From rbabaeecar at grad.kashanu.ac.ir Mon Aug 01 13:32:12 2011
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From: "Reza Babaee" <rbabaeecar at grad.kashanu.ac.ir>
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Date: Mon, 1 Aug 2011 17:53:03 +0430
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Subject: [isabelle] Isabelle and Runtime Verification
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Hello All Isabelle Users

I am a graduate student interested in runtime verification specifically in
distributed systems. I wonder if I can use "Isabelle" as a constraint prover
when system is on-the-fly. If there are any people working on the same topic
(runtime verification or monitoring) I would appreciate if they can provide
pertinent information on Isabelle usage in runtime monitoring or verification.
thanks in advance for your kind helps,
Bests,
Reza Babaee (grad.kashanu.ac.ir)

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From bertram.felgenhauer at googlemail.com Tue Aug 02 22:10:08 2011
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Date: Tue, 2 Aug 2011 23:10:01 +0200
From: Bertram Felgenhauer <bertram.felgenhauer at googlemail.com>
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Cc: Lars Noschinski <noschinl at in.tum.de>
Subject: Re: [isabelle] Odd failure to match local statement with pending goal.
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Hi,

> As Larry stated, this is indeed a strange problem. I tried to find a
> minimal example; here is what I came up with:
> 
> -------------------
> lemma
>   shows  "⋀c d. d ∈ Z ⟹ x = c ⟹
>         ∃e. e ∈ {_. ∃e. e ∈ Z ∧ y = e}"
>   apply (unfold mem_Collect_eq)
> proof -
>   fix s t
>   assume "x = s" and "t ∈ Z"
>   then show "∃s t. t ∈ Z ∧ y = t"
>     sorry
> qed
> -------------------
> The show statement fails with
[...]

So do we know whether this is an obscure feature or possibly a bug?
(If it's a feature I'd love to hear the underlying story.)

Best regards,

Bertram



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On Tue, Aug 2, 2011 at 2:10 PM, Bertram Felgenhauer
<bertram.felgenhauer at googlemail.com> wrote:
> Hi,
>
>> As Larry stated, this is indeed a strange problem. I tried to find a
>> minimal example; here is what I came up with:
>>
>> -------------------
>> lemma
>>   shows  "=E2=8B=80c d. d =E2=88=88 Z =E2=9F=B9 x =3D c =E2=9F=B9
>>         =E2=88=83e. e =E2=88=88 {_. =E2=88=83e. e =E2=88=88 Z =E2=88=A7 =
y =3D e}"
>>   apply (unfold mem_Collect_eq)
>> proof -
>>   fix s t
>>   assume "x =3D s" and "t =E2=88=88 Z"
>>   then show "=E2=88=83s t. t =E2=88=88 Z =E2=88=A7 y =3D t"
>>     sorry
>> qed
>> -------------------
>> The show statement fails with
> [...]
>
> So do we know whether this is an obscure feature or possibly a bug?
> (If it's a feature I'd love to hear the underlying story.)

It certainly looks like a bug to me. I don't have an idea yet of why
it happens, but I found an even smaller example. I constrained
everything to type "nat" just to rule out any weirdness with
polymorphism. Note the repeated bound variable name in the goal (the
argument to Q is the second "c", which pretty-prints as "ca"). This
seems to be necessary to make the error happen.

lemma
  shows "=E2=8B=80(a::nat) (b::nat). P a b =E2=9F=B9 =E2=88=80(c::nat) (c::=
nat). Q c"
proof -
  fix s t :: nat assume "P s t"
  thus "=E2=88=80(s::nat) (t::nat). Q t" (* Local statement will fail to re=
fine... *)

Swapping the order of the bound variable names in the conclusion also
gives the same error:

  thus "=E2=88=80(t::nat) (s::nat). Q s"

Just about any other modification to the lemma or proof that I could
think of seems to make it work again.

- Brian



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			   VSTTE 2012
Verified Software: Theories, Tools and Experiments
	 	      January 28-29, 2012
Philadelphia, USA (co-located with POPL and VMCAI)
https://sites.google.com/site/vstte2012/

The Fourth International Conference on Verified Software: Theories,
Tools, and Experiments  will take place on January 28-29, 2012.  The
focus of the conference is the development of systematic methods for
specifying, building, and verifying software.  The goal of
this conference is to advance the state of the art through the
interaction of theory development, tool evolution, and experimental
validation.  Historically,  the conference came out of the Verified
Software Initiative (VSI), a cooperative, international initiative
directed at the scientific challenges of large-scale software
verification.  An informal verification competition will be held in paralle=
l=20
to the conference. More information will be available from the=20
website.

Topics of interest include:

* Specification and verification techniques
* Tool support for specification languages
* Tool for various design methodologies
* Tool integration and plug-ins
* Automation in formal verification
* Tool comparisons and benchmark repositories
* Combination of tools and techniques
(e.g. formal vs. semiformal, software specification
vs. engineering techniques)
* Customizing tools for particular applications
* Challenge problems
* Refinement methodologies
* Requirements modeling
* Specification languages
* Specification/verification case-studies
* Software design methods
* Program logic

SUBMISSIONS

Submitted research papers and system descriptions must be original and
not submitted for publication elsewhere.  Research paper submissions
are limited to 15 proceedings pages in LNCS format and must include a
cogent and self-contained description of the ideas, methods and
results, together with a comparison to existing work. System
descriptions are also limited to 15 proceedings pages in LNCS
format. Authors are encouraged to submit work in progress, particularly if =
the
work involves collaboration, theory unification, and tool integration.
Papers can be submitted at

https://www.easychair.org/conferences/?conf=3Dvstte2012

Submissions that arrive late, are not in the proper format, or are too
long will not be considered.  The proceedings of VSTTE 2012 will be
published by Springer-Verlag in the LNCS series.  Authors of accepted
papers will be requested to sign a form transferring copyright of
their contribution to Springer-Verlag.


IMPORTANT DATES

August 31, 2011:     Conference Paper Submission Deadline
October 20, 2011:    Notification of acceptance
November 15, 2011:   Final conference paper versions due
January 28-29, 2012: Main conference


KEYNOTE SPEAKERS

Rupak Majumdar, Max Planck Institute for Software Systems
Wolfgang Paul,  Saarland University


TUTORIALS

Francesco Logozzo, Microsoft Research
Rustan Leino, Microsoft Research


CONFERENCE CHAIR

Ernie Cohen, European Microsoft Innovation Center=20


PROGRAM CHAIRS

Rajeev Joshi,  NASA Jet Propulsion Laboratory
Peter M=FCller, ETH Zurich
Andreas Podelski, University of Freiburg


PROGRAM COMMITTEE

Clark Barrett, New York University
Lars Birkedal, IT University of Copenhagen
Patrick Cousot, Ecole normale Sup=E9rieure, Paris and New York University
Leonardo De Moura, Microsoft Research
Jean-Christophe Filliatre, CNRS Universit=E9 Paris Sud
John Hatcliff, Kansas State University
Bart Jacobs, Katholieke Universiteit Leuven=20
Ranjit Jhala, University of California, San Diego
Rajeev Joshi,  NASA JPL
Gerwin Klein, NICTA=20
Viktor Kuncak, EPF Lausanne=20
Gary T. Leavens, University of Central Florida=20
Rustan Leino, Microsoft Research
Panagiotis Manolios, Northeastern University
Peter M=FCller, ETH Zurich
Tobias Nipkow, Technische Universit=E4t M=FCnchen=20
Matthew Parkinson, Microsoft Research
Corina Pasareanu, NASA Ames
Wolfgang Paul,  Saarland University
Andreas Podelski,  University of Freiburg
Natasha Sharygina, University of Lugano=20
Willem Visser, University of Stellenbosch
Thomas Wies, IST Austria


PUBLICITY CHAIR

Gudmund Grov, University of Edinburgh


VERIFICATION COMPETITION ORGANISER=20

Jean-Christophe Filliatre, CNRS Universit=E9 Paris Sud


STEERING COMMITTEE

Tony Hoare, Microsoft Research
Andrew Ireland, Heriot-Watt University
Jay Misra, UT Austin
Natarajan Shankar, SRI International
Jim Woodcock, University of York


--=20
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.




From Aart.Middeldorp at uibk.ac.at Wed Aug 03 13:21:58 2011
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Subject: [isabelle] postdoctoral researcher position in Innsbruck
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The University of Innsbruck invites applications for a 6 year position as

      postdoctoral researcher

at the Computational Logic research group.

Candidates must hold a PhD degree in computer science. A strong background
in computational logic (in particular SMT, automated and interactive
theorem proving) is desired. The ideal candidate complements existing
strengths and enjoys working with students at all levels. Candidates are
expected to conduct research leading to a habilitation and contribute to
teaching and administration. Knowledge of German is not essential.

The position is a full-time "B1/3 position" with teaching obligations of
4 hours per semester. The annual gross salary is approximately EUR 46,000.
The official job advert appeared in the "Mitteilungsblatt" of the
University on 3 August 2011 (code MIP-6659)

   http://orawww.uibk.ac.at/public_prod/owa/karriereportal.home

Applications (including CV, publication list, and two references) may
be mailed to the address stated there or, by email, to

   aart.middeldorp at uibk.ac.at

no later than 24 August 2011. Informal inquiries are also welcome at the
same email address. The preferred starting date is 2 November 2011.

The city of Innsbruck, which hosted the Olympic Winter Games in 1964 and
1976, is superbly located in the beautiful surroundings of the Tyrolean
Alps. The combination of the Alpine environment and urban life in this
historic town provides a high quality of living. The University of
Innsbruck has a long tradition dating back to the 16th century and offers
a wide spectrum of research and teaching activities with interesting
opportunities for interdisciplinary collaboration.

Further information is available from the following links:

Computational Logic:
   http://cl-informatik.uibk.ac.at/
Institute of Computer Science:
   http://informatik.uibk.ac.at/
University of Innsbruck:
   http://www.uibk.ac.at/
City of Innsbruck:
   http://www.innsbruck.at/

---

Univ.-Prof. Dr. Aart Middeldorp
Institute of Computer Science, University of Innsbruck
Technikerstr. 21a, 6020 Innsbruck, Austria
phone: +43 512 507 6430  fax: +43 512 507 9887

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From jonathan.von_schroeder at dfki.de Wed Aug 03 11:57:27 2011
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Date: Wed, 3 Aug 2011 12:57:26 +0200 (CEST)
From: Jonathan von Schroeder <jonathan.von_schroeder at dfki.de>
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Subject: [isabelle] Get an ML value from a theory context
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Hello all,
 I'm currently working on a way to export Isabelle/HOL type definitions and
their attached (user defined) axioms/theorems from a given theory in Isabel=
le. I
have already managed to get this workign by simply going through all the
constants, axioms and theorems present in the theories' context. But unluck=
ily I
currently get more axioms / theorems than I'm interested in, because the
theorems automatically generated by
http://isabelle.in.tum.de/repos/isabelle/file/6d736d983d5c/src/HOL/Tools/Da=
tatype/
are not really "user generated" and thus do not foll within the scope of
theorems I wish to export.

 Thus I'd really like to have (in the top-level raw ML loop) access to the
structure
http://isabelle.in.tum.de/repos/isabelle/file/6d736d983d5c/src/HOL/Tools/Da=
tatype/datatype_data.ML
(which lives in the context of
http://isabelle.in.tum.de/repos/isabelle/file/6d736d983d5c/src/HOL/Datatype=
.thy
from what i can tell) to be able to figure out which theorems were generate=
d by
the Datatype-Tool. Does anybody have any suggestions on how to do this, bec=
ause
the Manual http://isabelle.in.tum.de/doc/implementation.pdf only mentions o=
n
page 11 that "... [the function factorial] is not yet accessible in the
preceding paragraph, nor in a different theory that is independent from the
current one in the import hierarchy", but I wasn't able to find any informa=
tion
on how to "get" access to it (or for that matter to any ml functions /
structures defined within a theory). I'd greatly appreciate any information
anybody can provide on this matter.

 Jonathan
=C2=A0


From bulwahn at in.tum.de Thu Aug 04 12:50:18 2011
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Subject: Re: [isabelle] Get an ML value from a theory context
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On 08/03/2011 12:57 PM, Jonathan von Schroeder wrote:
> Hello all,
>   I'm currently working on a way to export Isabelle/HOL type definitions and
> their attached (user defined) axioms/theorems from a given theory in Isabelle. I
> have already managed to get this workign by simply going through all the
> constants, axioms and theorems present in the theories' context. But unluckily I
> currently get more axioms / theorems than I'm interested in, because thep,
> theorems automatically generated by
> http://isabelle.in.tum.de/repos/isabelle/file/6d736d983d5c/src/HOL/Tools/Datatype/
> are not really "user generated" and thus do not foll within the scope of
> theorems I wish to export.
>
>   Thus I'd really like to have (in the top-level raw ML loop) access to the
> structure
> http://isabelle.in.tum.de/repos/isabelle/file/6d736d983d5c/src/HOL/Tools/Datatype/datatype_data.ML
> (which lives in the context of
> http://isabelle.in.tum.de/repos/isabelle/file/6d736d983d5c/src/HOL/Datatype.thy
> from what i can tell) to be able to figure out which theorems were generated by
> the Datatype-Tool. Does anybody have any suggestions on how to do this, because
> the Manual http://isabelle.in.tum.de/doc/implementation.pdf only mentions on
> page 11 that "... [the function factorial] is not yet accessible in the
> preceding paragraph, nor in a different theory that is independent from the
> current one in the import hierarchy", but I wasn't able to find any information
> on how to "get" access to it (or for that matter to any ml functions /
> structures defined within a theory). I'd greatly appreciate any information
> anybody can provide on this matter.
>
If you work properly on the Isabelle/ML level, within the HOL image, the 
datatype package is loaded and set up.
Hence, you can then access the structure simply by its name "Datatype_Data".



Lukas
>   Jonathan
>




From jmaransay at gmail.com Thu Aug 04 12:56:04 2011
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Subject: [isabelle] A special notation for function application
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Dear all,

I was trying to introduce some additional notation for linear
functionals in vector spaces; the idea is to use:

"[x, f]" as an alternative notation for "f x", where "f" is a linear
functional (let's say, type "'a =3D> 'b") and "x" is an element of type
"'a" (note that the arguments f and x are interchanged in the proposed
notation).

I would like that all notation available for "f x" would still work
for the new notation "[x, f]", in such a way that

[x, f] \oplus [y, f]

would be equivalent to (without unfolding any particular definition):

f x \oplus f y

Is it possible to reach these behavior? How? Maybe brackets are
already a bit overloaded in terms of notation (lists, propositions...)
so a notation based for instance in "<x, f >" would be also
acceptable.

I tried the following approach (which does not interchange arguments)

abbreviation
  app :: "('b =3D> 'a) =3D> 'b =3D> 'a" ("<(_),(_)>" 90)
  where "<f, x> =3D=3D f x"

but then when I write, for instance, "term <f, x>" the system does not
seem to find the correct type of the expression.

Thanks for any hint,

Jesus

--=20
Jes=FAs Mar=EDa Aransay Azofra
Universidad de La Rioja
Dpto. de Matem=E1ticas y Computaci=F3n
tlf.: (+34) 941299438 fax: (+34) 941299460
mail: jesus-maria.aransay at unirioja.es ; web: http://www.unirioja.es/cu/jear=
ansa
Edificio Luis Vives, c/ Luis de Ulloa s/n, 26004 Logro=F1o, Espa=F1a



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Subject: Re: [isabelle] A special notation for function application
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Dear Jesus,

do you need your notation only as input syntax or do you want Isabelle to print 
function application this way, too? If it is for input only, you just have to 
restrict your abbreviation to the input parser and it works fine:

abbreviation (input)
    app :: "('b =>  'a) =>  'b =>  'a" ("<(_),(_)>" 90)
    where "<f, x> == f x"

term "<f, x>"

Without the (input) restriction, Isabelle's pretty printer loops when it tries 
to display the term again. I do not recommend that you use such syntax 
translations for output, because such a translation would apply to all function 
applications, which is probably not what you want. You could, however, restrict 
your translation to certain type classes (e.g., arbitrary functions from vector 
spaces to vector spaces). Still, you will have to install your own print 
translation to guarantee termination of the pretty printer.

By the way, any notation that works for "f x" also works for "[x, f]" even "[x, 
f]" is a proper constant instead of an abbreviation.

Hope this helps,
Andreas

Am 04.08.2011 13:55, schrieb Jesus Aransay:
> Dear all,
>
> I was trying to introduce some additional notation for linear
> functionals in vector spaces; the idea is to use:
>
> "[x, f]" as an alternative notation for "f x", where "f" is a linear
> functional (let's say, type "'a =>  'b") and "x" is an element of type
> "'a" (note that the arguments f and x are interchanged in the proposed
> notation).
>
> I would like that all notation available for "f x" would still work
> for the new notation "[x, f]", in such a way that
>
> [x, f] \oplus [y, f]
>
> would be equivalent to (without unfolding any particular definition):
>
> f x \oplus f y
>
> Is it possible to reach these behavior? How? Maybe brackets are
> already a bit overloaded in terms of notation (lists, propositions...)
> so a notation based for instance in "<x, f>" would be also
> acceptable.
>
> I tried the following approach (which does not interchange arguments)
>
> abbreviation
>    app :: "('b =>  'a) =>  'b =>  'a" ("<(_),(_)>" 90)
>    where "<f, x>  == f x"
>
> but then when I write, for instance, "term<f, x>" the system does not
> seem to find the correct type of the expression.
>
> Thanks for any hint,
>
> Jesus
>

-- 
Karlsruher Institut für Technologie
IPD Snelting

Andreas Lochbihler
wissenschaftlicher Mitarbeiter
Adenauerring 20a, Geb. 50.41, Raum 031
76131 Karlsruhe

Telefon: +49 721 608-47399
Fax: +49 721 608-48457
E-Mail: andreas.lochbihler at kit.edu
http://pp.info.uni-karlsruhe.de
KIT - Universität des Landes Baden-Württemberg und nationales Forschungszentrum 
in der Helmholtz-Gemeinschaft



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Dear Isabelle Users,

Usually, after a function f has been defined via fun or primrec, its
defining equations are available under the name
f.simps as theorems, e.g., thm "f.simps".
However, how could I access specifically each one of these equations
(simplification rules)?
I tried something as f.simps_1 (after seeing the trace example in the
tutorial), f.simps_2,  etc., but
it did not work.

Thanks!

-- 
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


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f.simps(2)

On Thu, Aug 4, 2011 at 5:39 PM, Alfio Martini <alfio.martini at acm.org> wrote=
:
> Dear Isabelle Users,
>
> Usually, after a function f has been defined via fun or primrec, its
> defining equations are available under the name
> f.simps as theorems, e.g., thm "f.simps".
> However, how could I access specifically each one of these equations
> (simplification rules)?
> I tried something as f.simps_1 (after seeing the trace example in the
> tutorial), f.simps_2, =A0etc., but
> it did not work.
>
> Thanks!
>
> --
> Alfio Ricardo Martini
> PhD in Computer Science (TU Berlin)
> Associate Professor at Faculty of Informatics (PUCRS)
> Porto Alegre - RS - Brasil
>
>



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Great!! Thanks for the quick reply!

On Thu, Aug 4, 2011 at 7:01 PM, Randy Pollack <rpollack at inf.ed.ac.uk> wrote:

> f.simps(2)
>
> On Thu, Aug 4, 2011 at 5:39 PM, Alfio Martini <alfio.martini at acm.org>
> wrote:
> > Dear Isabelle Users,
> >
> > Usually, after a function f has been defined via fun or primrec, its
> > defining equations are available under the name
> > f.simps as theorems, e.g., thm "f.simps".
> > However, how could I access specifically each one of these equations
> > (simplification rules)?
> > I tried something as f.simps_1 (after seeing the trace example in the
> > tutorial), f.simps_2,  etc., but
> > it did not work.
> >
> > Thanks!
> >
> > --
> > Alfio Ricardo Martini
> > PhD in Computer Science (TU Berlin)
> > Associate Professor at Faculty of Informatics (PUCRS)
> > Porto Alegre - RS - Brasil
> >
> >
>



-- 
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


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Cc: isabelle-users at cl.cam.ac.uk, Randy Pollack <rpollack at inf.ed.ac.uk>
Subject: Re: [isabelle] Accessing (individual) simplification rules of
	function definitions
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On 08/05/2011 12:13 AM, Alfio Martini wrote:
> Great!! Thanks for the quick reply!
>
>> f.simps(2)

You can also name the rules at definition time:

fun/primrec f :: "..."
where
   name1: "..."
| name2: "..."


Alex



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	function definitions
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Hi Alexander,

This is also very nice, because one now can refer to the specific rule
as f.name1 and so on. Very helpful.

Many thanks again!

On Fri, Aug 5, 2011 at 3:41 AM, Alexander Krauss <krauss at in.tum.de> wrote:

> On 08/05/2011 12:13 AM, Alfio Martini wrote:
>
>> Great!! Thanks for the quick reply!
>>
>>  f.simps(2)
>>>
>>
> You can also name the rules at definition time:
>
> fun/primrec f :: "..."
> where
>  name1: "..."
> | name2: "..."
>
>
> Alex
>



-- 
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


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Cc: isabelle-users at cl.cam.ac.uk, Randy Pollack <rpollack at inf.ed.ac.uk>
Subject: Re: [isabelle] Accessing (individual) simplification rules of
	function definitions
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Dear Isabelle  Users,

In order to keep it in the same thread, I am pasting an answer Alexander
gave me about a remaining doubt I had concerning the main topic of all
these messages.

Best!
----------------------------------------------xxxxxxxx--------------------------------------------------

Hi Alfio,


I have small problem. Using 'primrec" I can access the individual rules
> both using subscripts and tags, as you suggested.
> But If i define using 'fun" it works only with subscripts. In the
> following small script, Isabelle (2009-2) can not process
> the last thm command. It sends an error message: unknown fact. Thanks
> for any help!
>

theory playing_tags

imports Main
begin

   datatype Nat = Z | suc Nat

   primrec add::"Nat=>Nat=>Nat"
   where
      add01:  "(add x Z) = x" |
      add02:  "(add x (suc y)) = suc(add x y)"

   thm "add.simps"
   thm "add.simps"(2)
   thm "add.simps"(1)
   thm "add.add01"
   thm "add.add02"

  fun sum::"Nat * Nat => Nat"
    where
        sum01:  "sum(x,Z)=x" |
        sum02:  "sum(x,suc(y)) = suc(sum(x,y))"

  thm "sum.simps"
  thm "sum.simps"(1)
  thm "sum.simps"(2)
  thm "sum.sum01"
end


The function packages produces names without the function name as (optional)
qualifier. So plain "sum01" instead of "sum.sum01" works.
This should probably be made more uniform.

btw: you can inspect the theorems produced by a command by using
"print_theorems" afterwards.

Alex
--------------------------------------------xxxxxxxxxxxxxxxx------------------------------------------
On Fri, Aug 5, 2011 at 3:41 AM, Alexander Krauss <krauss at in.tum.de> wrote:

> On 08/05/2011 12:13 AM, Alfio Martini wrote:
>
>> Great!! Thanks for the quick reply!
>>
>>  f.simps(2)
>>>
>>
> You can also name the rules at definition time:
>
> fun/primrec f :: "..."
> where
>  name1: "..."
> | name2: "..."
>
>
> Alex
>



-- 
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


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Subject: [isabelle] MetiTarski 1.9 released!
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MetiTarski is an automatic theorem prover based on a combination of =
resolution and computer algebra technology. It is designed to prove =
theorems involving real-valued special functions such as ln, exp, sin, =
cos, arctan and sqrt. All variables are assumed to range over the real =
numbers.

MetiTarski can be downloaded from =
http://www.cl.cam.ac.uk/~lp15/papers/Arith/. You will be asked to leave =
your name and e-mail address so that we can have an idea how many users =
there are. You will not receive regular e-mails from us.

Version 1.9 represents over 6 months of development over the previous =
version, incorporating code by James Bridge and Grant Passmore, along =
with new problems supplied by William Denman. Please see the release =
notes for details.

Remark about CASC: The version run in the competition was 1.8. We did =
not push to release this version in time for CASC because most of our =
work would have been irrelevant. None of the problems used in the =
competition Involve real-valued special functions.

Please note that MetiTarski is experimental research software and may =
require a certain amount of effort to build on your machine. Feedback is =
welcome!!

Larry Paulson






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Subject: [isabelle] FFT.thy ?
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In Sascha's and Jasmin's talk at CADE they mentioned "FFT" in their 
benchmarks, i.e. fast fourier transform as they confirmed in personal 
communication.

 From the most recent clone 01d6ab227069 I get nothing by

     Isabelle/src$ find -name "F*.thy"
     Isabelle/src$ grep -r "ourier" *

I'd be grateful for another hint,
Walther



From gerwin.klein at nicta.com.au Sat Aug 06 09:31:57 2011
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Subject: Re: [isabelle] FFT.thy ?
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On 06/08/2011, at 10:11 AM, Walther Neuper wrote:

> In Sascha's and Jasmin's talk at CADE they mentioned "FFT" in their =
benchmarks, i.e. fast fourier transform as they confirmed in personal =
communication.
>=20
> =46rom the most recent clone 01d6ab227069 I get nothing by
>=20
>    Isabelle/src$ find -name "F*.thy"
>    Isabelle/src$ grep -r "ourier" *
>=20
> I'd be grateful for another hint,

It's an AFP entry:
http://afp.sourceforge.net/entries/FFT.shtml

(Harder to grep for, but to find things in the AFP, =
http://afp.sourceforge.net/search.shtml works fairly nicely)

Cheers,
Gerwin=



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From: Mamoun FILALI-AMINE <filali at irit.fr>
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--------------040508070603000006070804
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Hello,

   I wonder if it is possible to instantiate schematic variables
after unfolding (see example below).
thanks

Mamoun

--------

definition "ref P Q = (\<forall> s. P s \<longrightarrow> Q s)"

theorem
   assumes r1: "ref A A'"
   assumes r2: "ref B B'"
shows "ref (A \<union> B) (A' \<union> B')"
proof -
   have "?thesis" unfolding ref_def (* is "\<forall> s. ?L s 
\<longrightarrow> ?R s" *)


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begin:vcard
fn:Mamoun FILALI-AMINE
n:FILALI-AMINE;Mamoun
adr;quoted-printable:118 Route de Narbonne;;IRIT Universit=C3=A9 Paul Sabatier;Toulouse;;31062 cedex 9;France
email;internet:filali at irit.fr
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From boehmes at in.tum.de Sun Aug 07 12:26:17 2011
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Date: Sun, 7 Aug 2011 13:26:19 +0200
From: Sascha Boehme <boehmes at in.tum.de>
To: Mamoun FILALI-AMINE <filali at irit.fr>
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Subject: Re: [isabelle] schematic variables
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Hello Mamoun,

Your example does not contain schematic variables after unfolding with
ref_def.  Instead, the goal looks as follows:

  \<forall>s. (A \<union> B) s \<longrightarrow> (A' \<union> B') s

The most common form to instantiate schematic variables in facts is
via the "of" attribute, for example as follows:

  thm refl  (* is "?t = ?t" *)

  thm refl[of x]  (* is "x = x" *)

This can also be applied to intermediate steps in a proof:

  lemma "\<exists>n::nat. n \<ge> 0"
  proof -
    {
      fix n :: nat
      have "n \<ge> 0" by simp
    }
    (* we proved "?n \<ge> 0" *)
    note this[of "1 :: nat"]  (* is "1 \<ge> 0" *)
    then show ?thesis ..
  qed

A different form of this proof introduces schematic variables into the
goal, but in most cases it's best to let some tactic instantiate
these variables automatically:

  lemma "\<exists>n::nat. n \<ge> 0"
    apply (rule exI)  (* the goal is now "?n \<ge> 0" *)
    apply simp  (* instantiates "?n" appropriately and solves the goal *)
    done

Cheers,
Sascha


Mamoun FILALI-AMINE wrote:
> Hello,
> 
>   I wonder if it is possible to instantiate schematic variables
> after unfolding (see example below).
> thanks
> 
> Mamoun
> 
> --------
> 
> definition "ref P Q = (\<forall> s. P s \<longrightarrow> Q s)"
> 
> theorem
>   assumes r1: "ref A A'"
>   assumes r2: "ref B B'"
> shows "ref (A \<union> B) (A' \<union> B')"
> proof -
>   have "?thesis" unfolding ref_def (* is "\<forall> s. ?L s
> \<longrightarrow> ?R s" *)
> 

> begin:vcard
> fn:Mamoun FILALI-AMINE
> n:FILALI-AMINE;Mamoun
> adr;quoted-printable:118 Route de Narbonne;;IRIT Universit=C3=A9 Paul Sabatier;Toulouse;;31062 cedex 9;France
> email;internet:filali at irit.fr
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> 




From florian.haftmann at informatik.tu-muenchen.de Sun Aug 07 15:33:05 2011
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Date: Sun, 07 Aug 2011 16:32:55 +0200
From: Florian Haftmann <florian.haftmann at informatik.tu-muenchen.de>
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Subject: Re: [isabelle] code generation for saturated naturals
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Hi Peter, hi Brian,

> In his zest to ensure all uses of numerals are algebraically
well-organised, Brian manufactured the attached theory of "saturated"
arithmetic for the naturals for me.
>
> I'm now struggling to get it to work with the code generator. The
problem is that the CARD('a) construct leans on the card function, and
for some reason the code generator wants to enumerate nat while
calculating card. I can't see why it wants to do that. Can you suggest a
way forward? (The attached theory should break at an opportune point.)
>

find attached an experiment of mine which hopefully turn out to be helpfu=
l.

First, it is important that we keep such discussions on the public
mailing list, since more eyes see more than less and also to make sure
the generic Isabelle knowledge stays publicly available and is able to gr=
ow.

Here now, the answers proper to your issues:

a) avoiding CARD('a) in generated code

class len_card =3D len +
  assumes len_of_card: "len_of TYPE('a) =3D CARD('a)"

This connects len_of TYPE('a) to CARD('a) and allows you to generate
code for type 'a::len_card sat.  Of course you have to give appropriate
instantiations, or replace CARD('a) by len_of TYPE('a) in your
specification throughout to gain full flexibility.  @Brian: Did you ever
think about including such a class as len_card into the Word libraries
directly?

b) use abstract type for code generation

lemma Abs_Rep_sat' [simp, code abstype]:
  "Abs_sat' (Rep_sat n) =3D n"
  by (simp add: Abs_sat'_def min_CARD_Rep_sat Rep_sat_inverse)

(call on me again if this sounds like Bohemian villages for you)

c) prove simp rules for your "abtract" operation of the form:

lemma Rep_plus_sat [simp]:
  "Rep_sat (x + y) =3D min (Rep_sat x + Rep_sat y) CARD('a)"
  by (simp add: plus_sat_def)

Together with extensionality on sat values, this will greatly simplify
your proofs and make them less cumbersome.  Look at the theory to get
more ideas.

> I humbly suggest that a working version of this theory make its way
into HOL/Library. I'd be happy to round out the theory with some guidance=
=2E

Yes, indeed.  I'd first suggest to round up the proofs a little, and
maybe others want to comment also on that.

Hope this helps,
	Florian

--=20

Home:
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--------------070000050601010106080301
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 filename="Saturated.thy"

(* Author: Brian Huffman *)
(* Version: Isabelle2011 *)

header {* Saturated arithmetic *}

theory Saturated
imports Main "~~/src/HOL/Library/Numeral_Type" "~~/src/HOL/Word/Type_Leng=
th"
begin

typedef (open) 'a sat =3D "{.. CARD('a)}"
  by auto

definition Abs_sat' :: "nat \<Rightarrow> 'a sat" where
  "Abs_sat' n =3D Abs_sat (min (CARD('a)) n)"

text {* More simp rules are admissible and helpful *}

lemma Rep_Abs_sat' [simp]: "Rep_sat (Abs_sat' n :: 'a sat) =3D min (CARD(=
'a)) n"
  unfolding Abs_sat'_def
  by (rule Abs_sat_inverse) simp

lemma Rep_sat_le_CARD [simp]: "Rep_sat (n :: 'a sat) \<le> CARD('a)"
  using Rep_sat [where x=3Dn] by simp

lemma min_CARD_Rep_sat [simp]: "min CARD('a) (Rep_sat (n::'a sat)) =3D Re=
p_sat n"
  by (rule min_max.inf_absorb2 [OF Rep_sat_le_CARD])

lemma min_Rep_sat_CARD [simp]: "min (Rep_sat (n::'a sat)) CARD('a) =3D Re=
p_sat n"
  by (simp add: min_CARD_Rep_sat min_max.inf.commute)

text {* Suggestion: Use code generation for abstract types *}

lemma Abs_Rep_sat' [simp, code abstype]:
  "Abs_sat' (Rep_sat n) =3D n"
  by (simp add: Abs_sat'_def min_CARD_Rep_sat Rep_sat_inverse)

text {* Suggestion: use extensionality in primitive proofs about @{typ "'=
a sat"} *}

lemma sat_eqI:
  "Rep_sat m =3D Rep_sat n \<Longrightarrow> m =3D n"
  by (simp add: Rep_sat_inject)

lemma sat_eq_iff:
  "m =3D n \<longleftrightarrow> Rep_sat m =3D Rep_sat n"
  by (simp add: Rep_sat_inject)

text {* Suggestion: may can be generalized to class @{class linordered_se=
miring} *}

lemma nat_mult_min_left:
  fixes x y z :: nat
  shows "min x y * z =3D min (x * z) (y * z)"
  unfolding min_def by simp

lemma nat_mult_min_right:
  fixes x y z :: nat
  shows "x * min y z =3D min (x * y) (x * z)"
  unfolding min_def by simp

lemma nat_add_min_left:
  fixes x y z :: nat
  shows "min x y + z =3D min (x + z) (y + z)"
  unfolding min_def by simp

lemma nat_add_min_right:
  fixes x y z :: nat
  shows "x + min y z =3D min (x + y) (x + z)"
  unfolding min_def by simp

instantiation sat :: (type) "{minus, comm_semiring_0}"
begin

definition
  zero_sat_def: "0 =3D Abs_sat' 0"

text {* Prove the @{text "Rep ..."} lemmas immediately and use for code g=
eneration *}

lemma Rep_zero_sat [simp, code abstract]:
  "Rep_sat 0 =3D 0"
  by (simp add: zero_sat_def)

definition
  plus_sat_def: "x + y =3D Abs_sat' (Rep_sat x + Rep_sat y)"

lemma Rep_plus_sat [simp, code abstract]:
  "Rep_sat (x + y) =3D min (Rep_sat x + Rep_sat y) CARD('a)"
  by (simp add: plus_sat_def)

definition
  minus_sat_def: "x - y =3D Abs_sat' (Rep_sat x - Rep_sat y)"

lemma Rep_minus_sat [simp, code abstract]:
  "Rep_sat (x - y) =3D Rep_sat x - Rep_sat y"
proof -
  from Rep_sat_le_CARD [of x] have "Rep_sat x - Rep_sat y \<le> CARD('a)"=
 by arith
  then show ?thesis by (simp add: minus_sat_def)
qed

definition
  times_sat_def: "x * y =3D Abs_sat' (Rep_sat x * Rep_sat y)"

lemma Rep_times_sat [simp, code abstract]:
  "Rep_sat (x * y) =3D min (Rep_sat x * Rep_sat y) CARD('a)"
  by (simp add: times_sat_def)

instance
apply intro_classes
apply (simp_all add: sat_eq_iff mult.commute)
txt {* Here two subgoals algebraic goals about @{const min} survive, whic=
h should possible to be tracked to generic lemmas; still some work, but a=
 vast improvement over the previous apply proof *}
sorry

end

instantiation sat :: (type) ordered_comm_semiring
begin

definition
  less_eq_sat_def: "x \<le> y \<longleftrightarrow> Rep_sat x \<le> Rep_s=
at y"

text {* This formulation is much more nicer for unfolding *}

definition
  less_sat_def: "(x::'a sat) < y \<longleftrightarrow> Rep_sat x < Rep_sa=
t y"

instance
apply intro_classes
apply (auto simp add: less_eq_sat_def less_sat_def not_le sat_eq_iff)
txt {* use proper Isar proof *}
sorry

end

text {* Here an experiment on code generation: *}

code_thms "Saturated._" -- {* There is still @{text card} for @{const plu=
s} and @{const times} *}

class len_card =3D len +
  assumes len_of_card: "len_of TYPE('a) =3D CARD('a)"

lemma plus_sat_code [code abstract]:
  fixes x y :: "'a::len_card sat"
  shows "Rep_sat (x + y) =3D min (Rep_sat x + Rep_sat y) (len_of TYPE('a)=
)"
  by (simp add: len_of_card)

lemma times_sat_code [code abstract]:
  fixes x y :: "'a::len_card sat"
  shows "Rep_sat (x * y) =3D min (Rep_sat x * Rep_sat y) (len_of TYPE('a)=
)"
  by (simp add: len_of_card)

export_code "Saturated._" in Haskell file - -- {* Heureka! *}

instance sat :: (type) linorder
proof
  fix x y :: "'a sat"
  show "x \<le> y \<or> y \<le> x"
    unfolding less_eq_sat_def
    by (rule linear)
qed

instantiation sat :: (finite) comm_semiring_1
begin

definition
  one_sat_def: "1 =3D Abs_sat 1"

lemma Rep_sat_1: "Rep_sat 1 =3D 1"
  unfolding one_sat_def
  by (rule Abs_sat_inverse) simp

instance
apply intro_classes
apply (unfold times_sat_def)
apply (unfold Rep_sat_inject [symmetric])
apply (unfold Rep_Abs_sat' Rep_sat_0 Rep_sat_1)
apply (simp add: min_CARD_Rep_sat)
apply simp
done

end

instance sat :: (type) finite
proof
  show "finite (UNIV::'a sat set)"
    unfolding type_definition.univ [OF type_definition_sat]
    using finite by simp
qed

instantiation sat :: (type) number
begin

definition
  number_of_sat_def [code del]: "number_of =3D Abs_sat' \<circ> nat"

instance ..

end

instantiation sat :: (type) equal
(*<*)
begin

definition
  "HOL.equal A B \<longleftrightarrow> Rep_sat A =3D Rep_sat B"

instance proof
qed (simp add: equal_sat_def Rep_sat_inject)

end

text{* Code generator setup. *}

code_datatype number_sat_inst.number_of_sat

lemma zero_nat_code [code, code_unfold_post]:
  "0 =3D (Numeral0 :: 'a sat)"
  by (simp add: number_of_sat_def Abs_sat'_def Int.Pls_def zero_sat_def)

lemma one_nat_code [code, code_unfold_post]:
  "1 =3D (Numeral1 :: ('a :: card2) sat)"
  apply (simp add: number_of_sat_def Abs_sat'_def one_sat_def Int.Pls_def=
)
  apply (subst Abs_sat_inject)
  apply simp
  apply simp
  sorry

(*
lemma Suc_code [code]:
  "Suc n =3D n + 1"
  by simp
*)

declare plus_sat_def[code]

definition
  f :: "2 sat"
where
  "f \<equiv> 1 + 0"

code_thms f

export_code
  "f"
in -


lemma plus_sat_code[code]:
  "n + m =3D nat (of_nat n + of_nat m)"
  by simp


lemma minus_nat_code [code]:
  "n - m =3D nat (of_nat n - of_nat m)"
  by simp

end

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Btw. theory src/HOL/Library/Dlist.thy is a very nice example how to
establish what you could call =BBabstract types with invariants=AB and
corresponding code generation in Isabelle/HOL.
I suggest to follow the patterns which can be found there wrt.
to which auxiliary lemmas about Rep/Abs/Abs' to prove, which simp rules
to prove
and how to setup code generation.

Maybe your Abs_sat' can just be called Sat.

	Florian

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Subject: Re: [isabelle] the state of the lattice theories
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Hi Peter,

> OK. This being the case, could (/should) it be moved from the top-level=
, to e.g. HOL/Library/ or ex/, or maybe Proofs/?

here there are two misunderstandings mixed together:

a) Basically, everything inside HOL/ can be considered a library as long
it is a suitable development to build upon, be it HOL-Algebra or
HOL-Imperative_HOL.  Typically the developer of a (let's call it)
extension is able to tell you whether it can suit your purpose.

b) Proofs/ is not a directory, it is a particular image of the HOL
session run with proof terms.

> On a related note, HOL/Library/ is a zoo. Would it be reasonable to
introduce more structure there, ala Haskell's hierarchical libraries?

It would surely, but we have no hierarchical theory name space (yet).

> Indeed it was an entirely separate Isabelle logic (built on top of HOL)=
, but Brian's recent work has made HOLCF a HOL library. It provides conve=
nient ways of making recursive definitions over PCPOs that strike me as u=
seful for doing the same thing over complete lattices.

I dimly remember that once Brian and I discussed whether some ordering
stuff could be shared here, but AFAIR the major obstacle was that HOL
orderings have an explicit strict part <, which seems to be inconvenient
for HOLCF.

Hope this helps,
	Florian

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From florian.haftmann at informatik.tu-muenchen.de Sun Aug 07 19:35:28 2011
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> Maybe your Abs_sat' can just be called Sat.

When going through Dlist a further suggestion came to my mind:

I have modified the theory further: Abs_sat' is called Sat, and Rep_sat
nat_of.  Both are operations to be expected to be used in =BBuser space=AB=

and should therefore carry readable names.

Hope this helps,
	Florian

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(* Author: Brian Huffman *)
(* Version: Isabelle2011 *)

header {* Saturated arithmetic *}

theory Saturated
imports Main "~~/src/HOL/Library/Numeral_Type" "~~/src/HOL/Word/Type_Leng=
th"
begin

typedef (open) 'a sat =3D "{.. CARD('a)}"
  morphisms nat_of Abs_sat
  by auto

text {* Suggestion: use extensionality in primitive proofs about @{typ "'=
a sat"} *}

lemma sat_eqI:
  "nat_of m =3D nat_of n \<Longrightarrow> m =3D n"
  by (simp add: nat_of_inject)

lemma sat_eq_iff:
  "m =3D n \<longleftrightarrow> nat_of m =3D nat_of n"
  by (simp add: nat_of_inject)

text {* Suggestion: Use code generation for abstract types *}

lemma [code abstype]:
  "Abs_sat (nat_of n) =3D n"
  by (fact nat_of_inverse)

definition Sat :: "nat \<Rightarrow> 'a sat" where
  "Sat n =3D Abs_sat (min CARD('a) n)"

text {* More simp rules are admissible and helpful *}

lemma nat_of_Sat [simp]: "nat_of (Sat n :: 'a sat) =3D min (CARD('a)) n"
  unfolding Sat_def
  by (rule Abs_sat_inverse) simp

lemma nat_of_le_CARD [simp]: "nat_of (n :: 'a sat) \<le> CARD('a)"
  using nat_of [where x=3Dn] by simp

lemma min_CARD_nat_of [simp]: "min CARD('a) (nat_of (n::'a sat)) =3D nat_=
of n"
  by (rule min_max.inf_absorb2 [OF nat_of_le_CARD])

lemma min_nat_of_CARD [simp]: "min (nat_of (n::'a sat)) CARD('a) =3D nat_=
of n"
  by (simp add: min_max.inf.commute)

lemma Sat_nat_of [simp]:
  "Sat (nat_of n) =3D n"
  by (simp add: Sat_def nat_of_inverse)

text {* Suggestion: may can be generalized to class @{class linordered_se=
miring} *}

lemma nat_mult_min_left:
  fixes x y z :: nat
  shows "min x y * z =3D min (x * z) (y * z)"
  unfolding min_def by simp

lemma nat_mult_min_right:
  fixes x y z :: nat
  shows "x * min y z =3D min (x * y) (x * z)"
  unfolding min_def by simp

lemma nat_add_min_left:
  fixes x y z :: nat
  shows "min x y + z =3D min (x + z) (y + z)"
  unfolding min_def by simp

lemma nat_add_min_right:
  fixes x y z :: nat
  shows "x + min y z =3D min (x + y) (x + z)"
  unfolding min_def by simp

instantiation sat :: (type) "{minus, comm_semiring_0}"
begin

definition
  zero_sat_def: "0 =3D Sat 0"

text {* Prove the @{text "Rep ..."} lemmas immediately and use for code g=
eneration *}

lemma nat_of_zero_sat [simp, code abstract]:
  "nat_of 0 =3D 0"
  by (simp add: zero_sat_def)

definition
  plus_sat_def: "x + y =3D Sat (nat_of x + nat_of y)"

lemma nat_of_plus_sat [simp, code abstract]:
  "nat_of (x + y) =3D min (nat_of x + nat_of y) CARD('a)"
  by (simp add: plus_sat_def)

definition
  minus_sat_def: "x - y =3D Sat (nat_of x - nat_of y)"

lemma nat_of_minus_sat [simp, code abstract]:
  "nat_of (x - y) =3D nat_of x - nat_of y"
proof -
  from nat_of_le_CARD [of x] have "nat_of x - nat_of y \<le> CARD('a)" by=
 arith
  then show ?thesis by (simp add: minus_sat_def)
qed

definition
  times_sat_def: "x * y =3D Sat (nat_of x * nat_of y)"

lemma nat_of_times_sat [simp, code abstract]:
  "nat_of (x * y) =3D min (nat_of x * nat_of y) CARD('a)"
  by (simp add: times_sat_def)

instance
apply intro_classes
apply (simp_all add: sat_eq_iff mult.commute)
txt {* Here two subgoals algebraic goals about @{const min} survive, whic=
h should possible to be tracked to generic lemmas; still some work, but a=
 vast improvement over the previous apply proof *}
sorry

end

instantiation sat :: (type) ordered_comm_semiring
begin

definition
  less_eq_sat_def: "x \<le> y \<longleftrightarrow> nat_of x \<le> nat_of=
 y"

text {* This formulation is much more nicer for unfolding *}

definition
  less_sat_def: "(x::'a sat) < y \<longleftrightarrow> nat_of x < nat_of =
y"

instance
apply intro_classes
apply (auto simp add: less_eq_sat_def less_sat_def not_le sat_eq_iff)
txt {* use proper Isar proof *}
sorry

end

text {* Here an experiment on code generation: *}

code_thms "Saturated._" -- {* There is still @{text card} for @{const plu=
s} and @{const times} *}

class len_card =3D len +
  assumes len_of_card: "len_of TYPE('a) =3D CARD('a)"

lemma plus_sat_code [code abstract]:
  fixes x y :: "'a::len_card sat"
  shows "nat_of (x + y) =3D min (nat_of x + nat_of y) (len_of TYPE('a))"
  by (simp add: len_of_card)

lemma times_sat_code [code abstract]:
  fixes x y :: "'a::len_card sat"
  shows "nat_of (x * y) =3D min (nat_of x * nat_of y) (len_of TYPE('a))"
  by (simp add: len_of_card)

export_code "Saturated._" in Haskell file - -- {* Heureka! *}

instance sat :: (type) linorder
proof
  fix x y :: "'a sat"
  show "x \<le> y \<or> y \<le> x"
    unfolding less_eq_sat_def
    by (rule linear)
qed

instantiation sat :: (finite) comm_semiring_1
begin

definition
  one_sat_def: "1 =3D Abs_sat 1"

lemma nat_of_1 [simp, code abstract]: "nat_of 1 =3D 1"
  unfolding one_sat_def
  by (rule Abs_sat_inverse) simp

instance proof
qed (auto simp add: sat_eq_iff)

end

instance sat :: (type) finite
proof
  show "finite (UNIV::'a sat set)"
    unfolding type_definition.univ [OF type_definition_sat]
    using finite by simp
qed

instantiation sat :: (type) number
begin

definition
  number_of_sat_def [code del]: "number_of =3D Sat \<circ> nat"

instance ..

end

instantiation sat :: (type) equal
(*<*)
begin

definition
  "HOL.equal A B \<longleftrightarrow> nat_of A =3D nat_of B"

instance proof
qed (simp add: equal_sat_def nat_of_inject)

end

text{* Code generator setup. *}

lemma zero_nat_code [code, code_unfold_post]:
  "0 =3D (Numeral0 :: 'a sat)"
  by (simp add: sat_eq_iff number_of_sat_def Int.Pls_def)


lemma one_nat_code [code, code_unfold_post]:
  "1 =3D (Numeral1 :: ('a :: card2) sat)"
  apply (simp add: sat_eq_iff number_of_sat_def Int.Pls_def Int.Bit1_def)=

  apply (simp add: min_def) apply auto
  sorry

definition
  f :: "2 sat"
where
  "f \<equiv> 1 + 0"

text {* Add missing instantiations for @{class len_card} *}

end

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From jonathan.von_schroeder at dfki.de Tue Aug 09 00:28:30 2011
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Date: Tue, 9 Aug 2011 01:28:28 +0200 (CEST)
From: Jonathan von Schroeder <jonathan.von_schroeder at dfki.de>
To: Lukas Bulwahn <bulwahn at in.tum.de>
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Cc: cl-isabelle-users at lists.cam.ac.uk
Subject: Re: [isabelle] Get an ML value from a theory context
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Hi Lukas,
thanks for your response. It seems like I'm doing something wrong in "setti=
ng
up" the Isabelle/ML level or maybe I'm not "within the HOL image"? - Anyway=
s
this is what I'm currently doing. Maybe someone can point out the mistake(s=
) I'm
making:
=C2=A0
sternk at ubuntu:~/test$ wget
http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2011_bundle_x86-=
linux.tar.gz
 sternk at ubuntu:~/test$ tar xzf Isabelle2011_bundle_x86-linux.tar.gz
 sternk at ubuntu:~/test$ ./Isabelle2011/bin/isabelle-process HOL
 > val it =3D (): unit
 val commit =3D fn: unit -> bool
 ML> Datatype_Data;
 Error-Value or constructor (Datatype_Data) has not been declared
 Found near Datatype_Data
 Static Errors
=C2=A0
Jonathan
=C2=A0

 Lukas Bulwahn <bulwahn at in.tum.de> hat am 4. August 2011 um 13:50 geschrieb=
en:

 > On 08/03/2011 12:57 PM, Jonathan von Schroeder wrote:
 > > Hello all,
 > >=C2=A0 =C2=A0I'm currently working on a way to export Isabelle/HOL type=
 definitions
 > >and
 > > their attached (user defined) axioms/theorems from a given theory in
 > > Isabelle. I
 > > have already managed to get this workign by simply going through all t=
he
 > > constants, axioms and theorems present in the theories' context. But
 > > unluckily I
 > > currently get more axioms / theorems than I'm interested in, because t=
hep,
 > > theorems automatically generated by
 > > http://isabelle.in.tum.de/repos/isabelle/file/6d736d983d5c/src/HOL/Too=
ls/Datatype/
 > > are not really "user generated" and thus do not foll within the scope =
of
 > > theorems I wish to export.
 > >
 > >=C2=A0 =C2=A0Thus I'd really like to have (in the top-level raw ML loop=
) access to the
 > > structure
 > > http://isabelle.in.tum.de/repos/isabelle/file/6d736d983d5c/src/HOL/Too=
ls/Datatype/datatype_data.ML
 > > (which lives in the context of
 > > http://isabelle.in.tum.de/repos/isabelle/file/6d736d983d5c/src/HOL/Dat=
atype.thy
 > > from what i can tell) to be able to figure out which theorems were
 > > generated by
 > > the Datatype-Tool. Does anybody have any suggestions on how to do this=
,
 > > because
 > > the Manual http://isabelle.in.tum.de/doc/implementation.pdf only menti=
ons
 > > on
 > > page 11 that "... [the function factorial] is not yet accessible in th=
e
 > > preceding paragraph, nor in a different theory that is independent fro=
m the
 > > current one in the import hierarchy", but I wasn't able to find any
 > > information
 > > on how to "get" access to it (or for that matter to any ml functions /
 > > structures defined within a theory). I'd greatly appreciate any inform=
ation
 > > anybody can provide on this matter.
 > >
 > If you work properly on the Isabelle/ML level, within the HOL image, the
 > datatype package is loaded and set up.
 > Hence, you can then access the structure simply by its name "Datatype_Da=
ta".
 >
 >
 >
 > Lukas
 > >=C2=A0 =C2=A0Jonathan
 > >
 >


From krauss at in.tum.de Tue Aug 09 08:01:45 2011
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Cc: Lukas Bulwahn <bulwahn at in.tum.de>, cl-isabelle-users at lists.cam.ac.uk
Subject: Re: [isabelle] Get an ML value from a theory context
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> sternk at ubuntu:~/test$ wget
> http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2011_bundle_x86-linux.tar.gz
>   sternk at ubuntu:~/test$ tar xzf Isabelle2011_bundle_x86-linux.tar.gz
>   sternk at ubuntu:~/test$ ./Isabelle2011/bin/isabelle-process HOL

This gets you into the internal system toplevel, which is not suitable 
for most applications nowadays. Instead you want to write your ML 
literally inside a theory context like this:

theory Scratch
imports Main
begin

ML {*
   Datatype.get_info @{theory} @{type_name nat}
*}

end

Note the use of antiquotations @{theory} and @{type_name ...} to refer 
to formal entities from the context.

See also Chapter 0 of the Implementation manual for basic examples, as 
well as the Programming Tutorial (aka Cookbook).

Alex



From berghofe at in.tum.de Tue Aug 09 23:54:16 2011
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Subject: Re: [isabelle] Odd failure to match local statement with pending goal.
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Bertram Felgenhauer wrote:
> So do we know whether this is an obscure feature or possibly a bug?
> (If it's a feature I'd love to hear the underlying story.)

Hi,

this problem has now been fixed in the repository version of Isabelle (476a239d3e0e).
It was caused by some rather old code in Isabelle's theorem module that renamed
"all bound variables and some unknowns" in a rule during resolution, in order to preserve
as many of the variable names in the goal as possible. For example, when resolving the rule

  ?P ?x ==> \<exists>x. P x

with the proof state

  \<exists>foo. P foo

this will result in the new proof state

  ?P ?foo

because the schematic variable ?x in the rule has been renamed to match that of the
bound variable foo in the goal.
Unfortunately, such a renaming of schematic variables can cause two kinds of name clashes,
neither of which were detected by the old code:

1. If two bound variables in the goal happen to have the same name, this may cause
   two schematic variables in the rule to be mapped to the same variable:

   lemma R1: "P x ==> Q y ==> (\<exists>x. P x) \<and> (\<exists>y. Q y)"
     by auto

   lemma "(\<exists>z. P z) \<and> (\<exists>z. Q z)"
     apply (rule R1)
     oops

2. If a bound variable in the goal happens to have the same name as a schematic variable
   in the rule, it may clash with another schematic variable in the rule after the
   renaming.

   lemma R2: "P y ==> x = y ==> \<exists>x. P x"
     by auto

   lemma "\<exists>y. P y"
     apply (rule R2)
     oops

I have now introduced a check that filters out such problematic renamings.

Greetings,
Stefan




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Subject: [isabelle] Question regarding sequent calculi in Isabelle
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Hi all,

I currently work on implementing a sequent-style proof calculus over  
dynamic logic. To this end, I have given Isabelle a try (which I  
haven't used much before) and extended LK0.thy from the Sequents logic  
with my proof rules. This seems to work until I run into problems with  
a symbolic execution rule, where every symbol in a predicate needs to  
be replaced by a new symbol.

The rule is of the shape

|- p[v0/v'] --> q[v0/v]
-----------------------,
|- [p]q

where p[v0/v'] denotes the replacement of every primed symbol in p by  
a fresh symbol v0 (and similarly for q). This is not a problem as long  
as only a single symbol is to be substituted -- but I need to replace  
all primed symbols in v'. Is something like this possible with Isabelle?

Second, I have a more general question: it seems that the Sequents  
theory of Isabelle isn't used much and that the main work is on  
Isabelle/HOL. Does it nevertheless make sense to use the Sequents  
theory of Isabelle as a basis for a sequent-style calculus, or is  
Isabelle not the right choice for such a calculus?

I have already asked Makarius about this, who pointed me to this  
mailing list.

On 10 Jul 2011, Makarius wrote:
> This looks a bit too "syntactic".  The framework does not allow to  
> access
> the term structure as such, you somehow need to reason symbolically  
> within
> the minimal logic of Pure.
>
> There might be ways, say in Isabelle/HOL with a more detailed  
> syntactic
> model of the calculus.  But this also means you have to invest more  
> work
> in the formalization.
>
> The Sequents theories are really old.  I guess that quite a bit more
> expertise has emerged in the past decades how to do such things.  If  
> you
> ask on isbelle-users some experts might tell you more.


Many thanks for any help!

Johannes

--
Dipl.-Inform. Johannes Faber
Correct System Design Group
Department of Computing Science
Carl von Ossietzky University of Oldenburg
Phone: +49 441 798-4638
Fax:   +49 441 798-2965

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From: Mamoun FILALI-AMINE <filali at irit.fr>
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Hello,

   After discussing with Sascha Boehme, it seems to be technically
   impossible to match a goal against a pattern after unfolding with
   some rewrite rule:

     definition "foo x =3D bar x x"

     ...

     have "foo (f x)" (is "foo ?X")       [pattern is possible]
       unfolding foo_def (is "bar ?X _")  [pattern is not possible]

   However, according to Sascha, most of the time proofs can be
   restructured to avoid this need or Isabelle's proof methods (e.g.,
   simp or auto) can collapse relevant proof steps such that these
   patterns are not necessary.

Mamoun
Le 07dimanche/08/11 7 =E0 13:  19, Sascha Boehme a =E9crit :
> Hello Mamoun,
>
> Your example does not contain schematic variables after unfolding with
> ref_def.  Instead, the goal looks as follows:
>
>    \<forall>s. (A \<union>  B) s \<longrightarrow>  (A' \<union>  B') s
>
> The most common form to instantiate schematic variables in facts is
> via the "of" attribute, for example as follows:
>
>    thm refl  (* is "?t =3D ?t" *)
>
>    thm refl[of x]  (* is "x =3D x" *)
>
> This can also be applied to intermediate steps in a proof:
>
>    lemma "\<exists>n::nat. n \<ge>  0"
>    proof -
>      {
>        fix n :: nat
>        have "n \<ge>  0" by simp
>      }
>      (* we proved "?n \<ge>  0" *)
>      note this[of "1 :: nat"]  (* is "1 \<ge>  0" *)
>      then show ?thesis ..
>    qed
>
> A different form of this proof introduces schematic variables into the
> goal, but in most cases it's best to let some tactic instantiate
> these variables automatically:
>
>    lemma "\<exists>n::nat. n \<ge>  0"
>      apply (rule exI)  (* the goal is now "?n \<ge>  0" *)
>      apply simp  (* instantiates "?n" appropriately and solves the goal=
 *)
>      done
>
> Cheers,
> Sascha
>
>
> Mamoun FILALI-AMINE wrote:
>> Hello,
>>
>>    I wonder if it is possible to instantiate schematic variables
>> after unfolding (see example below).
>> thanks
>>
>> Mamoun
>>
>> --------
>>
>> definition "ref P Q =3D (\<forall>  s. P s \<longrightarrow>  Q s)"
>>
>> theorem
>>    assumes r1: "ref A A'"
>>    assumes r2: "ref B B'"
>> shows "ref (A \<union>  B) (A' \<union>  B')"
>> proof -
>>    have "?thesis" unfolding ref_def (* is "\<forall>  s. ?L s
>> \<longrightarrow>  ?R s" *)
>>
>> begin:vcard
>> fn:Mamoun FILALI-AMINE
>> n:FILALI-AMINE;Mamoun
>> adr;quoted-printable:118 Route de Narbonne;;IRIT Universit=3DC3=3DA9 P=
aul Sabatier;Toulouse;;31062 cedex 9;France
>> email;internet:filali at irit.fr
>> tel;work:00 33 5 61 55 69 26
>> tel;fax:00 33 5 61 55 64 48
>> version:2.1
>> end:vcard
>>
>
>


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To: Johannes Faber <johannesfaber at gmx.de>
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Subject: Re: [isabelle] Question regarding sequent calculi in Isabelle
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I hesitate to call anything impossible, because there are various ways =
to attach code to a theory. However, this kind of systematic renaming of =
non-variable symbols isn't directly supported by Isabelle's logical =
framework.

As for your second question, certainly most development focuses on =
Isabelle/HOL, but much of it involves strengthening the framework in =
general, which benefits all logics. We have retained a lot of ancient =
developments, such as CCL, and I would be very surprised if we got rid =
of the Sequents theory. Whether there exists an alternative out there I =
couldn't say. There are of course ready-made implementations of dynamic =
logic, http://www.key-project.org/ for example.

Larry Paulson


On 9 Aug 2011, at 10:34, Johannes Faber wrote:

>=20
> Hi all,
>=20
> I currently work on implementing a sequent-style proof calculus over =
dynamic logic. To this end, I have given Isabelle a try (which I haven't =
used much before) and extended LK0.thy from the Sequents logic with my =
proof rules. This seems to work until I run into problems with a =
symbolic execution rule, where every symbol in a predicate needs to be =
replaced by a new symbol.
>=20
> The rule is of the shape
>=20
> |- p[v0/v'] --> q[v0/v]
> -----------------------,
> |- [p]q
>=20
> where p[v0/v'] denotes the replacement of every primed symbol in p by =
a fresh symbol v0 (and similarly for q). This is not a problem as long =
as only a single symbol is to be substituted -- but I need to replace =
all primed symbols in v'. Is something like this possible with Isabelle?
>=20
> Second, I have a more general question: it seems that the Sequents =
theory of Isabelle isn't used much and that the main work is on =
Isabelle/HOL. Does it nevertheless make sense to use the Sequents theory =
of Isabelle as a basis for a sequent-style calculus, or is Isabelle not =
the right choice for such a calculus?
>=20
> I have already asked Makarius about this, who pointed me to this =
mailing list.
>=20
> On 10 Jul 2011, Makarius wrote:
>> This looks a bit too "syntactic".  The framework does not allow to =
access
>> the term structure as such, you somehow need to reason symbolically =
within
>> the minimal logic of Pure.
>>=20
>> There might be ways, say in Isabelle/HOL with a more detailed =
syntactic
>> model of the calculus.  But this also means you have to invest more =
work
>> in the formalization.
>>=20
>> The Sequents theories are really old.  I guess that quite a bit more
>> expertise has emerged in the past decades how to do such things.  If =
you
>> ask on isbelle-users some experts might tell you more.
>=20
>=20
> Many thanks for any help!
>=20
> Johannes
>=20
> --
> Dipl.-Inform. Johannes Faber
> Correct System Design Group
> Department of Computing Science
> Carl von Ossietzky University of Oldenburg
> Phone: +49 441 798-4638
> Fax:   +49 441 798-2965




From makarius at sketis.net Wed Aug 10 21:38:49 2011
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From: Makarius <makarius at sketis.net>
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To: Mamoun FILALI-AMINE <filali at irit.fr>
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Cc: isabelle-users at cl.cam.ac.uk
Subject: Re: [isabelle] schematic variables
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On Wed, 10 Aug 2011, Mamoun FILALI-AMINE wrote:

>  After discussing with Sascha Boehme, it seems to be technically
>  impossible to match a goal against a pattern after unfolding with
>  some rewrite rule:
>
>    definition "foo x = bar x x"
>
>    ...
>
>    have "foo (f x)" (is "foo ?X")       [pattern is possible]
>      unfolding foo_def (is "bar ?X _")  [pattern is not possible]

Strictly speaking it is not *technically* impossible, merely outside the 
scope of the structured proof language of Isar. Structure emerges by 
restricting low-level technical operations to something that conforms to 
certain higher concepts.  Take ML as programming language for example: it 
allows much less operations than machine language, and is thus far more 
powerful -- the compiler and runtime system can do smart things for you.

One of the key principles of Isar is the distinction of the proof text and 
the proof state.  Information may flow only from text to state, not the 
other way round.


Anyway, your example reminds me of the Ltac tactic definition language of 
Coq, with matching against the goal state.  After so many years, Isar 
still lacks a structured proof method definition language.  You have to 
use plain ML for that (via the 'method_setup' command, which is not really 
difficult).

When drafting the first versions of the Isar proof language, I was aware 
of this omission of a method definition language.  It made certain things 
easier, and the quality of proofs (readability and maintainability) has 
actually improved by making the language more restrictive.

Structured proof method definition languages are still an interesting area 
of research, but I see more potential for the future in sophisticated 
editing support of Isar text in the Prover IDE.  (The current 
Isabelle/jEdit implementation is a very modest beginning in that 
direction.)


This can be illustrated by looking again at what Coq has to offer.  Since 
I am myself located in France, I have the privilege to discuss with many 
Coq users first-hand.  I see two main movements of power-users at the 
moment:

   (1) Hardcore Ltac scripting according Chlipala.
       (This reminds me a lot of a tactical style that was popular in
       Isabelle/HOL in the late 1990-ies, e.g. see HOL/Bali or
       HOL/Hoare_Parallel).

   (2) Quick in-place tactic composition via ssreflect, according to
       Gonthier.  His language assigns a meaning to almost every character
       in the ASCII set, to make typing as efficient as possible.  This
       wins more and more converts, and recent versions of Matita seem to
       have adopted it as well.

Instead of imitating any of the above, I would eventually like to see a 
Prover IDE that allows very quick proof composition, but producing proper 
Isar proof text instead of recording the keystrokes in the script.  This 
would be analogous to a typical Java IDE: a relatively weak language (here 
Isar) is composed and maintained by relatively strong tooling.


 	Makarius



From florian.haftmann at informatik.tu-muenchen.de Thu Aug 11 14:00:51 2011
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Date: Thu, 11 Aug 2011 15:00:43 +0200
From: Florian Haftmann <florian.haftmann at informatik.tu-muenchen.de>
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Subject: [isabelle] Scala Code Generation
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Hi all,

since Isabelle2011 there is the possibility to generate Scala code from
HOL theories.  Some minor problems can be circumvented by a suitable
patch and will disappear in the next release.

Apart from that, is there any further feedback (positive or negative) on
code generation for Scala?  I would like to announce it on the Scala
mailing list after the next release, but for this I need some evidence
that it is really working.

Thanks for any feedback,
	Florian

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From nipkow at in.tum.de Thu Aug 11 15:15:43 2011
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Subject: [isabelle] Research Associate position at the University of York
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From: Jim Woodcock <jim at cs.york.ac.uk>

Applications are invited for one post of Research Associate in the
High-Integrity Systems Engineering and Real-time Systems Research Groups
in the Department of Computer Science, University of York.  The post,
which is limited to 3 years period in the first instance, is available
from October 2011.  Please the following for further details.

https://www22.i-grasp.com/fe/tpl_YorkUni01.asp?newms=jj&id=46061

The closing date for receipt of applications is midnight on Friday 26
August 2011.

James Woodcock FREng
Anniversary Professor of Software Engineering
Department of Computer Science
University of York




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Subject: [isabelle] CFP: Special Issue on Automated Verification of Critical
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(Apologies for duplicates)

Call For Papers

Science of Computer Programming

Special Issue on Automated Verification of Critical Systems
Guest editors: Jens Bendispoto, Michael Leuschel, Markus Roggenbach

Submission deadline: 9.9.2011

This special issue is devoted to the scope of the international
workshop on Automated Verification of Critical Systems (AVoCS 2010 -
see http://www.formal-methods.de/avocs2010/)
which Duesseldorf University hosted in September 2010. AVoCS is  
devoted to tools
and techniques for the verification of critical systems. These topics
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Florian,

On 08/08/2011, at 4:35 AM, Florian Haftmann wrote:

>> Maybe your Abs_sat' can just be called Sat.
>=20
> When going through Dlist a further suggestion came to my mind:
>=20
> I have modified the theory further: Abs_sat' is called Sat, and =
Rep_sat
> nat_of.  Both are operations to be expected to be used in =BBuser =
space=AB
> and should therefore carry readable names.

Thanks for this. I've tidied it up a bit. See the attached.

cheers
peter


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(* Author: Brian Huffman *)
(* Author: Peter Gammie *)
(* Author: Florian Haftmann *)
(* Version: Isabelle2011 *)

header {* Saturated arithmetic *}

theory Saturated
imports Main "~~/src/HOL/Library/Numeral_Type" "~~/src/HOL/Word/Type_Length"
begin

typedef (open) ('a::len) sat = "{.. len_of TYPE('a)}"
  morphisms nat_of Abs_sat
  by auto

lemma sat_eqI:
  "nat_of m = nat_of n \<Longrightarrow> m = n"
  by (simp add: nat_of_inject)

lemma sat_eq_iff:
  "m = n \<longleftrightarrow> nat_of m = nat_of n"
  by (simp add: nat_of_inject)

text {* Use code generation for abstract types. *}

lemma [code abstype]:
  "Abs_sat (nat_of n) = n"
  by (fact nat_of_inverse)

definition Sat :: "nat \<Rightarrow> ('a::len) sat" where
  "Sat n = Abs_sat (min (len_of TYPE('a)) n)"

lemma nat_of_Sat [simp]: "nat_of (Sat n :: ('a::len) sat) = min (len_of TYPE('a)) n"
  unfolding Sat_def
  by (rule Abs_sat_inverse) simp

lemma nat_of_le_len_of [simp]: "nat_of (n :: ('a::len) sat) \<le> len_of TYPE('a)"
  using nat_of [where x=n] by simp

lemma min_len_of_nat_of [simp]: "min (len_of TYPE('a)) (nat_of (n::('a::len) sat)) = nat_of n"
  by (rule min_max.inf_absorb2 [OF nat_of_le_len_of])

lemma min_nat_of_len_of [simp]: "min (nat_of (n::('a::len) sat)) (len_of TYPE('a)) = nat_of n"
  by (subst min_max.inf.commute) simp

lemma Sat_nat_of [simp]:
  "Sat (nat_of n) = n"
  by (simp add: Sat_def nat_of_inverse)

lemma nat_mult_min_left:
  fixes x y z :: nat
  shows "min x y * z = min (x * z) (y * z)"
  unfolding min_def by simp

lemma nat_mult_min_right:
  fixes x y z :: nat
  shows "x * min y z = min (x * y) (x * z)"
  unfolding min_def by simp

lemma nat_add_min_left:
  fixes x y z :: nat
  shows "min x y + z = min (x + z) (y + z)"
  unfolding min_def by simp

lemma nat_add_min_right:
  fixes x y z :: nat
  shows "x + min y z = min (x + y) (x + z)"
  unfolding min_def by simp

instantiation sat :: (len) linorder
begin

definition
  less_eq_sat_def: "x \<le> y \<longleftrightarrow> nat_of x \<le> nat_of y"

text {* This formulation is much nicer for unfolding *}

definition
  less_sat_def: "(x::'a sat) < y \<longleftrightarrow> nat_of x < nat_of y"

instance
by default (auto simp add: less_eq_sat_def less_sat_def not_le sat_eq_iff min_max.le_infI1 nat_mult_commute)

end

text {* Suggestion: may be generalized to class @{class linordered_semiring} *}

instantiation sat :: (len) "{minus, comm_semiring_0, comm_semiring_1}"
begin

definition
  zero_sat_def: "0 = Sat 0"

definition
  one_sat_def: "1 = Sat 1"

text {* Prove the @{text "Rep ..."} lemmas immediately and use for code generation *}

lemma nat_of_zero_sat [simp, code abstract]:
  "nat_of 0 = 0"
  by (simp add: zero_sat_def)

lemma nat_of_one_sat [simp, code abstract]:
  "nat_of 1 = min 1 (len_of TYPE('a))"
  by (simp add: one_sat_def)

definition
  plus_sat_def: "x + y = Sat (nat_of x + nat_of y)"

lemma nat_of_plus_sat [simp, code abstract]:
  "nat_of (x + y) = min (nat_of x + nat_of y) (len_of TYPE('a))"
  by (simp add: plus_sat_def)

definition
  minus_sat_def: "x - y = Sat (nat_of x - nat_of y)"

lemma nat_of_minus_sat [simp, code abstract]:
  "nat_of (x - y) = nat_of x - nat_of y"
proof -
  from nat_of_le_len_of [of x] have "nat_of x - nat_of y \<le> len_of TYPE('a)" by arith
  then show ?thesis by (simp add: minus_sat_def)
qed

definition
  times_sat_def: "x * y = Sat (nat_of x * nat_of y)"

lemma nat_of_times_sat [simp, code abstract]:
  "nat_of (x * y) = min (nat_of x * nat_of y) (len_of TYPE('a))"
  by (simp add: times_sat_def)

instance
proof
  fix a b c :: "('a::len) sat"
  show "a * b * c = a * (b * c)"
  proof(cases "a = 0")
    case True thus ?thesis by (simp add: sat_eq_iff)
  next
    case False show ?thesis
    proof(cases "c = 0")
      case True thus ?thesis by (simp add: sat_eq_iff)
    next
      case False with `a \<noteq> 0` show ?thesis
        by (simp add: sat_eq_iff nat_mult_min_left nat_mult_min_right mult_assoc min_max.inf_assoc min_max.inf_absorb2)
    qed
  qed
next
  fix a :: "('a::len) sat"
  show "1 * a = a"
    apply (simp add: sat_eq_iff)
    apply (metis One_nat_def len_gt_0 less_Suc0 less_zeroE linorder_not_less min_max.le_iff_inf min_nat_of_len_of nat_mult_1_right nat_mult_commute)
    done
next
  fix a b c :: "('a::len) sat"
  show "(a + b) * c = a * c + b * c"
  proof(cases "c = 0")
    case True thus ?thesis by (simp add: sat_eq_iff)
  next
    case False thus ?thesis
      by (simp add: sat_eq_iff nat_mult_min_left add_mult_distrib nat_add_min_left nat_add_min_right min_max.inf_assoc min_max.inf_absorb2)
  qed
qed (simp_all add: sat_eq_iff mult.commute)

end

instantiation sat :: (len) ordered_comm_semiring
begin

instance
by default (auto simp add: less_eq_sat_def less_sat_def not_le sat_eq_iff min_max.le_infI1 nat_mult_commute)

end

instantiation sat :: (len) number
begin

definition
  number_of_sat_def [code del]: "number_of = Sat \<circ> nat"

instance ..

end

lemma [code abstract]:
  "nat_of (number_of n :: ('a::len) sat) = min (nat n) (len_of TYPE('a))"
  unfolding number_of_sat_def by simp

instance sat :: (len) finite
proof
  show "finite (UNIV::'a sat set)"
    unfolding type_definition.univ [OF type_definition_sat]
    using finite by simp
qed

instantiation sat :: (len) equal
begin

definition
  "HOL.equal A B \<longleftrightarrow> nat_of A = nat_of B"

instance proof
qed (simp add: equal_sat_def nat_of_inject)

end

end

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Hi,

I just wanted to share a small script I created to have a more
convenient 'isabelle emacs' behavior: Especially when dealing with
different logic images, it is quite cumbersome to manually change the
image in PG each time you open a file needing a special image.

This script should change this:

1.) It can be passed a logic-pattern: This pattern is matched against
all logics as returned by `isabelle findlogics` and then the first match
is taken:
	So if you have 'HOL HOL-Cava-Libs HOL-Graphs HOL-Library Pure' as
images, "C" would match 'HOL-Cava-Libs' as would "L" (first match wins).

2.) This behavior is nice, but when working with the very same project
over and over, it is again cumbersome. Therefore the script also is able
to evaluate the file ".isabelle-logic" in the current directory. This
file should contain exactly one line with the image name (it is taken as
a pattern, but spelling out the complete name is probably better to
avoid surprises).
If the file contains "..", ../.isabelle-logic is looked up (this works
recursively).

So perhaps someone finds this useful. Feel free to edit/enhance it as
you like :).

- Ren=E9

P.S.: By specifiying the logic during startup the chooser in the menu in
PG is not altered(!), hence always states "HOL". The correct image is
nevertheless loaded when starting isabelle from PG.

P.P.S.: The script is a ported version of a personal zsh-script of mine.
It may therefore contain constructs which look strange to a bash-user :)


--------------080700020002010201010707
Content-Type: application/x-sh;
 name="IE.sh"
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 filename="IE.sh"

#!/bin/bash -x
# This script is a wrapper around 'isabelle emacs'
# Usage: ./IE.sh [logic-pattern] [file] [options]
#
# - logic-pattern: this is expanded to *logic-pattern* and matched
#                  against all logics as returned by `isabelle findlogics`
#                  the first match wins
# - file: file to open
# - options: options passed verbatim to 'isabelle emacs'
#
# If no logic-pattern is given, the file .isabelle-logic is
# evaluated: This file should contain one line, being either the logic to load,
# or '..', which makes the script take the .isabelle-logic in the parent directory.

# default arguments to isabelle emacs
declare defargs="-x true -m iff"
# fall-through logic
declare -r default="HOL"

# be nice and declare variables beforehand :)
declare file logic

# safety check to avoid failing later on
if [[ ! -x `type -P isabelle` ]]; then
    echo "Isabelle not found. Aborting"
    return 1
fi

# try to map the arguments to the correct option
# usage is: [logic] [file] [isabelle opts]
case x$1 in
    x*.thy) file=$1; shift;;
    x-*);; # argument to isabelle emacs -> ignore
    x) ;; # empty -> ignore
    x*) # a logic pattern :)
        logic=$1; shift
        if [[ -n $1 && $1 != -* ]]; then
            file=$1; shift
        fi
esac

# have a .isabelle-logic file that contains a logic-image pattern
# if it contains "..", the parent directory is searched
if [[ -z $logic && -e .isabelle-logic ]]; then
    declare p=.isabelle-logic
    declare line=$(head -1 $p)

    while [[ $line == .. ]]; do
        p=../$p
        if [[ -e $p ]]; then
            line=$(head -1 $p)
        else
            line=
        fi
    done

    if [[ -n $line ]]; then
        logic=$line
        echo "Setting logic to '$logic' as found in local settings."
    fi
fi

# try to find the correct logic
# special case HOL, just to be sure :)
if [[ -n $logic && $logic != 'HOL' ]]; then
    declare found

    for l in $(isabelle findlogics); do
        if [[ $l == *${logic}* ]]; then
            logic=$l; found=1
            echo "Using logic '$logic'"
            break
        fi
    done

    if [[ -z $found ]]; then
        echo "No logic found that matches the pattern *${logic}*"
        echo "Existing logics are: $(isabelle findlogics)"
        unset logic
    fi
fi

# fall-through if no logic could be determined
if [[ -z $logic ]]; then
    logic=$default
    echo "Defaulting to '$logic'."
fi

# AAAAND ... FIRE!
isabelle emacs ${defargs} -l $logic "$@" $file

# vim: ft=sh


--------------080700020002010201010707--



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Short correction ... the debugging slipped in.

- Ren=E9

--------------080104060002000009000302
Content-Type: application/x-sh;
 name="IE.sh"
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 filename="IE.sh"

#!/bin/bash
# This script is a wrapper around 'isabelle emacs'
# Usage: ./IE.sh [logic-pattern] [file] [options]
#
# - logic-pattern: this is expanded to *logic-pattern* and matched
#                  against all logics as returned by `isabelle findlogics`
#                  the first match wins
# - file: file to open
# - options: options passed verbatim to 'isabelle emacs'
#
# If no logic-pattern is given, the file .isabelle-logic is
# evaluated: This file should contain one line, being either the logic to load,
# or '..', which makes the script take the .isabelle-logic in the parent directory.

# default arguments to isabelle emacs
declare defargs="-x true -m iff"
# fall-through logic
declare -r default="HOL"

# be nice and declare variables beforehand :)
declare file logic

# safety check to avoid failing later on
if [[ ! -x `type -P isabelle` ]]; then
    echo "Isabelle not found. Aborting"
    return 1
fi

# try to map the arguments to the correct option
# usage is: [logic] [file] [isabelle opts]
case x$1 in
    x*.thy) file=$1; shift;;
    x-*);; # argument to isabelle emacs -> ignore
    x) ;; # empty -> ignore
    x*) # a logic pattern :)
        logic=$1; shift
        if [[ -n $1 && $1 != -* ]]; then
            file=$1; shift
        fi
esac

# have a .isabelle-logic file that contains a logic-image pattern
# if it contains "..", the parent directory is searched
if [[ -z $logic && -e .isabelle-logic ]]; then
    declare p=.isabelle-logic
    declare line=$(head -1 $p)

    while [[ $line == .. ]]; do
        p=../$p
        if [[ -e $p ]]; then
            line=$(head -1 $p)
        else
            line=
        fi
    done

    if [[ -n $line ]]; then
        logic=$line
        echo "Setting logic to '$logic' as found in local settings."
    fi
fi

# try to find the correct logic
# special case HOL, just to be sure :)
if [[ -n $logic && $logic != 'HOL' ]]; then
    declare found

    for l in $(isabelle findlogics); do
        if [[ $l == *${logic}* ]]; then
            logic=$l; found=1
            echo "Using logic '$logic'"
            break
        fi
    done

    if [[ -z $found ]]; then
        echo "No logic found that matches the pattern *${logic}*"
        echo "Existing logics are: $(isabelle findlogics)"
        unset logic
    fi
fi

# fall-through if no logic could be determined
if [[ -z $logic ]]; then
    logic=$default
    echo "Defaulting to '$logic'."
fi

# AAAAND ... FIRE!
isabelle emacs ${defargs} -l $logic "$@" $file

# vim: ft=sh

--------------080104060002000009000302--



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-----BEGIN PGP SIGNED MESSAGE-----
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On 12/08/11 23:53, René Neumann wrote:
> 1.) It can be passed a logic-pattern: This pattern is matched against
> all logics as returned by `isabelle findlogics` and then the first match
> is taken:
> 	So if you have 'HOL HOL-Cava-Libs HOL-Graphs HOL-Library Pure' as
> images, "C" would match 'HOL-Cava-Libs' as would "L" (first match wins).

I haven't looked at the script, but wouldn't "L" match 'HOL' first?

Tim
<><
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Date: Mon, 15 Aug 2011 11:19:57 +0200
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Subject: [isabelle] New AFP entry: 	Maximum Cardinality Matching
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Maximum Cardinality Matching
Christine Rizkallah

A matching in a graph G is a subset M of the edges of G such that no two
share an endpoint. A matching has maximum cardinality if its cardinality
is at least as large as that of any other matching. An odd-set cover OSC
of a graph G is a labeling of the nodes of G with integers such that
every edge of G is either incident to a node labeled 1 or connects two
nodes labeled with the same number i =E2=89=A5 2. This article proves Edm=
onds
theorem: Let M be a matching in a graph G and let OSC be an odd-set
cover of G. For any i =E2=89=A5 0, let n(i) be the number of nodes labele=
d i. If
|M| =3D n(1) + =E2=88=91i =E2=89=A5 2(n(i) div 2), then M is a maximum ca=
rdinality matching.

http://afp.sourceforge.net/entries/Max-Card-Matching.shtml



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Subject: Re: [isabelle] An 'isabelle emacs' wrapper
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Am 15.08.2011 00:28, schrieb Tim (McKenzie) Makarios:
> On 12/08/11 23:53, Ren=E9 Neumann wrote:
>> 1.) It can be passed a logic-pattern: This pattern is matched against
>> all logics as returned by `isabelle findlogics` and then the first mat=
ch
>> is taken:
>> 	So if you have 'HOL HOL-Cava-Libs HOL-Graphs HOL-Library Pure' as
>> images, "C" would match 'HOL-Cava-Libs' as would "L" (first match wins=
).
>=20
> I haven't looked at the script, but wouldn't "L" match 'HOL' first?

Uh - of course. My fault, sorry.

- Ren=E9



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Dear Isabelle Users,

Assuming the context of the declaration

datatype Nat = Z | suc Nat


the following antiquotation command produces a very nicely typeset inference
rule:

\begin{center}
@{thm [mode=Rule,show_types] Nat.induct [no_vars]}{\sc Ind-Nat}
\end{center}

However, Isabelle chooses the same name (in this case /\ Nat) for the bound
variable in the rule. In proof mode
one can rename such choices  using the rename_tac command. Unfortunately I
did not find how to do it in the
above. Took a careful look at chapter 4 of Isabelle reference manual (and
LaTex sugar too)
but I did not guess the way to do it.

Hope it is possible.

Many thanks
-- 
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


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Subject: [isabelle] VSTTE 2012: Final Call for Papers - Submission Deadline:
	August 31
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			   VSTTE 2012
Verified Software: Theories, Tools and Experiments
	 	      January 28-29, 2012
Philadelphia, USA (co-located with POPL and VMCAI)
     https://sites.google.com/site/vstte2012/

The Fourth International Conference on Verified Software: Theories,
Tools, and Experiments  will take place on January 28-29, 2012.  The
focus of the conference is the development of systematic methods for
specifying, building, and verifying software.  The goal of
this conference is to advance the state of the art through the
interaction of theory development, tool evolution, and experimental
validation.  Historically,  the conference came out of the Verified
Software Initiative (VSI), a cooperative, international initiative
directed at the scientific challenges of large-scale software
verification.  An informal verification competition will be held in paralle=
l=20
to the conference. More information will be available from the=20
website.

Topics of interest include:

* Specification and verification techniques
* Tool support for specification languages
* Tool for various design methodologies
* Tool integration and plug-ins
* Automation in formal verification
* Tool comparisons and benchmark repositories
* Combination of tools and techniques
   (e.g. formal vs. semiformal, software specification
    vs. engineering techniques)
* Customizing tools for particular applications
* Challenge problems
* Refinement methodologies
* Requirements modeling
* Specification languages
* Specification/verification case-studies
* Software design methods
* Program logic

SUBMISSIONS

Submitted research papers and system descriptions must be original and
not submitted for publication elsewhere.  Research paper submissions
are limited to 15 proceedings pages in LNCS format and must include a
cogent and self-contained description of the ideas, methods and
results, together with a comparison to existing work. System
descriptions are also limited to 15 proceedings pages in LNCS
format. Authors are encouraged to submit work in progress, particularly if =
the
work involves collaboration, theory unification, and tool integration.
Papers can be submitted at

https://www.easychair.org/conferences/?conf=3Dvstte2012

Submissions that arrive late, are not in the proper format, or are too
long will not be considered.  The proceedings of VSTTE 2012 will be
published by Springer-Verlag in the LNCS series.  Authors of accepted
papers will be requested to sign a form transferring copyright of
their contribution to Springer-Verlag.


IMPORTANT DATES

August 31, 2011:     Conference Paper Submission Deadline
October 20, 2011:    Notification of acceptance
November 15, 2011:   Final conference paper versions due
January 28-29, 2012: Main conference


KEYNOTE SPEAKERS

Rupak Majumdar, Max Planck Institute for Software Systems
Wolfgang Paul,  Saarland University


TUTORIALS

Francesco Logozzo, Microsoft Research
Rustan Leino, Microsoft Research


CONFERENCE CHAIR

Ernie Cohen, European Microsoft Innovation Center=20


PROGRAM CHAIRS

Rajeev Joshi,  NASA Jet Propulsion Laboratory
Peter M=FCller, ETH Zurich
Andreas Podelski, University of Freiburg


PROGRAM COMMITTEE

Clark Barrett, New York University
Lars Birkedal, IT University of Copenhagen
Patrick Cousot, Ecole normale Sup=E9rieure, Paris and New York University
Leonardo De Moura, Microsoft Research
Jean-Christophe Filliatre, CNRS Universit=E9 Paris Sud
John Hatcliff, Kansas State University
Bart Jacobs, Katholieke Universiteit Leuven=20
Ranjit Jhala, University of California, San Diego
Rajeev Joshi,  NASA JPL
Gerwin Klein, NICTA=20
Viktor Kuncak, EPF Lausanne=20
Gary T. Leavens, University of Central Florida=20
Rustan Leino, Microsoft Research
Panagiotis Manolios, Northeastern University
Peter M=FCller, ETH Zurich
Tobias Nipkow, Technische Universit=E4t M=FCnchen=20
Matthew Parkinson, Microsoft Research
Corina Pasareanu, NASA Ames
Wolfgang Paul,  Saarland University
Andreas Podelski,  University of Freiburg
Natasha Sharygina, University of Lugano=20
Willem Visser, University of Stellenbosch
Thomas Wies, IST Austria


PUBLICITY CHAIR

Gudmund Grov, University of Edinburgh


VERIFICATION COMPETITION ORGANISER=20

Jean-Christophe Filliatre, CNRS Universit=E9 Paris Sud


STEERING COMMITTEE

Tony Hoare, Microsoft Research
Andrew Ireland, Heriot-Watt University
Jay Misra, UT Austin
Natarajan Shankar, SRI International
Jim Woodcock, University of York


--=20
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.




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Subject: [isabelle] Renaming names of arbitrary values in document
	preparation (Answer)
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Dear Isabelle Users,

Looking again at LaTeXsugar, I found how to do it. It=B4s been always there=
,
right
in front of my nose. So  what I wanted is something like:

\begin{center}
@{thm [mode=3DRule,show_types] Nat.induct [where Nat =3D n,no_vars,rename_a=
bs
x0]}{\sc Ind-Nat}
\end{center}

Best!!

---------- Forwarded message ----------
From: Alfio Martini <alfio.martini at acm.org>
Date: Wed, Aug 17, 2011 at 11:51 AM
Subject: Renaming names of arbitrary values in document preparation
To: isabelle-users at cl.cam.ac.uk


Dear Isabelle Users,

Assuming the context of the declaration

datatype Nat =3D Z | suc Nat


the following antiquotation command produces a very nicely typeset inferenc=
e
rule:

\begin{center}
@{thm [mode=3DRule,show_types] Nat.induct [no_vars]}{\sc Ind-Nat}
\end{center}

However, Isabelle chooses the same name (in this case /\ Nat) for the bound
variable in the rule. In proof mode
one can rename such choices  using the rename_tac command. Unfortunately I
did not find how to do it in the
above. Took a careful look at chapter 4 of Isabelle reference manual (and
LaTex sugar too)
but I did not guess the way to do it.

Hope it is possible.

Many thanks
--=20
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil



--=20
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


From florian.haftmann at informatik.tu-muenchen.de Thu Aug 18 07:29:32 2011
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Subject: Re: [isabelle] code generation for saturated naturals
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Hi Peter,

> Thanks for this. I've tidied it up a bit. See the attached.

Thanks a lot.

One further remark: the lemmas nat_mult_min_left etc. are quite generic.
 These should go into a separate prelude section at the beginning of the
theory, from where, after becoming part of the library, they should be
move to appropriate theories in the HOL distribution.

What also comes to my mind is that saturated numbers seem to be a nice
example for complete lattices (with inf =3D min etc.).  Maybe you still
want to add those instances.

Cheers,
	Florian

--=20

Home:
http://www.in.tum.de/~haftmann

PGP available:
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Subject: Re: [isabelle] [isabelle-dev] (Re-)introducing set as a type
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I admit to a certain feeling surreality listening in on this exchange.

A blow-by-blow defence and repudiation of strong typing played out in the m=
inutiae of Isabelle's reasoning mechanisms.

It is especially amusing as I would also find it useful to distinguish pred=
icates from boolean-valued operators :-), using /\ ,\/ instead of cap,cup e=
tc.

Surely Isabelle-HOL is a logic for those who believe in the value of strong=
 typing and are willing to wear the need to use explicit type coercions?

Brendan
IMPORTANT: This email remains the property of the Department of Defence and=
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r and delete the email.



From nipkow at in.tum.de Fri Aug 19 16:32:23 2011
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Subject: [isabelle] New AFP entry: Gauss-Jordan Elimination for Matrices
	Represented as Functions
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Gauss-Jordan Elimination for Matrices Represented as Functions
Tobias Nipkow

This theory provides a compact formulation of Gauss-Jordan elimination
for matrices represented as functions. Its distinctive feature is
succinctness. It is not meant for large computations.

http://afp.sourceforge.net/entries/Gauss-Jordan-Elim-Fun.shtml



From makarius at sketis.net Sat Aug 20 15:16:34 2011
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Subject: Re: [isabelle] [isabelle-dev] (Re-)introducing set as a type
	constructor rather than as mere abbreviation[SEC=UNCLASSIFIED]
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On Fri, 19 Aug 2011, Dr. Brendan Patrick Mahony wrote:

> I admit to a certain feeling surreality listening in on this exchange.

Of course, anybody can join the discussion, either on isabelle-dev or 
isabelle-users.  See also 
http://news.gmane.org/gmane.science.mathematics.logic.isabelle.devel

Please chose exactly one list for your answers, to avoid crossposting and 
thus duplication for those on isabelle-dev (which is a subset of 
isabelle-users).


 	Makarius




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Subject: [isabelle] locale expressions?
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Consider the following (HOL/Main, Isabelle 2011)

locale preordX2 = le: preorder le lt + le': preorder le' lt'
  for le::"'a => 'a => bool" and lt::"'a => 'a => bool"
  and le'::"'b => 'b => bool" and lt'::"'b => 'b => bool"
  +
  fixes preordX2_opn:: "'a => 'b =>  'a"
begin

This locale is abstracted over two preorders.  I have an operation
"preordX2_opn" on objects of both preorders, so I need explicit type
variables 'a, 'b, for the constituent preorders in order to correctly
specify this operation.

Now consider the trivial lemma:

lemma
  fixes a::'a
  shows "~ (lt a a)"
  using less_irrefl .       --"less_irrefl from typeclass preorder"

This proof FAILS:
  *** Failed to finish proof
  *** At command "."

I suppose the failure is due to typing:

thm less_irrefl
\<not> (lt'\<Colon>'b \<Rightarrow> 'b \<Rightarrow> bool) (?x\<Colon>'b) ?x

It seems that type variable 'b is incorrect here;  less_irrefl should
have a generalized type.

Indeed, the following proof succeeds:

lemma
  fixes b::'b
  shows "~ (lt' b b)"
  using less_irrefl .

Randy



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Subject: Re: [isabelle] locale expressions?
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On Tue, Aug 23, 2011 at 12:41 PM, Randy Pollack <rpollack at inf.ed.ac.uk> wro=
te:
> Consider the following (HOL/Main, Isabelle 2011)
>
> locale preordX2 =3D le: preorder le lt + le': preorder le' lt'
> =A0for le::"'a =3D> 'a =3D> bool" and lt::"'a =3D> 'a =3D> bool"
> =A0and le'::"'b =3D> 'b =3D> bool" and lt'::"'b =3D> 'b =3D> bool"
> =A0+
> =A0fixes preordX2_opn:: "'a =3D> 'b =3D> =A0'a"
> begin

Within this locale, you have these two lemmas in scope:

le.less_irrefl: "~ lt x x"
le'.less_irrefl: "~ lt' x x"

> Now consider the trivial lemma:
>
> lemma
> =A0fixes a::'a
> =A0shows "~ (lt a a)"
> =A0using less_irrefl . =A0 =A0 =A0 --"less_irrefl from typeclass preorder=
"

The unqualified lemma name "less_irrefl" is ambiguous here. Isabelle
resolves the ambiguity by picking the most-recently-introduced name
that matches, which happens to be "le'.less_irrefl". If you explicitly
say "using le.less_irrefl" the proof will work.

- Brian



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Subject: [isabelle] Function Termination
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Hi all,

I had to define a function that needed its own proof of termination.
Thereby I noticed an issue, I'd like to show by example:

Let succs :: "('a =C3=97 'a) set =E2=87=92 'a =E2=87=92 'a set"
and then define some example function "foo":

function foo :: "('a =C3=97 'a) set =E2=87=92 'a =E2=87=92 nat =E2=87=92 =
nat" where
"foo E v n =3D (if n > 0 then
               fold (=CE=BBv'.=CE=BBn. if n =3D 0 then 0
                             else foo E v' n) (n - 1) (succs E v)
              else 0)"

This function might f.ex. being seen as walking depth-first through a
graph, doing at most n steps.

The problem now arises when showing termination: A 'termination proof'
wants me to show the following goal (the concrete measurement ?R should
be unimportant to my issue, but should probably rely on n):

=E2=8B=80E v n x xa. =E2=9F=A60 < n; xa =E2=89=A0 0=E2=9F=A7 =E2=9F=B9 ((=
E, x, xa), E, v, n) =E2=88=88 ?R

As you might notice there is no relation between xa and n, though it
should be something like "xa =3D n - 1".

Is it possible somehow to put the relation in again without doing some
heavy rewriting of the function? (As this might work for one case but
not for another)

Thanks,
Ren=C3=A9



From konrad.slind at gmail.com Tue Aug 23 23:59:14 2011
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Subject: Re: [isabelle] Function Termination
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Hi Rene,

  Since there is an occurrence of fold, you need to have
a congruence rule for fold installed so the termination
extraction machinery will do the right thing. I imagine
the documentation discusses this.

Cheers,
Konrad.


On Tue, Aug 23, 2011 at 4:19 PM, Ren=C3=A9 Neumann <lists at necoro.eu> wrote:
> Hi all,
>
> I had to define a function that needed its own proof of termination.
> Thereby I noticed an issue, I'd like to show by example:
>
> Let succs :: "('a =C3=97 'a) set =E2=87=92 'a =E2=87=92 'a set"
> and then define some example function "foo":
>
> function foo :: "('a =C3=97 'a) set =E2=87=92 'a =E2=87=92 nat =E2=87=92 =
nat" where
> "foo E v n =3D (if n > 0 then
> =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 fold (=CE=BBv'.=CE=BBn. =
if n =3D 0 then 0
> =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 else foo E v' n) (n - 1) (succs E v)
> =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0else 0)"
>
> This function might f.ex. being seen as walking depth-first through a
> graph, doing at most n steps.
>
> The problem now arises when showing termination: A 'termination proof'
> wants me to show the following goal (the concrete measurement ?R should
> be unimportant to my issue, but should probably rely on n):
>
> =E2=8B=80E v n x xa. =E2=9F=A60 < n; xa =E2=89=A0 0=E2=9F=A7 =E2=9F=B9 ((=
E, x, xa), E, v, n) =E2=88=88 ?R
>
> As you might notice there is no relation between xa and n, though it
> should be something like "xa =3D n - 1".
>
> Is it possible somehow to put the relation in again without doing some
> heavy rewriting of the function? (As this might work for one case but
> not for another)
>
> Thanks,
> Ren=C3=A9
>
>



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Hi,

I'm trying to define a function 'f' such that when the input is of
type 'A' it gives true, but when it's of type 'B' it gives false:
Would I need to make A and B subtypes of some parent type, say, 'P',
and that 'f' is of type "P => bool"? I can't seem to find much
documentation on subtyping.

If I use type classes instead:

class P
classes A < P
B < P

I can't seem to define the type of 'f' in terms of neither A, B, or P.

Any help on this will be much appreciated!

Thanks

John



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-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

On 24/08/11 11:03, John Munroe wrote:
> Hi,
> 
> I'm trying to define a function 'f' such that when the input is of
> type 'A' it gives true, but when it's of type 'B' it gives false:
> Would I need to make A and B subtypes of some parent type, say, 'P',
> and that 'f' is of type "P => bool"? I can't seem to find much
> documentation on subtyping.

It sounds like you might want to use a sum type, so that the type "'p"
is "'a + 'b".  There was a discussion about this quite recently on this
very list, starting here: http://tinyurl.com/3jzx3ny

Then you could have something like "f p = \<exists> a. p = Inl a" (but I
haven't tested this).

Tim
<><
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>
> On 24/08/11 11:03, John Munroe wrote:
>> Hi,
>>
>> I'm trying to define a function 'f' such that when the input is of
>> type 'A' it gives true, but when it's of type 'B' it gives false:
>> Would I need to make A and B subtypes of some parent type, say, 'P',
>> and that 'f' is of type "P =3D> bool"? I can't seem to find much
>> documentation on subtyping.
>
> It sounds like you might want to use a sum type, so that the type "'p"
> is "'a + 'b". =A0There was a discussion about this quite recently on this
> very list, starting here: http://tinyurl.com/3jzx3ny
>
> Then you could have something like "f p =3D \<exists> a. p =3D Inl a" (bu=
t I
> haven't tested this).

Thanks for that. I'm not certain if I properly understand "f p =3D
\<exists> a. p =3D Inl a". So, for my example, is the type of f "A + B
=3D> bool"? This is what I have:

typedecl A
typedecl B

axiomatization
f :: "A + B =3D> bool"
where
ax1 : "f p =3D (EX a. p =3D Inl a)"

consts a :: "A + 'b"

lemma "f a =3D True"
apply (simp add: ax1)
??

I can't seem to find out what Inl actually does. It's defined in
Sum_Type to be "Inl =3D Abs_sum \<circ> Inl_Rep", but I can't seem to
find where Abs_sum is defined.

Thanks

John

>
> Tim
> <><
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(sorry for multiple copies)
Hi there,

I would refrain from going into the "implementation" level of the sum 
type (Abs_sum, Inl_rep) and just use pattern matching.

The type A + B represents a type that incorporates values of type A 
/and/ values of type B. Since we are in a strongly typed setting we need 
a new type for this, which is essentially an algebraic datatype 
definable by (also the internal construction is different, I think)

datatype 'a + 'b = Inl 'a | Inr 'b

here the Inl and Inr are the left and right injections. To extract 
values you can just use pattern matching.

fun is_Inl where
   is_Inl (Inl _) = True"
| is_Inl (Inr _) = False"

Hope this helps.

cheers

chris


On 08/24/2011 05:32 AM, John Munroe wrote:
>>
>> On 24/08/11 11:03, John Munroe wrote:
>>> Hi,
>>>
>>> I'm trying to define a function 'f' such that when the input is of
>>> type 'A' it gives true, but when it's of type 'B' it gives false:
>>> Would I need to make A and B subtypes of some parent type, say, 'P',
>>> and that 'f' is of type "P =>  bool"? I can't seem to find much
>>> documentation on subtyping.
>>
>> It sounds like you might want to use a sum type, so that the type "'p"
>> is "'a + 'b".  There was a discussion about this quite recently on this
>> very list, starting here: http://tinyurl.com/3jzx3ny
>>
>> Then you could have something like "f p = \<exists>  a. p = Inl a" (but I
>> haven't tested this).
>
> Thanks for that. I'm not certain if I properly understand "f p =
> \<exists>  a. p = Inl a". So, for my example, is the type of f "A + B
> =>  bool"? This is what I have:
>
> typedecl A
> typedecl B
>
> axiomatization
> f :: "A + B =>  bool"
> where
> ax1 : "f p = (EX a. p = Inl a)"
>
> consts a :: "A + 'b"
>
> lemma "f a = True"
> apply (simp add: ax1)
> ??
>
> I can't seem to find out what Inl actually does. It's defined in
> Sum_Type to be "Inl = Abs_sum \<circ>  Inl_Rep", but I can't seem to
> find where Abs_sum is defined.
>
> Thanks
>
> John
>
>>
>> Tim
>> <><
>> -----BEGIN PGP SIGNATURE-----
>> Version: GnuPG v1.4.10 (GNU/Linux)
>> Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/
>>
>> iEYEARECAAYFAk5UZHMACgkQ/cBxZIxl6rmwnACfdWxXr+HPTl/8EOuAg0Y6j1Ai
>> 378An1HvQucFMwMdkCUv4a+PtWuAXzbO
>> =Z7Ie
>> -----END PGP SIGNATURE-----
>>
>
>




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To: Christian Sternagel <c.sternagel at gmail.com>
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Cc: isabelle-users at cl.cam.ac.uk,
	"Tim \(McKenzie\) Makarios" <tjm1983 at gmail.com>
Subject: Re: [isabelle] Subtyping
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Thanks for the reply. I've just tested

datatype 'a + 'b =3D Inl 'a | Inr 'b

but it complains about

*** Outer syntax error: name declaration expected,
*** but keyword + was found

It works if I instead have

datatype ('a, 'b) sum =3D Inl 'a | Inr 'b

Should this produce the same effect?

Using your is_Inl function, how should I then test that if a constant
is of the type A, then is_Inl returns True? is_Inl takes an input of
type 'a + 'b (or ('a,'b) sum, in my case), so how do I supply a
constant of type A?

Thanks

John

On Wed, Aug 24, 2011 at 9:46 AM, Christian Sternagel
<c.sternagel at gmail.com> wrote:
> Hi there,
>
> I would refrain from going into the "implementation" level of the sum typ=
e
> (Abs_sum, Inl_rep) and just use pattern matching.
>
> The type A + B represents a type that incorporates values of type A /and/
> values of type B. Since we are in a strongly typed setting we need a new
> type for this, which is essentially an algebraic datatype definable by (a=
lso
> the internal construction is different, I think)
>
> datatype 'a + 'b =3D Inl 'a | Inr 'b
>
> here the Inl and Inr are the left and right injections. To extract values
> you can just use pattern matching.
>
> fun is_Inl where
> =A0is_Inl (Inl _) =3D True"
> | is_Inl (Inr _) =3D False"
>
> Hope this helps.
>
> cheers
>
> chris
>
> On 08/24/2011 05:32 AM, John Munroe wrote:
>>>
>>> On 24/08/11 11:03, John Munroe wrote:
>>>>
>>>> Hi,
>>>>
>>>> I'm trying to define a function 'f' such that when the input is of
>>>> type 'A' it gives true, but when it's of type 'B' it gives false:
>>>> Would I need to make A and B subtypes of some parent type, say, 'P',
>>>> and that 'f' is of type "P =3D> =A0bool"? I can't seem to find much
>>>> documentation on subtyping.
>>>
>>> It sounds like you might want to use a sum type, so that the type "'p"
>>> is "'a + 'b". =A0There was a discussion about this quite recently on th=
is
>>> very list, starting here: http://tinyurl.com/3jzx3ny
>>>
>>> Then you could have something like "f p =3D \<exists> =A0a. p =3D Inl a=
" (but I
>>> haven't tested this).
>>
>> Thanks for that. I'm not certain if I properly understand "f p =3D
>> \<exists> =A0a. p =3D Inl a". So, for my example, is the type of f "A + =
B
>> =3D> =A0bool"? This is what I have:
>>
>> typedecl A
>> typedecl B
>>
>> axiomatization
>> f :: "A + B =3D> =A0bool"
>> where
>> ax1 : "f p =3D (EX a. p =3D Inl a)"
>>
>> consts a :: "A + 'b"
>>
>> lemma "f a =3D True"
>> apply (simp add: ax1)
>> ??
>>
>> I can't seem to find out what Inl actually does. It's defined in
>> Sum_Type to be "Inl =3D Abs_sum \<circ> =A0Inl_Rep", but I can't seem to
>> find where Abs_sum is defined.
>>
>> Thanks
>>
>> John
>>
>>>
>>> Tim
>>> <><
>>> -----BEGIN PGP SIGNATURE-----
>>> Version: GnuPG v1.4.10 (GNU/Linux)
>>> Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/
>>>
>>> iEYEARECAAYFAk5UZHMACgkQ/cBxZIxl6rmwnACfdWxXr+HPTl/8EOuAg0Y6j1Ai
>>> 378An1HvQucFMwMdkCUv4a+PtWuAXzbO
>>> =3DZ7Ie
>>> -----END PGP SIGNATURE-----
>>>
>>
>>
>
>



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Subject: Re: [isabelle] Subtyping
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OK. I suspect I'm doing something wrong here, but here's what I have:

typedecl A
typedecl B
datatype ('a, 'b) sum =3D Inl 'a | Inr 'b

fun is_Inl where
  is1: "is_Inl (Inl _) =3D True"
| is2: "is_Inl (Inr _) =3D False"

axiomatization
inst_parent_type :: "(A,B) sum" and
inst_child_type :: A
where
ax1: "Inl inst_child_type =3D inst_parent_type"


lemma "is_Inl inst_parent_type"
apply (simp add: is1 ax1)

I'm guessing that the lemma tests whether the type of
'inst_parent_type', i.e. (A,B) sum, has a left injection, i.e. whether
there exists an instance of the "left" child type. Axiom ax1 asserts
that 'inst_child_type' is the left injection. So, should the lemma be
provable?

This approach is supposed to imitate subtyping, but it seems to
require that an instance of the "parent type" to be constructed in
order to do any reasoning about subtypes. If I'm right, then it's
somewhat more restrictive because such an instance must be first
assumed to exist.

Any clarification on this will be much appreciated!

Thanks

John

On Wed, Aug 24, 2011 at 3:27 PM, John Munroe <munddr at gmail.com> wrote:
> Thanks for the reply. I've just tested
>
> datatype 'a + 'b =3D Inl 'a | Inr 'b
>
> but it complains about
>
> *** Outer syntax error: name declaration expected,
> *** but keyword + was found
>
> It works if I instead have
>
> datatype ('a, 'b) sum =3D Inl 'a | Inr 'b
>
> Should this produce the same effect?
>
> Using your is_Inl function, how should I then test that if a constant
> is of the type A, then is_Inl returns True? is_Inl takes an input of
> type 'a + 'b (or ('a,'b) sum, in my case), so how do I supply a
> constant of type A?
>
> Thanks
>
> John
>
> On Wed, Aug 24, 2011 at 9:46 AM, Christian Sternagel
> <c.sternagel at gmail.com> wrote:
>> Hi there,
>>
>> I would refrain from going into the "implementation" level of the sum ty=
pe
>> (Abs_sum, Inl_rep) and just use pattern matching.
>>
>> The type A + B represents a type that incorporates values of type A /and=
/
>> values of type B. Since we are in a strongly typed setting we need a new
>> type for this, which is essentially an algebraic datatype definable by (=
also
>> the internal construction is different, I think)
>>
>> datatype 'a + 'b =3D Inl 'a | Inr 'b
>>
>> here the Inl and Inr are the left and right injections. To extract value=
s
>> you can just use pattern matching.
>>
>> fun is_Inl where
>> =A0is_Inl (Inl _) =3D True"
>> | is_Inl (Inr _) =3D False"
>>
>> Hope this helps.
>>
>> cheers
>>
>> chris
>>
>> On 08/24/2011 05:32 AM, John Munroe wrote:
>>>>
>>>> On 24/08/11 11:03, John Munroe wrote:
>>>>>
>>>>> Hi,
>>>>>
>>>>> I'm trying to define a function 'f' such that when the input is of
>>>>> type 'A' it gives true, but when it's of type 'B' it gives false:
>>>>> Would I need to make A and B subtypes of some parent type, say, 'P',
>>>>> and that 'f' is of type "P =3D> =A0bool"? I can't seem to find much
>>>>> documentation on subtyping.
>>>>
>>>> It sounds like you might want to use a sum type, so that the type "'p"
>>>> is "'a + 'b". =A0There was a discussion about this quite recently on t=
his
>>>> very list, starting here: http://tinyurl.com/3jzx3ny
>>>>
>>>> Then you could have something like "f p =3D \<exists> =A0a. p =3D Inl =
a" (but I
>>>> haven't tested this).
>>>
>>> Thanks for that. I'm not certain if I properly understand "f p =3D
>>> \<exists> =A0a. p =3D Inl a". So, for my example, is the type of f "A +=
 B
>>> =3D> =A0bool"? This is what I have:
>>>
>>> typedecl A
>>> typedecl B
>>>
>>> axiomatization
>>> f :: "A + B =3D> =A0bool"
>>> where
>>> ax1 : "f p =3D (EX a. p =3D Inl a)"
>>>
>>> consts a :: "A + 'b"
>>>
>>> lemma "f a =3D True"
>>> apply (simp add: ax1)
>>> ??
>>>
>>> I can't seem to find out what Inl actually does. It's defined in
>>> Sum_Type to be "Inl =3D Abs_sum \<circ> =A0Inl_Rep", but I can't seem t=
o
>>> find where Abs_sum is defined.
>>>
>>> Thanks
>>>
>>> John
>>>
>>>>
>>>> Tim
>>>> <><
>>>> -----BEGIN PGP SIGNATURE-----
>>>> Version: GnuPG v1.4.10 (GNU/Linux)
>>>> Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/
>>>>
>>>> iEYEARECAAYFAk5UZHMACgkQ/cBxZIxl6rmwnACfdWxXr+HPTl/8EOuAg0Y6j1Ai
>>>> 378An1HvQucFMwMdkCUv4a+PtWuAXzbO
>>>> =3DZ7Ie
>>>> -----END PGP SIGNATURE-----
>>>>
>>>
>>>
>>
>>
>



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To: Florian Haftmann <florian.haftmann at informatik.tu-muenchen.de>,
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Subject: [isabelle] Overloading in locales
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Hi,

Thanks for the pointer to overloading. Can the class declaring the
class operation or the instantiation of the class be constructed
within a locale? i.e., using the example in the tutorial:

class plus =
  fixes plus :: "'a => 'a => 'a"

instantiation nat :: plus
begin
primrec plus_nat :: "nat => nat => nat" where ...

Can all or part of the overloading happen inside a locale rather than
at the top level, e.g., can the instantiation of plus be created
inside a locale?

Also, if I were to overload a function 'foo' that returns true if the
input is of type A and false if it's of type B, then is the following
correct?

class Foo =
  fixes foo :: "'a => bool"

typedecl A
typedecl B

instantiation A :: Foo
begin
fun foo :: "A => bool" where
  "foo x = True"
instance ..
end

instantiation B :: Foo
begin
fun foo :: "B => bool" where
  "foo x = False"
instance ..
end

I believe the second instantiation duplicates the declaration of foo.

Thanks for the help in advance.

John



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-----BEGIN PGP SIGNED MESSAGE-----
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On 25/08/11 06:08, John Munroe wrote:
> OK. I suspect I'm doing something wrong here, but here's what I have:
> 
> typedecl A
> typedecl B
> datatype ('a, 'b) sum = Inl 'a | Inr 'b
> 
> fun is_Inl where
>   is1: "is_Inl (Inl _) = True"
> | is2: "is_Inl (Inr _) = False"
> 
> axiomatization
> inst_parent_type :: "(A,B) sum" and
> inst_child_type :: A
> where
> ax1: "Inl inst_child_type = inst_parent_type"
> 
> 
> lemma "is_Inl inst_parent_type"
> apply (simp add: is1 ax1)
> 
> I'm guessing that the lemma tests whether the type of
> 'inst_parent_type', i.e. (A,B) sum, has a left injection, i.e. whether
> there exists an instance of the "left" child type. Axiom ax1 asserts
> that 'inst_child_type' is the left injection. So, should the lemma be
> provable?

The lemma asserts that inst_parent_type is of the form "Inl a" for some
a.  It is provable "by (simp add: ax1 [symmetric])".

> This approach is supposed to imitate subtyping, but it seems to
> require that an instance of the "parent type" to be constructed in
> order to do any reasoning about subtypes. If I'm right, then it's
> somewhat more restrictive because such an instance must be first
> assumed to exist.

You don't need to assume anything.  Whenever you've got an element a of
type 'a, you've got a corresponding element "Inl a" of type "'a + 'b";
you don't need to assume this.

Given any element c of type "'a + 'b", there is either
- - exactly one element a of type 'a such that "c = Inl a" or
- - exactly one element b of type 'b such that "c = Inr b"
but not both.  is_Inl tells you whether or not it's the first of these
two possibilities.

> Any clarification on this will be much appreciated!
> 
> Thanks
> 
> John

I hope this has helped.

Tim
<><
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Thanks so much. It surely has been helpful!

One thing though: I can't define the datatype "'a + 'b" with

datatype 'a + 'b =3D Inl 'a | Inr 'b

It doesn't seem to like the '+' operator. Is using "datatype ('a,'b)
sum" the only way? (I see that it doesn't have to be 'sum' but any
arbitrary name seems to do.)

Also, is the approach of using sum type more appropriate than
overloading for my application? Would overloading allow the same
effect to be produced, i.e. defining a function that gives True only
if the input is of a particular type?

Thanks again.

John

On Thu, Aug 25, 2011 at 1:52 AM, Tim (McKenzie) Makarios
<tjm1983 at gmail.com> wrote:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> On 25/08/11 06:08, John Munroe wrote:
>> OK. I suspect I'm doing something wrong here, but here's what I have:
>>
>> typedecl A
>> typedecl B
>> datatype ('a, 'b) sum =3D Inl 'a | Inr 'b
>>
>> fun is_Inl where
>> =A0 is1: "is_Inl (Inl _) =3D True"
>> | is2: "is_Inl (Inr _) =3D False"
>>
>> axiomatization
>> inst_parent_type :: "(A,B) sum" and
>> inst_child_type :: A
>> where
>> ax1: "Inl inst_child_type =3D inst_parent_type"
>>
>>
>> lemma "is_Inl inst_parent_type"
>> apply (simp add: is1 ax1)
>>
>> I'm guessing that the lemma tests whether the type of
>> 'inst_parent_type', i.e. (A,B) sum, has a left injection, i.e. whether
>> there exists an instance of the "left" child type. Axiom ax1 asserts
>> that 'inst_child_type' is the left injection. So, should the lemma be
>> provable?
>
> The lemma asserts that inst_parent_type is of the form "Inl a" for some
> a. =A0It is provable "by (simp add: ax1 [symmetric])".
>
>> This approach is supposed to imitate subtyping, but it seems to
>> require that an instance of the "parent type" to be constructed in
>> order to do any reasoning about subtypes. If I'm right, then it's
>> somewhat more restrictive because such an instance must be first
>> assumed to exist.
>
> You don't need to assume anything. =A0Whenever you've got an element a of
> type 'a, you've got a corresponding element "Inl a" of type "'a + 'b";
> you don't need to assume this.
>
> Given any element c of type "'a + 'b", there is either
> - - exactly one element a of type 'a such that "c =3D Inl a" or
> - - exactly one element b of type 'b such that "c =3D Inr b"
> but not both. =A0is_Inl tells you whether or not it's the first of these
> two possibilities.
>
>> Any clarification on this will be much appreciated!
>>
>> Thanks
>>
>> John
>
> I hope this has helped.
>
> Tim
> <><
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On 25/08/11 13:07, John Munroe wrote:
> Thanks so much. It surely has been helpful!
> 
> One thing though: I can't define the datatype "'a + 'b" with
> 
> datatype 'a + 'b = Inl 'a | Inr 'b
> 
> It doesn't seem to like the '+' operator. Is using "datatype ('a,'b)
> sum" the only way? (I see that it doesn't have to be 'sum' but any
> arbitrary name seems to do.)

I don't think you need to define it.  I'm pretty sure everything I said
is true of the built-in sum type.  However, Christian's suggestion of
how it could be defined is useful to help understand how it works.  If
you use the built-in sum type, you can still define is_Inl as Christian
suggested (a way I have little experience with), or you can define it
like this:

definition is_Inl :: "'a + 'b => bool" where
  "is_Inl x == \<exists> a. x = Inl a"

> Also, is the approach of using sum type more appropriate than
> overloading for my application? Would overloading allow the same
> effect to be produced, i.e. defining a function that gives True only
> if the input is of a particular type?

I don't have much experience with overloading, so I might let someone
else answer this.  But their answer might depend on what your intended
application really is --- what do you want to use this for?

Tim
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Subject: [isabelle] Various ways of overloading
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Hi all,

I'm looking into overloading and it seems that consts/axioms already
allow overloading:

typedecl A

consts
g :: "'a => bool"
a :: A

axioms
axA: "g (x::A) = True"
axB: "g (x::B) = False"

lemma "g a"
using axA
by auto

whereas, axiomatization doesn't:

axiomatization
g :: "'a => bool"
where axA: "g (x::A) = True"

which gives a type unification error:

*** Type unification failed
***
*** Type error in application: incompatible operand type
***
*** Operator:  g::'a => bool :: 'a => bool
*** Operand:   x::A :: A

Why is there such a discrepancy? Is it one of the reasons why
consts/axioms are legacy features? The documentation seems to imply
that overloading can only be achieved using type classes, but one
could also do a similar thing in locales:

consts
g :: "'a => bool"

locale L =
assumes "g (x::A) = True" and
  "g (y::B) = False"

Any advice on this will be much appreciated!

Thanks

John



From florian.haftmann at informatik.tu-muenchen.de Thu Aug 25 20:45:13 2011
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Hi John,

> Thanks for the pointer to overloading. Can the class declaring the
> class operation or the instantiation of the class be constructed
> within a locale?=20

> Can all or part of the overloading happen inside a locale rather than
> at the top level, e.g., can the instantiation of plus be created
> inside a locale?

Class instantiations are always global, since there is no concept of
=BBlocal sort algebra=AB or such in Isabelle.

> Also, if I were to overload a function 'foo' that returns true if the
> input is of type A and false if it's of type B, then is the following
> correct?

Rule of thumb: Try out and report if you get into problems ;-)

Regards,
	Florian

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Subject: Re: [isabelle] Various ways of overloading
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> I'm looking into overloading and it seems that consts/axioms already
> allow overloading:
>=20
> typedecl A
>=20
> consts
> g :: "'a =3D> bool"
> a :: A
>=20
> axioms
> axA: "g (x::A) =3D True"
> axB: "g (x::B) =3D False"

Well, no wonder: axioms allow you to specify everything.

Overloaded definitions are also part of the logical primitives, but type
classes provide a neat integrated interface, which internally maps again
on overloaded definitions.

> axiomatization
> g :: "'a =3D> bool"
> where axA: "g (x::A) =3D True"

By giving an explicit constant specification, you specify a *new*
constant to be declared, and its type signature (with type variables
locally fixed) must match its occurences in axiom propositions.

Without the constant specification, =BBaxiomatization=AB will just state =
an
axiom.

> The documentation seems to imply
> that overloading can only be achieved using type classes

The tutorial describes typical mechanisms for the end user.  The more
primitive interfaces are covered in the Isar Reference Manual.

> but one
> could also do a similar thing in locales:
>=20
> consts
> g :: "'a =3D> bool"
>=20
> locale L =3D
> assumes "g (x::A) =3D True" and
>   "g (y::B) =3D False"

In locale assumptions, you can state everything since it is only
hypothetical.  The question is whether you can give an interpretation
actually satisfying the assumptions.

Regards,
	Florian

--=20

Home:
http://www.in.tum.de/~haftmann

PGP available:
http://home.informatik.tu-muenchen.de/haftmann/pgp/florian_haftmann_at_in=
formatik_tu_muenchen_de


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From makarius at sketis.net Fri Aug 26 12:27:01 2011
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Date: Fri, 26 Aug 2011 13:26:47 +0200 (CEST)
From: Makarius <makarius at sketis.net>
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Subject: Re: [isabelle] [isabelle-dev] Malformed YXML encoding
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On Fri, 26 Aug 2011, Steve Wong wrote:

> I'm trying to generate a proof goal from string using the following:

I am answering this on isabelle-users, because it is a perfectly normal 
user question.  (Using ML alone does not mean it is relevant for 
isabelle-dev.)


> fun generate x lthy =
>    let
>        val thy = Local_Theory.exit_global lthy
>        val ctxt = ProofContext.init_global thy
>    in

This is a bit odd.  You can use lthy, which is called "auxiliary context" 
in local theory parlance directly as your context for the subsequent 
operations.  A lthy: local_theory is a semantic subtype of ctxt: 
Proof.context, and the lthy naming convention is used whenever actual 
local theory operations follow, like the subsequent 
Specification.theorem_cmd.

>        (Specification.theorem_cmd
>             Thm.lemmaK NONE (K I)
>             (Binding.name "", []) []
>
>             (Element.Shows [(Attrib.empty_binding,
>                              [(Syntax.string_of_term ctxt @{term "F"} ^ " =
> " ^
>                                Syntax.string_of_term ctxt @{term "G"}
>
> , [])])]) x lthy)
>    end

> *** Malformed YXML encoding: multiple results
> *** At command "verify_with"

Syntax.string_of_term turns internal formal entities (terms) into external 
text representation for user-consumption.  For historic reasons the string 
type is used here, but it is in fact some kind of quasi-abstract datatype 
for marked-up document content.  In general it is not allowed either to 
split text input that is passed in or paste together text that is passed 
out of the formal environment.

Working with string interfaces for formal entities was never robust, even 
20 years ago, but now the fragility has become immediately apparent. 
When "generating" things, you should always use the regular non-text 
versions of tools and packages.  (Sometines people forget to provide them, 
but for almost everything in the regular Isabelle distribution there is 
such a proper non-text version, taking directly typ and term values etc.)

Anyway, instead of Specification.theorem it is probably easier to use 
Proof.theorem, although you need to store the result yourself in the 
"after_qed" continuation.


 	Makarius




From alfio.martini at gmail.com Fri Aug 26 12:57:06 2011
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Subject: [isabelle] Isabelle2011: Where is that locked region (stronger)
	blue in PG?
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Dear Isabelle Users,

Yesterday I downloaded Isabelle2011 to give it a try. Everything works fine
(it is quite fast, indeed) up to
Proof General behavior
(at least to my expectations). The usual locked processed region is now with
a very faint blue (not the
usual classic one), which for me is almost impossible to see. Now we have a
(kind of)
black cursor at the left of the
window showing the next part of the buffer to be processed (?).

At the beginning I thought it was something to do with PG 4.1, but when I
use Isabelle2009-2 with PG 4.1,  that
lovely stronger blue is back.

Can anybody help me to get back that good-old fashioned PG stronger blue
when using Isabelle2011?
It is so catchy, at least for me, and without it ,the whole experience
becomes very questionable :-).

Thanks anyway!

PS: I expect it to be something very simple and almost silly.

-- 
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


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On Fri, Aug 26, 2011 at 12:26 PM, Makarius <makarius at sketis.net> wrote:

> On Fri, 26 Aug 2011, Steve Wong wrote:
>
>
> Syntax.string_of_term turns internal formal entities (terms) into external
> text representation for user-consumption.  For historic reasons the string
> type is used here, but it is in fact some kind of quasi-abstract datatype
> for marked-up document content.  In general it is not allowed either to
> split text input that is passed in or paste together text that is passed out
> of the formal environment.
>
> Working with string interfaces for formal entities was never robust, even
> 20 years ago, but now the fragility has become immediately apparent. When
> "generating" things, you should always use the regular non-text versions of
> tools and packages.  (Sometines people forget to provide them, but for
> almost everything in the regular Isabelle distribution there is such a
> proper non-text version, taking directly typ and term values etc.)
>
> Anyway, instead of Specification.theorem it is probably easier to use
> Proof.theorem, although you need to store the result yourself in the
> "after_qed" continuation.
>
>
Thanks a lot for that. So, which are the tools recommended for constructing
new terms (based on some existing terms)? Are you referring to functions
like dest_Free in term.ML, i.e. destruct a term into parts and then create a
new term from ground up?

Thanks again.

Steve


>        Makarius
>
>


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Subject: Re: [isabelle] Isabelle2011: Where is that locked region (stronger)
	blue in PG?
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On Fri, Aug 26, 2011 at 4:56 AM, Alfio Martini <alfio.martini at acm.org> wrote:
> Can anybody help me to get back that good-old fashioned PG stronger blue
> when using Isabelle2011?

In emacs, try customizing the face called "proof-locked-face". If you
have a setting for this saved in your .emacs file, it should override
any defaults that the various Isabelle versions may have.

- Brian



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Hi,

What is a better way to beta-apply two terms without using betapply, which
can cause a type mismatch. For example:

consts
a :: nat
F :: "'a => nat"
ML {*
val ftrm = @{term "F"};
val atrm = @{term "a"};
val res = betapply((ftrm,atrm));
type_of res
*}

The application succeeds, but the resulting term isn't well-typed (thus
type_of fails). betapply doesn't seem to change the input type of F from a
variable to "Nat.nat". Is there a better way of beta applying such that the
input type can automatically be updated?

Thanks for the help in advance!

Steve


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Le 11/08/11 15:00, Florian Haftmann a écrit :
> Hi all,
>
> since Isabelle2011 there is the possibility to generate Scala code from
> HOL theories.  Some minor problems can be circumvented by a suitable
> patch and will disappear in the next release.
>
> Apart from that, is there any further feedback (positive or negative) on
> code generation for Scala?  I would like to announce it on the Scala
> mailing list after the next release, but for this I need some evidence
> that it is really working.
>
> Thanks for any feedback,
> 	Florian


	Dear Florian,


as I already mentioned to you, we will use Isabelle2011 and Scala export 
for teaching on the second semester here at Rennes 1 University at 
master level. We already experimented a bit with the scala export in 
order to integrate formally developed components (in Isabelle) into Java 
software. For the moment everything is OK... but it is true that we will 
use only simple things: integers, strings, lists, etc... no exotic 
Isabelle theory :-)

Best regards,

Thomas
-- 
Thomas Genet
ISTIC/IRISA
Campus de Beaulieu, 35042 Rennes cedex, France
Tél: +33 (0) 2 99 84 73 44   E-mail: genet at irisa.fr
http://www.irisa.fr/celtique/genet



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Subject: Re: [isabelle] Isabelle2011: Where is that locked region (stronger)
	blue in PG?
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Thanks Brian. I found it: "Cornflower Blue". Now I can rest in piece.

Cheers

On Fri, Aug 26, 2011 at 10:11 AM, Brian Huffman <brianh at cs.pdx.edu> wrote:

> On Fri, Aug 26, 2011 at 4:56 AM, Alfio Martini <alfio.martini at acm.org>
> wrote:
> > Can anybody help me to get back that good-old fashioned PG stronger blue
> > when using Isabelle2011?
>
> In emacs, try customizing the face called "proof-locked-face". If you
> have a setting for this saved in your .emacs file, it should override
> any defaults that the various Isabelle versions may have.
>
> - Brian
>



-- 
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


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Hi,

Does anyone know why there's a type error in

ML {*
val trm = @{term "(f::'a=>nat) (a::nat)"};
*}

but not in

consts
f:: "'a => nat"
a :: nat

ML {* @{term "f a" *}

Why are the two cases treated differently?

Thanks

John


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Because 'a is not equal to nat and in the first case you are asking for them
to be the same.

In the second case, f is first specified to be polymorphic then the use, in
"f a", is instantiated appropriately by type inference, that is, you really
have "(f::nat => nat) a", which is allowed because "nat => nat" refines "'a
=> nat".

On Aug 29, 2011 7:42 AM, "John Munroe" <munddr at gmail.com> wrote:
>
> Hi,
>
> Does anyone know why there's a type error in
>
> ML {*
> val trm = @{term "(f::'a=>nat) (a::nat)"};
> *}
>
> but not in
>
> consts
> f:: "'a => nat"
> a :: nat
>
> ML {* @{term "f a" *}
>
> Why are the two cases treated differently?
>
> Thanks
>
> John


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			   VSTTE 2012
Verified Software: Theories, Tools and Experiments
	 	      January 28-29, 2012
Philadelphia, USA (co-located with POPL and VMCAI)
https://sites.google.com/site/vstte2012/

(*** NEW SUBMISSION DEADLINE:  September 10, 2011 ***)

The Fourth International Conference on Verified Software: Theories,
Tools, and Experiments  will take place on January 28-29, 2012.  The
focus of the conference is the development of systematic methods for
specifying, building, and verifying software.  The goal of
this conference is to advance the state of the art through the
interaction of theory development, tool evolution, and experimental
validation.  Historically,  the conference came out of the Verified
Software Initiative (VSI), a cooperative, international initiative
directed at the scientific challenges of large-scale software
verification.  An informal verification competition will be held in paralle=
l=20
to the conference. More information will be available from the=20
website.

Topics of interest include:

* Specification and verification techniques
* Tool support for specification languages
* Tool for various design methodologies
* Tool integration and plug-ins
* Automation in formal verification
* Tool comparisons and benchmark repositories
* Combination of tools and techniques
(e.g. formal vs. semiformal, software specification
vs. engineering techniques)
* Customizing tools for particular applications
* Challenge problems
* Refinement methodologies
* Requirements modeling
* Specification languages
* Specification/verification case-studies
* Software design methods
* Program logic

SUBMISSIONS

Submitted research papers and system descriptions must be original and
not submitted for publication elsewhere.  Research paper submissions
are limited to 15 proceedings pages in LNCS format and must include a
cogent and self-contained description of the ideas, methods and
results, together with a comparison to existing work. System
descriptions are also limited to 15 proceedings pages in LNCS
format. Authors are encouraged to submit work in progress, particularly if =
the
work involves collaboration, theory unification, and tool integration.
Papers can be submitted at

https://www.easychair.org/conferences/?conf=3Dvstte2012

Submissions that arrive late, are not in the proper format, or are too
long will not be considered.  The proceedings of VSTTE 2012 will be
published by Springer-Verlag in the LNCS series.  Authors of accepted
papers will be requested to sign a form transferring copyright of
their contribution to Springer-Verlag.


IMPORTANT DATES

September 10, 2011:     Conference Paper Submission Deadline
October 20, 2011:    Notification of acceptance
November 15, 2011:   Final conference paper versions due
January 28-29, 2012: Main conference


KEYNOTE SPEAKERS

Rupak Majumdar, Max Planck Institute for Software Systems
Wolfgang Paul,  Saarland University


TUTORIALS

Francesco Logozzo, Microsoft Research
Rustan Leino, Microsoft Research


CONFERENCE CHAIR

Ernie Cohen, European Microsoft Innovation Center=20


PROGRAM CHAIRS

Rajeev Joshi,  NASA Jet Propulsion Laboratory
Peter M=FCller, ETH Zurich
Andreas Podelski, University of Freiburg


PROGRAM COMMITTEE

Clark Barrett, New York University
Lars Birkedal, IT University of Copenhagen
Patrick Cousot, Ecole normale Sup=E9rieure, Paris and New York University
Leonardo De Moura, Microsoft Research
Jean-Christophe Filliatre, CNRS Universit=E9 Paris Sud
John Hatcliff, Kansas State University
Bart Jacobs, Katholieke Universiteit Leuven=20
Ranjit Jhala, University of California, San Diego
Rajeev Joshi,  NASA JPL
Gerwin Klein, NICTA=20
Viktor Kuncak, EPF Lausanne=20
Gary T. Leavens, University of Central Florida=20
Rustan Leino, Microsoft Research
Panagiotis Manolios, Northeastern University
Peter M=FCller, ETH Zurich
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It should be said that types explicitly provided in type annotations in term
quotations are not unified by the type checker, they are simply left as they
are, whereas implicit types in term quotations are unified.

on 29/8/11 8:07 AM, Ramana Kumar <rk436 at cam.ac.uk> wrote:

> Because 'a is not equal to nat and in the first case you are asking for
them
> to be the same.
>
> In the second case, f is first specified to be polymorphic then the use,
in
> "f a", is instantiated appropriately by type inference, that is, you
really
> have "(f::nat =3D> nat) a", which is allowed because "nat =3D> nat" refines
"'a
> =3D> nat".
>
> On Aug 29, 2011 7:42 AM, "John Munroe" <munddr at gmail.com> wrote:
>>
>> Hi,
>>
>> Does anyone know why there's a type error in
>>
>> ML {*
>> val trm =3D @{term "(f::'a=3D>nat) (a::nat)"};
>> *}
>>
>> but not in
>>
>> consts
>> f:: "'a =3D> nat"
>> a :: nat
>>
>> ML {* @{term "f a" *}
>>
>> Why are the two cases treated differently?
>>
>> Thanks
>>
>> John
>
>
>



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Subject: Re: [isabelle] Type unification failed
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One more aspect: the language of type constraints admits nameless dummies 
that *are* unified.  For example

   term "(f :: _ => nat) (a::nat)"

Sort constraints may be also added here:

   term "(f :: _::plus => nat) (a::nat)"

The ML interfaces of the "term check" phase also admits named unification 
parameters (via Type_Infer.param), but this is an advanced concept without 
notation for end-users (as in ML/Haskell).


 	Makarius


On Mon, 29 Aug 2011, "Mark" wrote:

> It should be said that types explicitly provided in type annotations in term
> quotations are not unified by the type checker, they are simply left as they
> are, whereas implicit types in term quotations are unified.
>
> on 29/8/11 8:07 AM, Ramana Kumar <rk436 at cam.ac.uk> wrote:
>
>> Because 'a is not equal to nat and in the first case you are asking for
> them
>> to be the same.
>>
>> In the second case, f is first specified to be polymorphic then the use,
> in
>> "f a", is instantiated appropriately by type inference, that is, you
> really
>> have "(f::nat => nat) a", which is allowed because "nat => nat" refines
> "'a
>> => nat".
>>
>> On Aug 29, 2011 7:42 AM, "John Munroe" <munddr at gmail.com> wrote:
>>>
>>> Hi,
>>>
>>> Does anyone know why there's a type error in
>>>
>>> ML {*
>>> val trm = @{term "(f::'a=>nat) (a::nat)"};
>>> *}
>>>
>>> but not in
>>>
>>> consts
>>> f:: "'a => nat"
>>> a :: nat
>>>
>>> ML {* @{term "f a" *}
>>>
>>> Why are the two cases treated differently?
>>>
>>> Thanks
>>>
>>> John
>>
>>
>>
>



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Subject: Re: [isabelle] Better way to beta apply two terms
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On Fri, 26 Aug 2011, Steve Wong wrote:

> What is a better way to beta-apply two terms without using betapply, which
> can cause a type mismatch. For example:
>
> consts
> a :: nat
> F :: "'a => nat"
> ML {*
> val ftrm = @{term "F"};
> val atrm = @{term "a"};
> val res = betapply((ftrm,atrm));
> type_of res
> *}
>
> The application succeeds, but the resulting term isn't well-typed (thus 
> type_of fails). betapply doesn't seem to change the input type of F from 
> a variable to "Nat.nat". Is there a better way of beta applying such 
> that the input type can automatically be updated?

Term.betapply is not used that often, although there is nothing wrong with 
it.  Other term constructions (even plain Abs and $) are used more 
frequently.

The experiment above has failed for other reasons: the example terms are 
internalized independently, i.e. the system did not know they are 
correlated.  Normally you use something like Syntax.read_terms, 
Syntax.check_terms or even Specification.read_specification / 
check_specification for simultaneous processing of formal input in an 
shared syntactic context.

An alternative is to compose untyped preterms (using dummyT) in some 
places and then let Syntax.check_term(s) work out the details.  (It also 
requires some care because many basic term operations assume fully typed 
terms.)

Another note concerning readability of ML sources: "ftrm" and "atrm" are 
rather long and unwieldy names for plain formal entities that could be 
just called "f" and "a", or "t" and "u".


 	Makarius



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On Fri, 26 Aug 2011, Steve Wong wrote:

> On Fri, Aug 26, 2011 at 12:26 PM, Makarius <makarius at sketis.net> wrote:
>
>> On Fri, 26 Aug 2011, Steve Wong wrote:
>>
>>
>> Working with string interfaces for formal entities was never robust, even
>> 20 years ago, but now the fragility has become immediately apparent. When
>> "generating" things, you should always use the regular non-text versions of
>> tools and packages.

> So, which are the tools recommended for constructing new terms (based on 
> some existing terms)? Are you referring to functions like dest_Free in 
> term.ML, i.e. destruct a term into parts and then create a new term from 
> ground up?

Either using directly the datype constructors of typ/term (e.g. in pattern 
matching) or some derived functions from src/Pure/term.ML, 
src/Pure/logic.ML, src/HOL/Tools/hologic.ML.

The "tools and packages" that I mentioned above are more complex things 
like Function_Fun.add_fun (the regular ML version) instead of the 
add_fun_cmd as string version for end-users.


 	Makarius



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Subject: [isabelle] Gaussian Elimination
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Thank you Tobias for the theory file about the Gauss-Seidel algorithm.
I'll try to build on this result in my project. My aim is to have an
automatically transformed PL(1) formula from the algorithm, although I
do not know when and how the goal can be reached.

Regards,
Jens Doll




From Thomas.Genet at irisa.fr Mon Aug 29 16:01:03 2011
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Subject: [isabelle] Open Post-doc position at INRIA Rennes, France
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Dear all Isabelle users,

here is a Postdoc position available at INRIA Rennes, France

--------------------------------------------------------------------------------------------------

A postdoc position for 1 year is available at INRIA Rennes - Bretagne 
Atlantique.
The research will take place in the Celtique team 
(http://www.irisa.fr/celtique/).
The task will consist in developing certificates of software which makes 
it possible
for a user to check a downloaded code, in an automatic manner and extremely
quickly.  A program producer can hence verify the security of his 
program with a
large amount of computation resource before distributing it with a 
certificate that
helps the consumer to replay the verification program but with very far 
fewer resources.

Candidates should have a background in program verification. Additional
knowledge in one or more of the following topics will be appreciated:
  - static analysis,
  - theory of abstract interpretation,
  - language-based security,
  - deductive verification,
  - decision procedures,
  - probabilistic verification
  Knowledge of the French language is not required.

Start of contract: ideally, the candidate will start working in 
september or october, but
we can accomodate a later date.
Salaries: usual INRIA postdoc salary (2,357.30 euros gross/month, i.e. 
1923,26 euros net/month).
Social security benefits:
   - Entitled to unemployment benefit at the end of the contract;
   - Affiliated to the French social security system.

Candidates should submit to david.pichardie[at]irisa.fr, 
thomas.genet[at]irisa.fr and thomas.jensen[at]irisa.fr
   - A CV including a list of publications
   - A one-page research statement
   - Referee reports for the PhD thesis if any
   - Contact information for two references (including the PhD supervisor)


-- 
Thomas Genet
ISTIC/IRISA
Campus de Beaulieu, 35042 Rennes cedex, France
Tél: +33 (0) 2 99 84 73 44   E-mail: genet at irisa.fr
http://www.irisa.fr/celtique/genet




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Subject: [isabelle] Unify.matchers and term representation
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Hello,

I see that the instantiations Unify.matchers finds may not necessarily
have the simplest internal representation. For example:

ML {*
  val trm = @{term "(bar::nat set) = bar"};
  val pat = @{cpat "(?foo::(?'a => ?'b) => ?'c) (bar::(?'a => ?'b))"}
|> term_of;
  val mtchsq = Unify.matchers @{theory} [(pat,trm)];
  val mtchs = Seq.list_of mtchsq;
*}

The first match gives this instantiation for ?foo:

[?foo::(nat => bool) => ?'c := %a::nat => bool. a = a]

Now, if we look at the internal representation of the term, it actually is:

   Abs ("", "Nat.nat => HOL.bool",
     Const ("HOL.eq", "(Nat.nat => HOL.bool) => (Nat.nat => HOL.bool)
=> HOL.bool") $
       Abs ("", "Nat.nat", Bound 1 $ Bound 0) $ Abs ("", "Nat.nat",
Bound 1 $ Bound 0))

It is unnecessarily large. A simpler representation would be:

   Abs ("", "Nat.nat  => HOL.bool",
     Const ("HOL.eq", "(Nat.nat => HOL.bool) => (Nat.nat => HOL.bool)
=> HOL.bool") $ Bound 0 $
       Bound 0)

My question is: Is there a way to reduce the internal representation
of a term from one that contains "reducible" lambda expressions (like
in the first) to one that is leaner (like in the second) in general?
Or, is there a simple way to make the matcher algorithm spit out
leaner internal representations?

Thank you for the help in advance.

John



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The unification algorithm operates on eta-expanded terms. Is there any =
compelling reason why you need them to be eta-contracted?
Larry Paulson


On 29 Aug 2011, at 22:06, John Munroe wrote:

> Hello,
>=20
> I see that the instantiations Unify.matchers finds may not necessarily
> have the simplest internal representation. For example:
>=20
> ML {*
>  val trm =3D @{term "(bar::nat set) =3D bar"};
>  val pat =3D @{cpat "(?foo::(?'a =3D> ?'b) =3D> ?'c) (bar::(?'a =3D> =
?'b))"}
> |> term_of;
>  val mtchsq =3D Unify.matchers @{theory} [(pat,trm)];
>  val mtchs =3D Seq.list_of mtchsq;
> *}
>=20
> The first match gives this instantiation for ?foo:
>=20
> [?foo::(nat =3D> bool) =3D> ?'c :=3D %a::nat =3D> bool. a =3D a]
>=20
> Now, if we look at the internal representation of the term, it =
actually is:
>=20
>   Abs ("", "Nat.nat =3D> HOL.bool",
>     Const ("HOL.eq", "(Nat.nat =3D> HOL.bool) =3D> (Nat.nat =3D> =
HOL.bool)
> =3D> HOL.bool") $
>       Abs ("", "Nat.nat", Bound 1 $ Bound 0) $ Abs ("", "Nat.nat",
> Bound 1 $ Bound 0))
>=20
> It is unnecessarily large. A simpler representation would be:
>=20
>   Abs ("", "Nat.nat  =3D> HOL.bool",
>     Const ("HOL.eq", "(Nat.nat =3D> HOL.bool) =3D> (Nat.nat =3D> =
HOL.bool)
> =3D> HOL.bool") $ Bound 0 $
>       Bound 0)
>=20
> My question is: Is there a way to reduce the internal representation
> of a term from one that contains "reducible" lambda expressions (like
> in the first) to one that is leaner (like in the second) in general?
> Or, is there a simple way to make the matcher algorithm spit out
> leaner internal representations?
>=20
> Thank you for the help in advance.
>=20
> John
>=20




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Subject: [isabelle] list_size_pointwise
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Dear all,

when looking at the thm in Libary List

lemma list_size_pointwise: assumes "!! x. x : set xs =3D=3D> f x < g x"
  shows "list_size f xs <=3D list_size g xs"

I was wondering why the strict inequality is used in the assumption. =
Indeed,
the lemma also holds in its stronger version where only <=3D is used in =
the assumption.

lemma list_size_pointwise': assumes "\<And> x. x \<in> set xs =
\<Longrightarrow> f x \<le> g x"
  shows "list_size f xs \<le> list_size g xs"
  using assms=20
proof (induct xs)
  case Nil thus ?case by auto
next
  case (Cons x xs)
  have "list_size f xs \<le> list_size g xs"=20
    by (rule Cons(1), insert Cons(2), auto)
  with Cons(2)[of x]
  show ?case by auto
qed

So, one might consider to replace the current lemma list_size_pointwise
by the stronger version list_size_pointwise'.

Cheers,
Ren=E9
--=20
Ren=E9 Thiemann                    mailto:rene.thiemann at uibk.ac.at
Computational Logic Group        =
http://cl-informatik.uibk.ac.at/~thiemann/
Institute of Computer Science    phone: +43 512 507-6434
University of Innsbruck




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I agree. The current version is unnecessarily week.
Larry Paulson


On 30 Aug 2011, at 10:44, Ren=E9 Thiemann wrote:

> Dear all,
>=20
> when looking at the thm in Libary List
>=20
> lemma list_size_pointwise: assumes "!! x. x : set xs =3D=3D> f x < g =
x"
>  shows "list_size f xs <=3D list_size g xs"
>=20
> I was wondering why the strict inequality is used in the assumption. =
Indeed,
> the lemma also holds in its stronger version where only <=3D is used =
in the assumption.
>=20
> lemma list_size_pointwise': assumes "\<And> x. x \<in> set xs =
\<Longrightarrow> f x \<le> g x"
>  shows "list_size f xs \<le> list_size g xs"
>  using assms=20
> proof (induct xs)
>  case Nil thus ?case by auto
> next
>  case (Cons x xs)
>  have "list_size f xs \<le> list_size g xs"=20
>    by (rule Cons(1), insert Cons(2), auto)
>  with Cons(2)[of x]
>  show ?case by auto
> qed
>=20
> So, one might consider to replace the current lemma =
list_size_pointwise
> by the stronger version list_size_pointwise'.
>=20
> Cheers,
> Ren=E9
> --=20
> Ren=E9 Thiemann                    mailto:rene.thiemann at uibk.ac.at
> Computational Logic Group        =
http://cl-informatik.uibk.ac.at/~thiemann/
> Institute of Computer Science    phone: +43 512 507-6434
> University of Innsbruck
>=20
>=20




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Subject: Re: [isabelle] Unify.matchers and term representation
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On Tue, 30 Aug 2011, Lawrence Paulson wrote:

> The unification algorithm operates on eta-expanded terms. Is there any 
> compelling reason why you need them to be eta-contracted?

Larry is right that according to the natural order of things it is better 
to leave things as they are produced, and work conceptually with arbitrary 
representatives of the alpha/beta/eta equivalence classes.

In some boundary cases this might fails, because certain tools do not 
observe this equivalence.  Here you can contract or expand manually to 
achieve a certain standard form, e.g. via Envir.eta_contract, 
Envir.beta_eta_contract, Patter.eta_long.  The Thm module also provides 
some variants for actual theorems.


 	Makarius



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Subject: [isabelle] Struggling with type unification
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Dear Isabelle Users,

In the following simple script, the Isar proof only works if I fix the types
of
both subtrees,  like I did. If I let their types unspecified (like in: fix
x0 and lt0 and rt0) it
gives a type unification error. From the proof state, one can see that it
happens
because the two induction hypothesis are assigned different type variables.

Could anyone elaborate a bit more on that for me?

Many Thanks!
---------------------------------------------------------------------------------------------------------------
theory newbies_tree_demo

imports Main

begin
 datatype 'a Tree = Leaf | Br  'a "'a Tree" "'a Tree"

 primrec reflect::"'a Tree => 'a Tree"
   where
     ref01:"reflect Leaf = Leaf" |
     rev02:"reflect (Br label lt rt) = Br label (reflect rt) (reflect lt)"

theorem th_refl01isA: "reflect (reflect t) = t"
  proof (induct t)
     show  "reflect (reflect Leaf) = Leaf" by simp
  next
     fix x0 and lt0::"'a Tree" and rt0::"'a Tree"
     assume IH1: "reflect (reflect lt0) = lt0"
     assume IH2: "reflect (reflect rt0) = rt0"
     show "reflect (reflect (Br x0 lt0 rt0)) = Br x0 lt0 rt0" by (simp
add:IH1 IH2)
  qed


-- 
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


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Subject: Re: [isabelle] Struggling with type unification
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The problem is that the function reflect is polymorphic, and when you =
simply state the induction hypotheses as you do, there is no reason to =
assume that the variables have the same types. To eliminate this =
difficulty, the Isar language includes abbreviations letting you refer =
to the various inductive cases. Then types are assigned correctly. I =
suggest writing your proof as follows:

theorem th_refl01isA: "reflect (reflect t) =3D t"
 proof (induct t)
   case Leaf
    show ?case by simp
 next
   case (Br x0 lt0 rt0)
     thus ?case by simp
 qed

Larry Paulson


On 30 Aug 2011, at 15:07, Alfio Martini wrote:

> Dear Isabelle Users,
>=20
> In the following simple script, the Isar proof only works if I fix the =
types
> of
> both subtrees,  like I did. If I let their types unspecified (like in: =
fix
> x0 and lt0 and rt0) it
> gives a type unification error. =46rom the proof state, one can see =
that it
> happens
> because the two induction hypothesis are assigned different type =
variables.
>=20
> Could anyone elaborate a bit more on that for me?
>=20
> Many Thanks!
> =
--------------------------------------------------------------------------=
-------------------------------------
> theory newbies_tree_demo
>=20
> imports Main
>=20
> begin
> datatype 'a Tree =3D Leaf | Br  'a "'a Tree" "'a Tree"
>=20
> primrec reflect::"'a Tree =3D> 'a Tree"
>   where
>     ref01:"reflect Leaf =3D Leaf" |
>     rev02:"reflect (Br label lt rt) =3D Br label (reflect rt) (reflect =
lt)"
>=20
> theorem th_refl01isA: "reflect (reflect t) =3D t"
>  proof (induct t)
>     show  "reflect (reflect Leaf) =3D Leaf" by simp
>  next
>     fix x0 and lt0::"'a Tree" and rt0::"'a Tree"
>     assume IH1: "reflect (reflect lt0) =3D lt0"
>     assume IH2: "reflect (reflect rt0) =3D rt0"
>     show "reflect (reflect (Br x0 lt0 rt0)) =3D Br x0 lt0 rt0" by =
(simp
> add:IH1 IH2)
>  qed
>=20
>=20
> --=20
> Alfio Ricardo Martini
> PhD in Computer Science (TU Berlin)
> Associate Professor at Faculty of Informatics (PUCRS)
> Porto Alegre - RS - Brasil




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To: Lawrence Paulson <lp15 at cam.ac.uk>
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Dear Lawrence,

Many thanks for the quick and  helpful reply!

Best!

On Tue, Aug 30, 2011 at 11:17 AM, Lawrence Paulson <lp15 at cam.ac.uk> wrote:

> The problem is that the function reflect is polymorphic, and when you
> simply state the induction hypotheses as you do, there is no reason to
> assume that the variables have the same types. To eliminate this difficulty,
> the Isar language includes abbreviations letting you refer to the various
> inductive cases. Then types are assigned correctly. I suggest writing your
> proof as follows:
>
> theorem th_refl01isA: "reflect (reflect t) = t"
>  proof (induct t)
>    case Leaf
>    show ?case by simp
>  next
>   case (Br x0 lt0 rt0)
>     thus ?case by simp
>  qed
>
> Larry Paulson
>
>
> On 30 Aug 2011, at 15:07, Alfio Martini wrote:
>
> > Dear Isabelle Users,
> >
> > In the following simple script, the Isar proof only works if I fix the
> types
> > of
> > both subtrees,  like I did. If I let their types unspecified (like in:
> fix
> > x0 and lt0 and rt0) it
> > gives a type unification error. From the proof state, one can see that it
> > happens
> > because the two induction hypothesis are assigned different type
> variables.
> >
> > Could anyone elaborate a bit more on that for me?
> >
> > Many Thanks!
> >
> ---------------------------------------------------------------------------------------------------------------
> > theory newbies_tree_demo
> >
> > imports Main
> >
> > begin
> > datatype 'a Tree = Leaf | Br  'a "'a Tree" "'a Tree"
> >
> > primrec reflect::"'a Tree => 'a Tree"
> >   where
> >     ref01:"reflect Leaf = Leaf" |
> >     rev02:"reflect (Br label lt rt) = Br label (reflect rt) (reflect lt)"
> >
> > theorem th_refl01isA: "reflect (reflect t) = t"
> >  proof (induct t)
> >     show  "reflect (reflect Leaf) = Leaf" by simp
> >  next
> >     fix x0 and lt0::"'a Tree" and rt0::"'a Tree"
> >     assume IH1: "reflect (reflect lt0) = lt0"
> >     assume IH2: "reflect (reflect rt0) = rt0"
> >     show "reflect (reflect (Br x0 lt0 rt0)) = Br x0 lt0 rt0" by (simp
> > add:IH1 IH2)
> >  qed
> >
> >
> > --
> > Alfio Ricardo Martini
> > PhD in Computer Science (TU Berlin)
> > Associate Professor at Faculty of Informatics (PUCRS)
> > Porto Alegre - RS - Brasil
>
>


-- 
Alfio Ricardo Martini
PhD in Computer Science (TU Berlin)
Associate Professor at Faculty of Informatics (PUCRS)
Porto Alegre - RS - Brasil


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Is anyone already changing this to the stronger version right now?

Otherwise I would tackle this change this evening, in two hours from now.

Lukas


On 08/30/2011 11:52 AM, Lawrence Paulson wrote:
> I agree. The current version is unnecessarily week.
> Larry Paulson
>
>
> On 30 Aug 2011, at 10:44, Ren=E9 Thiemann wrote:
>
>> Dear all,
>>
>> when looking at the thm in Libary List
>>
>> lemma list_size_pointwise: assumes "!! x. x : set xs =3D=3D>  f x<  g =
x"
>>   shows "list_size f xs<=3D list_size g xs"
>>
>> I was wondering why the strict inequality is used in the assumption. I=
ndeed,
>> the lemma also holds in its stronger version where only<=3D is used in=
 the assumption.
>>
>> lemma list_size_pointwise': assumes "\<And>  x. x \<in>  set xs \<Long=
rightarrow>  f x \<le>  g x"
>>   shows "list_size f xs \<le>  list_size g xs"
>>   using assms
>> proof (induct xs)
>>   case Nil thus ?case by auto
>> next
>>   case (Cons x xs)
>>   have "list_size f xs \<le>  list_size g xs"
>>     by (rule Cons(1), insert Cons(2), auto)
>>   with Cons(2)[of x]
>>   show ?case by auto
>> qed
>>
>> So, one might consider to replace the current lemma list_size_pointwis=
e
>> by the stronger version list_size_pointwise'.
>>
>> Cheers,
>> Ren=E9
>> --=20
>> Ren=E9 Thiemann                    mailto:rene.thiemann at uibk.ac.at
>> Computational Logic Group        http://cl-informatik.uibk.ac.at/~thie=
mann/
>> Institute of Computer Science    phone: +43 512 507-6434
>> University of Innsbruck
>>
>>
>




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Subject: Re: [isabelle] Unify.matchers and term representation
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On Tue, Aug 30, 2011 at 5:12 AM, Makarius <makarius at sketis.net> wrote:
>
> Larry is right that according to the natural order of things it is better to
> leave things as they are produced, and work conceptually with arbitrary
> representatives of the alpha/beta/eta equivalence classes.
>
> In some boundary cases this might fails, because certain tools do not
> observe this equivalence.

I want to point out that the *simplifier* is one of those "certain
tools" whose behavior depends on whether or not terms are
eta-expanded. (This includes not only the "simp" method, but also
"unfold", "auto", "fastsimp", etc.)

Many simplification rules, such as "id x = x" or "(f o g) x = f (g
x)", are intended to unfold a definition of a constant *only* when it
is applied to an argument. Eta expansion can cause the simplifier to
apply these rules in unexpected situations. (When users have the "eta
contract" pretty printing option enabled, as is the default,
replacements like "f o g" -> "%x. f (g x)" can appear to happen at
random.)

Eta-expansion can cause some confusion with congruence rules in the
simplifier, since a congruence rule only applies when the given
constant is applied to a sufficient number of arguments.

https://lists.cam.ac.uk/pipermail/cl-isabelle-users/2010-May/msg00032.html
https://lists.cam.ac.uk/pipermail/cl-isabelle-users/2010-May/msg00046.html

Eta expansion also interferes with the feature of the "rule" tactic
where it tries to preserve bound variable names:

https://mailmanbroy.informatik.tu-muenchen.de/pipermail/isabelle-dev/2011-August/001803.html

With type "'a set" being an abbreviation for "'a => bool",
eta-expansion can happen to set expressions, which causes other
problems. For example, "A \<inter> B" might get expanded to "%a. (A
\<inter> B) a". Because of this, the otherwise-entirely-reasonable
simp rule "inf f g x = inf (f x) (g x)" would cause  "%a. (A \<inter>
B) a" (which pretty-prints as "A \<inter> B") to simplify to "%x. A x
& B x", violating the set/predicate discipline and messing up a lot of
proofs.

https://mailmanbroy.informatik.tu-muenchen.de/pipermail/isabelle-dev/2011-August/001687.html
https://mailmanbroy.informatik.tu-muenchen.de/pipermail/isabelle-dev/2011-August/001733.html

> On Tue, 30 Aug 2011, Lawrence Paulson wrote:
>
>> The unification algorithm operates on eta-expanded terms. Is there any
>> compelling reason why you need them to be eta-contracted?

For reasons including (but not limited to) the ones listed above, I
would greatly prefer to have a unification algorithm that preserves
terms as much as possible, performing NO unnecessary eta-expansions OR
eta-contractions.

(Implementation idea: When eta-expanding, mark all of the
newly-introduced bound variables in some way; then do an
eta-contraction at the end, contracting *only* newly-introduced
variables.)

A unification algorithm with this property would allow us to simplify
Isabelle's pretty printer quite a bit: The ridiculous "eta contract"
pretty-printing option would no longer be needed, and we could also
get rid of a lot of ML code used for preventing or reversing
eta-contraction with binders (e.g. the print translations for "split"
in Product_Type.thy).

- Brian



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changesets f3635643a376 and fd520fa2fb09 are the result of this thread.

Lukas


On 08/30/2011 04:57 PM, Lukas Bulwahn wrote:
> Is anyone already changing this to the stronger version right now?
>
> Otherwise I would tackle this change this evening, in two hours from no=
w.
>
> Lukas
>
>
> On 08/30/2011 11:52 AM, Lawrence Paulson wrote:
>> I agree. The current version is unnecessarily week.
>> Larry Paulson
>>
>>
>> On 30 Aug 2011, at 10:44, Ren=E9 Thiemann wrote:
>>
>>> Dear all,
>>>
>>> when looking at the thm in Libary List
>>>
>>> lemma list_size_pointwise: assumes "!! x. x : set xs =3D=3D>  f x<  g=
 x"
>>>   shows "list_size f xs<=3D list_size g xs"
>>>
>>> I was wondering why the strict inequality is used in the assumption.=20
>>> Indeed,
>>> the lemma also holds in its stronger version where only<=3D is used i=
n=20
>>> the assumption.
>>>
>>> lemma list_size_pointwise': assumes "\<And>  x. x \<in>  set xs=20
>>> \<Longrightarrow>  f x \<le>  g x"
>>>   shows "list_size f xs \<le>  list_size g xs"
>>>   using assms
>>> proof (induct xs)
>>>   case Nil thus ?case by auto
>>> next
>>>   case (Cons x xs)
>>>   have "list_size f xs \<le>  list_size g xs"
>>>     by (rule Cons(1), insert Cons(2), auto)
>>>   with Cons(2)[of x]
>>>   show ?case by auto
>>> qed
>>>
>>> So, one might consider to replace the current lemma list_size_pointwi=
se
>>> by the stronger version list_size_pointwise'.
>>>
>>> Cheers,
>>> Ren=E9
>>> --=20
>>> Ren=E9 Thiemann                    mailto:rene.thiemann at uibk.ac.at
>>> Computational Logic Group       =20
>>> http://cl-informatik.uibk.ac.at/~thiemann/
>>> Institute of Computer Science    phone: +43 512 507-6434
>>> University of Innsbruck
>>>
>>>
>>
>
>




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Hi Viorel,

>>> There are some aspects of the lattice theories which creates problems=

>>> for my developments. The fact that inf and sup constants are part
>>> of the lattice itself, rather than being defined just as classes with=

>>> only inf and sup constants. All other constants (*, +, ...) are defin=
ed
>>> in separate classes and their reuse is much easier.
>>> Do you know if the same technique is going to be used for inf and sup=
?

> Ultimately the structure is a (semi-) lattice, but the axioms are
> different.
> Imagine an algebraic structure with some operations *, left_imp which
> satisfies
> some properties and in which inf can be defined
>=20
> class left_inf =3D inf + times + left_imp + order +
>   assumes some axioms for times and left_imp
>   and inf_l_def: "(inf a b) =3D (left_imp a b) * a"
>   and definition of order
>=20
> begin
>=20
> in this setting the fact that inf is a semi-lattice operation can be
> proved from the axioms of times and left_imp.
>=20
> in the context of left_inf I would state
>=20
> subclass semilattice_inf
>=20
> If I assume that left_inf is a semilattice_inf, then I would need to
> prove this fact for every instantiation of it.

> One more comment. Now in the Isabelle/HOL library the operations
> Inf and Sup of complete lattices are defined in their own classes.
> If the same is done for inf and sup, their use via semilattice will
> be the same, but it would be easier to reuse them in contexts
> where one does not want to assume the semilattice structure.=20

the answer to your issue has many facets.

Historically, syntactic classes where necessary since the class +
operations & instantiation infrastructure has not yet emerged.  With the
class package my first thought was to avoid syntactic classes entirely,
since they allow to write down things for which one might expect certain
properties to hold, which, in fact, do not, only with more specific sort
constraints:

	(a + b) + c =3D a + (b + c)
        2 + 2 =3D 4 -- an Isabelle classic!

(an aside: there is a similar issue with min/max which are defined
purely syntactical, not only on linear orders)

I kept the then existing syntactic classes a) for backward compatibility
and b) since they carry syntax by default.  The case for inf and sup
then was different.

Nowadays I have to admit that in situations like yours syntactic classes
for inf and sup would allow a more liberal building of the class
hierarchy.  Indeed, I recently had some thoughts how you could achieve
something like =BBimport class parameters, but with different
specification from which the original specification follows=AB, in essenc=
e
a class with simultaneous subclass.  But it looked rather complicated.

I have no strong opinion whether to turn inf and sup into syntactic
classes.  But note that to simplify your instantiation proofs you can
prove a specific introduction rule for P =3D=3D> OFCLASS('a, left_inf) wh=
ere
P is the body of your left_inf class.

Hope this helps,
	Florian

--=20

Home:
http://www.in.tum.de/~haftmann

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http://home.informatik.tu-muenchen.de/haftmann/pgp/florian_haftmann_at_in=
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Subject: Re: [isabelle] Lattices and syntactic classes
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On Wed, Aug 31, 2011 at 11:53 AM, Florian Haftmann
<florian.haftmann at informatik.tu-muenchen.de> wrote:
> Hi Viorel,
>
>> Ultimately the structure is a (semi-) lattice, but the axioms are
>> different.
>> Imagine an algebraic structure with some operations *, left_imp which
>> satisfies
>> some properties and in which inf can be defined
>>
>> class left_inf =3D inf + times + left_imp + order +
>> =A0 assumes some axioms for times and left_imp
>> =A0 and inf_l_def: "(inf a b) =3D (left_imp a b) * a"
>> =A0 and definition of order
>>
>> begin
>>
>> in this setting the fact that inf is a semi-lattice operation can be
>> proved from the axioms of times and left_imp.

There are several similar situations that arise in Isabelle's real
analysis class hierarchy. For example, RealVector.thy introduces type
classes topological_space and metric_space. Every metric space is also
a topological space, so we definitely want a subclass relationship
topological_space < metric_space. The naive way to formalize these
classes is shown below.

class topological_space =3D
  fixes "open" :: "'a set =3D> bool"
  assumes open_UNIV: "open UNIV"
  assumes open_Int: "open S =3D=3D> open T =3D=3D> open (S \<inter> T)"
  assumes open_Union:: "ALL S:K. open S =3D=3D> open (Union K)"

class metric_space =3D topological_space +
  fixes dist :: "'a =3D> 'a =3D> real"
  assumes dist_eq_0_iff: "(dist x y =3D 0) =3D (x =3D y)"
  assumes dist_triangle2: "dist x y \<le> dist x z + dist y z"
  assumes open_dist: "open S =3D (ALL x:S. EX e>0. ALL y. dist y x < e --> =
y : S)"

Of course, the problem here is that whenever we want to prove an
instance of the metric_space class, Isabelle expects us to re-prove
all the topological_space axioms as well, even though they are implied
by the metric_space axioms! To avoid this, I broke up the class
definitions using some syntactic classes:

class "open" =3D fixes "open" :: "'a set =3D> bool"

class topological_space =3D "open" +
  assumes open_UNIV: "open UNIV"
  assumes open_Int: "open S =3D=3D> open T =3D=3D> open (S \<inter> T)"
  assumes open_Union:: "ALL S:K. open S =3D=3D> open (Union K)"

class dist =3D fixes dist :: "'a =3D> 'a =3D> real"

class open_dist =3D "open" + dist +
  assumes open_dist: "open S =3D (ALL x:S. EX e>0. ALL y. dist y x < e --> =
y : S)"

class metric_space =3D open_dist +
  assumes dist_eq_0_iff: "(dist x y =3D 0) =3D (x =3D y)"
  assumes dist_triangle2: "dist x y \<le> dist x z + dist y z"

Then we can prove a subclass relationship:

instance topological_space < metric_space
proof ...

Now instance proofs for metric_space give us exactly the proof
obligations we want.

Similar relationships exist among a whole sequence of classes, and
they are set up in a similar manner:
topological_space < metric_space < real_normed_vector < real_inner

> Historically, syntactic classes where necessary since the class +
> operations & instantiation infrastructure has not yet emerged.  With the
> class package my first thought was to avoid syntactic classes entirely,
> since they allow to write down things for which one might expect certain
> properties to hold, which, in fact, do not, only with more specific sort
> constraints:
>
>        (a + b) + c =3D a + (b + c)
>        2 + 2 =3D 4 -- an Isabelle classic!

The redefined class hierarchy as I presented it above still has this
same kind of problem: If you write something like "dist x y =3D dist y
x", the inferred sort for x and y is "dist", and not "metric_space" as
you would like. I solve this problem with the following ML command:

setup {* Sign.add_const_constraint
  (@{const_name dist}, SOME @{typ "'a::metric_space =3D> 'a =3D> real"}) *}

This tells Isabelle's parser/typechecker to automatically infer a
metric_space class constraint whenever the "dist" constant is used.
This works great most of the time, but there are rare occasions when I
need to temporarily turn off the extra constraints (see
Library/Inner_Product.thy) which is a pain.

> Nowadays I have to admit that in situations like yours syntactic classes
> for inf and sup would allow a more liberal building of the class
> hierarchy.  Indeed, I recently had some thoughts how you could achieve
> something like =BBimport class parameters, but with different
> specification from which the original specification follows=AB, in essenc=
e
> a class with simultaneous subclass.  But it looked rather complicated.

Such a feature might be worthwhile; after all, my workaround for the
problem is rather complicated too! This feature would let us radically
simplify the class hierarchy in the real analysis theories. It would
also let us simplify the group/ring class hierarchy a bit. But perhaps
most importantly, it would let users define classes like Viorel's
"left_inf" class in the most natural way.

- Brian