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The adapt(T, x) function acts like convert(T, x), but without the restriction of returning a T. This allows you to "convert" wrapper types like Adjoint to be GPU compatible (for example) without throwing away the wrapper.

For example:

adapt(CuArray, ::Adjoint{Array})::Adjoint{CuArray}

New wrapper types like Adjoint should overload adapt_structure(T, ::Adjoint) (usually just to forward the call to adapt):

Adapt.adapt_structure(to, x::Adjoint) = Adjoint(adapt(to, parent(x)))

A similar function, adapt_storage, can be used to define the conversion behavior for the innermost storage types:

adapt_storage(::Type{<:CuArray}, xs::AbstractArray) = convert(CuArray, xs)

Implementations of adapt_storage will typically be part of libraries that use Adapt. For example, CUDA.jl defines methods of adapt_storage(::Type{<:CuArray}, ...) and uses that to convert different kinds of arrays, while CUDAnative.jl provides implementations of adapt_storage(::CUDAnative.Adaptor, ...) to convert various values to GPU-compatible alternatives.

Packages that define new wrapper types and want to be compatible with packages that use Adapt.jl should provide implementations of adapt_structure that preserve the wrapper type. Adapt.jl already provides such methods for array wrappers that are part of the Julia standard library.