--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/LazyTensors/lazy_tensor.jl	Fri Mar 18 21:17:01 2022 +0100
@@ -0,0 +1,80 @@
+export LazyTensor
+export apply
+export apply_transpose
+export range_dim, domain_dim
+export range_size, domain_size
+
+"""
+    LazyTensor{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
+```julia
+    apply(t::LazyTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg) where {R,D,T}
+```
+
+The size of the range and domain that the operator works with should be returned by
+the functions
+```julia
+    range_size(::LazyTensor)
+    domain_size(::LazyTensor)
+```
+to allow querying for one or the other.
+
+Optionally the action of the transpose may be defined through
+```julia
+    apply_transpose(t::LazyTensor{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T}
+```
+"""
+abstract type LazyTensor{T,R,D} end
+
+"""
+    apply(t::LazyTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg) where {R,D,T}
+
+Return the result of the mapping for a given index.
+"""
+function apply end
+
+"""
+    apply_transpose(t::LazyTensor{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg) where {R,D,T}
+
+Return the result of the transposed mapping for a given index.
+"""
+function apply_transpose end
+
+"""
+    range_dim(::LazyTensor)
+Return the dimension of the range space of a given mapping
+"""
+range_dim(::LazyTensor{T,R,D}) where {T,R,D} = R
+
+"""
+    domain_dim(::LazyTensor)
+Return the dimension of the domain space of a given mapping
+"""
+domain_dim(::LazyTensor{T,R,D}) where {T,R,D} = D
+
+
+"""
+    range_size(M::LazyTensor)
+
+Return the range size for the mapping.
+"""
+function range_size end
+
+"""
+    domain_size(M::LazyTensor)
+
+Return the domain size for the mapping.
+"""
+function domain_size end
+
+
+"""
+    eltype(::LazyTensor{T})
+
+The type of elements the LazyTensor acts on.
+"""
+Base.eltype(::LazyTensor{T}) where T = T
+
+# TODO: Think about boundschecking!