diff --git a/benchmark/supports.jl b/benchmark/supports.jl
index 23dd55bc75..b65738dfb0 100644
--- a/benchmark/supports.jl
+++ b/benchmark/supports.jl
@@ -15,7 +15,7 @@ for set_type in (Ball1, BallInf, Hyperrectangle)
     for n in (2, 10, 100, 1000)
         rng = MersenneTwister(n)
         d = rand(rng, n)
-        X = rand(set_type, dim=n, rng=rng)
+        X = LazySets.rand(set_type, dim=n, rng=rng)
         SUITE["ρ"][string(set_type), "dense", n] = @benchmarkable ρ($d, $X)
         SUITE["σ"][string(set_type), "dense", n] = @benchmarkable σ($d, $X)
         A = tridiagm(1, -2, 0.5, n)
diff --git a/src/ConcreteOperations/convex_hull.jl b/src/ConcreteOperations/convex_hull.jl
index 55b7e8df20..51cc983f98 100644
--- a/src/ConcreteOperations/convex_hull.jl
+++ b/src/ConcreteOperations/convex_hull.jl
@@ -387,7 +387,7 @@ end
 function _convex_hull_2d!(points::Vector{VN};
                           algorithm="monotone_chain"
                          ) where {N, VN<:AbstractVector{N}}
-    if algorithm == nothing
+    if isnothing(algorithm)
         algorithm = default_convex_hull_algorithm(points)
     end
     if algorithm == "monotone_chain"
diff --git a/src/ConcreteOperations/isdisjoint.jl b/src/ConcreteOperations/isdisjoint.jl
index 47ad3fff38..1876b56c85 100644
--- a/src/ConcreteOperations/isdisjoint.jl
+++ b/src/ConcreteOperations/isdisjoint.jl
@@ -865,7 +865,7 @@ function _isdisjoint_polyhedron(P::AbstractPolyhedron, X::LazySet,
         end
         clist_P = _normal_Vector(P) # TODO
         clist_X = _normal_Vector(X) # TODO
-        if solver == nothing
+        if isnothing(solver)
             solver = default_lp_solver(N)
         end
         return _isempty_polyhedron_lp([clist_P; clist_X], witness; solver=solver)
diff --git a/src/ConcreteOperations/issubset.jl b/src/ConcreteOperations/issubset.jl
index 13b65e829b..b5667fa354 100644
--- a/src/ConcreteOperations/issubset.jl
+++ b/src/ConcreteOperations/issubset.jl
@@ -831,7 +831,7 @@ function ⊆(∅::EmptySet, X::LazySet, witness::Bool=false)
     return _issubset_emptyset(∅, X, witness)
 end
 
-function _issubset_emptyset(∅, X, witness)
+function _issubset_emptyset(∅::EmptySet, X::LazySet, witness::Bool=false)
     N = promote_type(eltype(∅), eltype(X))
     return witness ? (true, N[]) : true
 end
@@ -867,7 +867,7 @@ function ⊆(X::LazySet, ∅::EmptySet, witness::Bool=false)
     return _issubset_in_emptyset(X, ∅, witness)
 end
 
-function _issubset_in_emptyset(X, ∅, witness)
+function _issubset_in_emptyset(X::LazySet, ∅::EmptySet, witness::Bool=false)
     if isempty(X)
         N = promote_type(eltype(∅), eltype(X))
         return witness ? (true, N[]) : true
@@ -987,7 +987,7 @@ function ⊆(X::LazySet, U::Universe, witness::Bool=false)
     return _issubset_universe(X, U, witness)
 end
 
-function _issubset_universe(X, U, witness)
+function _issubset_universe(X::LazySet, U::Universe, witness::Bool=false)
     if !witness
         return true
     end
@@ -998,7 +998,8 @@ end
 # disambiguations
 for ST in [:AbstractPolytope, :AbstractHyperrectangle, :AbstractSingleton,
            :LineSegment, :EmptySet, :UnionSet, :UnionSetArray]
-    @eval ⊆(X::($ST), U::Universe, witness::Bool=false) = _issubset_universe(X, U, witness)
+    @eval ⊆(X::($ST), U::Universe, witness::Bool=false) =
+        _issubset_universe(X, U, witness)
 end
 
 """
@@ -1025,7 +1026,7 @@ compute a witness.
 
 We fall back to `isuniversal(X)`.
 """
-function ⊆(U::Universe, X::LazySet, witness::Bool=false)
+function ⊆(::Universe, X::LazySet, witness::Bool=false)
     return isuniversal(X, witness)
 end
 
@@ -1037,7 +1038,7 @@ end
 # disambiguations
 for ST in [:AbstractPolyhedron, :AbstractPolytope, :AbstractHyperrectangle,
            :AbstractSingleton, :EmptySet, :UnionSetArray, :Complement]
-    @eval ⊆(U::Universe, X::($ST), witness::Bool=false) = isuniversal(X, witness)
+    @eval ⊆(::Universe, X::($ST), witness::Bool=false) = isuniversal(X, witness)
 end
 
 """
diff --git a/src/ConcreteOperations/minkowski_sum.jl b/src/ConcreteOperations/minkowski_sum.jl
index 75fadf15c5..ff4ebc0925 100644
--- a/src/ConcreteOperations/minkowski_sum.jl
+++ b/src/ConcreteOperations/minkowski_sum.jl
@@ -161,12 +161,12 @@ function _minkowski_sum_hrep(A::AbstractMatrix, b::AbstractVector,
                              C::AbstractMatrix, d::AbstractVector;
                              backend=nothing, algorithm=nothing, prune=true)
 
-    if backend == nothing
+    if isnothing(backend)
         N = promote_type(eltype(A), eltype(b), eltype(C), eltype(d))
         backend = default_cddlib_backend(N)
     end
 
-    if algorithm == nothing
+    if isnothing(algorithm)
         algorithm = Polyhedra.FourierMotzkin()
     elseif !(algorithm isa Polyhedra.EliminationAlgorithm)
         error("algorithm $algorithm is not a valid elimination algorithm; " *
@@ -433,7 +433,7 @@ function _minkowski_sum_vrep_nd(vlist1::Vector{VT}, vlist2::Vector{VT};
         end
     end
     if apply_convex_hull
-        if backend == nothing
+        if isnothing(backend)
             require(@__MODULE__, :Polyhedra; fun_name="minkowski_sum")
             backend = default_polyhedra_backend_nd(N)
             solver = default_lp_solver_polyhedra(N)
diff --git a/src/Interfaces/AbstractHyperrectangle.jl b/src/Interfaces/AbstractHyperrectangle.jl
index 8e7a4e82bc..f659476887 100644
--- a/src/Interfaces/AbstractHyperrectangle.jl
+++ b/src/Interfaces/AbstractHyperrectangle.jl
@@ -624,7 +624,7 @@ function split(H::AbstractHyperrectangle{N},
     centers = Vector{StepRangeLen{N}}(undef, dim(H))
     @inbounds for (i, m) in enumerate(num_blocks)
         if m <= 0
-            throw(ArgumentError(m, "each dimension needs at least one block"))
+            throw(ArgumentError("each dimension needs at least one block, got $m"))
         elseif m == one(N)
             centers[i] = range(lo[i] + radius[i], length=1)
         else
diff --git a/src/Interfaces/AbstractPolyhedron_functions.jl b/src/Interfaces/AbstractPolyhedron_functions.jl
index f155566834..75a66e7b39 100644
--- a/src/Interfaces/AbstractPolyhedron_functions.jl
+++ b/src/Interfaces/AbstractPolyhedron_functions.jl
@@ -32,7 +32,7 @@ end
 # default LP solver for Polyhedra (fallback method)
 # NOTE: exists in parallel to `default_lp_solver` because we use different
 # interfaces (see #1493)
-function default_lp_solver_polyhedra(N, varargs...)
+function default_lp_solver_polyhedra(N; kwargs...)
     require(@__MODULE__, :Polyhedra; fun_name="default_lp_solver_polyhedra")
     error("no default solver for numeric type $N")
 end
@@ -416,11 +416,11 @@ end
 
 function _get_elimination_instance(N, backend, elimination_method)
     require(@__MODULE__, :Polyhedra; fun_name="linear_map with elimination")
-    if backend == nothing
+    if isnothing(backend)
         require(@__MODULE__, :CDDLib; fun_name="linear_map with elimination")
         backend = default_cddlib_backend(N)
     end
-    if elimination_method == nothing
+    if isnothing(elimination_method)
         elimination_method = Polyhedra.BlockElimination()
     end
     return LinearMapElimination(backend, elimination_method)
@@ -647,12 +647,12 @@ function _linear_map_polyhedron(M::AbstractMatrix{NM},
     size(M, 2) != dim(P) && throw(ArgumentError("a linear map of size " *
                 "$(size(M)) cannot be applied to a set of dimension $(dim(P))"))
 
-    got_algorithm = algorithm != nothing
+    got_algorithm = !isnothing(algorithm)
     got_inv = got_algorithm && (algorithm == "inv" || algorithm == "inverse")
     got_inv_right = got_algorithm && (algorithm ==
         "inv_right" || algorithm == "inverse_right")
 
-    if inverse != nothing
+    if !isnothing(inverse)
         if !got_algorithm || got_inv
             algo = LinearMapInverse(inverse)
         elseif got_inv_right
@@ -726,7 +726,7 @@ function _linear_map_vrep(M::AbstractMatrix, P::AbstractPolyhedron,
 
     P_hpoly = HPolytope(constraints_list(P), check_boundedness=false)
     backend = algo.backend
-    if backend == nothing
+    if isnothing(backend)
         backend = default_polyhedra_backend(P)
     end
     P = tovrep(P_hpoly, backend=backend)
@@ -1168,7 +1168,7 @@ function project(P::AbstractPolyhedron{N}, block::AbstractVector{Int};
         elseif status == 1
             # simple projection of half-space
             hs = HalfSpace(c.a[block], c.b)
-            if clist == nothing
+            if isnothing(clist)
                 clist = [hs]  # get the right type of the constraints
             else
                 push!(clist, hs)
diff --git a/src/Interfaces/AbstractZonotope.jl b/src/Interfaces/AbstractZonotope.jl
index 50a0bbfc41..e2498f2876 100644
--- a/src/Interfaces/AbstractZonotope.jl
+++ b/src/Interfaces/AbstractZonotope.jl
@@ -84,7 +84,7 @@ function genmat_fallback(Z::AbstractZonotope{N};
                          gens=generators(Z), ngens=nothing) where {N}
     if isempty(gens)
         return Matrix{N}(undef, dim(Z), 0)
-    elseif ngens == nothing
+    elseif isnothing(ngens)
         return _genmat_fallback_generic(Z, gens)
     else
         return _genmat_fallback_ngens(Z, gens, ngens)
@@ -280,7 +280,7 @@ function ∈(x::AbstractVector, Z::AbstractZonotope; solver=nothing)
     sense = ['>'; fill('=', n)]
     obj = [one(N); zeros(N, p)]
 
-    if solver == nothing
+    if isnothing(solver)
         solver = default_lp_solver(N)
     end
     lp = linprog(obj, A, sense, b, lbounds, ubounds, solver)
diff --git a/src/Interfaces/LazySet.jl b/src/Interfaces/LazySet.jl
index 1c7409c356..64f4c8cc31 100644
--- a/src/Interfaces/LazySet.jl
+++ b/src/Interfaces/LazySet.jl
@@ -1848,7 +1848,7 @@ function _isempty_polyhedron_polyhedra(P::LazySet{N}, witness::Bool=false;
     require(@__MODULE__, :Polyhedra; fun_name="isempty",
             explanation="with the active option `use_polyhedra_interface`")
 
-    if backend == nothing
+    if isnothing(backend)
         backend = default_polyhedra_backend(P)
     end
 
diff --git a/src/LazyOperations/Intersection.jl b/src/LazyOperations/Intersection.jl
index 528e0e74aa..1e6a98c162 100644
--- a/src/LazyOperations/Intersection.jl
+++ b/src/LazyOperations/Intersection.jl
@@ -926,7 +926,7 @@ function _projection(ℓ, X::S, H::Union{Hyperplane{N}, Line2D{N}};
     Xnℓ = lazy_linear_map ? LinearMap(Πnℓ, X) : linear_map(Πnℓ, X)
     Xnℓ⋂Lγ = lazy_2d_intersection ? Intersection(Xnℓ, Lγ) : intersection(Xnℓ, Lγ)
 
-    if algorithm_2d_intersection == nothing
+    if isnothing(algorithm_2d_intersection)
         return ρ(y_dir, Xnℓ⋂Lγ; kwargs...)
     else
         return ρ(y_dir, Xnℓ⋂Lγ, algorithm=algorithm_2d_intersection; kwargs...)
diff --git a/src/LazyOperations/Rectification.jl b/src/LazyOperations/Rectification.jl
index 887d394f31..79a90b4990 100644
--- a/src/LazyOperations/Rectification.jl
+++ b/src/LazyOperations/Rectification.jl
@@ -116,7 +116,7 @@ isoperationtype(::Type{<:Rectification}) = true
 isconvextype(::Type{<:Rectification}) = false
 
 function _compute_exact_representation!(R::Rectification)
-    if R.cache.set == nothing
+    if isnothing(R.cache.set)
         R.cache.set = to_union_of_projections(R)
     end
     return R.cache.set
diff --git a/src/Plotting/mesh.jl b/src/Plotting/mesh.jl
index b205a385b0..c8309bf841 100644
--- a/src/Plotting/mesh.jl
+++ b/src/Plotting/mesh.jl
@@ -119,7 +119,7 @@ function plot3d(S::LazySet; backend=default_polyhedra_backend(S), alpha=1.0,
                 transparency=true, visible=true)
     require(@__MODULE__, [:Makie, :Polyhedra]; fun_name="plot3d")
 
-    if colorrange == nothing
+    if isnothing(colorrange)
         colorrange = Automatic()
     end
     P_poly_mesh = _plot3d_helper(S, backend)
@@ -152,7 +152,7 @@ function plot3d!(S::LazySet; backend=default_polyhedra_backend(S), alpha=1.0,
                  transparency=true, visible=true)
     require(@__MODULE__, [:Makie, :Polyhedra]; fun_name="plot3d!")
 
-    if colorrange == nothing
+    if isnothing(colorrange)
         colorrange = Automatic()
     end
     P_poly_mesh = _plot3d_helper(S, backend)
diff --git a/src/Sets/HPolyhedron.jl b/src/Sets/HPolyhedron.jl
index 814c81f0df..e22ce48e70 100644
--- a/src/Sets/HPolyhedron.jl
+++ b/src/Sets/HPolyhedron.jl
@@ -156,7 +156,7 @@ end
 
 # construct the solution from the solver's ray result
 function _σ_unbounded_lp(d, P::HPoly{N}, lp) where {N}
-    if lp == nothing
+    if isnothing(lp)
         ray = d
     elseif has_lp_infeasibility_ray(lp.model)
         ray = lp.sol  # infeasibility ray is stored as the solution
diff --git a/src/Sets/HPolytope.jl b/src/Sets/HPolytope.jl
index 9b510701cc..e0eb295b6c 100644
--- a/src/Sets/HPolytope.jl
+++ b/src/Sets/HPolytope.jl
@@ -230,12 +230,12 @@ function vertices_list(P::HPolytope;
     N = eltype(P)
     if isempty(P.constraints)
         return Vector{N}(Vector{N}(undef, 0))  # illegal polytope
-    elseif dim(P) == 2 && backend == nothing
+    elseif dim(P) == 2 && isnothing(backend)
         # use efficient 2D implementation
         return vertices_list(convert(HPolygon, P, prune=prune))
     else
         require(@__MODULE__, :Polyhedra; fun_name="vertices_list")
-        if backend == nothing
+        if isnothing(backend)
             backend = default_polyhedra_backend(P)
         end
         Q = polyhedron(P; backend=backend)
diff --git a/src/Sets/VPolytope.jl b/src/Sets/VPolytope.jl
index d6403ddbc7..2db3f1172d 100644
--- a/src/Sets/VPolytope.jl
+++ b/src/Sets/VPolytope.jl
@@ -440,12 +440,12 @@ function remove_redundant_vertices(P::VPolytope{N};
                                    backend=nothing,
                                    solver=nothing) where {N}
     require(@__MODULE__, :Polyhedra; fun_name="remove_redundant_vertices")
-    if backend == nothing
+    if isnothing(backend)
         backend = default_polyhedra_backend(P)
     end
     Q = polyhedron(P; backend=backend)
     if Polyhedra.supportssolver(typeof(Q))
-        if solver == nothing
+        if isnothing(solver)
             solver = default_lp_solver_polyhedra(N)
         end
         vQ = Polyhedra.vrep(Q)
@@ -555,7 +555,7 @@ function polyhedron(P::VPolytope;
                     backend=default_polyhedra_backend(P),
                     relative_dimension=nothing)
     if isempty(P)
-        if relative_dimension == nothing
+        if isnothing(relative_dimension)
             error("the conversion to a `Polyhedra.polyhedron` requires the " *
                 "(relative) dimension of the `VPolytope` to be known, but it " *
                 "cannot be inferred from an empty set; use the keyword " *
diff --git a/src/Utils/helper_functions.jl b/src/Utils/helper_functions.jl
index 542307e6f0..97e2832bf7 100644
--- a/src/Utils/helper_functions.jl
+++ b/src/Utils/helper_functions.jl
@@ -124,7 +124,7 @@ function implementing_sets(op::Function;
             if type_args isa Type
                 augmented_set_type = set_type{type_args}
             else
-                @assert type_args == nothing "for binary functions, " *
+                @assert isnothing(type_args) "for binary functions, " *
                     "`type_args` must not be a list"
             end
         catch e
@@ -164,7 +164,7 @@ function _implementing_sets_unary!(dict, op, signature, index, type_args)
         try
             if type_args isa Type
                 augmented_set_type = set_type{type_args}
-            elseif type_args != nothing
+            elseif !isnothing(type_args)
                 augmented_set_type = set_type{type_args...}
             end
         catch e
diff --git a/test/Sets/Hyperrectangle.jl b/test/Sets/Hyperrectangle.jl
index c4b6d7bc9d..273a1af48c 100644
--- a/test/Sets/Hyperrectangle.jl
+++ b/test/Sets/Hyperrectangle.jl
@@ -160,6 +160,7 @@ for N in [Float64, Rational{Int}, Float32]
     H = Hyperrectangle(N[0, 0], N[1, 2])
     S = split(H, [2, 2])
     @test S isa Vector{typeof(H)}
+    @test_throws ArgumentError split(H, [0, 4])
     H = Hyperrectangle(SA[N(0), N(0)], SA[N(1), N(2)])
     S = split(H, [2, 2])
     @test S isa Vector{typeof(H)}
diff --git a/test/Sets/Zonotope.jl b/test/Sets/Zonotope.jl
index 4f7a982368..bbcff1bfd9 100644
--- a/test/Sets/Zonotope.jl
+++ b/test/Sets/Zonotope.jl
@@ -253,7 +253,7 @@ for N in [Float64, Rational{Int}, Float32]
         if N<:AbstractFloat || test_suite_polyhedra
             @test isequivalent(Z, Z2)
         end
-        if G2 != nothing
+        if !isnothing(G2)
             @test genmat(remove_redundant_generators(Z)) == G2
         end