Re: [isabelle] efficient code for ('a, 'b) map (as opposed to ('a, 'b) mapping



Dear Andreas and Ondřej,

here is my "report" ;) (I did however not systematically investigate my options, but stopped immediately after having the first working solution).

For ease of reference please consult the attached theory file (Matching_Test) which is (together with Andreas' Map_To_Mapping) self-contained but is only concerned with code generation; thus a "sorry" and no soundness or completeness statements for matching (but this all exists of course on my local machine as part of IsaFoR).

A short explanation of the used functions and what I intended to do with them:

- match_term_list: matching on lists of term pairs, but with an accumulator that builds the result; thus depending on the initial value of this accumulator this might not really compute a matcher

- match_list: the above where the accumulator is initialized to the empty map (thus it really is matching on the given list of term pairs)

- for code generation only "match_list" is important (since "match_term_list" is just an auxiliary function that is not used directly); hence my goal was to get efficient code for "match_list"

- first get an efficient variant of "match_term_list" (called "match_term_list'" and then prove a code equation which replaces "match_term_list" inside the definition of "match_list" by "match_term_list'" (together with necessary glue); what I wanted to avoid at all cost, was to have to create a duplicate of "match_list" for code generation (since than I would also have to "transfer" all existing proofs to this constant)

Since I'm a newbie w.r.t. to lifting/transfer (well, I've read about it, but never used it myself) I can only give some comments (which might be trivial):

Andreas' "transferred_mapping" attribute worked "as advertised" in order to get code equations for "match_term_list'"!

Afterwards I manually proved that

  match_term_list E σ =
    Option.map Mapping.lookup (match_term_list' E (Mapping σ))

(maybe this could also be done automatically?) and finally the code equation for "match_list"

  match_list E =
    Option.map (subst_of_map undefined ∘ Mapping.lookup)
      (match_term_list' E Mapping.empty)

I could have stopped after the first equation, but in the generated code "Mapping sigma" was used to initialize "match_term_list" which I understood to mean that the generated code would actually *not* use an efficient version of maps, since maps are represented by an AST

  data Mapping a b = Assoc_List_Mapping (DAList.Alist a b)
  | RBT_Mapping (RBT_Mapping2.Mapping_rbt a b) | Mapping (a -> Maybe b);

cheers

chris

On 10/25/2013 12:19 AM, Ondřej Kunčar wrote:
lift_definition gives you a logical definition of the new function. But
you have to still provide a code equation for this new function (as it
is described in the paper I've already referred to).
Then you have two options:
A) state the new code equation by yourself and prove it by transfer
(Isabelle 2013).
B) Since Isabelle 2013-1, there is a limited support for transferring
"in the other direction" by the attribute Transfer.transferred. The
problem in this solution is that the raw terms for map operations are
very general terms like term application (for map lookup) and so on.
Andreas showed us in his file a trick that actually Peter Lammich does
in his autoref framework, namely rewriting these term applications to an
ad-hoc constants by simplifier and then using Transfer.transferred. The
question is, of course how, much this solution scale. I am curious to
hear some report about that from you.

Ondrej

On 10/24/2013 03:43 PM, Christian Sternagel wrote:
Dear all,

Thanks for the useful answers. For my concrete case: does
"lift_definition" also work for recursive functions (whith "match_list"
is). With my first attempt using "lift_definition" I just got a
"wrapper" around the recursive function that changed the type, which
doesn't solve the efficiency problem.

cheers

chris

On 10/24/2013 06:59 PM, Ondřej Kunčar wrote:
Hi Christian,
Peter has already explained the situation in general. I just want to add
that Lifting/Transfer can indeed help you a bit in moving your
specification from 'a => 'b option to ('a, 'b) mapping. Please see
Chapter 4 in our ITP 2013 paper: Data Refinement in Isabelle/HOL.

Best,
Ondrej

On 10/24/2013 11:35 AM, Peter Lammich wrote:
Hi Christian.

The problem is, that ('a,'b) map is just syntactic sugar for the type
'a => 'b option. The code-generator replacement of types by efficient
implementations only works for types represented by a single
type-constant (like ('a,'b) mapping or 'a set).

Moreover, note that, in general, you do not want to translate all
occurences of "'a -> 'b option" by a map implementation, as there are
also functions that return option-values, which are intended to be
translated as functions.


The automatic refinement framework [1] tries to tackle this problem,
however, it has to be employed manually before code generation, and
usually requires some setup overhead.

In order to use Containers, I believe that you should transform your
functions to use mapping. Maybe the transfer+lifting package of Brian
and Ondra may help you to automate this task.


Best,
   Peter

[1]: Peter Lammich, Automatic Data Refinement, Proc. of ITP 2013


On Do, 2013-10-24 at 18:10 +0900, Christian Sternagel wrote:
Dear all (especially Andreas ;)),

is it possible to automatically get efficient code when code
generating
a function involving the "('a, 'b) map" type (i.e., "'a => 'b
option").

If I import AFP/Containers I can have this for "('a, 'b) mapping"
(which
is a type-copy of "('a, 'b) map").

But in the actual formalization "('a, 'b) map" is more convenient to
use
since we have nice syntax like "m x" for lookup and "m (x |-> t)" for
update.

Since according to the user guide the above is possible w.r.t. "'a
set",
I was wondering what the obstacle is for "('a, 'b) map" (or maybe I
just
misunderstood something).

More concretely, what is your advice for a function like

    match_list ::
      (('f, 'v) term * ('f, 'v) term) list =>
        ('v => ('f, 'v) term option) => ('f, 'v) subst

where "match_list E Map.empty" gives a matcher for all equations in
"E".
Would you change this to use "('v, ('f, 'v) term) mapping" instead, or
is there a way to get efficient code as it is? Thanks in advance!

cheers

chris








Attachment: Matching_Test.thy
Description: application/example



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