Re: [isabelle] Code generation from abstract types



Hi Jesus,

> When we try to generate code for operations over matrices which return
> a matrix (for instance, matrix multiplication), we do not know how to
> define the "code abstract" lemma for such operation, since it involves
> a "vec_nth of a vec_lambda of a vec_nth", for which the code generator
> produces a "violation abstraction error":
> 
> lemma mat_mult [code abstract]: "vec_nth (m ** m') = (%f. vec_lambda
> (%c. setsum (%k. ((m$f)$k) * ((m'$k)$c)) (UNIV :: 'n::finite set)))"
>   unfolding matrix_matrix_mult_def
>   using vec_lambda_beta by auto
> 
> Is there a way to express the previous lemma and that code generation
> for matrix multiplication is still possible? Is anybody aware of any
> possible workaround?

there is no support for nested abstract datatypes.  To achieve abstract
matrices, you would need to provide an explicit type for matrices (e.g.
using datatype ('a, 'm, 'n) matrix = Matrix "'a ^ 'm ^ 'n" (*)) and then
lift all operations you want to that explicit matrix type.  When doing
this, the recently emerged lifting and transfer infrastructure could be
helpful – unfortunately, I have no canonical reference for this at hand
and have not used it myself, but others on this mailing list will know
better.

I hope these meagure hints show the way.  Feel free to ask again if you
are still lost.

Cheers,
	Florian

(*) I am not familiar with the vectors/matrix stuff, so this might be wrong.

-- 

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http://home.informatik.tu-muenchen.de/haftmann/pgp/florian_haftmann_at_informatik_tu_muenchen_de

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