--- a/LazyTensors/src/lazy_operations.jl	Thu Jun 20 23:05:12 2019 +0200
+++ b/LazyTensors/src/lazy_operations.jl	Thu Jun 20 23:11:30 2019 +0200
@@ -55,6 +55,83 @@
 
 
 
+"""
+    LazyElementwiseOperation{T,D,Op, T1<:AbstractArray{T,D}, T2 <: AbstractArray{T,D}} <: AbstractArray{T,D}
+
+Struct allowing for lazy evaluation of elementwise operations on AbstractArrays.
+
+A LazyElementwiseOperation contains two AbstractArrays of equal size,
+together with an operation. The operations are carried out when the
+LazyElementwiseOperation is indexed.
+"""
+struct LazyElementwiseOperation{T,D,Op, T1<:AbstractArray{T,D}, T2 <: AbstractArray{T,D}} <: AbstractArray{T,D}
+    a::T1
+    b::T2
+
+    function LazyElementwiseOperation{T,D,Op}(a::T1,b::T2) where {T,D,Op, T1<:AbstractArray{T,D}, T2<:AbstractArray{T,D}}
+        return new{T,D,Op,T1,T2}(a,b)
+    end
+end
+
+Base.size(v::LazyElementwiseOperation) = size(v.a)
+
+# TODO: Make sure boundschecking is done properly and that the lenght of the vectors are equal
+# NOTE: Boundschecking in getindex functions now assumes that the size of the
+# vectors in the LazyElementwiseOperation are the same size. If we remove the
+# size assertion in the constructor we might have to handle
+# boundschecking differently.
+Base.@propagate_inbounds @inline function Base.getindex(leo::LazyElementwiseOperation{T,D,:+}, I...) where {T,D}
+    @boundscheck if !checkbounds(Bool,leo.a,I...)
+        throw(BoundsError([leo],[I...]))
+    end
+    return leo.a[I...] + leo.b[I...]
+end
+Base.@propagate_inbounds @inline function Base.getindex(leo::LazyElementwiseOperation{T,D,:-}, I...) where {T,D}
+    @boundscheck if !checkbounds(Bool,leo.a,I...)
+        throw(BoundsError([leo],[I...]))
+    end
+    return leo.a[I...] - leo.b[I...]
+end
+Base.@propagate_inbounds @inline function Base.getindex(leo::LazyElementwiseOperation{T,D,:*}, I...) where {T,D}
+    @boundscheck if !checkbounds(Bool,leo.a,I...)
+        throw(BoundsError([leo],[I...]))
+    end
+    return leo.a[I...] * leo.b[I...]
+end
+Base.@propagate_inbounds @inline function Base.getindex(leo::LazyElementwiseOperation{T,D,:/}, I...) where {T,D}
+    @boundscheck if !checkbounds(Bool,leo.a,I...)
+        throw(BoundsError([leo],[I...]))
+    end
+    return leo.a[I...] / leo.b[I...]
+end
+
+# Define lazy operations for AbstractArrays. Operations constructs a LazyElementwiseOperation which
+# can later be indexed into. Lazy operations are denoted by the usual operator followed by a tilde
+@inline +̃(a::AbstractArray{T,D},b::AbstractArray{T,D}) where {T,D} = LazyElementwiseOperation{T,D,:+}(a,b)
+@inline -̃(a::AbstractArray{T,D},b::AbstractArray{T,D}) where {T,D} = LazyElementwiseOperation{T,D,:-}(a,b)
+@inline *̃(a::AbstractArray{T,D},b::AbstractArray{T,D}) where {T,D} = LazyElementwiseOperation{T,D,:*}(a,b)
+@inline /̃(a::AbstractArray{T,D},b::AbstractArray{T,D}) where {T,D} = LazyElementwiseOperation{T,D,:/}(a,b)
+
+# Abstract type for which the normal operations are defined by their
+# lazy counterparts
+abstract type LazyArray{T,D} <: AbstractArray{T,D} end;
+
+Base.:+(a::LazyArray{T,D},b::AbstractArray{T,D}) where {T,D} = a +̃ b
+Base.:+(a::AbstractArray{T,D}, b::LazyArray{T,D}) where {T,D} = b + a
+Base.:-(a::LazyArray{T,D},b::AbstractArray{T,D}) where {T,D} = a -̃ b
+Base.:-(a::AbstractArray{T,D}, b::LazyArray{T,D}) where {T,D} = a -̃ b
+Base.:*(a::LazyArray{T,D},b::AbstractArray{T,D}) where {T,D} = a *̃ b
+Base.:*(a::AbstractArray{T,D},b::LazyArray{T,D}) where {T,D} = b * a
+# TODO: / seems to be ambiguous
+# Base.:/(a::LazyArray{T,D},b::AbstractArray{T,D}) where {T,D} = a /̃ b
+# Base.:/(a::AbstractArray{T,D},b::LazyArray{T,D}) where {T,D} = a /̃ b
+
+export +̃, -̃, *̃, /̃, +, -, * #, /
+
+
+
+
+
 # TODO: Write tests and documentation for LazyTensorMappingComposition
 # struct LazyTensorMappingComposition{T,R,K,D} <: TensorMapping{T,R,D}
 #     t1::TensorMapping{T,R,K}