--- layout: fc_discuss_archives title: Message 9 from Frama-C-discuss on May 2016 ---
ACSL is a specification language with a two-valued logic (see Section 2.2.2). So predicates can definitely be valid or invalid. Here, Maurice's assert is equivalent to the lemma \forall double x; -1 <= x <= 1 ==> x*x - .2 * x + 0.01 >= 0.; This lemma is invalid because it is refuted by the double value 0x1.9999998p-4. (i.e. 1.5999999940395355*2^-4 or approximately 0.0999999996275). See my message on May 1 for more floating-point gory details :-) On Thu, May 5, 2016 at 3:31 AM, David R. Cok <dcok at grammatech.com> wrote: > Sorry: when you say "invalid in ACSL" do you actually mean it is invalid > (because it is floating point, not real?) or do you mean it is not provable > (and by what) or do you mean it is not a well-formed ACSL statement? ACSL > is just a language, not a proof tool. If the first, is it actually the case > that there are double precision numbers for which the assertion does not > hold? > > - David > > On 5/4/2016 2:14 PM, Boris Yakobowski wrote: > > My mistake. I coalesced two different things when replying to Maurice : > > - the validity of the lemma /*@ lemma sq_double: \forall real x; x*x - .2 > * x + 0.01 >= 0.; */. It is indeed valid in ACSL, should be proven by WP > whatever the model (since, as Loïc mentioned, it involves only real) , > and (as all lemmas) is completely ignored by Value; > > - the validity status of the assert in double x1 = x*x - .2 * x + 0.01; /*@ > assert x1 >= 0; */, which is invalid in ACSL, but can be proven by the > Float model of WP. > > On Wed, May 4, 2016 at 2:07 PM, Claude Marché <Claude.Marche at inria.fr> > wrote: > >> >> Sorry to interfere, but I don't understand the meaning of "wrong in WP" >> >> According to ACSL manual, this lemma is a statement expressed purely in >> mathematical real arithmetic, and as such it is valid. It is indeed >> proved automatically by Z3 4.4.1. >> >> If you want to state a similar property talking about floating-point >> arithmetic, it should be stated differently, typically using a program >> >> void f(double x) { >> double y = x*x - .2 * x + 0.01; >> //@ assert y >= 0.0; >> } >> >> But I guess it probably wrong because of rounding, even with a >> precondition like \abs(x) <= 1.0 >> >> My two cents, >> >> - Claude >> >> Le 04/05/2016 13:54, Loïc Correnson a écrit : >> >> /*@ lemma sq_double: \forall real x; x*x - .2 * x + 0.01 >= 0.; */ >> > >> > This lemma is definitely wrong in WP with Real model (not float there). >> > At least, it is not provable in the forthcoming release of Frama-C. >> > Is there a bug in some existing release? >> > L. >> > >> > >> > _______________________________________________ >> > Frama-c-discuss mailing list >> > Frama-c-discuss at lists.gforge.inria.fr >> > http://lists.gforge.inria.fr/mailman/listinfo/frama-c-discuss >> > >> >> -- >> Claude Marché | tel: +33 1 69 15 66 08 >> INRIA Saclay - Ãle-de-France | >> Université Paris-sud, Bat. 650 | >> <http://www.lri.fr/%7Emarche/%0AF-91405>http://www.lri.fr/~marche/ >> F-91405 ORSAY Cedex | >> _______________________________________________ >> Frama-c-discuss mailing list >> Frama-c-discuss at lists.gforge.inria.fr >> http://lists.gforge.inria.fr/mailman/listinfo/frama-c-discuss >> > > > > -- > Boris > > > _______________________________________________ > Frama-c-discuss mailing listFrama-c-discuss at lists.gforge.inria.frhttp://lists.gforge.inria.fr/mailman/listinfo/frama-c-discuss > > > > _______________________________________________ > Frama-c-discuss mailing list > Frama-c-discuss at lists.gforge.inria.fr > http://lists.gforge.inria.fr/mailman/listinfo/frama-c-discuss > -- Boris -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.gforge.inria.fr/pipermail/frama-c-discuss/attachments/20160506/31fa76ea/attachment.html>