To print theory "foo" as html :
DB.html_theory "foo";
Konrad.
On Fri, Apr 7, 2017 at 6:50 AM, Chun Tian (binghe) <binghe.l...@gmail.com>
wrote:
> yes, I know these signature files, I use them too (when the proofs do not
> interest me), but I found that, in signatures, all theorems and definitions
> are sorted in lexicographic order, which is sometimes very different from
> the source scripts. But the source scripts well preserved the relationships
> (and dependences) between theorems, i.e. later theorems were proved by
> previous theorems, they're kind of very useful information to me.
>
> By the way, is it possible to generate HTML files from any theory
> signature? I know how to use EmitTeX.print_theories_as_tex_doc() to
> print my theory into PDF finally. But I find HOL's HTML outputs beautiful
> and compat, I would like have the same for my own theories ... (sorry for
> bring this last question to you, today ^_^)
>
> Regards,
>
> Chun
>
> On 7 April 2017 at 13:17, Thomas Tuerk <tho...@tuerk-brechen.de> wrote:
>
>> Hi Chun,
>>
>> learning Holyhammer is also on my TODO list.
>>
>> One minor trick. I often look at the theory signature instead of the
>> Script-file. So I read "relationTheory.sig". For the theories comming with
>> HOL, the signature is available in the HTML help. For my own theories, I
>> just open the "*Theory.sig" file.
>>
>> https://hol-theorem-prover.org/kananaskis-10-helpdocs/help/
>> src-sml/htmlsigs/relationTheory.html#LinearOrder-val
>>
>> Best
>>
>> Thomas
>>
>> On 07.04.2017 13:07, Chun Tian (binghe) wrote:
>>
>> Thanks again, this is really convenient.
>>
>> Actually a large piece of my time was spent on reading HOL's
>> relationScript.sml and other scripts that I needed, I try to find useful
>> theorems by their name (otherwise I couldn't know RTC_CASES*, RTC_INDUCT,
>> RTC_SINGLE, etc.), but maybe the scripts are too long, I don't know how to
>> I missed RTC_INDUCT_RIGHT1, etc.)
>>
>> I hope one day I could learn to use the Holyhammer ...
>>
>> Regards,
>>
>> Chun
>>
>>
>> On 7 April 2017 at 12:57, Thomas Tuerk <tho...@tuerk-brechen.de> wrote:
>>
>>> Hi Chun,
>>>
>>> by the way. I always find DB.match and DB.find very helpful. You can for
>>> example try
>>>
>>> DB.print_match [] ``RTC``
>>> DB.print_match [] ``RTC _ x x``
>>> DB.print_find "RTC"
>>> to find interesting theorems about RTC.
>>>
>>> Cheers
>>>
>>> Thomas
>>>
>>>
>>> On 07.04.2017 12:51, Chun Tian (binghe) wrote:
>>>
>>> Hi Thomas,
>>>
>>> Thank you very much!! Obviously I didn't know those RTC_ALT* and
>>> RTC_RIGHT* series of theorems before. Now I can prove something new:)
>>>
>>> Best regards,
>>>
>>> Chun
>>>
>>>
>>> On 7 April 2017 at 12:08, Thomas Tuerk <tho...@tuerk-brechen.de> wrote:
>>>
>>>> Hi,
>>>>
>>>> 1) They are the same. You can easily proof with induction (see below).
>>>>
>>>> 2) Yes you can prove it. You would also do it via some kind of
>>>> induction proof. However there is no need, since it is already present in
>>>> the relationTheory as RTC_INDUCT_RIGHT1.
>>>>
>>>> Cheers
>>>>
>>>> Thomas
>>>>
>>>>
>>>>
>>>> open relationTheory
>>>>
>>>> val (RTC1_rules, RTC1_ind, RTC1_cases) = Hol_reln `
>>>> (!x. RTC1 R x x) /\
>>>> (!x y z. R x y /\ RTC1 R y z ==> RTC1 R x z)`;
>>>>
>>>> val (RTC2_rules, RTC2_ind, RTC2_cases) = Hol_reln `
>>>> (!x. RTC2 R x x) /\
>>>> (!x y z. RTC2 R x y /\ R y z ==> RTC2 R x z)`;
>>>>
>>>> val RTC1_ALT_DEF = prove (``RTC1 = RTC``,
>>>>
>>>> `!R. (!x y. RTC1 R x y ==> RTC R x y) /\
>>>> (!x y. RTC R x y ==> RTC1 R x y)` suffices_by (
>>>> SIMP_TAC std_ss [FUN_EQ_THM] THEN METIS_TAC[FUN_EQ_THM])
>>>> THEN
>>>>
>>>> GEN_TAC THEN CONJ_TAC THENL [
>>>> Induct_on `RTC1` THEN
>>>> METIS_TAC [RTC_RULES],
>>>>
>>>> MATCH_MP_TAC RTC_INDUCT THEN
>>>> METIS_TAC[RTC1_rules]
>>>> ]);
>>>>
>>>>
>>>> val RTC2_ALT_DEF = prove (``RTC2 = RTC``,
>>>>
>>>> `!R. (!x y. RTC2 R x y ==> RTC R x y) /\
>>>> (!x y. RTC R x y ==> RTC2 R x y)` suffices_by (
>>>> SIMP_TAC std_ss [FUN_EQ_THM] THEN METIS_TAC[FUN_EQ_THM])
>>>> THEN
>>>>
>>>> GEN_TAC THEN CONJ_TAC THENL [
>>>> Induct_on `RTC2` THEN
>>>> METIS_TAC [RTC_RULES_RIGHT1],
>>>>
>>>> MATCH_MP_TAC RTC_INDUCT_RIGHT1 THEN
>>>> METIS_TAC[RTC2_rules]
>>>> ]);
>>>>
>>>>
>>>>
>>>> On 07.04.2017 11:49, Chun Tian (binghe) wrote:
>>>>
>>>> Hi,
>>>>
>>>> If I try to define RTC manually (like those in HOL tutorial, chapter 6,
>>>> page 74):
>>>>
>>>> val (RTC1_rules, RTC1_ind, RTC1_cases) = Hol_reln `
>>>> (!x. RTC1 R x x) /\
>>>> (!x y z. R x y /\ RTC1 R y z ==> RTC1 R x z)`;
>>>>
>>>> It seems that (maybe) I can also define the "same" relation with a
>>>> different transitive rule:
>>>>
>>>> val (RTC2_rules, RTC2_ind, RTC2_cases) = Hol_reln `
>>>> (!x. RTC2 R x x) /\
>>>> (!x y z. RTC2 R x y /\ R y z ==> RTC2 R x z)`;
>>>>
>>>> Here are some observations:
>>>>
>>>> 1. If I directly use the RTC definition from HOL's relationTheory,
>>>> above two transitive rules are both true, easily provable by theorems
>>>> RTC_CASES1 and RTC_CASES2 (relationTheory):
>>>>
>>>> > RTC_CASES1;
>>>> val it =
>>>> |- ∀R x y. R^* x y ⇔ (x = y) ∨ ∃u. R x u ∧ R^* u y:
>>>> thm
>>>> > RTC_CASES2;
>>>> val it =
>>>> |- ∀R x y. R^* x y ⇔ (x = y) ∨ ∃u. R^* x u ∧ R u y:
>>>> thm
>>>>
>>>> 2. The theorem RTC1_ind (generated by Hol_reln) is the same as theorem
>>>> RTC_INDUCT (relationTheory):
>>>>
>>>> val RTC1_ind =
>>>> |- ∀R RTC1'.
>>>> (∀x. RTC1' x x) ∧ (∀x y z. R x y ∧ RTC1' y z ⇒ RTC1' x z) ⇒
>>>> ∀a0 a1. RTC1 R a0 a1 ⇒ RTC1' a0 a1:
>>>> thm
>>>>
>>>> > RTC_INDUCT;
>>>> val it =
>>>> |- ∀R P.
>>>> (∀x. P x x) ∧ (∀x y z. R x y ∧ P y z ⇒ P x z) ⇒
>>>> ∀x y. R^* x y ⇒ P x y:
>>>> thm
>>>>
>>>> Now my questions are:
>>>>
>>>> 1. Given any R, are the two relations (RTC1 R) and (RTC2 R) really the
>>>> same? i.e. is ``!R x y. RTC1 R x y = RTC2 R x y`` a theorem? (and if so,
>>>> how to prove it?)
>>>>
>>>> 2. (If the answer of last question is yes) Is it possible to prove the
>>>> following theorem RTC_INDUCT2 in relationTheory? (which looks like RTC2_ind
>>>> generated in above definition)
>>>>
>>>> val RTC_INDUCT2 = store_thm(
>>>> "RTC_INDUCT2",
>>>> ``!R P. (!x. P x x) /\ (!x y z. P x y /\ R y z ==> P x z) ==>
>>>> (!x (y:'a). RTC R x y ==> P x y)``,
>>>> cheat);
>>>>
>>>> (and the corresponding RTC_STRONG_INDUCT2).
>>>>
>>>> Regards,
>>>>
>>>> --
>>>> Chun Tian (binghe)
>>>> University of Bologna (Italy)
>>>>
>>>>
>>>>
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>>>
>>> --
>>> ---
>>> Chun Tian (binghe)
>>> University of Bologna (Italy)
>>>
>>> ------------------------------------------------------------------------------
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>>
>> --
>> ---
>> Chun Tian (binghe)
>> University of Bologna (Italy)
>>
>> ------------------------------------------------------------------------------
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>>
>>
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>>
>
>
> --
> Chun Tian (binghe)
> University of Bologna (Italy)
>
>
> ------------------------------------------------------------
> ------------------
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>
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