diff --git a/src/forward.jl b/src/forward.jl
index 22e54e5..b3db6b9 100644
--- a/src/forward.jl
+++ b/src/forward.jl
@@ -10,9 +10,9 @@
 # a general DAG. If we have a DAG, then need to associate storage with each edge of the DAG.
 # user_input_buffer and user_output_buffer are used as temporary storage
 # when handling user-defined functions
-function forward_eval(storage::Vector{T}, partials_storage::AbstractVector{T},
+function forward_eval(storage::AbstractVector{T}, partials_storage::AbstractVector{T},
                       nd::AbstractVector{NodeData}, adj, const_values,
-                      parameter_values, x_values::Vector{T},
+                      parameter_values, x_values::AbstractVector{T},
                       subexpression_values, user_input_buffer=[],
                       user_output_buffer=[];
                       user_operators::UserOperatorRegistry=UserOperatorRegistry()) where T
@@ -215,7 +215,7 @@ export forward_eval
 # need to recompute the real components.
 # Computes partials_storage_ϵ as well
 # We assume that forward_eval has already been called.
-function forward_eval_ϵ(storage::Vector{T},
+function forward_eval_ϵ(storage::AbstractVector{T},
                         storage_ϵ::AbstractVector{ForwardDiff.Partials{N, T}},
                         partials_storage::AbstractVector{T},
                         partials_storage_ϵ::AbstractVector{ForwardDiff.Partials{N, T}},
diff --git a/src/reverse.jl b/src/reverse.jl
index 2e13c88..b27cf6b 100644
--- a/src/reverse.jl
+++ b/src/reverse.jl
@@ -5,7 +5,7 @@
 # assumes partials_storage is already updated
 # dense gradient output, assumes initialized to zero
 # if subexpressions are present, must run reverse_eval on subexpression tapes afterwards
-function reverse_eval(reverse_storage::Vector{T}, partials_storage::Vector{T},
+function reverse_eval(reverse_storage::AbstractVector{T}, partials_storage::AbstractVector{T},
                       nd::Vector{NodeData},adj) where {T}
 
     @assert length(reverse_storage) >= length(nd)
@@ -38,7 +38,7 @@ export reverse_eval
 
 # assume we've already run the reverse pass, now just extract the answer
 # given the scaling value
-function reverse_extract(output::Vector{T}, reverse_storage::Vector{T}, nd::Vector{NodeData},
+function reverse_extract(output::AbstractVector{T}, reverse_storage::AbstractVector{T}, nd::Vector{NodeData},
                          adj, subexpression_output, scale_value::T) where {T}
 
     @assert length(reverse_storage) >= length(nd)
@@ -62,7 +62,7 @@ export reverse_extract
 # Compute directional derivatives of the reverse pass, goes with forward_eval_ϵ
 # to compute hessian-vector products.
 function reverse_eval_ϵ(output_ϵ::AbstractVector{ForwardDiff.Partials{N,T}},
-                        reverse_storage::Vector{T}, reverse_storage_ϵ, partials_storage::Vector{T},
+                        reverse_storage::AbstractVector{T}, reverse_storage_ϵ, partials_storage::AbstractVector{T},
                         partials_storage_ϵ, nd::Vector{NodeData}, adj, subexpression_output,
                         subexpression_output_ϵ, scale_value::T, scale_value_ϵ::ForwardDiff.Partials{N,T}) where {N,T}
 
diff --git a/test/runtests.jl b/test/runtests.jl
index d0d96d0..af7a80e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -27,6 +27,23 @@ reverse_extract(grad,reverse_storage,nd,adj,[],1.0)
 true_grad = [2*x[1]*cos(x[1]^2), -4*sin(x[2]*4)/5]
 @test isapprox(grad,true_grad)
 
+# Testing view
+xx = [1.0,2.0,3.0,4.0,5.0]
+xv = @view xx[2:3]
+fval_view = forward_eval(storage,partials_storage,nd,adj,const_values,[],xv,[])
+@test fval_view == fval
+
+grad_view = zeros(2)
+reverse_eval(reverse_storage,partials_storage,nd,adj)
+reverse_extract(grad_view,reverse_storage,nd,adj,[],1.0)
+@test grad_view == grad
+
+grad_view = zeros(5)
+gv = @view grad_view[2:2:end]
+reverse_eval(reverse_storage,partials_storage,nd,adj)
+reverse_extract(gv,reverse_storage,nd,adj,[],1.0)
+@test gv == grad
+
 # subexpressions
 
 nd_outer = [NodeData(SUBEXPRESSION,1,-1)]