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 01c5b07..f0c2c85 100644
--- a/src/common.jl
+++ b/src/common.jl
@@ -104,6 +104,14 @@ 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"
+    @assert is_points(isf) str
+
+    return make_vector_fold([value(pattern(isf), :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..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
@@ -52,6 +54,18 @@ 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)
+
+# 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
@@ -114,3 +128,5 @@ 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 461c96e..0361d0b 100644
--- a/test/vector.jl
+++ b/test/vector.jl
@@ -43,4 +43,8 @@
     v22 = fold(w2)
 
     @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