Merge pull request #649 from JuliaReach/schillic/639

#639 - Compact sets

docs/src/lib/interfaces.md

@@ -59,6 +59,13 @@ an_element(::LazySet{Real})
 ==(::LazySet, ::LazySet)
 ```
 
+### Aliases for set types
+
+```@docs
+CompactSet
+NonCompactSet
+```
+
 ## Centrally symmetric set
 
 Centrally symmetric sets such as balls of different norms are characterized by a

src/LazySets.jl

@@ -73,6 +73,11 @@ include("concrete_intersection.jl")
 include("is_intersection_empty.jl")
 include("is_subset.jl")
 
+# =======
+# Aliases
+# =======
+include("aliases.jl")
+
 # =====================
 # Approximations module
 # =====================

src/aliases.jl

@@ -0,0 +1,34 @@
+export CompactSet,
+       NonCompactSet
+
+"""
+    CompactSet
+
+An alias for compact set types.
+
+### Notes
+
+Most lazy operations are not captured by this alias because whether their result
+is compact or not depends on the argument(s).
+"""
+const CompactSet = Union{
+    AbstractCentrallySymmetric,
+    AbstractPolytope,
+    EmptySet
+    }
+
+"""
+    NonCompactSet
+
+An alias for non-compact set types.
+
+### Notes
+
+Most lazy operations are not captured by this alias because whether their result
+is non-compact or not depends on the argument(s).
+"""
+const NonCompactSet = Union{
+    HalfSpace,
+    Hyperplane,
+    Line    
+    }

test/runtests.jl

@@ -78,6 +78,11 @@ if test_suite_basic
     @time @testset "LazySets.CartesianProduct" begin include("unit_CartesianProduct.jl") end
     @time @testset "LazySets.SymmetricIntervalHull" begin include("unit_SymmetricIntervalHull.jl") end
 
+    # ======================
+    # Testing set interfaces
+    # ======================
+    @time @testset "LazySets.CompactSet" begin include("unit_CompactSet.jl") end
+
     # =================================================================
     # Algorithms for approximation of convex sets using support vectors
     # =================================================================

test/unit_CompactSet.jl

@@ -0,0 +1,16 @@
+for N in [Float64, Rational{Int}, Float32]
+    # compact set
+    @test Ball1 <: CompactSet && !(Ball1 <: NonCompactSet)
+    b = Ball1(N[0, 1], N(1))
+    @test b isa CompactSet && !(b isa NonCompactSet)
+
+    # non-compact set
+    @test Line <: NonCompactSet && !(Line <: CompactSet)
+    l = Line(N[0, 1], N(1))
+    @test l isa NonCompactSet && !(l isa CompactSet)
+
+    # lazy operations are neither compact nor non-compact by default
+    @test !(MinkowskiSum <: CompactSet) && !(MinkowskiSum <: NonCompactSet)
+    ms = b + l
+    @test !(ms isa CompactSet) && !(ms isa NonCompactSet)
+end