--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/LazyTensor/src/LazyTensor.jl	Thu Jun 20 15:23:21 2019 +0200
@@ -0,0 +1,165 @@
+module LazyTensor
+
+
+"""
+    Mapping{T,R,D}
+
+Describes a mapping of a D dimension tensor to an R dimension tensor.
+The action of the mapping is implemented through the method
+
+    apply(t::Mapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T}
+
+The size of range tensor should be dependent on the size of the domain tensor
+and the type should implement the methods
+
+    range_size(::Mapping{T,R,D}, domain_size::NTuple{D,Integer}) where {T,R,D}
+    domain_size(::Mapping{T,R,D}, range_size::NTuple{R,Integer}) where {T,R,D}
+
+to allow querying for one or the other.
+
+Optionally the action of the transpose may be defined through
+    apply_transpose(t::Mapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T}
+"""
+abstract type Mapping{T,R,D} end
+
+"""
+    apply(t::Mapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T}
+
+Return the result of the mapping for a given index.
+"""
+function apply end
+export apply
+
+"""
+    apply_transpose(t::Mapping{T,R,D}, v::AbstractArray{T,R}, I::Vararg) where {R,D,T}
+
+Return the result of the transposed mapping for a given index.
+"""
+function apply_transpose end
+export apply_transpose
+
+"""
+Return the dimension of the range space of a given mapping
+"""
+range_dim(::Mapping{T,R,D}) where {T,R,D} = R
+
+"""
+Return the dimension of the domain space of a given mapping
+"""
+domain_dim(::Mapping{T,R,D}) where {T,R,D} = D
+
+export range_dim, domain_dim
+
+"""
+    range_size(M::Mapping, domain_size)
+
+Return the resulting range size for the mapping applied to a given domain_size
+"""
+function range_size end
+
+"""
+    domain_size(M::Mapping, range_size)
+
+Return the resulting domain size for the mapping applied to a given range_size
+"""
+function domain_size end
+
+export range_size, domain_size
+# TODO: Think about boundschecking!
+
+
+"""
+    Operator{T,D}
+
+A `Mapping{T,D,D}` where the range and domain tensor have the same number of
+dimensions and the same size.
+"""
+abstract type Operator{T,D} <: Mapping{T,D,D} end
+domain_size(::Operator{T,D}, range_size::NTuple{D,Integer}) where {T,D} = range_size
+range_size(::Operator{T,D}, domain_size::NTuple{D,Integer}) where {T,D} = domain_size
+
+
+
+"""
+    MappingTranspose{T,R,D} <: Mapping{T,D,R}
+
+Struct for lazy transpose of a Mapping.
+
+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 Mapping lazily calling
+the appropriate methods of `m`.
+"""
+struct MappingTranspose{T,R,D} <: Mapping{T,D,R}
+    tm::Mapping{T,R,D}
+end
+
+# # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors?
+Base.adjoint(t::Mapping) = MappingTranspose(t)
+Base.adjoint(t::MappingTranspose) = t.tm
+
+apply(tm::MappingTranspose{T,R,D}, v::AbstractArray{T,R}, I::Vararg) where {T,R,D} = apply_transpose(tm.tm, v, I...)
+apply_transpose(tm::MappingTranspose{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {T,R,D} = apply(tm.tm, v, I...)
+
+range_size(tmt::MappingTranspose{T,R,D}, d_size::NTuple{R,Integer}) where {T,R,D} = domain_size(tmt.tm, domain_size)
+domain_size(tmt::MappingTranspose{T,R,D}, r_size::NTuple{D,Integer}) where {T,R,D} = range_size(tmt.tm, range_size)
+
+
+"""
+    Application{T,R,D} <: AbstractArray{T,R}
+
+Struct for lazy application of a Mapping. Created using `*`.
+
+Allows the result of a `Mapping` applied to a vector to be treated as an `AbstractArray`.
+With a mapping `m` and a vector `v` the Application object can be created by `m*v`.
+The actual result will be calcualted when indexing into `m*v`.
+"""
+struct Application{T,R,D} <: AbstractArray{T,R}
+    t::Mapping{T,R,D}
+    o::AbstractArray{T,D}
+end
+
+Base.:*(tm::Mapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = Application(tm,o)
+
+Base.getindex(ta::Application{T,R,D}, I::Vararg) where {T,R,D} = apply(ta.t, ta.o, I...)
+Base.size(ta::Application{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.:*(args::Union{Mapping{T}, AbstractArray{T}}...) where T = foldr(*,args)
+# # Should we overload some other infix binary operator?
+# →(tm::Mapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = Application(tm,o)
+# TODO: We need to be really careful about good error messages.
+# For example what happens if you try to multiply Application with a Mapping(wrong order)?
+
+
+
+# struct TensorMappingComposition{T,R,K,D} <: Mapping{T,R,D}
+#     t1::Mapping{T,R,K}
+#     t2::Mapping{T,K,D}
+# end
+
+# Base.:∘(s::Mapping{T,R,K}, t::Mapping{T,K,D}) where {T,R,K,D} = TensorMappingComposition(s,t)
+
+# function range_size(tm::TensorMappingComposition{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::TensorMappingComposition{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::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::Vararg) where {T,R,K,D}
+#     apply(c.t1, Application(c.t2,v), I...)
+# end
+
+# function apply_transpose(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{T,D}, I::Vararg) where {T,R,K,D}
+#     apply_transpose(c.t2, Application(c.t1',v), I...)
+# end
+
+# # Have i gone too crazy with the type parameters? Maybe they aren't all needed?
+
+# export →
+
+
+end # module