Le 27/12/12 06:55, Ramana Kumar a écrit :
Do you have a clone of the HOL4 git repository? You could make a pull
request on github after adding HINT_EXISTS_TAC in an appropriate place.
I'd totally be ready to do this, but I would like, first of all, to be
sure people share my interest in the features of HINT_EXISTS_TAC: I
don't want to pollute the repo with new tactics that I am the only one
to find useful.
In particular, it seems from this discussion that there are several
"close" solutions in HOL4.
However, none of them allows to just make progress in a goal without
solving it completely.
In my opinion, that's an essential aspect of HINT_EXISTS_TAC, but I'm
not sure this opinion is shared by any of you guys? :-)
In addition to match_assum_abbrev_tac, there is
match_assum_rename_tac. Both of them could do with some improvement,
e.g. see https://github.com/mn200/HOL/issues/81. If you happen to
delve into this code, your patches would be warmly welcomed :)
On Thu, Dec 27, 2012 at 6:48 PM, Vincent Aravantinos
<vincent.aravanti...@gmail.com <mailto:vincent.aravanti...@gmail.com>>
wrote:
Hi Michael,
I'm regularly amazed by the pearls that HOL4 contains...
I did not know about the SatisfySimps module!
Now, from my first tests, this can only be used to conclude a goal.
Concretely, if I have a goal of the following form:
?x. P x /\ Q x
--------------------
0. P t
...
where Q x cannot be solved immediatly (assume it can be solved
from other theorems or the other assumptions, but not automatically).
Then SATISFY_ss won't do anything because of Q x.
On the other hand, HINT_EXISTS_TAC will instantiate x by t, just
leaving Q t as a new goal to prove (of course the new goal is not
equivalent to the previous one, but the purpose of the tactic is
just to make some progress and help the user reducing parts of the
goal easily).
Am I right about this behaviour of SATISFY_ss or did I miss something?
V.
Le 26/12/12 23:17, Michael Norrish a écrit :
HOL4’s SATISFY_ss (from SatisfySimps) should solve this problem
(particularly now that Thomas Türk has fixed a bug in its code).
Michael
On 27/12/2012, at 11:42, Ramana Kumar <ram...@member.fsf.org
<mailto:ram...@member.fsf.org>> wrote:
For what it's worth, my usual move in this situation is to do
qmatch_assum_abbrev_tac 'P t' >>
qexists_tac 't' >>
simp[Abbr'X']
Note that P is a metavariable, i.e. I have to type it out, but I
avoid typing the large term abbreviated by t. The X stands for
pieces of P I want unabbreviated after.
HINT_EXISTS_TAC might still be an improvement.
Sorry for no proper backquotes, using my phone.
On Dec 26, 2012 10:57 PM, "Vincent Aravantinos"
<vincent.aravanti...@gmail.com
<mailto:vincent.aravanti...@gmail.com>> wrote:
Hi list,
here is another situation which I don't like and often meet
(both in
HOL-Light and HOL4), and a potential solution.
Please tell me if you also often meet the situation, if you
agree that
it is annoying, and if there is already a solution which I
don't know of
(I'm pretty sure there is no solution in HOL-Light, but I'm
not familiar
with all its extensions over there).
SITUATION:
goal of the form `?x. ... /\ P x /\ ...`
+ one of the assumptions is of the form `P t` (t is a big
a term)
+ one wants to use t as the witness for x
USUAL MOVE:
e (EXISTS_TAC `t`)
(*Then rewrite with the assumptions in order to remove
the now
trivial P t:*)
e(ASM_REWRITE_TAC[])
PROBLEM WITH THIS:
Annoying to write explicitly the big term t.
Plus the subsequent ASM_REWRITE_TAC is trivial and can
thus be
systematized.
Not really annoying if it only appears from time to time,
but I
personally often face this situation.
SOLUTION:
A tactic HINT_EXISTS_TAC which looks for an assumption
matching one
(or more) of the conjuncts in the conclusion and applies
EXISTS_TAC with
the corresponding term.
EXAMPLE IN HOL-LIGHT:
(* Consider the following goal:*)
0 [`P m`]
1 [`!x. P x ==> x <= m`]
`?x. P x`
(* Usual move: *)
# e (EXISTS_TAC `m:num`);;
val it : goalstack = 1 subgoal (1 total)
0 [`P m`]
1 [`!x. P x ==> x <= m`]
`P m`
# e (ASM_REWRITE_TAC[]);;
val it : goalstack = No subgoals
(* New solution, which finds the witness automatically
and removes
the trivial conjunct : *)
# b (); b (); e HINT_EXISTS_TAC;;
val it : goalstack = No subgoals
(* Notes:
* - The use case gets more interesting when m is
actually a big term.
* - Though, in this example, the tactic allows to
conclude the goal,
it can also be used just to make progress in the proof
without necessary
concluding.
*)
A HOL-Light implementation for HINT_EXISTS_TAC is provided
below the
signature.
One for HOL4 can easily be implemented if anyone expresses
some interest
for it.
Cheers,
V.
--
Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia
University, Hardware
Verification Group
http://users.encs.concordia.ca/~vincent/
<http://users.encs.concordia.ca/%7Evincent/>
let HINT_EXISTS_TAC (hs,c as g) =
let hs = map snd hs in
let v,c' = dest_exists c in
let vs,c' = strip_exists c' in
let hyp_match c h =
ignore (check (not o exists (C mem vs) o frees) c);
term_match (subtract (frees c) [v]) c (concl h), h
in
let (_,subs,_),h = tryfind (C tryfind hs o hyp_match)
(binops `/\` c') in
let witness =
match subs with
|[] -> v
|[t,u] when u = v -> t
|_ -> failwith "HINT_EXISTS_TAC not applicable"
in
(EXISTS_TAC witness THEN REWRITE_TAC hs) g;;
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Verification Group
http://users.encs.concordia.ca/~vincent/
<http://users.encs.concordia.ca/%7Evincent/>
--
Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware
Verification Group
http://users.encs.concordia.ca/~vincent/
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