Re: [isabelle] Code generation from abstract types

Hi Andreas,

thanks for your help, your proposed solution was really helpful, it
worked perfectly. Let's
see if we can successfully apply it to some other operations on matrices!

Thanks again,


On Fri, Jan 4, 2013 at 12:59 PM,  <andreas.lochbihler at> wrote:
> Hi Jesus and Florian,
> The code generator does support nested abstract datatypes in this case,
> although only indirectly. As the abstraction function vec_lambda must not
> appear in any code equation, you have to promote any such subterm to a
> proper constant and prove the corresponding code equation. The following
> works:
> definition mat_mult_row where
>  "mat_mult_row m m' f = vec_lambda   (%c. setsum (%k. ((m$f)$k) *
> ((m'$k)$c)) (UNIV :: 'n::finite set))"
> lemma mat_mult_row_code [code abstract]:
>  "vec_nth (mat_mult_row m m' f) =   (%c. setsum (%k. ((m$f)$k) * ((m'$k)$c))
> (UNIV :: 'n::finite set))"
> by(simp add: mat_mult_row_def fun_eq_iff)
> lemma mat_mult [code abstract]: "vec_nth (m ** m') = mat_mult_row m m'"
>  unfolding matrix_matrix_mult_def mat_mult_row_def[abs_def]
>  using vec_lambda_beta by auto
> export_code "op **" in SML file -
> So there is no need to wrap all types and do the lifting.
> Hope this helps,
> Andreas
> Zitat von Florian Haftmann <florian.haftmann at>:
>> 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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