bh/set-algebra #416
bh/set-algebra #416
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Looks great, but I think a lot of what you have here could be significantly simplified by writing the functions as composites of more primitive intersection and union operations. You already have a type that represents the union of a FiniteSet and N IntervalSets, and you could be using it a lot more liberally to simplify these functions. You have lots of special case logic for each of these types that probably isn't necessary and seems like premature optimization. For example I would replace most of the interval squashing code you have here with a single Canonicalize() method on the Set interface, which does nothing for the simple types but squashes the intervals in a CompositeSet. Even that might be overkill though. None of these optimizations are necessary for correctness as far as I can tell, and the times you're going to see significantly better performance from any of them seem like they are probably rare. (Although Canonicalize() will probably make it easier to write tests, so maybe it's worth it just for that).
| // * EmptySet for an interval defined as: N < X < N | ||
| // * EmptySet for an interval where end < start | ||
| // * an unchanged interval will be returned for all other conditions | ||
| func simplifyInterval(in Interval) (Set, error) { |
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I would consider removing this, not sure it's pulling its weight. Seems like a premature optimization.
| // unionWithMultipleIntervals takes an interval and a slice of intervals and returns a slice of intervals containing | ||
| // the minimum number of intervals required to represent the union. The src []Interval argument must be in sorted | ||
| // order and only contain non-overlapping intervals. | ||
| func unionWithMultipleIntervals(in Interval, src []Interval) ([]Interval, error) { |
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If this returned a Set (which would be a CompositeSet in practice) then you could use it as a primitive to compose other union operations
Package setalgebra provides the ability to perform algebraic set operations on mathematical sets built directly on noms
types. Unlike standard sets in computer science, which define a finitely sized collection of unordered unique values,
sets in mathematics are defined as a well-defined collection of distint objects. This can include infinitely sized
groupings such as the set of all real numbers greater than 0.
See https://en.wikipedia.org/wiki/Set_(mathematics)
There are 3 types of sets defined in this package: FiniteSet, Interval, and CompositeSet.
FiniteSet is your typical computer science set representing a finite number of unique objects stored in a map. An
example would be the set of strings {"red","blue","green"}, or the set of numbers {5, 73, 127}.
Interval is a set which can be written as an inequality such as {n | n > 0} (set of all numbers n such that n > 0) or a
chained comparison {n | 0.0 <= n <= 1.0 } (set of all floating point values between 0.0 and 1.0)
CompositeSet is a set which is made up of a FiniteSet and one or more non overlapping intervals such as
{n | n < 0 or n > 100} (set of all numbers n below 0 or greater than 100) this set contains 2 non overlapping intervals
and an empty finite set. Alternatively {n | n < 0 or {5,10,15}} (set of all numbers n below 0 or n equal to 5, 10 or 15)
which would be represented by one Interval and a FiniteSet containing 5,10, and 15.
There are 2 special sets also defined in this package: EmptySet, UniversalSet.
The EmptySet is a set that has no values in it. It has the property that when unioned with any set X, X will be the
result, and if intersected with any set X, EmptySet will be returned.
The UniversalSet is the set containing all values. It has the property that when unioned with any set X, UniversalSet is
returned and when intersected with any set X, X will be returned.