--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/LazyTensors/src/lazy_tensor_operations.jl	Thu Dec 05 09:28:04 2019 +0100
@@ -0,0 +1,101 @@
+"""
+    LazyTensorMappingApplication{T,R,D} <: LazyArray{T,R}
+
+Struct for lazy application of a TensorMapping. Created using `*`.
+
+Allows the result of a `TensorMapping` applied to a vector to be treated as an `AbstractArray`.
+With a mapping `m` and a vector `v` the LazyTensorMappingApplication object can be created by `m*v`.
+The actual result will be calcualted when indexing into `m*v`.
+"""
+struct LazyTensorMappingApplication{T,R,D} <: LazyArray{T,R}
+    t::TensorMapping{T,R,D}
+    o::AbstractArray{T,D}
+end
+export LazyTensorMappingApplication
+
+Base.:*(tm::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = LazyTensorMappingApplication(tm,o)
+
+Base.getindex(ta::LazyTensorMappingApplication{T,R,D}, I::Vararg{Int,R}) where {T,R,D} = apply(ta.t, ta.o, I)
+Base.size(ta::LazyTensorMappingApplication{T,R,D}) where {T,R,D} = range_size(ta.t,size(ta.o))
+# TODO: What else is needed to implement the AbstractArray interface?
+
+# # We need the associativity to be a→b→c = a→(b→c), which is the case for '→'
+Base.:*(a::TensorMapping{T,R,D}, b::TensorMapping{T,D,K}, args::Union{TensorMapping{T}, AbstractArray{T}}...) where {T,R,D,K} = foldr(*,(a,b,args...))
+# # Should we overload some other infix binary operator?
+# →(tm::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = LazyTensorMappingApplication(tm,o)
+# TODO: We need to be really careful about good error messages.
+# For example what happens if you try to multiply LazyTensorMappingApplication with a TensorMapping(wrong order)?
+
+"""
+    LazyTensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R}
+
+Struct for lazy transpose of a TensorMapping.
+
+If a mapping implements the the `apply_transpose` method this allows working with
+the transpose of mapping `m` by using `m'`. `m'` will work as a regular TensorMapping lazily calling
+the appropriate methods of `m`.
+"""
+struct LazyTensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R}
+    tm::TensorMapping{T,R,D}
+end
+export LazyTensorMappingTranspose
+
+# # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors?
+Base.adjoint(t::TensorMapping) = LazyTensorMappingTranspose(t)
+Base.adjoint(t::LazyTensorMappingTranspose) = t.tm
+
+apply(tm::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{T,R}, I::NTuple{D,Int}) where {T,R,D} = apply_transpose(tm.tm, v, I)
+apply_transpose(tm::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{T,D}, I::NTuple{R,Int}) where {T,R,D} = apply(tm.tm, v, I)
+
+range_size(tmt::LazyTensorMappingTranspose{T,R,D}, d_size::NTuple{R,Integer}) where {T,R,D} = domain_size(tmt.tm, d_size)
+domain_size(tmt::LazyTensorMappingTranspose{T,R,D}, r_size::NTuple{D,Integer}) where {T,R,D} = range_size(tmt.tm, r_size)
+
+
+
+
+struct LazyTensorMappingBinaryOperation{Op,T,R,D,T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
+    A::T1
+    B::T2
+
+    @inline function LazyTensorMappingBinaryOperation{Op,T,R,D}(A::T1,B::T2) where {Op,T,R,D, T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}}
+        return new{Op,T,R,D,T1,T2}(A,B)
+    end
+end
+
+apply(mb::LazyTensorMappingBinaryOperation{:+,T,R,D}, v::AbstractArray{T,D}, I::NTuple{R,Int}) where {T,R,D} = apply(mb.A, v, I...) + apply(mb.B,v,I...)
+apply(mb::LazyTensorMappingBinaryOperation{:-,T,R,D}, v::AbstractArray{T,D}, I::NTuple{R,Int}) where {T,R,D} = apply(mb.A, v, I...) - apply(mb.B,v,I...)
+
+range_size(mp::LazyTensorMappingBinaryOperation{Op,T,R,D}, domain_size::NTuple{D,Integer}) where {Op,T,R,D} = range_size(mp.A, domain_size)
+domain_size(mp::LazyTensorMappingBinaryOperation{Op,T,R,D}, range_size::NTuple{R,Integer}) where {Op,T,R,D} = domain_size(mp.A, range_size)
+
+Base.:+(A::TensorMapping{T,R,D}, B::TensorMapping{T,R,D}) where {T,R,D} = LazyTensorMappingBinaryOperation{:+,T,R,D}(A,B)
+Base.:-(A::TensorMapping{T,R,D}, B::TensorMapping{T,R,D}) where {T,R,D} = LazyTensorMappingBinaryOperation{:-,T,R,D}(A,B)
+
+
+# TODO: Write tests and documentation for LazyTensorMappingComposition
+# struct LazyTensorMappingComposition{T,R,K,D} <: TensorMapping{T,R,D}
+#     t1::TensorMapping{T,R,K}
+#     t2::TensorMapping{T,K,D}
+# end
+
+# Base.:∘(s::TensorMapping{T,R,K}, t::TensorMapping{T,K,D}) where {T,R,K,D} = LazyTensorMappingComposition(s,t)
+
+# function range_size(tm::LazyTensorMappingComposition{T,R,K,D}, domain_size::NTuple{D,Integer}) where {T,R,K,D}
+#     range_size(tm.t1, domain_size(tm.t2, domain_size))
+# end
+
+# function domain_size(tm::LazyTensorMappingComposition{T,R,K,D}, range_size::NTuple{R,Integer}) where {T,R,K,D}
+#     domain_size(tm.t1, domain_size(tm.t2, range_size))
+# end
+
+# function apply(c::LazyTensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::NTuple{R,Int}) where {T,R,K,D}
+#     apply(c.t1, LazyTensorMappingApplication(c.t2,v), I...)
+# end
+
+# function apply_transpose(c::LazyTensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::NTuple{D,Int}) where {T,R,K,D}
+#     apply_transpose(c.t2, LazyTensorMappingApplication(c.t1',v), I...)
+# end
+
+# # Have i gone too crazy with the type parameters? Maybe they aren't all needed?
+
+# export →