--- a/test/LazyTensors/lazy_tensor_operations_test.jl	Fri Mar 18 16:57:00 2022 +0100
+++ b/test/LazyTensors/lazy_tensor_operations_test.jl	Mon Mar 21 09:51:07 2022 +0100
@@ -4,17 +4,28 @@
 
 using Tullio
 
-@testset "Mapping transpose" begin
-    struct DummyMapping{T,R,D} <: TensorMapping{T,R,D} end
+struct DummyMapping{T,R,D} <: LazyTensor{T,R,D} end
 
-    LazyTensors.apply(m::DummyMapping{T,R}, v, I::Vararg{Any,R}) where {T,R} = :apply
-    LazyTensors.apply_transpose(m::DummyMapping{T,R,D}, v, I::Vararg{Any,D}) where {T,R,D} = :apply_transpose
+LazyTensors.apply(m::DummyMapping{T,R}, v, I::Vararg{Any,R}) where {T,R} = :apply
+LazyTensors.apply_transpose(m::DummyMapping{T,R,D}, v, I::Vararg{Any,D}) where {T,R,D} = :apply_transpose
+
+LazyTensors.range_size(m::DummyMapping) = :range_size
+LazyTensors.domain_size(m::DummyMapping) = :domain_size
+
 
-    LazyTensors.range_size(m::DummyMapping) = :range_size
-    LazyTensors.domain_size(m::DummyMapping) = :domain_size
+struct SizeDoublingMapping{T,R,D} <: LazyTensor{T,R,D}
+    domain_size::NTuple{D,Int}
+end
 
+LazyTensors.apply(m::SizeDoublingMapping{T,R}, v, i::Vararg{Any,R}) where {T,R} = (:apply,v,i)
+LazyTensors.range_size(m::SizeDoublingMapping) = 2 .* m.domain_size
+LazyTensors.domain_size(m::SizeDoublingMapping) = m.domain_size
+
+
+
+@testset "Mapping transpose" begin
     m = DummyMapping{Float64,2,3}()
-    @test m' isa TensorMapping{Float64, 3,2}
+    @test m' isa LazyTensor{Float64, 3,2}
     @test m'' == m
     @test apply(m',zeros(Float64,(0,0)), 0, 0, 0) == :apply_transpose
     @test apply(m'',zeros(Float64,(0,0,0)), 0, 0) == :apply
@@ -24,91 +35,91 @@
     @test domain_size(m') == :range_size
 end
 
-@testset "TensorApplication" begin
-    struct SizeDoublingMapping{T,R,D} <: TensorMapping{T,R,D}
-        domain_size::NTuple{D,Int}
-    end
 
-    LazyTensors.apply(m::SizeDoublingMapping{T,R}, v, i::Vararg{Any,R}) where {T,R} = (:apply,v,i)
-    LazyTensors.range_size(m::SizeDoublingMapping) = 2 .* m.domain_size
-    LazyTensors.domain_size(m::SizeDoublingMapping) = m.domain_size
-
-
+@testset "LazyTensorApplication" begin
     m = SizeDoublingMapping{Int, 1, 1}((3,))
+    mm = SizeDoublingMapping{Int, 1, 1}((6,))
     v = [0,1,2]
     @test size(m*v) == 2 .*size(v)
-    @test (m*v)[0] == (:apply,v,(0,))
-    @test (m*m*v)[1] == (:apply,m*v,(1,))
-    @test (m*m*v)[3] == (:apply,m*v,(3,))
-    @test (m*m*v)[6] == (:apply,m*v,(6,))
-    @test_broken BoundsError == (m*m*v)[0]
-    @test_broken BoundsError == (m*m*v)[7]
+    @test (m*v)[1] == (:apply,v,(1,))
+    @test (mm*m*v)[1] == (:apply,m*v,(1,))
+    @test (mm*m*v)[3] == (:apply,m*v,(3,))
+    @test (mm*m*v)[6] == (:apply,m*v,(6,))
     @test_throws MethodError m*m
 
     @test (m*v)[CartesianIndex(2)] == (:apply,v,(2,))
-    @test (m*m*v)[CartesianIndex(2)] == (:apply,m*v,(2,))
-
-    m = SizeDoublingMapping{Int, 2, 1}((3,))
-    @test_throws MethodError m*ones(Int,2,2)
-    @test_throws MethodError m*m*v
+    @test (mm*m*v)[CartesianIndex(2)] == (:apply,m*v,(2,))
 
     m = SizeDoublingMapping{Float64, 2, 2}((3,3))
+    mm = SizeDoublingMapping{Float64, 2, 2}((6,6))
     v = ones(3,3)
     @test size(m*v) == 2 .*size(v)
     @test (m*v)[1,2] == (:apply,v,(1,2))
 
     @test (m*v)[CartesianIndex(2,3)] == (:apply,v,(2,3))
-    @test (m*m*v)[CartesianIndex(4,3)] == (:apply,m*v,(4,3))
+    @test (mm*m*v)[CartesianIndex(4,3)] == (:apply,m*v,(4,3))
 
-    struct ScalingOperator{T,D} <: TensorMapping{T,D,D}
-        λ::T
-        size::NTuple{D,Int}
-    end
-
-    LazyTensors.apply(m::ScalingOperator{T,D}, v, I::Vararg{Any,D}) where {T,D} = m.λ*v[I...]
-    LazyTensors.range_size(m::ScalingOperator) = m.size
-    LazyTensors.domain_size(m::ScalingOperator) = m.size
-
-    m = ScalingOperator{Int,1}(2,(3,))
+    m = ScalingTensor(2,(3,))
     v = [1,2,3]
     @test m*v isa AbstractVector
     @test m*v == [2,4,6]
 
-    m = ScalingOperator{Int,2}(2,(2,2))
+    m = ScalingTensor(2,(2,2))
     v = [[1 2];[3 4]]
     @test m*v == [[2 4];[6 8]]
     @test (m*v)[2,1] == 6
 
+    @testset "Error on index out of bounds" begin
+        m = SizeDoublingMapping{Int, 1, 1}((3,))
+        v = [0,1,2]
+
+        @test_throws BoundsError (m*v)[0]
+        @test_throws BoundsError (m*v)[7]
+    end
+
+    @testset "Error on unmatched dimensions" begin
+        v = [0,1,2]
+        m = SizeDoublingMapping{Int, 2, 1}((3,))
+        @test_throws MethodError m*ones(Int,2,2)
+        @test_throws MethodError m*m*v
+    end
+
+    @testset "Error on unmatched sizes" begin
+        @test_throws DomainSizeMismatch ScalingTensor(2,(2,))*ones(3)
+        @test_throws DomainSizeMismatch ScalingTensor(2,(2,))*ScalingTensor(2,(3,))*ones(3)
+    end
+
+
     @testset "Type calculation" begin
-        m = ScalingOperator{Int,1}(2,(3,))
+        m = ScalingTensor(2,(3,))
         v = [1.,2.,3.]
         @test m*v isa AbstractVector{Float64}
         @test m*v == [2.,4.,6.]
         @inferred m*v
         @inferred (m*v)[1]
 
-        m = ScalingOperator{Int,2}(2,(2,2))
+        m = ScalingTensor(2,(2,2))
         v = [[1. 2.];[3. 4.]]
         @test m*v == [[2. 4.];[6. 8.]]
         @test (m*v)[2,1] == 6.
         @inferred m*v
         @inferred (m*v)[1]
 
-        m = ScalingOperator{ComplexF64,1}(2. +2. *im,(3,))
+        m = ScalingTensor(2. +2. *im,(3,))
         v = [1.,2.,3.]
         @test m*v isa AbstractVector{ComplexF64}
         @test m*v == [2. + 2. *im, 4. + 4. *im, 6. + 6. *im]
         @inferred m*v
         @inferred (m*v)[1]
 
-        m = ScalingOperator{ComplexF64,1}(1,(3,))
+        m = ScalingTensor(1,(3,))
         v = [2. + 2. *im, 4. + 4. *im, 6. + 6. *im]
         @test m*v isa AbstractVector{ComplexF64}
         @test m*v == [2. + 2. *im, 4. + 4. *im, 6. + 6. *im]
         @inferred m*v
         @inferred (m*v)[1]
 
-        m = ScalingOperator{Float64,1}(2., (3,))
+        m = ScalingTensor(2., (3,))
         v = [[1,2,3], [3,2,1],[1,3,1]]
         @test m*v isa AbstractVector{Vector{Float64}}
         @test m*v == [[2.,4.,6.], [6.,4.,2.],[2.,6.,2.]]
@@ -117,19 +128,10 @@
     end
 end
 
-@testset "TensorMapping binary operations" begin
-    struct ScalarMapping{T,R,D} <: TensorMapping{T,R,D}
-        λ::T
-        range_size::NTuple{R,Int}
-        domain_size::NTuple{D,Int}
-    end
 
-    LazyTensors.apply(m::ScalarMapping{T,R}, v, I::Vararg{Any,R}) where {T,R} = m.λ*v[I...]
-    LazyTensors.range_size(m::ScalarMapping) = m.domain_size
-    LazyTensors.domain_size(m::ScalarMapping) = m.range_size
-
-    A = ScalarMapping{Float64,1,1}(2.0, (3,), (3,))
-    B = ScalarMapping{Float64,1,1}(3.0, (3,), (3,))
+@testset "LazyTensor binary operations" begin
+    A = ScalingTensor(2.0, (3,))
+    B = ScalingTensor(3.0, (3,))
 
     v = [1.1,1.2,1.3]
     for i ∈ eachindex(v)
@@ -140,24 +142,34 @@
         @test ((A-B)*v)[i] == 2*v[i] - 3*v[i]
     end
 
+
     @test range_size(A+B) == range_size(A) == range_size(B)
     @test domain_size(A+B) == domain_size(A) == domain_size(B)
 
     @test ((A+B)*ComplexF64[1.1,1.2,1.3])[3] isa ComplexF64
+
+    @testset "Error on unmatched sizes" begin
+        @test_throws Union{DomainSizeMismatch, RangeSizeMismatch} ScalingTensor(2.0, (3,)) + ScalingTensor(2.0, (4,))
+
+        @test_throws DomainSizeMismatch ScalingTensor(2.0, (4,)) + SizeDoublingMapping{Float64,1,1}((2,))
+        @test_throws DomainSizeMismatch SizeDoublingMapping{Float64,1,1}((2,)) + ScalingTensor(2.0, (4,))
+        @test_throws RangeSizeMismatch ScalingTensor(2.0, (2,)) + SizeDoublingMapping{Float64,1,1}((2,))
+        @test_throws RangeSizeMismatch SizeDoublingMapping{Float64,1,1}((2,)) + ScalingTensor(2.0, (2,))
+    end
 end
 
 
-@testset "TensorMappingComposition" begin
+@testset "LazyTensorComposition" begin
     A = rand(2,3)
     B = rand(3,4)
 
     Ã = LazyLinearMap(A, (1,), (2,))
     B̃ = LazyLinearMap(B, (1,), (2,))
 
-    @test Ã∘B̃ isa TensorMappingComposition
+    @test Ã∘B̃ isa LazyTensorComposition
     @test range_size(Ã∘B̃) == (2,)
     @test domain_size(Ã∘B̃) == (4,)
-    @test_throws SizeMismatch B̃∘Ã
+    @test_throws DomainSizeMismatch B̃∘Ã
 
     # @test @inbounds B̃∘Ã # Should not error even though dimensions don't match. (Since ]test runs with forced boundschecking this is currently not testable 2020-10-16)
 
@@ -171,100 +183,9 @@
     @test ((Ã∘B̃)'*ComplexF64[1.,2.])[1] isa ComplexF64
 end
 
-@testset "LazyLinearMap" begin
-    # Test a standard matrix-vector product
-    # mapping vectors of size 4 to vectors of size 3.
-    A = rand(3,4)
-    Ã = LazyLinearMap(A, (1,), (2,))
-    v = rand(4)
-    w = rand(3)
 
-    @test à isa LazyLinearMap{T,1,1} where T
-    @test à isa TensorMapping{T,1,1} where T
-    @test range_size(Ã) == (3,)
-    @test domain_size(Ã) == (4,)
-
-    @test Ã*ones(4) ≈ A*ones(4) atol=5e-13
-    @test Ã*v ≈ A*v atol=5e-13
-    @test Ã'*w ≈ A'*w
-
-    A = rand(2,3,4)
-    @test_throws DomainError LazyLinearMap(A, (3,1), (2,))
-
-    # Test more exotic mappings
-    B = rand(3,4,2)
-    # Map vectors of size 2 to matrices of size (3,4)
-    B̃ = LazyLinearMap(B, (1,2), (3,))
-    v = rand(2)
-
-    @test range_size(B̃) == (3,4)
-    @test domain_size(B̃) == (2,)
-    @test B̃ isa TensorMapping{T,2,1} where T
-    @test B̃*ones(2) ≈ B[:,:,1] + B[:,:,2] atol=5e-13
-    @test B̃*v ≈ B[:,:,1]*v[1] + B[:,:,2]*v[2] atol=5e-13
-
-    # Map matrices of size (3,2) to vectors of size 4
-    B̃ = LazyLinearMap(B, (2,), (1,3))
-    v = rand(3,2)
-
-    @test range_size(B̃) == (4,)
-    @test domain_size(B̃) == (3,2)
-    @test B̃ isa TensorMapping{T,1,2} where T
-    @test B̃*ones(3,2) ≈ B[1,:,1] + B[2,:,1] + B[3,:,1] +
-                        B[1,:,2] + B[2,:,2] + B[3,:,2] atol=5e-13
-    @test B̃*v ≈ B[1,:,1]*v[1,1] + B[2,:,1]*v[2,1] + B[3,:,1]*v[3,1] +
-                B[1,:,2]v[1,2] + B[2,:,2]*v[2,2] + B[3,:,2]*v[3,2] atol=5e-13
-
-
-    # TODO:
-    # @inferred (B̃*v)[2]
-end
-
-
-@testset "IdentityMapping" begin
-    @test IdentityMapping{Float64}((4,5)) isa IdentityMapping{T,2} where T
-    @test IdentityMapping{Float64}((4,5)) isa TensorMapping{T,2,2} where T
-    @test IdentityMapping{Float64}((4,5)) == IdentityMapping{Float64}(4,5)
-
-    @test IdentityMapping(3,2) isa IdentityMapping{Float64,2}
-
-    for sz ∈ [(4,5),(3,),(5,6,4)]
-        I = IdentityMapping{Float64}(sz)
-        v = rand(sz...)
-        @test I*v == v
-        @test I'*v == v
-
-        v = rand(ComplexF64,sz...)
-        @test I*v == v
-        @test I'*v == v
-
-        @test range_size(I) == sz
-        @test domain_size(I) == sz
-    end
-
-    I = IdentityMapping{Float64}((4,5))
-    v = rand(4,5)
-    @inferred (I*v)[3,2]
-    @inferred (I'*v)[3,2]
-    @inferred range_size(I)
-
-    @inferred range_dim(I)
-    @inferred domain_dim(I)
-
-    Ã = rand(4,2)
-    A = LazyLinearMap(Ã,(1,),(2,))
-    I1 = IdentityMapping{Float64}(2)
-    I2 = IdentityMapping{Float64}(4)
-    @test A∘I1 == A
-    @test I2∘A == A
-    @test I1∘I1 == I1
-    @test_throws SizeMismatch I1∘A
-    @test_throws SizeMismatch A∘I2
-    @test_throws SizeMismatch I1∘I2
-end
-
-@testset "InflatedTensorMapping" begin
-    I(sz...) = IdentityMapping(sz...)
+@testset "InflatedLazyTensor" begin
+    I(sz...) = IdentityTensor(sz...)
 
     Ã = rand(4,2)
     B̃ = rand(4,2,3)
@@ -275,99 +196,89 @@
     C = LazyLinearMap(C̃,(1,),(2,3))
 
     @testset "Constructors" begin
-        @test InflatedTensorMapping(I(3,2), A, I(4)) isa TensorMapping{Float64, 4, 4}
-        @test InflatedTensorMapping(I(3,2), B, I(4)) isa TensorMapping{Float64, 5, 4}
-        @test InflatedTensorMapping(I(3), C, I(2,3)) isa TensorMapping{Float64, 4, 5}
-        @test InflatedTensorMapping(C, I(2,3)) isa TensorMapping{Float64, 3, 4}
-        @test InflatedTensorMapping(I(3), C) isa TensorMapping{Float64, 2, 3}
-        @test InflatedTensorMapping(I(3), I(2,3)) isa TensorMapping{Float64, 3, 3}
+        @test InflatedLazyTensor(I(3,2), A, I(4)) isa LazyTensor{Float64, 4, 4}
+        @test InflatedLazyTensor(I(3,2), B, I(4)) isa LazyTensor{Float64, 5, 4}
+        @test InflatedLazyTensor(I(3), C, I(2,3)) isa LazyTensor{Float64, 4, 5}
+        @test InflatedLazyTensor(C, I(2,3)) isa LazyTensor{Float64, 3, 4}
+        @test InflatedLazyTensor(I(3), C) isa LazyTensor{Float64, 2, 3}
+        @test InflatedLazyTensor(I(3), I(2,3)) isa LazyTensor{Float64, 3, 3}
     end
 
     @testset "Range and domain size" begin
-        @test range_size(InflatedTensorMapping(I(3,2), A, I(4))) == (3,2,4,4)
-        @test domain_size(InflatedTensorMapping(I(3,2), A, I(4))) == (3,2,2,4)
+        @test range_size(InflatedLazyTensor(I(3,2), A, I(4))) == (3,2,4,4)
+        @test domain_size(InflatedLazyTensor(I(3,2), A, I(4))) == (3,2,2,4)
 
-        @test range_size(InflatedTensorMapping(I(3,2), B, I(4))) == (3,2,4,2,4)
-        @test domain_size(InflatedTensorMapping(I(3,2), B, I(4))) == (3,2,3,4)
+        @test range_size(InflatedLazyTensor(I(3,2), B, I(4))) == (3,2,4,2,4)
+        @test domain_size(InflatedLazyTensor(I(3,2), B, I(4))) == (3,2,3,4)
 
-        @test range_size(InflatedTensorMapping(I(3), C, I(2,3))) == (3,4,2,3)
-        @test domain_size(InflatedTensorMapping(I(3), C, I(2,3))) == (3,2,3,2,3)
+        @test range_size(InflatedLazyTensor(I(3), C, I(2,3))) == (3,4,2,3)
+        @test domain_size(InflatedLazyTensor(I(3), C, I(2,3))) == (3,2,3,2,3)
 
-        @inferred range_size(InflatedTensorMapping(I(3,2), A, I(4))) == (3,2,4,4)
-        @inferred domain_size(InflatedTensorMapping(I(3,2), A, I(4))) == (3,2,2,4)
+        @inferred range_size(InflatedLazyTensor(I(3,2), A, I(4))) == (3,2,4,4)
+        @inferred domain_size(InflatedLazyTensor(I(3,2), A, I(4))) == (3,2,2,4)
     end
 
     @testset "Application" begin
         # Testing regular application and transposed application with inflation "before", "after" and "before and after".
         # The inflated tensor mappings are chosen to preserve, reduce and increase the dimension of the result compared to the input.
-        tests = [
+        cases = [
             (
-                InflatedTensorMapping(I(3,2), A, I(4)),
+                InflatedLazyTensor(I(3,2), A, I(4)),
                 (v-> @tullio res[a,b,c,d] := Ã[c,i]*v[a,b,i,d]), # Expected result of apply
                 (v-> @tullio res[a,b,c,d] := Ã[i,c]*v[a,b,i,d]), # Expected result of apply_transpose
             ),
             (
-                InflatedTensorMapping(I(3,2), B, I(4)),
+                InflatedLazyTensor(I(3,2), B, I(4)),
                 (v-> @tullio res[a,b,c,d,e] := B̃[c,d,i]*v[a,b,i,e]),
                 (v-> @tullio res[a,b,c,d] := B̃[i,j,c]*v[a,b,i,j,d]),
             ),
             (
-                InflatedTensorMapping(I(3,2), C, I(4)),
+                InflatedLazyTensor(I(3,2), C, I(4)),
                 (v-> @tullio res[a,b,c,d] := C̃[c,i,j]*v[a,b,i,j,d]),
                 (v-> @tullio res[a,b,c,d,e] := C̃[i,c,d]*v[a,b,i,e]),
             ),
             (
-                InflatedTensorMapping(I(3,2), A),
+                InflatedLazyTensor(I(3,2), A),
                 (v-> @tullio res[a,b,c] := Ã[c,i]*v[a,b,i]),
                 (v-> @tullio res[a,b,c] := Ã[i,c]*v[a,b,i]),
             ),
             (
-                InflatedTensorMapping(I(3,2), B),
+                InflatedLazyTensor(I(3,2), B),
                 (v-> @tullio res[a,b,c,d] := B̃[c,d,i]*v[a,b,i]),
                 (v-> @tullio res[a,b,c] := B̃[i,j,c]*v[a,b,i,j]),
             ),
             (
-                InflatedTensorMapping(I(3,2), C),
+                InflatedLazyTensor(I(3,2), C),
                 (v-> @tullio res[a,b,c] := C̃[c,i,j]*v[a,b,i,j]),
                 (v-> @tullio res[a,b,c,d] := C̃[i,c,d]*v[a,b,i]),
             ),
             (
-                InflatedTensorMapping(A,I(4)),
+                InflatedLazyTensor(A,I(4)),
                 (v-> @tullio res[a,b] := Ã[a,i]*v[i,b]),
                 (v-> @tullio res[a,b] := Ã[i,a]*v[i,b]),
             ),
             (
-                InflatedTensorMapping(B,I(4)),
+                InflatedLazyTensor(B,I(4)),
                 (v-> @tullio res[a,b,c] := B̃[a,b,i]*v[i,c]),
                 (v-> @tullio res[a,b] := B̃[i,j,a]*v[i,j,b]),
             ),
             (
-                InflatedTensorMapping(C,I(4)),
+                InflatedLazyTensor(C,I(4)),
                 (v-> @tullio res[a,b] := C̃[a,i,j]*v[i,j,b]),
                 (v-> @tullio res[a,b,c] := C̃[i,a,b]*v[i,c]),
             ),
         ]
 
-        @testset "apply" begin
-            for i ∈ 1:length(tests)
-                tm = tests[i][1]
-                v = rand(domain_size(tm)...)
-                true_value = tests[i][2](v)
-                @test tm*v ≈ true_value rtol=1e-14
-            end
-        end
+        @testset "$tm" for (tm, true_apply, true_apply_transpose) ∈ cases
+            v = rand(domain_size(tm)...)
+            @test tm*v ≈ true_apply(v) rtol=1e-14
 
-        @testset "apply_transpose" begin
-            for i ∈ 1:length(tests)
-                tm = tests[i][1]
-                v = rand(range_size(tm)...)
-                true_value = tests[i][3](v)
-                @test tm'*v ≈ true_value rtol=1e-14
-            end
+            v = rand(range_size(tm)...)
+            @test tm'*v ≈ true_apply_transpose(v) rtol=1e-14
         end
 
         @testset "application to other type" begin
-            tm = InflatedTensorMapping(I(3,2), A, I(4))
+            tm = InflatedLazyTensor(I(3,2), A, I(4))
 
             v = rand(ComplexF64, domain_size(tm)...)
             @test (tm*v)[1,2,3,1] isa ComplexF64
@@ -377,16 +288,7 @@
         end
 
         @testset "Inference of application" begin
-            struct ScalingOperator{T,D} <: TensorMapping{T,D,D}
-                λ::T
-                size::NTuple{D,Int}
-            end
-
-            LazyTensors.apply(m::ScalingOperator{T,D}, v, I::Vararg{Any,D}) where {T,D} = m.λ*v[I...]
-            LazyTensors.range_size(m::ScalingOperator) = m.size
-            LazyTensors.domain_size(m::ScalingOperator) = m.size
-
-            tm = InflatedTensorMapping(I(2,3),ScalingOperator(2.0, (3,2)),I(3,4))
+            tm = InflatedLazyTensor(I(2,3),ScalingTensor(2.0, (3,2)),I(3,4))
             v = rand(domain_size(tm)...)
 
             @inferred apply(tm,v,1,2,3,2,2,4)
@@ -394,94 +296,24 @@
         end
     end
 
-    @testset "InflatedTensorMapping of InflatedTensorMapping" begin
-        A = ScalingOperator(2.0,(2,3))
-        itm = InflatedTensorMapping(I(3,2), A, I(4))
-        @test  InflatedTensorMapping(I(4), itm, I(2)) == InflatedTensorMapping(I(4,3,2), A, I(4,2))
-        @test  InflatedTensorMapping(itm, I(2)) == InflatedTensorMapping(I(3,2), A, I(4,2))
-        @test  InflatedTensorMapping(I(4), itm) == InflatedTensorMapping(I(4,3,2), A, I(4))
+    @testset "InflatedLazyTensor of InflatedLazyTensor" begin
+        A = ScalingTensor(2.0,(2,3))
+        itm = InflatedLazyTensor(I(3,2), A, I(4))
+        @test  InflatedLazyTensor(I(4), itm, I(2)) == InflatedLazyTensor(I(4,3,2), A, I(4,2))
+        @test  InflatedLazyTensor(itm, I(2)) == InflatedLazyTensor(I(3,2), A, I(4,2))
+        @test  InflatedLazyTensor(I(4), itm) == InflatedLazyTensor(I(4,3,2), A, I(4))
 
-        @test InflatedTensorMapping(I(2), I(2), I(2)) isa InflatedTensorMapping # The constructor should always return its type.
+        @test InflatedLazyTensor(I(2), I(2), I(2)) isa InflatedLazyTensor # The constructor should always return its type.
     end
 end
 
-@testset "split_index" begin
-    @test LazyTensors.split_index(Val(2),Val(1),Val(2),Val(2),1,2,3,4,5,6) == ((1,2,:,5,6),(3,4))
-    @test LazyTensors.split_index(Val(2),Val(3),Val(2),Val(2),1,2,3,4,5,6) == ((1,2,:,:,:,5,6),(3,4))
-    @test LazyTensors.split_index(Val(3),Val(1),Val(1),Val(2),1,2,3,4,5,6) == ((1,2,3,:,5,6),(4,))
-    @test LazyTensors.split_index(Val(3),Val(2),Val(1),Val(2),1,2,3,4,5,6) == ((1,2,3,:,:,5,6),(4,))
-    @test LazyTensors.split_index(Val(1),Val(1),Val(2),Val(3),1,2,3,4,5,6) == ((1,:,4,5,6),(2,3))
-    @test LazyTensors.split_index(Val(1),Val(2),Val(2),Val(3),1,2,3,4,5,6) == ((1,:,:,4,5,6),(2,3))
-
-    @test LazyTensors.split_index(Val(0),Val(1),Val(3),Val(3),1,2,3,4,5,6) == ((:,4,5,6),(1,2,3))
-    @test LazyTensors.split_index(Val(3),Val(1),Val(3),Val(0),1,2,3,4,5,6) == ((1,2,3,:),(4,5,6))
-
-    @inferred LazyTensors.split_index(Val(2),Val(3),Val(2),Val(2),1,2,3,2,2,4)
-end
-
-@testset "slice_tuple" begin
-    @test LazyTensors.slice_tuple((1,2,3),Val(1), Val(3)) == (1,2,3)
-    @test LazyTensors.slice_tuple((1,2,3,4,5,6),Val(2), Val(5)) == (2,3,4,5)
-    @test LazyTensors.slice_tuple((1,2,3,4,5,6),Val(1), Val(3)) == (1,2,3)
-    @test LazyTensors.slice_tuple((1,2,3,4,5,6),Val(4), Val(6)) == (4,5,6)
-end
-
-@testset "split_tuple" begin
-    @testset "2 parts" begin
-        @test LazyTensors.split_tuple((),Val(0)) == ((),())
-        @test LazyTensors.split_tuple((1,),Val(0)) == ((),(1,))
-        @test LazyTensors.split_tuple((1,),Val(1)) == ((1,),())
-
-        @test LazyTensors.split_tuple((1,2,3,4),Val(0)) == ((),(1,2,3,4))
-        @test LazyTensors.split_tuple((1,2,3,4),Val(1)) == ((1,),(2,3,4))
-        @test LazyTensors.split_tuple((1,2,3,4),Val(2)) == ((1,2),(3,4))
-        @test LazyTensors.split_tuple((1,2,3,4),Val(3)) == ((1,2,3),(4,))
-        @test LazyTensors.split_tuple((1,2,3,4),Val(4)) == ((1,2,3,4),())
-
-        @test LazyTensors.split_tuple((1,2,true,4),Val(3)) == ((1,2,true),(4,))
-
-        @inferred LazyTensors.split_tuple((1,2,3,4),Val(3))
-        @inferred LazyTensors.split_tuple((1,2,true,4),Val(3))
-    end
-
-    @testset "3 parts" begin
-        @test LazyTensors.split_tuple((),Val(0),Val(0)) == ((),(),())
-        @test LazyTensors.split_tuple((1,2,3),Val(1), Val(1)) == ((1,),(2,),(3,))
-        @test LazyTensors.split_tuple((1,true,3),Val(1), Val(1)) == ((1,),(true,),(3,))
-
-        @test LazyTensors.split_tuple((1,2,3,4,5,6),Val(1),Val(2)) == ((1,),(2,3),(4,5,6))
-        @test LazyTensors.split_tuple((1,2,3,4,5,6),Val(3),Val(2)) == ((1,2,3),(4,5),(6,))
-
-        @inferred LazyTensors.split_tuple((1,2,3,4,5,6),Val(3),Val(2))
-        @inferred LazyTensors.split_tuple((1,true,3),Val(1), Val(1))
-    end
-end
-
-@testset "flatten_tuple" begin
-    @test LazyTensors.flatten_tuple((1,)) == (1,)
-    @test LazyTensors.flatten_tuple((1,2,3,4,5,6)) == (1,2,3,4,5,6)
-    @test LazyTensors.flatten_tuple((1,2,(3,4),5,6)) == (1,2,3,4,5,6)
-    @test LazyTensors.flatten_tuple((1,2,(3,(4,5)),6)) == (1,2,3,4,5,6)
-    @test LazyTensors.flatten_tuple(((1,2),(3,4),(5,),6)) == (1,2,3,4,5,6)
-end
-
-
 @testset "LazyOuterProduct" begin
-    struct ScalingOperator{T,D} <: TensorMapping{T,D,D}
-        λ::T
-        size::NTuple{D,Int}
-    end
-
-    LazyTensors.apply(m::ScalingOperator{T,D}, v, I::Vararg{Any,D}) where {T,D} = m.λ*v[I...]
-    LazyTensors.range_size(m::ScalingOperator) = m.size
-    LazyTensors.domain_size(m::ScalingOperator) = m.size
-
-    A = ScalingOperator(2.0, (5,))
-    B = ScalingOperator(3.0, (3,))
-    C = ScalingOperator(5.0, (3,2))
+    A = ScalingTensor(2.0, (5,))
+    B = ScalingTensor(3.0, (3,))
+    C = ScalingTensor(5.0, (3,2))
 
     AB = LazyOuterProduct(A,B)
-    @test AB isa TensorMapping{T,2,2} where T
+    @test AB isa LazyTensor{T,2,2} where T
     @test range_size(AB) == (5,3)
     @test domain_size(AB) == (5,3)
 
@@ -490,7 +322,7 @@
 
     ABC = LazyOuterProduct(A,B,C)
 
-    @test ABC isa TensorMapping{T,4,4} where T
+    @test ABC isa LazyTensor{T,4,4} where T
     @test range_size(ABC) == (5,3,3,2)
     @test domain_size(ABC) == (5,3,3,2)
 
@@ -515,32 +347,21 @@
     @test B̃Ã*v₂ ≈ BAv
 
     @testset "Indentity mapping arguments" begin
-        @test LazyOuterProduct(IdentityMapping(3,2), IdentityMapping(1,2)) == IdentityMapping(3,2,1,2)
+        @test LazyOuterProduct(IdentityTensor(3,2), IdentityTensor(1,2)) == IdentityTensor(3,2,1,2)
 
         Ã = LazyLinearMap(A,(1,),(2,))
-        @test LazyOuterProduct(IdentityMapping(3,2), Ã) == InflatedTensorMapping(IdentityMapping(3,2),Ã)
-        @test LazyOuterProduct(Ã, IdentityMapping(3,2)) == InflatedTensorMapping(Ã,IdentityMapping(3,2))
+        @test LazyOuterProduct(IdentityTensor(3,2), Ã) == InflatedLazyTensor(IdentityTensor(3,2),Ã)
+        @test LazyOuterProduct(Ã, IdentityTensor(3,2)) == InflatedLazyTensor(Ã,IdentityTensor(3,2))
 
-        I1 = IdentityMapping(3,2)
-        I2 = IdentityMapping(4)
-        @test I1⊗Ã⊗I2 == InflatedTensorMapping(I1, Ã, I2)
+        I1 = IdentityTensor(3,2)
+        I2 = IdentityTensor(4)
+        @test I1⊗Ã⊗I2 == InflatedLazyTensor(I1, Ã, I2)
     end
-
 end
 
 @testset "inflate" begin
-    struct ScalingOperator{T,D} <: TensorMapping{T,D,D}
-        λ::T
-        size::NTuple{D,Int}
-    end
-
-    LazyTensors.apply(m::ScalingOperator{T,D}, v, I::Vararg{Any,D}) where {T,D} = m.λ*v[I...]
-    LazyTensors.range_size(m::ScalingOperator) = m.size
-    LazyTensors.domain_size(m::ScalingOperator) = m.size
-
-
-    I = LazyTensors.inflate(IdentityMapping(),(3,4,5,6), 2)
-    @test I isa TensorMapping{Float64, 3,3}
+    I = LazyTensors.inflate(IdentityTensor(),(3,4,5,6), 2)
+    @test I isa LazyTensor{Float64, 3,3}
     @test range_size(I) == (3,5,6)
     @test domain_size(I) == (3,5,6)