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|
%****************************************************************************%
% %
% File: tools.ml %
% %
% Editor: Paul Curzon %
% %
% Date: May 1991 %
% %
% Description: General Purpose Stuff that can be loaded without %
% having to load any other library/file %
% %
%****************************************************************************%
%********************************* HISTORY ********************************%
% %
% This file is the amalgamation of general purpose tool files from %
% Mike Benjamin %
% Paul Curzon %
% Wim Ploegaerts %
% The files have been trimmed to include only those tools used by the %
% more_arithmetic and more_lists libraries %
% %
%***************************** END OF HISTORY *****************************%
%****************************************************************************%
% %
% File: general_purp.ml %
% %
% Author: Wim Ploegaerts (ploegaer@imec.be) %
% %
% Date: Mon Feb 11 1991 %
% %
% Organization: Imec vzw. %
% Kapeldreef 75 %
% 3001 Leuven - Belgium %
% %
% Description: General Purpose Stuff that can be loaded without %
% having to load any other library/file %
% %
%****************************************************************************%
%----------------------------------------------------------------------------%
% %
% CONVERSIONS %
% %
%----------------------------------------------------------------------------%
let LHS_CONV = RATOR_CONV o RAND_CONV;;
let CONJ1 = fst o CONJ_PAIR;;
let CONJ2 = snd o CONJ_PAIR;;
let SPEC_SYM = SYM o SPEC_ALL;;
%----------------------------------------------------------------------------%
% %
% RULES %
% %
%----------------------------------------------------------------------------%
let SYM_RULE =
CONV_RULE (ONCE_DEPTH_CONV SYM_CONV)
? failwith `SYM_RULE`;;
%----------------------------------------------------------------------------%
% %
% TACTICS %
% %
%----------------------------------------------------------------------------%
%============================================================================%
% %
% PROTECT_REWRITE_CONV: %
% %
% Conversion for rewrite rules of the form |- !x1 ... xn. t == u %
% Matches x1 ... xn : t' ----> |- t' == u' %
% Matches all types in conclusion except those mentioned in hypotheses %
% %
%============================================================================%
% %
% `REWRITE_CONV` behandelt alle vrije variabelen met vervanging door %
% generieke variabelen (`genvars`). De volgende protected functies %
% leggen hieraan restricties op. %
% %
letrec PROTECT_GSPEC tml th =
let wl,w = dest_thm th in
if is_forall w then
let tm = fst(dest_forall w) in
let tm' = (mem tm tml) => (genvar (type_of tm)) | tm in
PROTECT_GSPEC tml (SPEC tm' th)
else th;;
% %
% Match a given part of "th" to a term, instantiating "th". %
% The part should be free in the theorem, except for outer bound variables %
% %
let PROTECT_PART_MATCH tml partfn th =
let pth = PROTECT_GSPEC tml (GEN_ALL th) in
let pat = partfn(concl pth) in
let matchfn = match pat in
\tm. INST_TY_TERM (matchfn tm) pth;;
let PROTECT_REWRITE_CONV tml =
set_fail_prefix `PROTECT_REWRITE_CONV`
(PROTECT_PART_MATCH tml (fst o dest_eq));;
% %
% Example of the use: %
% ------------------ %
% %
% TRANSLATION_LEQ_EQ: %
% " !z x y . (x leq y) = (x plus z) leq (y plus z)" %
% %
% let thm = SPEC "n:zet" TRANSLATION_LEQ_EQ;; %
% thm = |- !x y. x leq y = (x plus n) leq (y plus n) : thm %
% %
% (PROTECT_REWRITE_CONV ["x:zet";"y:zet"] thm) "a leq b";; %
% |- a leq b = (a plus n) leq (b plus n) %
% %
% (REWR_CONV thm) "a leq b";; %
% |- a leq b = (a plus GEN_VAR_871) leq (b plus GEN_VAR_871) %
% %
%<-------------------------------------------------------------------------->%
%****************************************************************************%
% %
% File: tactics.ml %
% %
% Author: Paul Curzon %
% %
% Date: May 1991 %
% %
% %
%****************************************************************************%
%****************************************************************************%
% %
% Tactic to rewrite using the last added assumption and general rewrites %
% %
%****************************************************************************%
let POP_REWRITE_TAC = POP_ASSUM (\th.REWRITE_TAC[th]);;
%****************************************************************************%
% %
% Tactic to remove the last added assumption from the assumption list %
% %
%****************************************************************************%
let POP_JUNK_TAC = POP_ASSUM (\th. ALL_TAC);;
%****************************************************************************%
% %
% Tactics to apply rules to the last added assumption from the %
% assumption list %
% %
%****************************************************************************%
let POP_TAC rule = POP_ASSUM (\th . ASSUME_TAC (rule th));;
let PEEK_ASSUM (thm_tac:thm_tactic) ((asl,g):goal) =
thm_tac (ASSUME (hd asl))
(asl, g);;
let PEEK_TAC rule = PEEK_ASSUM (\th . ASSUME_TAC (rule th));;
%****************************************************************************%
% %
% Specialize a single named variable t1 to t2 %
% %
%****************************************************************************%
let SPEC1 t1 t2 th =
(GEN_ALL (SPEC t2 (GEN t1 (SPEC_ALL th))));;
%****************************************************************************%
% %
% Rewrite the last assumption with the second last %
% %
%****************************************************************************%
let REWRITE_A1_WITH_A2_THEN (tac:thm_tactic) =
(POP_ASSUM (\th1 . (POP_ASSUM (\th2. tac
(REWRITE_RULE[th2] th1)))));;
%****************************************************************************%
% %
% Rewrite the second last assumption with the last %
% %
%****************************************************************************%
let REWRITE_A2_WITH_A1_THEN (tac:thm_tactic) =
(POP_ASSUM (\th1 . (POP_ASSUM (\th2. tac
(REWRITE_RULE[th1] th2)))));;
%****************************************************************************%
% %
% Versions of RES_TAC and IMP_RES_TAC which only add a single new %
% assumption to the assumption list. It must be identical to the term %
% given orelse no new assumption is added %
% %
%****************************************************************************%
let FILTER_THM f target th =
if (snd (dest_thm th)) = target
then f th
else ALL_TAC;;
letrec filter_assume_tac th (asl,c) g =
if (asl = []) then ASSUME_TAC th g
else if ((snd (dest_thm th)) = (hd asl)) then ALL_TAC g
else filter_assume_tac th ((tl asl),c) g ;;
let FILTER_ASSUME_TAC th1 g =
filter_assume_tac th1 g g;;
let FILTER_IMP_RES_TAC t =
REPEAT_GTCL IMP_RES_THEN (FILTER_THM FILTER_ASSUME_TAC t);;
let FILTER_RES_TAC t =
let FILTER_THM f target th =
if (snd (dest_thm th)) = target
then f th
else FILTER_IMP_RES_TAC target th
in
RES_THEN (FILTER_THM FILTER_ASSUME_TAC t);;
%****************************************************************************%
% %
% STRIP_TAC except do not split CONJUNCTS apart. %
% %
%****************************************************************************%
let NC_STRIP_TAC (asl,t) =
if is_conj t
then NO_TAC (asl,t)
else (STRIP_TAC (asl,t)) ;;
% ***************************************************************************
* *
* Mike Benjamin *
* FPC 267 *
* British Aerospace Sowerby Research Centre *
* PO BOX 5 *
* Filton *
* Bristol BS12 7QW *
* *
* Tel: (0272) 366198 *
* EMAIL: benjamin@src.bae.co.uk *
* *
**************************************************************************%
% **************************************************************************
* *
* GENERAL PURPOSE TACTICS. *
* *
* These are based on existing tactics in Cambrideg-LCF that don't seem
to have been implemented *
* in HOL. *
* *
* !!! WARNING !!! *
* No provision has been made in these routines for exception handling. *
* *
**************************************************************************%
% ***************************************************************************
* *
* CUT : thm -> thm -> thm *
* *
* X |- A Y, A |- B *
* ------------------- *
* X, Y |- B *
* *
**************************************************************************%
let CUT ath bth = MP (DISCH (concl ath) bth) ath;;
% ***************************************************************************
* *
* Introduce a lemma. *
* *
* CUT_TAC : form -> tactic *
* A *
* *
* X |- A X, A |- B *
* ------------------- *
* X |- B *
* *
**************************************************************************%
let CUT_TAC A :tactic (asl,B) =
([(asl,A);(A.asl,B)], (\ [thA;thB]. CUT thA thB));;
% ***************************************************************************
* *
* Add a theorem to the assumption list. *
* *
* CUT_TAC : thm -> tactic *
* A *
* *
* Y, A |- B *
* --------- *
* Y |- B *
* *
**************************************************************************%
let CUT_THM_TAC bth :tactic (asl,w) =
([(((concl bth).asl),w)],(\ [th]. CUT bth th));;
% ***************************************************************************
* *
* Disjunction elimination in the assumption list, generating two subgoals.*
* *
* DISJ_LEFT_TAC : tactic *
* *
* X, A |- C X ,B |- C *
* ---------------------- *
* X, A \/ B |- C *
* *
**************************************************************************%
letrec take p (rxs, xxs) = if
(length xxs = 0)
then
([], rev rxs)
else
(if
p (hd xxs)
then
([hd xxs], rev rxs @ (tl xxs))
else
take p ((hd xxs).rxs, (tl xxs)));;
let take_first p xs = take p ([],xs);;
let DISJ_LEFT_TAC :tactic (asl,C) =
let
([asm], asl') = (take_first is_disj asl)
in
let
(A,B) = (dest_disj asm)
in
([(A.asl',C); (B.asl',C)], \[thA;thB]. DISJ_CASES (ASSUME asm) thA thB);;
% ***************************************************************************
* *
* Specialise forall. *
* *
* FORALL_LEFT_TAC : term X term -> tactic *
* *
* Y, !x.A, A[t/x] |- B *
* -------------------- *
* Y, !x.A |- B *
* *
**************************************************************************%
let isvar_forall x C =
is_forall C &
let (y,_) = dest_forall C in x=y;;
let FORALL_LEFT_TAC (t:term,x:term) :tactic ((asl,C):goal) =
let ([asm], z) = take_first (isvar_forall x) asl in
let specth = SPEC t (ASSUME asm)
in ([(concl specth . asl, C)],
\ [th]. CUT specth th);;
% ***************************************************************************
* *
* Specialise exists. *
* *
* EXISTS_LEFT_TAC : tactic *
* *
* Y, A[x'/x] |- B *
* --------------- (provided x' is not free in ?x.A, Y, or B) *
* Y, ?x.A |- B *
* *
**************************************************************************%
let terml_frees wl = itlist (\ w . union (frees w)) wl [];;
let EXISTS_LEFT_TAC :tactic (asl,C) =
let ([asm], asl') = take_first is_exists asl in
let (x,A) = dest_exists asm in
let x' = variant (terml_frees(C.asl)) x in
let A' = subst [(x',x)] A
in ([(A'.asl',C)],
\ [th]. CHOOSE (x', ASSUME asm) th);;
% ***************************************************************************
* *
* Solve a goal provided the result to be proven is in the assumption list.*
* *
* ACCEPT_ASM_TAC : tactic *
* *
**************************************************************************%
let ACCEPT_ASM_TAC : tactic ((asl,a):goal) = ([], \[]. ASSUME a);;
% ***************************************************************************
* *
* A set of tactics that rewrite the goal using *
* assumptions identified by index numbers. *
* *
* N_REWRITE_TAC : integer -> tactic *
* S_REWRITE_TAC : integer list -> tactic *
* ONCE_N_REWRITE_TAC :integer -> tactic *
* *
**************************************************************************%
letrec index i (x.xs) = if (i = 1) then x else (index (i-1) xs);;
letrec indexes is xs = if (is = []) then [] else ((index (hd is) xs).(indexes (tl is) xs));;
let N_REWRITE_TAC n = ASSUM_LIST (\ (x:thm list). REWRITE_TAC [index n x]);;
let S_REWRITE_TAC n = ASSUM_LIST (\ (x:thm list). REWRITE_TAC (indexes n x));;
let ONCE_N_REWRITE_TAC n = ASSUM_LIST (\ (x:thm list). ONCE_REWRITE_TAC [index n x]);;
% ***************************************************************************
* *
* A tactic that adds the inverse of an assumption to the assumption list. *
* It is based on the law that equality is symmetric. *
* *
* N_REVERSE_TAC : integer -> tactic *
* *
**************************************************************************%
let N_REVERSE_TAC n = ASSUM_LIST (\ (x:thm list). CUT_THM_TAC (ONCE_REWRITE_RULE [EQ_SYM_EQ] (index n x)));;
let autoload_defs_and_thms thy =
map (\name. autoload_theory(`definition`,thy,name))
(map fst (definitions thy));
map (\name. autoload_theory(`theorem`,thy,name))
(map fst (theorems thy));;
let LEMMA_PROOF term tacticl (asl,g) =
(MP_TAC (TAC_PROOF ((asl,term), (EVERY tacticl))) THEN STRIP_TAC) (asl,g);;
let MATCH_EQ_MP eqth =
let match = PART_MATCH (fst o dest_eq) eqth ? failwith `MATCH_MP`
in
\th. EQ_MP (match (concl th)) th;;
|
