:~v))(-inf,0)| (3,4)| (8,+inf)>>># Replace infinities with -10 and 10>>>conv=lambdav:-10ifv==-P.infelse (10ifv==P.infelsev)>>>i.apply(lambdax:x.replace(lower=conv,upper=conv,ignore_inf=False))(-10,0]| [3,4]| [8,10)

Thanks to theapply andreplace methods, several advanced operations or transformations of intervals can be easily expressed.Seethis comment for an example of a morphological opening and closing of intervals with dilatation/erosion using these two methods.

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Theiterate function takes an interval, and returns a generator to iterate over the values of an interval. Obviously, as intervals are continuous, it is required to specify thestep between consecutive values. The iteration then starts from the lower bound and ends on the upper one. Only values contained by the interval are returned this way.

>>>list(P.iterate(P.closed(0,3),step=1))[0,1,2,3]>>>list(P.iterate(P.closed(0,3),step=2))[0,2]>>>list(P.iterate(P.open(0,3),step=2))[2]

When an interval is not atomic,iterate consecutively iterates on all underlying atomic intervals, starting from each lower bound and ending on each upper one:

>>>list(P.iterate(P.singleton(0)|P.singleton(3)|P.singleton(5),step=2))# Won't be [0][0,3,5]>>>list(P.iterate(P.closed(0,2)|P.closed(4,6),step=3))# Won't be [0, 6][0,4]

By default, the iteration always starts on the lower bound of each underlying atomic interval.Thebase parameter can be used to change this behaviour, by specifying how the initial value to start the iteration from must be computed. This parameter accepts a callable that is called with the lower bound of each underlying atomic interval, and that returns the initial value to start the iteration from.It can be helpful to deal with (semi-)infinite intervals, or toalign the generated values of the iterator:

>>># Align on integers>>>list(P.iterate(P.closed(0.3,4.9),step=1,base=int))[1,2,3,4]>>># Restrict values of a (semi-)infinite interval>>>list(P.iterate(P.openclosed(-P.inf,2),step=1,base=lambdax:max(0,x)))[0,1,2]

Thebase parameter can be used to change howiterate applies on unions of atomic interval, by specifying a function that returns a single value, as illustrated next:

>>>base=lambdax:0>>>list(P.iterate(P.singleton(0)|P.singleton(3)|P.singleton(5),step=2,base=base))[0]>>>list(P.iterate(P.closed(0,2)|P.closed(4,6),step=3,base=base))[0,6]

Notice that definingbase such that it returns a single value can be extremely inefficient in terms of performance when the intervals are "far apart" each other (i.e., when thegaps between atomic intervals are large).

Finally, iteration can be performed in reverse order by specifyingreverse=True.

>>>list(P.iterate(P.closed(0,3),step=-1,reverse=True))# Mind step=-1[3,2,1,0]>>>list(P.iterate(P.closed(0,3),step=-2,reverse=True))# Mind step=-2[3,1]

Again, this library does not make any assumption about the objects being used in an interval, as long as they are comparable. However, it is not always possible to provide a meaningful value forstep (e.g., what would be the step between two consecutive characters?). In these cases, a callable can be passed instead of a value.This callable will be called with the current value, and is expected to return the next possible value.

>>>list(P.iterate(P.closed('a','d'),step=lambdad:chr(ord(d)+1)))['a','b','c','d']>>># Since we reversed the order, we changed "+" to "-" in the lambda.>>>list(P.iterate(P.closed('a','d'),step=lambdad:chr(ord(d)-1),reverse=True))['d','c','b','a']

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The library provides anIntervalDict class, adict-like data structure to store and query data along with intervals. Any value can be stored in such data structure as long as it supports equality.

>>>d=P.IntervalDict()>>>d[P.closed(0,3)]='banana'>>>d[4]='apple'>>>d{[0,3]:'banana', [4]:'apple'}

When a value is defined for an interval that overlaps an existing one, it is automatically updated to take the new value into account:

>>>d[P.closed(2,4)]='orange'>>>d{[0,2):'banana', [2,4]:'orange'}

AnIntervalDict can be queried using single values or intervals. If a single value is used as a key, its behaviour corresponds to the one of a classicaldict:

>>>d[2]'orange'>>>d[5]# Key does not existTraceback (mostrecentcalllast): ...KeyError:5>>>d.get(5,default=0)0

When the key is an interval, a newIntervalDict containing the values for the specified key is returned:

>>>d[~P.empty()]# Get all values, similar to d.copy(){[0,2):'banana', [2,4]:'orange'}>>>d[P.closed(1,3)]{[1,2):'banana', [2,3]:'orange'}>>>d[P.closed(-2,1)]{[0,1]:'banana'}>>>d[P.closed(-2,-1)]{}

By using.get, a default value (defaulting toNone) can be specified.This value is used to "fill the gaps" if the queried interval is not completely covered by theIntervalDict:

>>>d.get(P.closed(-2,1),default='peach'){[-2,0):'peach', [0,1]:'banana'}>>>d.get(P.closed(-2,-1),default='peach'){[-2,-1]:'peach'}>>>d.get(P.singleton(1),default='peach')# Key is covered, default is not used{[1]:'banana'}

For convenience, anIntervalDict provides a way to look for specific data values.The.find method always returns a (possibly empty)Interval instance for which given value is defined:

>>>d.find('banana')[0,2)>>>d.find('orange')[2,4]>>>d.find('carrot')()

The active domain of anIntervalDict can be retrieved with its.domain method.This method always returns a singleInterval instance, where.keys returns a sorted view of disjoint intervals.

>>>d.domain()[0,4]>>>list(d.keys())[[0,2), [2,4]]>>>list(d.values())['banana','orange']>>>list(d.items())[([0,2),'banana'), ([2,4],'orange')]

The.keys,.values and.items methods return exactly one element for each stored value (i.e., if two intervals share a value, they are merged into a disjunction), as illustrated next.See#44 to know how to obtain a sorted list of atomic intervals instead.

>>>d=P.IntervalDict()>>>d[P.closed(0,1)]=d[P.closed(2,3)]='peach'>>>list(d.items())[([0,1]| [2,3],'peach')]

TwoIntervalDict instances can be combined using the.combine method.This method returns a newIntervalDict whose keys and values are taken from the two sourceIntervalDict.The values corresponding to intersecting keys (i.e., when the two instances overlap) are combined using the providedhow function, while values corresponding to non-intersecting keys are simply copied (i.e., thehow function is not called for them), as illustrated hereafter:

>>>d1=P.IntervalDict({P.closed(0,2):'banana'})>>>d2=P.IntervalDict({P.closed(1,3):'orange'})>>>concat=lambdax,y:x+'/'+y>>>d1.combine(d2,how=concat){[0,1):'banana', [1,2]:'banana/orange', (2,3]:'orange'}

Thehow function can also receive the current interval as third parameter, by enabling thepass_interval parameter of.combine.Thecombine method also accepts amissing parameter. Whenmissing is set, thehow function is called even for non-intersecting keys, using the value ofmissing to replace the missing values:

>>>d1.combine(d2,how=concat,missing='kiwi'){[0,1):'banana/kiwi', [1,2]:'banana/orange', (2,3]:'kiwi/orange'}

Resulting keys always correspond to an outer join. Other joins can be easily simulated by querying the resultingIntervalDict as follows:

>>>d=d1.combine(d2,how=concat)>>>d[d1.domain()]# Left join{[0,1):'banana', [1,2]:'banana/orange'}>>>d[d2.domain()]# Right join{[1,2]:'banana/orange', (2,3]:'orange'}>>>d[d1.domain()&d2.domain()]# Inner join{[1,2]:'banana/orange'}

While.combine accepts a singleIntervalDict, it can be generalized to support an arbitrary number ofIntervalDicts, as illustrated in#95.

Finally, similarly to adict, anIntervalDict also supportslen,in anddel, and defines.clear,.copy,.update,.pop,.popitem, and.setdefault.For convenience, one can export the content of anIntervalDict to a classical Pythondict using theas_dict method. This method accepts an optionalatomic parameter (whose default isFalse).When set toTrue, the keys of the resultingdict instance are atomic intervals.

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Intervals can be exported to string, either usingrepr (as illustrated above) or with theto_string function.

>>>P.to_string(P.closedopen(0,1))'[0,1)'

The way string representations are built can be easily parametrized using the various parameters supported byto_string:

>>>params= {...'disj':' or ',...'sep':' - ',...'left_closed':'<',...'right_closed':'>',...'left_open':'..',...'right_open':'..',...'pinf':'+oo',...'ninf':'-oo',...'conv':lambdav:'"{}"'.format(v),... }>>>x=P.openclosed(0,1)|P.closed(2,P.inf)>>>P.to_string(x,**params)'.."0" - "1"> or <"2" - +oo..'

Similarly, intervals can be created from a string using thefrom_string function.A conversion function (conv parameter) has to be provided to convert a bound (as string) to a value.

>>>P.from_string('[0, 1]',conv=int)==P.closed(0,1)True>>>P.from_string('[1.2]',conv=float)==P.singleton(1.2)True>>>converter=lambdas:datetime.datetime.strptime(s,'%Y/%m/%d')>>>P.from_string('[2011/03/15, 2013/10/10]',conv=converter)[datetime.datetime(2011,3,15,0,0),datetime.datetime(2013,10,10,0,0)]

Similarly toto_string, functionfrom_string can be parametrized to deal with more elaborated inputs.Notice that asfrom_string expects regular expression patterns, we need to escape some characters.

>>>s='.."0" - "1"> or <"2" - +oo..'>>>params= {...'disj':' or ',...'sep':' - ',...'left_closed':'<',...'right_closed':'>',...'left_open':r'\.\.',# from_string expects regular expression patterns...'right_open':r'\.\.',# from_string expects regular expression patterns...'pinf':r'\+oo',# from_string expects regular expression patterns...'ninf':'-oo',...'conv':lambdav:int(v[1:-1]),... }>>>P.from_string(s,**params)(0,1]| [2,+inf)

When a bound contains a comma or has a representation that cannot be automatically parsed withfrom_string, thebound parameter can be used to specify the regular expression that should be used to match its representation.

>>>s='[(0, 1), (2, 3)]'# Bounds are expected to be tuples>>>P.from_string(s,conv=eval,bound=r'\(.+?\)')[(0,1),(2,3)]

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Intervals can also be exported to a list of 4-uples withto_data, e.g., to support JSON serialization.P.CLOSED andP.OPEN are represented by Boolean valuesTrue (inclusive) andFalse (exclusive).

>>>P.to_data(P.openclosed(0,2))[(False,0,2,True)]

The values used to represent positive and negative infinities can be specified withpinf andninf. They default tofloat('inf') andfloat('-inf') respectively.

>>>x=P.openclosed(0,1)|P.closedopen(2,P.inf)>>>P.to_data(x)[(False,0,1,True), (True,2,inf,False)]

The function to convert bounds can be specified with theconv parameter.

>>>x=P.closedopen(datetime.date(2011,3,15),datetime.date(2013,10,10))>>>P.to_data(x,conv=lambdav: (v.year,v.month,v.day))[(True, (2011,3,15), (2013,10,10),False)]

Intervals can be imported from such a list of 4-tuples withfrom_data.The same set of parameters can be used to specify how bounds and infinities are converted.

>>>x= [(True, (2011,3,15), (2013,10,10),False)]>>>P.from_data(x,conv=lambdav:datetime.date(*v))[datetime.date(2011,3,15),datetime.date(2013,10,10))

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Disclaimer: the features explained in this section are still experimental and are subject to backward incompatible changes even in minor or patch updates ofportion.

The intervals provided byportion already cover a wide range of use cases.However, in some situations, it might be interesting to specialize or customize these intervals.One typical example would be to support discrete intervals such as intervals of integers.

While it is definitely possible to rely on the default intervals provided byportion to encode discrete intervals, there are a few edge cases that lead some operations to return unexpected results:

>>>P.singleton(0)|P.singleton(1)# Case 1: should be [0,1] for discrete numbers[0]| [1]>>>P.open(0,1)# Case 2: should be empty(0,1)>>>P.closedopen(0,1)# Case 3: should be singleton [0][0,1)

Theportion library makes its best to ease defining and using subclasses ofInterval to address these situations. In particular,Interval instances always produce new intervals usingself.__class__, and the class is written in a way that most of its methods can be easily extended.

To implement a class for intervals of discrete numbers and to cover the three aforementioned cases, we need to change the behaviour of theInterval._mergeable class method (to address first case) and of theInterval.from_atomic class method (for cases 2 and 3).The former is used to detect whether two atomic intervals can be merged into a single interval, while the latter is used to create atomic intervals.

Thankfully, since discrete intervals are expected to be a frequent use case,portion provides anAbstractDiscreteInterval class that already makes the appropriate changes to these two methods.As indicated by its name, this class cannot be used directly and should be inherited.In particular, one has either to provide a_step class attribute to define the step between consecutive discrete values, or to define the_incr and_decr class methods:

>>>classIntInterval(P.AbstractDiscreteInterval):..._step=1

That's all!We can now use this class to manipulate intervals of discrete numbers and see it covers the three problematic cases:

>>>IntInterval.from_atomic(P.CLOSED,0,0,P.CLOSED)|IntInterval.from_atomic(P.CLOSED,1,1,P.CLOSED)[0,1]>>>IntInterval.from_atomic(P.OPEN,0,1,P.OPEN)()>>>IntInterval.from_atomic(P.CLOSED,0,1,P.OPEN)[0]

As an example of using_incr and_decr, consider the followingCharInterval subclass tailored to manipulate intervals of characters:

>>>classCharInterval(P.AbstractDiscreteInterval):..._incr=lambdav:chr(ord(v)+1)..._decr=lambdav:chr(ord(v)-1)>>>CharInterval.from_atomic(P.OPEN,'a','z',P.OPEN)['b','y']

Having to callfrom_atomic on the subclass to create intervals is quite verbose.For convenience, all the functions that create interval instances accept an additionalklass parameter to specify the class that creates intervals, circumventing the direct use of the class constructors.However, having to specify theklass parameter in each call toP.closed or other helpers that create intervals is still a bit too verbose to be convenient.Consequently,portion provides acreate_api function that, given a subclass ofInterval, returns a dynamically generated module whose API is similar to the one ofportion but configured to use the subclass instead:

>>>D=P.create_api(IntInterval)>>>D.singleton(0)|D.singleton(1)[0,1]>>>D.open(0,1)()>>>D.closedopen(0,1)[0]

This makes it easy to use our newly definedIntInterval subclass while still benefiting fromportion's API.

Let's extend our example to support intervals of natural numbers.Such intervals are quite similar to the above ones, except they cannot go over negative values.We can prevent the bounds of an interval to be negative by slightly changing thefrom_atomic class method as follows:

>>>classNaturalInterval(IntInterval):...    @classmethod...deffrom_atomic(cls,left,lower,upper,right):...returnsuper().from_atomic(...P.CLOSEDiflower<0elseleft,...max(0,lower),...upper,...right,...        )

We can now define and use theN module to check whether our newly definedNaturalInterval does the job:

>>>N=P.create_api(NaturalInterval)>>>N.closed(-10,2)[0,2]>>>N.open(-10,2)[0,1]>>>~N.empty()[0,+inf)

Keep in mind that just becauseNaturalInterval has semantics associated with natural numbers does not mean that all possible operations on these intervals strictly comply the semantics.The following examples illustrate some of the cases where additional checks should be implemented to strictly adhere to these semantics:

>>>N.closed(1.5,2.5)# Bounds are not natural numbers[1.5,2.5]>>>0.5inN.closed(0,1)# Given value is not a natural numberTrue>>>~N.singleton(0.5)[1.5,+inf)

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This library adheres to asemantic versioning scheme (except for the experimental features as mentionned in the documentation).SeeCHANGELOG.md for the list of changes.

Feel free to report bugs or suggest new features using GitHub issues and/or pull requests.Contributions are very welcome, but please open an issue before, especially for new features ;-)

Distributed underLGPLv3 - GNU Lesser General Public License, version 3.

You can refer to this library using:

@software{portion,  author = {Decan, Alexandre},  title = {portion: Python data structure and operations for intervals},  url = {https://github.com/AlexandreDecan/portion},}