diff --git a/Project.toml b/Project.toml
index 2cb2686b..50baa5ad 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,11 +3,11 @@ uuid = "774a0091-654f-5c65-bbdc-ad5b67b45832"
 version = "0.2.0"
 
 [deps]
-Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 Expokit = "a1e7a1ef-7a5d-5822-a38c-be74e1bb89f4"
 HybridSystems = "2207ec0c-686c-5054-b4d2-543502888820"
 IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 LazySets = "b4f0291d-fe17-52bc-9479-3d1a343d9043"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MathematicalSystems = "d14a8603-c872-5ed3-9ece-53e0e82e39da"
 Memento = "f28f55f0-a522-5efc-85c2-fe41dfb9b2d9"
 Optim = "429524aa-4258-5aef-a3af-852621145aeb"
@@ -23,7 +23,6 @@ TaylorSeries = "6aa5eb33-94cf-58f4-a9d0-e4b2c4fc25ea"
 
 [compat]
 julia = "≥ 1.0.0"
-Compat = "≥ 2.1.0"
 Expokit = "≥ 0.2.0"
 HybridSystems = "≥ 0.3.0"
 IntervalArithmetic = "≥ 0.15.2"
diff --git a/src/ReachSets/ContinuousPost/BFFPS19/reach_blocks.jl b/src/ReachSets/ContinuousPost/BFFPS19/reach_blocks.jl
index 7f0059f4..d5649251 100644
--- a/src/ReachSets/ContinuousPost/BFFPS19/reach_blocks.jl
+++ b/src/ReachSets/ContinuousPost/BFFPS19/reach_blocks.jl
@@ -273,10 +273,10 @@ function reach_blocks!(ϕ::AbstractMatrix{NUM},
             end
         end
 
-         _A_mul_B!(ϕpowerk_cache, ϕpowerk, ϕ)
+        mul!(ϕpowerk_cache, ϕpowerk, ϕ)
         copyto!(ϕpowerk, ϕpowerk_cache)
 
-         k += 1
+        k += 1
     end
 
     return k, skip
diff --git a/src/ReachSets/ContinuousPost/BFFPSV18/check_blocks.jl b/src/ReachSets/ContinuousPost/BFFPSV18/check_blocks.jl
index c4e85dd7..062a6fbc 100644
--- a/src/ReachSets/ContinuousPost/BFFPSV18/check_blocks.jl
+++ b/src/ReachSets/ContinuousPost/BFFPSV18/check_blocks.jl
@@ -174,7 +174,7 @@ function check_blocks(ϕ::AbstractMatrix{NUM},
             end
         end
 
-        _A_mul_B!(ϕpowerk_cache, ϕpowerk, ϕ)
+        mul!(ϕpowerk_cache, ϕpowerk, ϕ)
         copyto!(ϕpowerk, ϕpowerk_cache)
         k += 1
     end
diff --git a/src/ReachSets/ContinuousPost/BFFPSV18/reach_blocks.jl b/src/ReachSets/ContinuousPost/BFFPSV18/reach_blocks.jl
index c1d1c4da..3cd08e5d 100644
--- a/src/ReachSets/ContinuousPost/BFFPSV18/reach_blocks.jl
+++ b/src/ReachSets/ContinuousPost/BFFPSV18/reach_blocks.jl
@@ -210,7 +210,7 @@ function reach_blocks!(ϕ::AbstractMatrix{NUM},
             end
         end
 
-        _A_mul_B!(ϕpowerk_cache, ϕpowerk, ϕ)
+        mul!(ϕpowerk_cache, ϕpowerk, ϕ)
         copyto!(ϕpowerk, ϕpowerk_cache)
 
         k += 1
diff --git a/src/ReachSets/ContinuousPost/GLGM06/reach.jl b/src/ReachSets/ContinuousPost/GLGM06/reach.jl
index c8421475..2b4d718a 100644
--- a/src/ReachSets/ContinuousPost/GLGM06/reach.jl
+++ b/src/ReachSets/ContinuousPost/GLGM06/reach.jl
@@ -57,7 +57,7 @@ function reach_inhomog!(X::Vector{ReachSet{Zonotope{Float64}}},
 
         Wk₊ = reduce_order(Wk₊, max_order)
 
-        _A_mul_B!(Φ_power_k_cache, Φ_power_k, Φ)
+        mul!(Φ_power_k_cache, Φ_power_k, Φ)
         copyto!(Φ_power_k, Φ_power_k_cache)
         k += 1
     end
diff --git a/src/ReachSets/ReachSets.jl b/src/ReachSets/ReachSets.jl
index 8a504a27..62a9b27f 100644
--- a/src/ReachSets/ReachSets.jl
+++ b/src/ReachSets/ReachSets.jl
@@ -6,20 +6,13 @@ module ReachSets
 
 using ..Utils, ..Properties
 using LazySets, MathematicalSystems, HybridSystems, Expokit, Optim,
-      ProgressMeter
+      LinearAlgebra, SparseArrays, ProgressMeter
 
 # fix namespace conflicts with MathematicalSystems
-using LazySets: LinearMap
+using LazySets: LinearMap, AffineMap, ResetMap
 using Reachability: info, warn
 
-include("../compat.jl")
-
-using LazySets.Approximations: symmetric_interval_hull,
-                               decompose,
-                               overapproximate,
-                               box_approximation,
-                               AbstractDirections
-
+using LazySets.Approximations: AbstractDirections
 import LazySets.Approximations: project
 
 using Reachability: @timing,
diff --git a/src/ReachSets/discretize.jl b/src/ReachSets/discretize.jl
index ff4a99ad..85948f61 100644
--- a/src/ReachSets/discretize.jl
+++ b/src/ReachSets/discretize.jl
@@ -138,7 +138,7 @@ A matrix.
 """
 function exp_Aδ(A::AbstractMatrix{Float64}, δ::Float64; exp_method="base")
     if exp_method == "base"
-        return expmat(Matrix(A*δ))
+        return exp(Matrix(A*δ))
     elseif exp_method == "lazy"
         return SparseMatrixExp(A*δ)
     elseif exp_method == "pade"
@@ -210,7 +210,7 @@ Heidelberg, 2011.
 function Φ₁(A, δ; exp_method="base")
     n = size(A, 1)
     if exp_method == "base"
-        P = expmat(Matrix(Pmatrix(A, δ, n)))
+        P = exp(Matrix(Pmatrix(A, δ, n)))
         Φ₁_Aδ = P[1:n, (n+1):2*n]
 
     elseif exp_method == "lazy"
@@ -285,7 +285,7 @@ Heidelberg, 2011.
 function Φ₂(A, δ; exp_method="base")
     n = size(A, 1)
     if exp_method == "base"
-        P = expmat(Matrix(Pmatrix(A, δ, n)))
+        P = exp(Matrix(Pmatrix(A, δ, n)))
         Φ₂_Aδ = P[1:n, (2*n+1):3*n]
 
     elseif exp_method == "lazy"
diff --git a/src/Reachability.jl b/src/Reachability.jl
index ebdeec59..e7186af3 100644
--- a/src/Reachability.jl
+++ b/src/Reachability.jl
@@ -5,13 +5,12 @@ This is the main module and provides interfaces for specifying and solving reach
 module Reachability
 
 using Reexport, RecipesBase, Memento, MathematicalSystems, HybridSystems,
-      Compat, Suppressor
+      LinearAlgebra, Suppressor, SparseArrays, Printf
+
 @reexport using LazySets
-using LazySets.Approximations: overapproximate
+import LazySets: use_precise_ρ
+using LazySets: LinearMap, AffineMap, ResetMap
 
-import LazySets.use_precise_ρ
-import LazySets: LinearMap, AffineMap, ResetMap
- 
 include("logging.jl")
 include("Options/dictionary.jl")
 include("Options/validation.jl")
diff --git a/src/Utils/Utils.jl b/src/Utils/Utils.jl
index b8eea655..73ee95e2 100644
--- a/src/Utils/Utils.jl
+++ b/src/Utils/Utils.jl
@@ -4,9 +4,12 @@ decompositions and visualization.
 """
 module Utils
 
-using LazySets, MathematicalSystems, HybridSystems
+using LazySets, MathematicalSystems, HybridSystems, Printf
 
-include("../compat.jl")
+# fix namespace conflicts with MathematicalSystems
+using LazySets: LinearMap, AffineMap, ResetMap
+
+import LinearAlgebra: normalize
 
 using Reachability: Options
 
diff --git a/src/compat.jl b/src/compat.jl
deleted file mode 100644
index e2379e8f..00000000
--- a/src/compat.jl
+++ /dev/null
@@ -1,19 +0,0 @@
-#=
-This file defines internal functions for compatibility across
-different Julia versions.
-=#
-
-using Compat
-using Compat: copyto!, axes, argmax
-import Compat.String
-using Compat.LinearAlgebra
-import Compat.LinearAlgebra: norm, checksquare, LAPACKException,
-                             SingularException, ×
-import Compat.InteractiveUtils.subtypes
-
-using SparseArrays, Printf
-@inline _At_mul_B(A, B) = transpose(A) * B
-@inline _A_mul_B!(C, A, B) = mul!(C, A, B)
-expmat = exp
-export eye
-
diff --git a/test/runtests.jl b/test/runtests.jl
index 3086ec3d..fb1e02a9 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,22 +1,8 @@
-#!/usr/bin/env julia
-using LazySets, Reachability, MathematicalSystems,
-      LinearAlgebra, SparseArrays
+using Test, LazySets, Reachability, MathematicalSystems, LinearAlgebra,
+      SparseArrays
 
 # fix namespace conflicts with MathematicalSystems
-using LazySets: LinearMap
-
-# common aliases
-const CLCCS = ConstrainedLinearControlContinuousSystem
-const CLCDS = ConstrainedLinearControlDiscreteSystem
-const LCS = LinearContinuousSystem
-const LDS = LinearDiscreteSystem
-
-# compatibility between Julia versions
-include("../src/compat.jl")
-using Compat.Test
-
-# Note: CDDLib is only required for v0.6; for v0.7 or later the default Polyhedra
-# library is used and CDDLib can be removed from REQUIRE
+using LazySets: LinearMap, AffineMap, ResetMap
 
 include("Systems/alltests.jl")
 include("ReachSets/alltests.jl")