Re: [isabelle] Code generation from abstract types



Dear Jesus,

there is also the possibility to use the matrices from the AFP which are fully
executable, but where all lemmas are guarded by their dimension, as in 

"mat n m m1 ==> mat n m m2 ==> mat_plus m1 m2 = mat_plus m2 m1"

Cheers,
René

Am 27.12.2012 um 10:17 schrieb Florian Haftmann <florian.haftmann at informatik.tu-muenchen.de>:

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






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