From f4b5fd8352e1bade92b3381ffff1542f5175cd71 Mon Sep 17 00:00:00 2001
From: schillic <schillic@informatik.uni-freiburg.de>
Date: Mon, 1 Oct 2018 16:36:44 +0200
Subject: [PATCH 1/2] made 'Interval' an 'AbstractHyperrectangle'

---
 src/AbstractCentrallySymmetricPolytope.jl |  3 +-
 src/AbstractHyperrectangle.jl             |  3 +-
 src/Interval.jl                           | 49 ++++++++++++++++++++---
 3 files changed, 47 insertions(+), 8 deletions(-)

diff --git a/src/AbstractCentrallySymmetricPolytope.jl b/src/AbstractCentrallySymmetricPolytope.jl
index 486f62af48..114fde97ad 100644
--- a/src/AbstractCentrallySymmetricPolytope.jl
+++ b/src/AbstractCentrallySymmetricPolytope.jl
@@ -25,10 +25,9 @@ functions:
 
 ```jldoctest
 julia> subtypes(AbstractCentrallySymmetricPolytope)
-5-element Array{Any,1}:
+4-element Array{Any,1}:
  AbstractHyperrectangle
  Ball1
- Interval
  LineSegment
  Zonotope
 ```
diff --git a/src/AbstractHyperrectangle.jl b/src/AbstractHyperrectangle.jl
index b9c6e74704..09abb52537 100644
--- a/src/AbstractHyperrectangle.jl
+++ b/src/AbstractHyperrectangle.jl
@@ -19,10 +19,11 @@ Every concrete `AbstractHyperrectangle` must define the following functions:
 
 ```jldoctest
 julia> subtypes(AbstractHyperrectangle)
-4-element Array{Any,1}:
+5-element Array{Any,1}:
  AbstractSingleton
  BallInf
  Hyperrectangle
+ Interval
  SymmetricIntervalHull
 ```
 """
diff --git a/src/Interval.jl b/src/Interval.jl
index 7a0ff742d7..8dada4ffe6 100644
--- a/src/Interval.jl
+++ b/src/Interval.jl
@@ -7,11 +7,10 @@ export Interval,
        low, high, vertices_list
 
 """
-    Interval{N<:Real, IN <: AbstractInterval{N}}
-        <: AbstractCentrallySymmetricPolytope{N}
+    Interval{N<:Real, IN <: AbstractInterval{N}} <: AbstractHyperrectangle{N}
 
-Type representing an interval on the real line. Mathematically, it is of the
-form
+Type representing an interval on the real line.
+Mathematically, it is of the form
 
 ```math
 [a, b] := \\{ a ≤ x ≤ b \\} ⊆ \\mathbb{R}.
@@ -75,7 +74,7 @@ julia> Interval(0//1, 2//1)
 Interval{Rational{Int64},IntervalArithmetic.AbstractInterval{Rational{Int64}}}([0//1, 2//1])
 ```
 """
-struct Interval{N<:Real, IN <: AbstractInterval{N}} <: AbstractCentrallySymmetricPolytope{N}
+struct Interval{N<:Real, IN <: AbstractInterval{N}} <: AbstractHyperrectangle{N}
    dat::IN
 end
 
@@ -303,3 +302,43 @@ Return the list of vertices of this interval.
 The list of vertices of the interval represented as two one-dimensional vectors.
 """
 vertices_list(x::Interval) = [[low(x)], [high(x)]]
+
+
+# --- AbstractHyperrectangle interface functions ---
+
+
+"""
+    radius_hyperrectangle(I::Interval{N}, i::Int)::N where {N<:Real}
+
+Return the box radius of an interval in a given dimension.
+
+### Input
+
+- `I` -- interval
+- `i` -- dimension index (must be `1`)
+
+### Output
+
+The box radius in the given dimension.
+"""
+function radius_hyperrectangle(I::Interval{N}, i::Int)::N where {N<:Real}
+    @assert i == 1 "an interval is one-dimensional"
+    return high(x) - low(x)
+end
+
+"""
+    radius_hyperrectangle(I::Interval{N})::Vector{N} where {N<:Real}
+
+Return the box radius of an interval in every dimension.
+
+### Input
+
+- `I` -- interval
+
+### Output
+
+The box radius of the interval (a one-dimensional vector).
+"""
+function radius_hyperrectangle(I::Interval{N})::Vector{N} where {N<:Real}
+    return [high(x) - low(x)]
+end

From f2207c035080482ef0468b6a19db7b137a1d27b5 Mon Sep 17 00:00:00 2001
From: schillic <schillic@informatik.uni-freiburg.de>
Date: Mon, 1 Oct 2018 16:41:35 +0200
Subject: [PATCH 2/2] fix method ambiguity

---
 src/Interval.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/Interval.jl b/src/Interval.jl
index 8dada4ffe6..0907f6b26f 100644
--- a/src/Interval.jl
+++ b/src/Interval.jl
@@ -210,7 +210,7 @@ The product of the intervals as a new `Interval` set.
 *(x::Interval, y::Interval) = Interval(x.dat * y.dat)
 
 """
-    ∈(v::AbstractVector, x::Interval)
+    ∈(v::AbstractVector{N}, x::Interval{N}) where {N<:Real})
 
 Return whether a vector is contained in the interval.
 
@@ -223,7 +223,7 @@ Return whether a vector is contained in the interval.
 
 `true` iff `x` contains `v`'s first component.
 """
-∈(v::AbstractVector, x::Interval) = v[1] ∈ x.dat
+∈(v::AbstractVector{N}, x::Interval{N}) where {N<:Real} = v[1] ∈ x.dat
 
 """
     ∈(v::N, x::Interval) where {N}