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

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.


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.



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.


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.


[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"
is a type-copy of "('a, 'b) map").

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

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



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