diff --git a/src/Approximations/decompositions.jl b/src/Approximations/decompositions.jl
index 5e6f0f6d6b..3a8a252f56 100644
--- a/src/Approximations/decompositions.jl
+++ b/src/Approximations/decompositions.jl
@@ -37,7 +37,7 @@ end
               [ε]::Real=Inf,
               [blocks]::AbstractVector{Int}=default_block_structure(S, set_type),
               [block_types]::Dict{Type{<:LazySet}, AbstractVector{<:AbstractVector{Int}}}(),
-              [directions]::Union{Type{<:AbstractDirections}, Void}=nothing
+              [directions]::Union{Type{<:AbstractDirections}, Nothing}=nothing
              )::CartesianProductArray where {N<:Real}
 
 Decompose a high-dimensional set into a Cartesian product of overapproximations
@@ -221,7 +221,7 @@ function decompose(S::LazySet{N};
                    ε::Real=Inf,
                    blocks::AbstractVector{Int}=default_block_structure(S, set_type),
                    block_types=Dict{Type{<:LazySet}, AbstractVector{<:AbstractVector{Int}}}(),
-                   directions::Union{Type{<:AbstractDirections}, Void}=nothing
+                   directions::Union{Type{<:AbstractDirections}, Nothing}=nothing
                   )::CartesianProductArray where {N<:Real}
     n = dim(S)
     result = Vector{LazySet{N}}()
diff --git a/src/CartesianProduct.jl b/src/CartesianProduct.jl
index caac9d6b0e..b18fbbbd67 100644
--- a/src/CartesianProduct.jl
+++ b/src/CartesianProduct.jl
@@ -1,4 +1,4 @@
-import Base:*, ×, ∈
+import Base:*, ∈
 
 export CartesianProduct,
        CartesianProductArray,
diff --git a/src/ExponentialMap.jl b/src/ExponentialMap.jl
index c7ad082c41..0aae0f5ca8 100644
--- a/src/ExponentialMap.jl
+++ b/src/ExponentialMap.jl
@@ -61,7 +61,7 @@ end
 SparseMatrixExp(M::Matrix) =
         error("only sparse matrices can be used to create a `SparseMatrixExp`")
 
-Base.eye(spmexp::SparseMatrixExp) = SparseMatrixExp(spzeros(size(spmexp.M)...))
+eye(spmexp::SparseMatrixExp) = SparseMatrixExp(spzeros(size(spmexp.M)...))
 
 Base.IndexStyle(::Type{<:SparseMatrixExp}) = IndexCartesian()
 Base.getindex(spmexp::SparseMatrixExp, I::Vararg{Int, 2}) = get_column(spmexp, I[2])[I[1]]
diff --git a/src/compat.jl b/src/compat.jl
index 4a951fca12..1e28425400 100644
--- a/src/compat.jl
+++ b/src/compat.jl
@@ -8,9 +8,10 @@ import Compat.String
 
 if VERSION < v"0.7-"
     import Base.LinAlg:norm, checksquare
+    import Base: eye, ×
 else
     using SparseArrays, LinearAlgebra
-    import LinearAlgebra:norm, checksquare
+    import LinearAlgebra:norm, checksquare, eye, ×
 end
 
 export _At_mul_B