From b3caa0c6352c0b7295ef7e9594e5a318769a110c Mon Sep 17 00:00:00 2001
From: Azzaare <jf@baffier.fr>
Date: Fri, 13 Aug 2021 15:43:03 +0900
Subject: [PATCH 1/3] Add a conversion from IntervalsFold to VectorFold when
 the interval is a point

---
 src/common.jl    | 9 +++++++++
 src/intervals.jl | 6 ++++++
 test/vector.jl   | 3 +++
 3 files changed, 18 insertions(+)

diff --git a/src/common.jl b/src/common.jl
index 01c5b07..4e62020 100644
--- a/src/common.jl
+++ b/src/common.jl
@@ -104,6 +104,15 @@ A dispatcher to construct a folded vector. The `kind` of vector can be set to ei
 function make_vector_fold(pattern, gap, fold, kind = :mutable)
     return make_vector_fold(pattern, gap, fold, Val(kind))
 end
+function make_vector_fold(isf; kind = :mutable)
+    vf = kind == :mutable ? "VectorFold" : "IVectorFold"
+    str = "The pattern of the interval is not a point." *
+        " The IntervalsFold cannot be converted to a $vf"
+    pt = pattern(isf)
+    @assert is_point(pt) str
+
+    return make_vector_fold([value(pt, :a)], gap(isf), folds(isf), kind)
+end
 
 function Base.print_array(io::IO, X::AbstractVectorFold)
     print(io, "\tPattern: $(pattern(X))\n\tGap: $(gap(X))\n\tFolds: $(folds(X))")
diff --git a/src/intervals.jl b/src/intervals.jl
index ad028cf..9efffe6 100644
--- a/src/intervals.jl
+++ b/src/intervals.jl
@@ -52,6 +52,12 @@ Base.isempty(i::Interval) = size(i) == 0 && (opened(i, :a) || opened(i, :b))
 Base.ndims(::Interval) = 1
 Base.rand(i::Interval) = rand() * size(i) + value(i, :a)
 
+"""
+    is_point(i::Interval)
+Check if the interval `i` is simple point.
+"""
+is_point(i) = value(i, :a) == value(i, :b) && !isempty(i)
+
 mutable struct IntervalsFold{T <: Real} #<: PatternFold{T, Interval{T}}
     pattern::Interval{T}
     gap::T
diff --git a/test/vector.jl b/test/vector.jl
index 461c96e..4f2a7c6 100644
--- a/test/vector.jl
+++ b/test/vector.jl
@@ -43,4 +43,7 @@
     v22 = fold(w2)
 
     @test unfold(v22) == w2
+
+    isf = IntervalsFold(Interval((0.0, true), (0.0, true)), 1.0, 5)
+    @test unfold(make_vector_fold(isf)) == [i for i in 0.0:4.0]
 end

From 63bfbe148b97fc3cf594ffefbc9a44f782b39c18 Mon Sep 17 00:00:00 2001
From: Azzaare <jf@baffier.fr>
Date: Fri, 13 Aug 2021 15:53:45 +0900
Subject: [PATCH 2/3] Add is_points

---
 src/PatternFolds.jl | 2 ++
 src/common.jl       | 5 ++---
 src/intervals.jl    | 2 ++
 test/vector.jl      | 1 +
 4 files changed, 7 insertions(+), 3 deletions(-)

diff --git a/src/PatternFolds.jl b/src/PatternFolds.jl
index c0af992..7d1945f 100644
--- a/src/PatternFolds.jl
+++ b/src/PatternFolds.jl
@@ -18,6 +18,8 @@ export closed
 export fold
 export folds
 export gap
+export is_point
+export is_points
 export length
 export make_vector_fold
 export opened
diff --git a/src/common.jl b/src/common.jl
index 4e62020..f0c2c85 100644
--- a/src/common.jl
+++ b/src/common.jl
@@ -108,10 +108,9 @@ function make_vector_fold(isf; kind = :mutable)
     vf = kind == :mutable ? "VectorFold" : "IVectorFold"
     str = "The pattern of the interval is not a point." *
         " The IntervalsFold cannot be converted to a $vf"
-    pt = pattern(isf)
-    @assert is_point(pt) str
+    @assert is_points(isf) str
 
-    return make_vector_fold([value(pt, :a)], gap(isf), folds(isf), kind)
+    return make_vector_fold([value(pattern(isf), :a)], gap(isf), folds(isf), kind)
 end
 
 function Base.print_array(io::IO, X::AbstractVectorFold)
diff --git a/src/intervals.jl b/src/intervals.jl
index 9efffe6..cbf27b6 100644
--- a/src/intervals.jl
+++ b/src/intervals.jl
@@ -120,3 +120,5 @@ end
 Base.size(isf::IntervalsFold) = size(isf.pattern) * folds(isf)
 
 Base.eltype(::Type{<:IntervalsFold{T}}) where {T} = Interval{T}
+
+is_points(isf) = is_point(pattern(isf))
diff --git a/test/vector.jl b/test/vector.jl
index 4f2a7c6..0361d0b 100644
--- a/test/vector.jl
+++ b/test/vector.jl
@@ -45,5 +45,6 @@
     @test unfold(v22) == w2
 
     isf = IntervalsFold(Interval((0.0, true), (0.0, true)), 1.0, 5)
+    @test is_points(isf)
     @test unfold(make_vector_fold(isf)) == [i for i in 0.0:4.0]
 end

From 5aa6f9014ea26a4255c9c4bf56f76af75fffd6b0 Mon Sep 17 00:00:00 2001
From: Azzaare <jf@baffier.fr>
Date: Fri, 13 Aug 2021 16:51:33 +0900
Subject: [PATCH 3/3] Add b_equal_a

---
 src/intervals.jl | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/src/intervals.jl b/src/intervals.jl
index cbf27b6..2c8dfe8 100644
--- a/src/intervals.jl
+++ b/src/intervals.jl
@@ -39,6 +39,8 @@ end
 
 b_isless(i₁, i₂) = b_ismore(i₂, i₁)
 
+b_eq_a(i₁, i₂) = b(i₁) == a(i₂)
+
 function Base.in(val, i::Interval)
     (x, y) = (value(i, :a), value(i, :b))
     lesser = closed(i, :a) ? x ≤ val : x < val
@@ -58,6 +60,12 @@ Check if the interval `i` is simple point.
 """
 is_point(i) = value(i, :a) == value(i, :b) && !isempty(i)
 
+# function Base.intersect(i₁::Interval, i₂::Interval)
+#     !a_isless(i₁, i₂) && return intersect(i₂, i₁)
+#     b_ismore(i₁, i₂) && return i₂
+#     value(i₁, :b) ∈ i₂
+# end
+
 mutable struct IntervalsFold{T <: Real} #<: PatternFold{T, Interval{T}}
     pattern::Interval{T}
     gap::T