diff --git a/src/intervals/arithmetic/basic.jl b/src/intervals/arithmetic/basic.jl
index 7f4887541..5b056b4c4 100644
--- a/src/intervals/arithmetic/basic.jl
+++ b/src/intervals/arithmetic/basic.jl
@@ -8,17 +8,9 @@
 
 +(a::Interval) = a  # Not in the IEEE standard
 
-"""
-    -(a::Interval)
-
-Implement the `neg` function of the IEEE Std 1788-2015 (Table 9.1).
-"""
--(a::F) where {F<:Interval} = F(-sup(a), -inf(a))
-
-
 """
     +(a::Interval, b::Real)
-    +(a::Real, a::Interval)
+    +(a::Real, b::Interval)
     +(a::Interval, b::Interval)
 
 Implement the `add` function of the IEEE Std 1788-2015 (Table 9.1).
@@ -34,10 +26,18 @@ function +(a::F, b::F) where {F<:Interval}
     (isempty(a) || isempty(b)) && return emptyinterval(F)
     return @round(F, inf(a) + inf(b), sup(a) + sup(b))
 end
++(a::Interval, b::Interval) = +(promote(a, b)...)
+
+"""
+    -(a::Interval)
+
+Implement the `neg` function of the IEEE Std 1788-2015 (Table 9.1).
+"""
+-(a::F) where {F<:Interval} = F(-sup(a), -inf(a))
 
 """
     -(a::Interval, b::Real)
-    -(a::Real, a::Interval)
+    -(a::Real, b::Interval)
     -(a::Interval, b::Interval)
 
 Implement the `sub` function of the IEEE Std 1788-2015 (Table 9.1).
@@ -46,19 +46,18 @@ function -(a::F, b::T) where {T<:Real, F<:Interval{T}}
     isempty(a) && return emptyinterval(F)
     return @round(F, inf(a) - b, sup(a) - b)
 end
-
 function -(b::T, a::F) where {T, F<:Interval{T}}
     isempty(a) && return emptyinterval(F)
     return @round(F, b - sup(a), b - inf(a))
 end
+-(a::F, b::Real) where {F<:Interval} = a - F(b)
+-(a::Real, b::F) where {F<:Interval} = F(a) - b
 
 function -(a::F, b::F) where {F<:Interval}
     (isempty(a) || isempty(b)) && return emptyinterval(F)
     return @round(F, inf(a) - sup(b), sup(a) - inf(b))
 end
-
--(a::F, b::Real) where {F<:Interval} = a - F(b)
--(a::Real, b::F) where {F<:Interval} = F(a) - b
+-(a::Interval, b::Interval) = -(promote(a, b)...)
 
 """
     scale(α, a::Interval)
@@ -71,7 +70,7 @@ For efficiency, does not check that the constant is positive.
 
 """
     *(a::Interval, b::Real)
-    *(a::Real, a::Interval)
+    *(a::Real, b::Interval)
     *(a::Interval, b::Interval)
 
 Implement the `mul` function of the IEEE Std 1788-2015 (Table 9.1).
@@ -88,25 +87,21 @@ function *(x::T, a::F) where {T<:Real, F<:Interval{T}}
         return @round(F, sup(a)*x, inf(a)*x)
     end
 end
-
 *(x::T, a::F) where {T<:Real, S, F<:Interval{S}} = Interval{S}(x) * a
 *(a::F, x::T) where {T<:Real, S, F<:Interval{S}} = x*a
 
 function *(a::F, b::F) where {F<:Interval}
     (isempty(a) || isempty(b)) && return emptyinterval(F)
-
     (isthinzero(a) || isthinzero(b)) && return zero(F)
-
     (isbounded(a) && isbounded(b)) && return mult(*, a, b)
-
     return mult((x, y, r) -> unbounded_mult(F, x, y, r), a, b)
 end
-
+*(a::Interval, b::Interval) = *(promote(a, b)...)
 
 # Helper functions for multiplication
 function unbounded_mult(::Type{F}, x::T, y::T, r::RoundingMode) where {T, F<:Interval{T}}
-    iszero(x) && return sign(y)*zero_times_infinity(T)
-    iszero(y) && return sign(x)*zero_times_infinity(T)
+    iszero(x) && return sign(y) * zero_times_infinity(T)
+    iszero(y) && return sign(x) * zero_times_infinity(T)
     return *(x, y, r)
 end
 
@@ -114,11 +109,11 @@ function mult(op, a::F, b::F) where {T, F<:Interval{T}}
     if inf(b) >= zero(T)
         inf(a) >= zero(T) && return @round(F, op(inf(a), inf(b)), op(sup(a), sup(b)))
         sup(a) <= zero(T) && return @round(F, op(inf(a), sup(b)), op(sup(a), inf(b)))
-        return @round(F, inf(a)*sup(b), sup(a)*sup(b))   # when zero(T) ∈ a
+        return @round(F, inf(a)*sup(b), sup(a)*sup(b))   # zero(T) ∈ a
     elseif sup(b) <= zero(T)
         inf(a) >= zero(T) && return @round(F, op(sup(a), inf(b)), op(inf(a), sup(b)))
         sup(a) <= zero(T) && return @round(F, op(sup(a), sup(b)), op(inf(a), inf(b)))
-        return @round(F, sup(a)*inf(b), inf(a)*inf(b))   # when zero(T) ∈ a
+        return @round(F, sup(a)*inf(b), inf(a)*inf(b))   # zero(T) ∈ a
     else
         inf(a) > zero(T) && return @round(F, op(sup(a), inf(b)), op(sup(a), sup(b)))
         sup(a) < zero(T) && return @round(F, op(inf(a), sup(b)), op(inf(a), inf(b)))
@@ -129,7 +124,7 @@ end
 
 """
     /(a::Interval, b::Real)
-    /(a::Real, a::Interval)
+    /(a::Real, b::Interval)
     /(a::Interval, b::Interval)
 
 Implement the `div` function of the IEEE Std 1788-2015 (Table 9.1).
@@ -182,6 +177,7 @@ function /(a::F, b::F) where {T, F<:Interval{T}}
         end
     end
 end
+/(a::Interval, b::Interval) = /(promote(a, b)...)
 
 """
     inv(a::Interval)
diff --git a/src/intervals/construction.jl b/src/intervals/construction.jl
index 51fdd2739..bf5f36404 100644
--- a/src/intervals/construction.jl
+++ b/src/intervals/construction.jl
@@ -115,6 +115,11 @@ Interval(x::Irrational) = Interval{default_bound()}(x)
     return :(return $res)  # Set body of the function to return the precomputed result
 end
 
+# promotion
+
+Base.promote_rule(::Type{Interval{T}}, ::Type{Interval{S}}) where {T,S} =
+    Interval{promote_type(T, S)}
+
 """
     interval(a, b)
 
@@ -123,15 +128,13 @@ If so, then an `Interval(a, b)` object is returned;
 if not, a warning is printed and the empty interval is returned.
 """
 function interval(a::T, b::S) where {T<:Real, S<:Real}
-    if !is_valid_interval(a, b)
-        @warn "Invalid input, empty interval is returned"
-        return emptyinterval(promote_type(T, S))
-    end
-
-    return Interval(a, b)
+    is_valid_interval(a, b) && return Interval(a, b)
+    @warn "Invalid input, empty interval is returned"
+    return emptyinterval(promote_type(T, S))
 end
 
 interval(a::Real) = interval(a, a)
+interval(a::Interval) = interval(inf(a), sup(a))  # Check the validity of the interval
 
 const checked_interval = interval
 
@@ -240,4 +243,4 @@ function bigequiv(x::AbstractFloat)
 end
 
 float(x::Interval{T}) where T = atomic(Interval{float(T)}, x)
-big(x::Interval) = atomic(Interval{BigFloat}, x)
\ No newline at end of file
+big(x::Interval) = atomic(Interval{BigFloat}, x)
diff --git a/test/interval_tests/construction.jl b/test/interval_tests/construction.jl
index d8c9a6e91..32d46979c 100644
--- a/test/interval_tests/construction.jl
+++ b/test/interval_tests/construction.jl
@@ -39,6 +39,9 @@ using Test
     @test big(ℯ) in Interval{Float32}(0, ℯ)
     @test big(π) in Interval{Float32}(π, 4)
 
+    @test interval(Interval(pi)) ≛ Interval(pi)
+    @test interval(Interval(NaN, -Inf)) ≛ emptyinterval()
+
     # a < Inf and b > -Inf
     @test @interval("1e300") ≛ Interval(9.999999999999999e299, 1.0e300)
     @test @interval("-1e307") ≛ Interval(-1.0000000000000001e307, -1.0e307)
@@ -164,6 +167,16 @@ end
     @test convert(Interval{BigFloat}, x) === x
 end
 
+@testset "Promotion between intervals" begin
+    x = Interval{Float64}(π)
+    y = Interval{BigFloat}(π)
+    x_, y_ = promote(x, y)
+
+    @test promote_type(typeof(x), typeof(y)) == Interval{BigFloat}
+    @test bounds(x_) == (BigFloat(inf(x), RoundDown), BigFloat(sup(x), RoundUp))
+    @test y_ ≛ y
+end
+
 @testset "Typed intervals" begin
     @test typeof(@interval Float64 1 2) == Interval{Float64}
     @test typeof(@interval         1 2) == Interval{Float64}
@@ -185,6 +198,11 @@ end
 
     a = convert(Interval{Float64}, @biginterval(3, 4))
     @test typeof(a) == Interval{Float64}
+
+    pi64, pi32 = Interval{Float64}(pi), Interval{Float32}(pi)
+    x, y = promote(pi64, pi32)
+    @test x ≛ pi64
+    @test y ≛ Interval{Float64}(pi32)
 end
 
 @testset "Interval{T} constructor" begin
diff --git a/test/interval_tests/numeric.jl b/test/interval_tests/numeric.jl
index 22c5a0d4c..2d43835d7 100644
--- a/test/interval_tests/numeric.jl
+++ b/test/interval_tests/numeric.jl
@@ -40,6 +40,12 @@ end
     @test a + b ≛ Interval(+(a.lo, b.lo, RoundDown), +(a.hi, b.hi, RoundUp))
     @test -a ≛ Interval(-a.hi, -a.lo)
     @test a - b ≛ Interval(-(a.lo, b.hi, RoundDown), -(a.hi, b.lo, RoundUp))
+    for f in (:+, :-, :*, :/)
+        @eval begin
+            @test $f(Interval{Float64}(pi), Interval{Float32}(pi)) ≛
+                $f(Interval{Float64}(pi), Interval{Float64}(Interval{Float32}(pi)))
+        end
+    end
     @test Interval(1//4,1//2) + Interval(2//3) ≛ Interval(11//12, 7//6)
     @test_broken Interval(1//4,1//2) - Interval(2//3) ≛ Interval(-5//12, -1//6)