On 23/06/11 21:33, Tom N wrote:
 
> I have a set of hypotheses involving the words library that I would
> like to prove automatically. My first attempt at this was to ask HOL
> to prove them against the entirety of wordsTheory, using:

>   > prove(hypothesis, METIS_TAC(map snd (DB.theorems "words")));

Wow.  How long do these attempts take?  I'd be very surprised if you got many 
interesting results out of this.  
 
> While this appeared to work at first, it seems that it is able to
> 'prove' obviously-incorrect hypotheses, for example:

>   > load "wordsTheory"; open wordsTheory;
>   > show_assums := true;
>   > prove(``F``, METIS_TAC(map snd (DB.theorems "words")));
>   [%%genvar%%8939 = @m. dimindex (:'XXfolXX_40996) = SUC m,
>    %%genvar%%8939 = @m. dimindex (:2) = SUC m,
>    %%genvar%%8939 = @m. dimindex (:unit) = SUC m] |- F:
>      thm
 
> Is this more likely to indicate an inconsistency in wordsTheory, or me
> doing something wrong?  I've only started using HOL recently, so it's
> probably the latter ;)

It's a bug in METIS_TAC, strictly. 

The theorem is OK (though not informative); the second and third assumptions 
are equivalent to the statements 

  %%genvar%%8939 = 1

and 

  %%genvar%%8939 = 0

which is how false can be derived.

It's a bug because METIS_TAC should not be adding assumptions to the goal it's 
trying to prove.

It would be interesting to know just which theorems in wordsTheory were giving 
rise to this derivation; they would help us track down the problem in METIS_TAC.

In general, METIS_TAC is designed to be used with smallish numbers of theorems.

I hope this helps,
Michael

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