Introduce an IntervalSet type.

src/Intervals.jl

@@ -42,6 +42,7 @@ export Bound,
        Unbounded,
        AbstractInterval,
        Interval,
+       IntervalSet,
        AnchoredInterval,
        HourEnding,
        HourBeginning,

src/deprecated.jl

@@ -195,4 +195,8 @@ function HB(anchor, inc::Inclusivity)
     return HourBeginning{L,R}(floor(anchor, Hour))
 end
 
+@deprecate union(intervals::AbstractVector{<:AbstractInterval}) collect(union(IntervalSet(intervals)))
+@deprecate union!(intervals::AbstractVector{<:AbstractInterval}) collect(union!(IntervalSet(intervals)))
+@deprecate superset(intervals::AbstractVector{<:AbstractInterval}) superset(IntervalSet(intervals))
+
 # END Intervals 1.X.Y deprecations

src/interval_sets.jl

@@ -1,7 +1,22 @@
 
 ###### Set-related Helpers #####
 
-const IntervalSet = AbstractVector{<:AbstractInterval}
+struct IntervalSet{T<:AbstractInterval}
+    items::Vector{<:AbstractInterval}
+end
+
+IntervalSet(v::AbstractVector) = IntervalSet{eltype(v)}(v)
+IntervalSet(interval::T) where T <: AbstractInterval = IntervalSet{T}([interval])
+IntervalSet(interval::IntervalSet) = interval
+IntervalSet(itr) = IntervalSet{eltype(itr)}(collect(itr))
+
+Base.copy(intervals::IntervalSet{T}) where T = IntervalSet{T}(copy(intervals.items))
+Base.length(intervals::IntervalSet) = length(intervals.items)
+Base.iterate(intervals::IntervalSet, args...) = iterate(intervals.items, args...)
+Base.eltype(::IntervalSet{T}) where T = T
+Base.:(==)(a::IntervalSet, b::IntervalSet) = a.items == b.items
+Base.isequal(a::IntervalSet, b::IntervalSet) = isequal(a, b)
+
 const AbstractIntervals = Union{AbstractInterval, IntervalSet}
 
 # During merge operations used to compute unions, intersections etc...,
@@ -39,9 +54,13 @@ function endpoint_tracking(
 )
     return TrackEachEndpoint()
 end
-endpoint_tracking(a::AbstractVector, b::AbstractVector) = endpoint_tracking(eltype(a), eltype(b))
+
+endpoint_tracking(a::IntervalSet, b::IntervalSet) = endpoint_tracking(eltype(a), eltype(b))
 endpoint_tracking(a::AbstractInterval, b::AbstractInterval) = endpoint_tracking(typeof(a), typeof(b))
 
+# TODO: Delete once union deprecation is gone.
+endpoint_tracking(a::AbstractVector, b::AbstractVector) = endpoint_tracking(eltype(a), eltype(b))
+
 # track: run a thunk, but only if we are tracking endpoints dynamically
 track(fn::Function, ::TrackEachEndpoint, args...) = fn(args...)
 track(_, tracking::TrackStatically, args...) = tracking
@@ -58,11 +77,11 @@ interval_type(::TrackRightOpen{T}) where T = Interval{T, Closed, Open}
 # all vectors of sets be represented by their endpoints. The functions unbunch
 # and bunch convert between an interval and an endpoint representation
 
-function unbunch(interval::AbstractInterval, tracking::EndpointTracking; lt=isless) 
+function unbunch(interval::AbstractInterval, tracking::EndpointTracking; lt=isless)
     return endpoint_type(tracking)[LeftEndpoint(interval), RightEndpoint(interval)]
 end
 unbunch_by_fn(_) = identity
-function unbunch(intervals::Union{AbstractIntervals, Base.Iterators.Enumerate{<:AbstractIntervals}}, 
+function unbunch(intervals::Union{AbstractIntervals, Base.Iterators.Enumerate{<:AbstractIntervals}},
                  tracking::EndpointTracking; lt=isless)
     by = unbunch_by_fn(intervals)
     filtered = Iterators.filter(!isempty ∘ by, intervals)
@@ -72,7 +91,7 @@ function unbunch(intervals::Union{AbstractIntervals, Base.Iterators.Enumerate{<:
 end
 # support for `unbunch(enumerate(vcat(x)))` (transforming [(i, interval)] -> [(i, endpoint), (i,endpoint)])
 unbunch_by_fn(::Base.Iterators.Enumerate) = last
-function unbunch((i, interval)::Tuple, tracking; lt=isless) 
+function unbunch((i, interval)::Tuple, tracking; lt=isless)
     eltype = Tuple{Int, endpoint_type(tracking)}
     return eltype[(i, LeftEndpoint(interval)), (i, RightEndpoint(interval))]
 end
@@ -84,19 +103,25 @@ function unbunch(a::AbstractIntervals, b::AbstractIntervals; kwargs...)
     return a_, b_, tracking
 end
 
+# TODO: Delete fallback once union deprecation is removed
+function unbunch(a::Vector{<:AbstractInterval}, b::Vector{<:AbstractInterval}; kwargs...)
+    return unbunch(IntervalSet(a), IntervalSet(b); kwargs...)
+end
+
 # represent a sequence of endpoints as a sequence of one or more intervals
 function bunch(endpoints, tracking)
     @assert iseven(length(endpoints))
-    isempty(endpoints) && return interval_type(tracking)[]
-    return map(Iterators.partition(endpoints, 2)) do pair
+    isempty(endpoints) && return IntervalSet(interval_type(tracking)[])
+    res = map(Iterators.partition(endpoints, 2)) do pair
         return Interval(pair..., tracking)
     end
+    return IntervalSet(res)
 end
 Interval(a::Endpoint, b::Endpoint, ::TrackEachEndpoint) = Interval(a, b)
 Interval(a::Endpoint, b::Endpoint, ::TrackLeftOpen{T}) where T = Interval{T,Open,Closed}(a.endpoint, b.endpoint)
 Interval(a::Endpoint, b::Endpoint, ::TrackRightOpen{T}) where T = Interval{T,Closed,Open}(a.endpoint, b.endpoint)
 
-# the sentinel endpoint reduces the number of edgecases 
+# the sentinel endpoint reduces the number of edgecases
 # we have to deal with when comparing endpoints during a merge
 # NOTE: it's tempting to replace this with an unbounded endpoint
 # but if we ever want to support unbounded endpoints in mergesets
@@ -108,7 +133,7 @@ function first_endpoint(x)
     return eltype(x) <: Tuple ? last(first(x)) : first(x)
 end
 function last_endpoint(x)
-    isempty(x) && return SentinelEndpoint() 
+    isempty(x) && return SentinelEndpoint()
     # if the endpoints are enumerated, eltype will be a tuple
     return eltype(x) <: Tuple ? last(last(x)) : last(x)
 end
@@ -139,7 +164,7 @@ isleft(::RightEndpoint) = false
 # will remain unchanged moving left to right along the real-number line until we encounter a
 # new endpoint.
 #
-# For each endpoint, we determine two things: 
+# For each endpoint, we determine two things:
 #   1. whether subsequent points should be included in the merge operation or not (based on
 #        its membership in both `x` and `y`) by using `op`
 #   2. whether the next step will define a left (start including) or right endpoint (stop
@@ -264,35 +289,35 @@ right_endpoint(t, ::TrackRightOpen{T}) where T = RightEndpoint{T,Open}(endpoint(
 
 # There is power in a union.
 """
-    union(intervals::AbstractVector{<:AbstractInterval})
+    union(intervals::IntervalSets)
 
-Flattens a vector of overlapping intervals into a new, smaller vector containing only
-non-overlapping intervals.
+Flattens any overlapping intervals within the `IntervalSet` into a new, smaller set
+containing only non-overlapping intervals.
 """
-function Base.union(intervals::AbstractVector{<:AbstractInterval})
-    return union!(convert(Vector{AbstractInterval}, intervals))
-end
+Base.union(intervals::IntervalSet{<:Interval}) = union!(copy(intervals))
 
-# allow a concretely typed array for `Interval` objects (as opposed to e.g. anchored intervals
-# which may change type during the union process)
-function Base.union(intervals::AbstractVector{T}) where T <: Interval
-    return union!(copy(intervals))
+# In the case where we're dealing with a non-concrete interval type like AnchoredIntervals then simply
+# allocate a AbstractInterval vector
+function Base.union(intervals::IntervalSet{<:AbstractInterval})
+    T = AbstractInterval
+    return union!(IntervalSet{T}(convert(Vector{T}, intervals.items)))
 end
 
 """
-    union!(intervals::AbstractVector{<:AbstractInterval})
+    union!(intervals::IntervalSet)
 
 Flattens a vector of overlapping intervals in-place to be a smaller vector containing only
 non-overlapping intervals.
 """
-function Base.union!(intervals::AbstractVector{<:AbstractInterval})
-    sort!(intervals)
+function Base.union!(intervals::IntervalSet)
+    items = intervals.items
+    sort!(items)
 
     i = 2
-    n = length(intervals)
+    n = length(items)
     while i <= n
-        prev = intervals[i - 1]
-        curr = intervals[i]
+        prev = items[i - 1]
+        curr = items[i]
 
         # If the current and previous intervals don't meet then move along
         if !overlaps(prev, curr) && !contiguous(prev, curr)
@@ -301,8 +326,8 @@ function Base.union!(intervals::AbstractVector{<:AbstractInterval})
         # If the two intervals meet then we absorb the current interval into
         # the previous one.
         else
-            intervals[i - 1] = merge(prev, curr)
-            deleteat!(intervals, i)
+            items[i - 1] = merge(prev, curr)
+            deleteat!(items, i)
             n -= 1
         end
     end
@@ -311,13 +336,13 @@ function Base.union!(intervals::AbstractVector{<:AbstractInterval})
 end
 
 """
-    superset(intervals::AbstractArray{<:AbstractInterval}) -> Interval
+    superset(intervals::IntervalSet) -> Interval
 
 Create the smallest single interval which encompasses all of the provided intervals.
 """
-function superset(intervals::AbstractArray{<:AbstractInterval})
-    left = minimum(LeftEndpoint.(intervals))
-    right = maximum(RightEndpoint.(intervals))
+function superset(intervals::IntervalSet)
+    left = minimum(LeftEndpoint.(intervals.items))
+    right = maximum(RightEndpoint.(intervals.items))
 
     return Interval(left, right)
 end
@@ -332,14 +357,14 @@ Base.issubset(x::AbstractIntervals, y::AbstractIntervals) = isempty(setdiff(x, y
 Base.isdisjoint(x::AbstractIntervals, y::AbstractIntervals) = isempty(intersect(x, y))
 
 function Base.issetequal(x::AbstractIntervals, y::AbstractIntervals)
-    x, y, tracking = unbunch(union(vcat(x)), union(vcat(y)))
+    x, y, tracking = unbunch(union(IntervalSet(x)), union(IntervalSet(y)))
     return x == y || all(isempty, bunch(x, tracking)) && all(isempty, bunch(y, tracking))
 end
 
 # order edges so that closed boundaries are on the outside: e.g. [( )]
 intersection_order(x::Endpoint) = isleft(x) ? !isclosed(x) : isclosed(x)
 intersection_isless_fn(::TrackStatically) = isless
-function intersection_isless_fn(::TrackEachEndpoint) 
+function intersection_isless_fn(::TrackEachEndpoint)
     function (x,y)
         if isequal(x, y)
             return isless(intersection_order(x), intersection_order(y))
@@ -351,15 +376,15 @@ end
 
 """
     find_intersections(
-        x::Union{AbstractInterval, AbstractVector{<:AbstractInterval}},
-        y::Union{AbstractInterval, AbstractVector{<:AbstractInterval}},
+        x::Union{AbstractInterval, IntervalSet},
+        y::Union{AbstractInterval, IntervalSet},
     )
 
 Returns a `Vector{Vector{Int}}` where the value at index `i` gives the indices to all
 intervals in `y` that intersect with `x[i]`.
 """
 function find_intersections(x_::AbstractIntervals, y_::AbstractIntervals)
-    xa, ya = vcat(x_), vcat(y_)
+    xa, ya = IntervalSet(x_), IntervalSet(y_)
     tracking = endpoint_tracking(xa, ya)
     lt = intersection_isless_fn(tracking)
     x = unbunch(enumerate(xa), tracking; lt)
@@ -402,4 +427,3 @@ function find_intersections_helper!(result, x, y, lt)
 
     return unique!.(result)
 end
-