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From: =?utf-8?Q?Yannick_Duch=C3=AAne_=28Hibou57?=
 =?utf-8?Q?=29?=
 <yannick_duchene@yahoo.fr>
Newsgroups: comp.lang.ada
Subject: Re: SPARK : surprising failure with implication
Date: Wed, 02 Jun 2010 06:34:54 +0200
Organization: Ada At Home
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Date: 2010-06-02T06:34:54+02:00
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Le Tue, 01 Jun 2010 20:51:04 +0200, Yannick Duch=C3=AAne (Hibou57)  =

<yannick_duchene@yahoo.fr> a =C3=A9crit:

> Hi all,
>
> In an Ada/SPARK source, I had something like this:
>
>     --# check (Source =3D 1) -> ((Source mod 2) =3D 1); -- (1)
>     --# check (Source mod 2) /=3D 1;                  -- (2)
>     --# check Source /=3D 1;                          -- (3)
>
> 1) Was proved by the simplifier (note that I needed a user rule for  =

> that).
> 2) Is a valid hypothesis ; an already proved conclusion (in some prior=
  =

> check clauses)
> 3) Failed to be proved, while I expected this to be proved from (1) an=
d  =

> (2).
>
> [...]

Although late, I'm back to this topic.

I added this user rule:

    my_logic(1): not B -> not A may_be_deduced_from [ (A -> B) ].

While this was looking so much obvious, I though the Simplifier already =
 =

knew it and this would probably change nothing. But this did change  =

something! Now the above sequence of hypothesis->conclusion is proved.

Did I made something wrong somewhere ? Did I brake something somewhere ?=
  =

Why is not this fundamental rule embedded in the Simplifier ?

I was so much surprised, that I checked it (yes, what looks obvious is  =

sometimes good to check). Can't say anything else that =E2=80=9Cyes, thi=
s is true=E2=80=9D.

(A) (B) (A->B)
  F   F    T
  F   T    T
  T   F    F
  T   T    T

(not B) (not A) (not B -> not A)
  T       T       T
  F       T       T
  T       F       F
  F       F       T

(A -> B) (not B -> not A) ((A -> B) -> (not B -> not A))
  T        T                T
  T        T                T
  F        F                T
  T        T                T

This is indeed tautology.

OK, that is solved, but I'm still somewhat frightened by what I don't  =

understand in this experience : why did I need to add a user rule for th=
at  =

? What was wrong ?


-- =

There is even better than a pragma Assert: a SPARK --# check.
--# check C and WhoKnowWhat and YouKnowWho;
--# assert Ada;
--  i.e. forget about previous premises which leads to conclusion
--  and start with new conclusion as premise.