diff --git a/src/AbstractTensor.jl b/src/AbstractTensor.jl
index cb401e82..c644d24f 100644
--- a/src/AbstractTensor.jl
+++ b/src/AbstractTensor.jl
@@ -1,6 +1,6 @@
 abstract type AbstractTensor{S <: Tuple, T, N} <: AbstractArray{T, N} end
 
-Base.size(::Type{TT}) where {S, TT <: AbstractTensor{S}} = Dims(Space(S))
+Base.size(::Type{TT}) where {S, TT <: AbstractTensor{S}} = tensorsize(Space(S))
 Base.size(x::AbstractTensor) = size(typeof(x))
 
 # indices
@@ -23,11 +23,11 @@ end
 # to SArray
 @generated function convert_to_SArray(x::AbstractTensor)
     S = Space(x)
-    NewS = Space(Dims(S)) # remove Symmetry
+    NewS = Space(tensorsize(S)) # remove Symmetry
     exps = [getindex_expr(:x, x, i) for i in indices(NewS)]
     quote
         @_inline_meta
-        @inbounds SArray{Tuple{$(Dims(NewS)...)}}(tuple($(exps...)))
+        @inbounds SArray{Tuple{$(tensorsize(NewS)...)}}(tuple($(exps...)))
     end
 end
 
diff --git a/src/Space.jl b/src/Space.jl
index 8dde9f33..d018680b 100644
--- a/src/Space.jl
+++ b/src/Space.jl
@@ -22,10 +22,15 @@ _ncomponents(x::Symmetry) = ncomponents(x)
 @pure Base.Dims(::Space{S}) where {S} = flatten_tuple(map(Dims, S))
 @pure Base.Tuple(::Space{S}) where {S} = S
 
-@pure Base.ndims(s::Space) = length(Dims(s))
 @pure Base.length(s::Space) = length(Tuple(s))
 Base.getindex(s::Space, i::Int) = Tuple(s)[i]
 
+@pure tensorsize(s::Space) = Dims(s)
+@pure tensororder(s::Space) = length(tensorsize(s))
+# don't allow to use `size` and `ndims` because their names are confusing.
+Base.size(s::Space) = throw(ArgumentError("use `tensorsize` to get size of a tensor instead of `size`"))
+Base.ndims(s::Space) = throw(ArgumentError("use `tensororder` to get order of a tensor instead of `ndims`"))
+
 function Base.show(io::IO, ::Space{S}) where {S}
     print(io, "Space", S)
 end
@@ -46,21 +51,23 @@ for op in (:dropfirst, :droplast)
     end
 end
 
-# otimes/contraction
-@pure otimes(x::Space, y::Space) = Space(Tuple(x)..., Tuple(y)...)
+# contractions
 @pure function contraction(x::Space, y::Space, ::Val{N}) where {N}
-    if !(0 ≤ N ≤ ndims(x) && 0 ≤ N ≤ ndims(y) && Dims(x)[end-N+1:end] === Dims(y)[1:N])
+    if !(0 ≤ N ≤ tensororder(x) && 0 ≤ N ≤ tensororder(y) && tensorsize(x)[end-N+1:end] === tensorsize(y)[1:N])
         throw(DimensionMismatch("dimensions must match"))
     end
     otimes(droplast(x, Val(N)), dropfirst(y, Val(N)))
 end
+@pure otimes(x::Space, y::Space) = Space(Tuple(x)..., Tuple(y)...)
+@pure dot(x::Space, y::Space) = contraction(x, y, Val(1))
+@pure double_contraction(x::Space, y::Space) = contraction(x, y, Val(2))
 
 # promote_space
 promote_space(x::Space) = x
 @generated function promote_space(x::Space{S1}, y::Space{S2}) where {S1, S2}
     S = _promote_space(S1, S2, ())
     quote
-        Dims(x) == Dims(y) || throw(DimensionMismatch("dimensions must match"))
+        tensorsize(x) == tensorsize(y) || throw(DimensionMismatch("dimensions must match"))
         Space($S)
     end
 end
@@ -97,10 +104,10 @@ end
 _typeof(x::Int) = x
 _typeof(x::Symmetry) = typeof(x)
 @pure function tensortype(x::Space)
-    Tensor{Tuple{map(_typeof, Tuple(x))...}, T, ndims(x), ncomponents(x)} where {T}
+    Tensor{Tuple{map(_typeof, Tuple(x))...}, T, tensororder(x), ncomponents(x)} where {T}
 end
 
 # LinearIndices/CartesianIndices
 for IndicesType in (LinearIndices, CartesianIndices)
-    @eval (::Type{$IndicesType})(x::Space) = $IndicesType(Dims(x))
+    @eval (::Type{$IndicesType})(x::Space) = $IndicesType(tensorsize(x))
 end
diff --git a/src/Tensor.jl b/src/Tensor.jl
index 74e983fd..4e51d57a 100644
--- a/src/Tensor.jl
+++ b/src/Tensor.jl
@@ -8,8 +8,8 @@ end
 
 @generated function check_tensor_parameters(::Type{S}, ::Type{T}, ::Val{N}, ::Val{L}) where {S, T, N, L}
     check_size_parameters(S)
-    if ndims(Space(S)) != N
-        return :(throw(ArgumentError("Number of dimensions must be $(ndims(Space(S))) for $S size, got $N.")))
+    if tensororder(Space(S)) != N
+        return :(throw(ArgumentError("Number of dimensions must be $(tensororder(Space(S))) for $S size, got $N.")))
     end
     if ncomponents(Space(S)) != L
         return :(throw(ArgumentError("Length of tuple data must be $(ncomponents(Space(S))) for $S size, got $L.")))
@@ -26,11 +26,11 @@ const Vec{dim, T} = Tensor{Tuple{dim}, T, 1, dim}
 
 # constructors
 @inline function Tensor{S, T}(data::Tuple{Vararg{Any, L}}) where {S, T, L}
-    N = ndims(Space(S))
+    N = tensororder(Space(S))
     Tensor{S, T, N, L}(data)
 end
 @inline function Tensor{S}(data::Tuple{Vararg{Any, L}}) where {S, L}
-    N = ndims(Space(S))
+    N = tensororder(Space(S))
     T = promote_ntuple_eltype(data)
     Tensor{S, T, N, L}(data)
 end
diff --git a/src/simd.jl b/src/simd.jl
index 2297b65e..6ebda297 100644
--- a/src/simd.jl
+++ b/src/simd.jl
@@ -3,12 +3,12 @@ const SIMDTypes = Union{Float16, Float32, Float64}
 @generated function contraction(x::Tensor{<: Any, T, order1}, y::Tensor{<: Any, T, order2}, ::Val{N}) where {T <: SIMDTypes, N, order1, order2}
     S1 = Space(x)
     S2 = Space(y)
-    S_Inner = Space((Dims(S2)[i] for i in 1:N)...)
+    S_Inner = Space((tensorsize(S2)[i] for i in 1:N)...)
     S1 = otimes(droplast(S1, Val(N)), S_Inner)
     S2 = otimes(S_Inner, dropfirst(S2, Val(N)))
     s1 = [:(Tuple(x)[$i]) for i in 1:ncomponents(S1)]
     s2 = [:(Tuple(y)[$i]) for i in 1:ncomponents(S2)]
-    K = prod(Dims(S_Inner))
+    K = prod(tensorsize(S_Inner))
     I = length(s1) ÷ K
     J = length(s2) ÷ K
     s1′ = reshape(s1, I, K)
diff --git a/test/Space.jl b/test/Space.jl
index 6cea9749..bf213706 100644
--- a/test/Space.jl
+++ b/test/Space.jl
@@ -2,10 +2,14 @@
     # basic
     @test (@inferred length(Space(3,3))) == 2
     @test (@inferred length(Space(Symmetry(3,3),3))) == 2
-    @test (@inferred ndims(Space(Symmetry(3,3),3))) == 3
+    @test (@inferred Tensorial.tensorsize(Space(Symmetry(3,3),3))) == (3,3,3)
+    @test (@inferred Tensorial.tensororder(Space(Symmetry(3,3),3))) == 3
     @test (@inferred Tuple(Space(Symmetry(3,3),3))) == (Symmetry(3,3),3)
     @test Space(3,2)[1] == 3
     @test Space(3,2)[2] == 2
+    # prohibited
+    @test_throws Exception size(Space(Symmetry(3,3),3))
+    @test_throws Exception ndims(Space(Symmetry(3,3),3))
     # promotion
     @test (@inferred Tensorial.promote_space(Space(3,2), Space(3,2))) == Space(3,2)
     @test (@inferred Tensorial.promote_space(Space(3,3,3), Space(Symmetry(3,3),3))) == Space(3,3,3)