/usr/share/hol88-2.02.19940316/Library/pair/both2.ml is in hol88-library-source 2.02.19940316-19.
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% Copyright (c) Jim Grundy 1992 %
% All rights reserved %
% %
% Jim Grundy, hereafter referred to as `the Author', retains the %
% copyright and all other legal rights to the Software contained in %
% this file, hereafter referred to as `the Software'. %
% %
% The Software is made available free of charge on an `as is' basis. %
% No guarantee, either express or implied, of maintenance, reliability %
% or suitability for any purpose is made by the Author. %
% %
% The user is granted the right to make personal or internal use %
% of the Software provided that both: %
% 1. The Software is not used for commercial gain. %
% 2. The user shall not hold the Author liable for any consequences %
% arising from use of the Software. %
% %
% The user is granted the right to further distribute the Software %
% provided that both: %
% 1. The Software and this statement of rights is not modified. %
% 2. The Software does not form part or the whole of a system %
% distributed for commercial gain. %
% %
% The user is granted the right to modify the Software for personal or %
% internal use provided that all of the following conditions are %
% observed: %
% 1. The user does not distribute the modified software. %
% 2. The modified software is not used for commercial gain. %
% 3. The Author retains all rights to the modified software. %
% %
% Anyone seeking a licence to use this software for commercial purposes %
% is invited to contact the Author. %
% --------------------------------------------------------------------- %
% CONTENTS: Functions which are common to both paried universal and %
% existential quantifications and which rely on more %
% primitive functions from all.ml and exi.ml. %
% --------------------------------------------------------------------- %
%$Id: both2.ml,v 3.1 1993/12/07 14:42:10 jg Exp $%
% ------------------------------------------------------------------------- %
% Paired stiping tactics, same as basic ones, but they use PGEN_TAC %
% and PCHOOSE_THEN rather than GEN_TAC and CHOOSE_THEN %
% ------------------------------------------------------------------------- %
let PSTRIP_THM_THEN =
FIRST_TCL [CONJUNCTS_THEN; DISJ_CASES_THEN; PCHOOSE_THEN];;
let PSTRIP_ASSUME_TAC =
(REPEAT_TCL PSTRIP_THM_THEN) CHECK_ASSUME_TAC;;
let PSTRUCT_CASES_TAC =
REPEAT_TCL PSTRIP_THM_THEN
(\th. SUBST1_TAC th ORELSE ASSUME_TAC th);;
let PSTRIP_GOAL_THEN ttac = FIRST [PGEN_TAC; CONJ_TAC; DISCH_THEN ttac];;
let FILTER_PSTRIP_THEN ttac tm =
FIRST [
FILTER_PGEN_TAC tm;
FILTER_DISCH_THEN ttac tm;
CONJ_TAC ];;
let PSTRIP_TAC = PSTRIP_GOAL_THEN PSTRIP_ASSUME_TAC;;
let FILTER_PSTRIP_TAC = FILTER_PSTRIP_THEN PSTRIP_ASSUME_TAC;;
% ------------------------------------------------------------------------- %
% A |- !p. (f p) = (g p) %
% ------------------------ PEXT %
% A |- f = g %
% ------------------------------------------------------------------------- %
let PEXT th =
(let (p,_) = dest_pforall (concl th) in
let p' = pvariant (thm_frees th) p in
let th1 = PSPEC p' th in
let th2 = PABS p' th1 in
let th3 = (CONV_RULE (RATOR_CONV (RAND_CONV PETA_CONV))) th2 in
(CONV_RULE (RAND_CONV PETA_CONV)) th3
) ? failwith `PEXT`;;
% ------------------------------------------------------------------------- %
% P_FUN_EQ_CONV "p" "f = g" = |- (f = g) = (!p. (f p) = (g p)) %
% ------------------------------------------------------------------------- %
let P_FUN_EQ_CONV =
let gpty = ":*" in
let grange = ":**" in
let gfty = ":*->**" in
let gf = genvar gfty in
let gg = genvar gfty in
let gp = genvar gpty in
let imp1 = DISCH_ALL (GEN gp (AP_THM (ASSUME (mk_eq(gf,gg))) gp)) in
let imp2 =
DISCH_ALL
(EXT (ASSUME (mk_forall(gp, mk_eq(mk_comb(gf,gp),mk_comb(gg,gp))))))
in
let ext_thm = (IMP_ANTISYM_RULE imp1 imp2) in
\p tm.
let (f,g) = dest_eq tm in
let fty = type_of f
and pty = type_of p in
let gfinst = mk_var(fst (dest_var gf), fty)
and gginst = mk_var(fst (dest_var gg), fty) in
let range = hd (tl(snd(dest_type fty))) in
let th =
INST_TY_TERM
([(f,gfinst);(g,gginst)],
[(pty,gpty);(range,grange)])
ext_thm in
(CONV_RULE (RAND_CONV (RAND_CONV (PALPHA_CONV p)))) th ;;
% ------------------------------------------------------------------------- %
% A |- !p. t = u %
% ------------------------ MK_PABS %
% A |- (\p. t) = (\p. u) %
% ------------------------------------------------------------------------- %
let MK_PABS th =
(let (p,_) = dest_pforall (concl th) in
let th1 = (CONV_RULE (RAND_CONV (PABS_CONV (RATOR_CONV (RAND_CONV
(UNPBETA_CONV p)))))) th in
let th2 = (CONV_RULE (RAND_CONV (PABS_CONV (RAND_CONV
(UNPBETA_CONV p))))) th1 in
let th3 = PEXT th2 in
let th4 = (CONV_RULE (RATOR_CONV (RAND_CONV (PALPHA_CONV p)))) th3 in
(CONV_RULE (RAND_CONV (PALPHA_CONV p))) th4
) ? failwith `MK_PABS`;;
% ------------------------------------------------------------------------- %
% A |- !p. t p = u %
% ------------------ HALF_MK_PABS %
% A |- t = (\p. u) %
% ------------------------------------------------------------------------- %
let HALF_MK_PABS th =
(let (p,_) = dest_pforall (concl th) in
let th1 = (CONV_RULE (RAND_CONV (PABS_CONV (RAND_CONV
(UNPBETA_CONV p))))) th in
let th2 = PEXT th1 in
(CONV_RULE (RAND_CONV (PALPHA_CONV p))) th2
) ? failwith `HALF_MK_PABS` ;;
% ------------------------------------------------------------------------- %
% A |- !p. t = u %
% ------------------------ MK_PFORALL %
% A |- (!p. t) = (!p. u) %
% ------------------------------------------------------------------------- %
let MK_PFORALL th =
(let (p,_) = dest_pforall (concl th) in
AP_TERM
(mk_const
(`!`, mk_type(`fun`, [mk_type(`fun`, [type_of p; bool_ty]); bool_ty])))
(MK_PABS th)) ? failwith `MK_PFORALL` ;;
% ------------------------------------------------------------------------- %
% A |- !p. t = u %
% ------------------------ MK_PEXISTS %
% A |- (?p. t) = (?p. u) %
% ------------------------------------------------------------------------- %
let MK_PEXISTS th =
(let (p,_) = dest_pforall (concl th) in
AP_TERM
(mk_const
(`?`, mk_type(`fun`, [mk_type(`fun`, [type_of p; bool_ty]); bool_ty])))
(MK_PABS th)) ? failwith `MK_PEXISTS` ;;
% ------------------------------------------------------------------------- %
% A |- !p. t = u %
% ------------------------ MK_PSELECT %
% A |- (@p. t) = (@p. u) %
% ------------------------------------------------------------------------- %
let MK_PEXISTS th =
(let (p,_) = dest_pforall (concl th) in
let pty = type_of p in
AP_TERM
(mk_const
(`@`, mk_type(`fun`, [mk_type(`fun`, [pty; bool_ty]); pty])))
(MK_PABS th)) ? failwith `MK_PSELECT` ;;
% ------------------------------------------------------------------------- %
% A |- t = u %
% ------------------------ PFORALL_EQ "p" %
% A |- (!p. t) = (!p. u) %
% ------------------------------------------------------------------------- %
let PFORALL_EQ p th =
(let pty = type_of p in
AP_TERM
(mk_const
(`!`, mk_type(`fun`, [mk_type(`fun`, [pty; bool_ty ]); bool_ty])))
(PABS p th)) ? failwith `PFORALL_EQ` ;;
% ------------------------------------------------------------------------- %
% A |- t = u %
% ------------------------ PEXISTS_EQ "p" %
% A |- (?p. t) = (?p. u) %
% ------------------------------------------------------------------------- %
let PEXISTS_EQ p th =
(let pty = type_of p in
AP_TERM
(mk_const
(`?`, mk_type(`fun`, [mk_type(`fun`, [pty; bool_ty ]); bool_ty])))
(PABS p th)) ? failwith `PEXISTS_EQ` ;;
% ------------------------------------------------------------------------- %
% A |- t = u %
% ------------------------ PSELECT_EQ "p" %
% A |- (@p. t) = (@p. u) %
% ------------------------------------------------------------------------- %
let PSELECT_EQ p th =
(let pty = type_of p in
AP_TERM
(mk_const
(`@`, mk_type(`fun`, [mk_type(`fun`, [pty; bool_ty ]); pty])))
(PABS p th)) ? failwith `PSELECT_EQ` ;;
% ------------------------------------------------------------------------- %
% A |- t = u %
% ---------------------------------------- LIST_MK_PFORALL [p1;...pn] %
% A |- (!p1 ... pn. t) = (!p1 ... pn. u) %
% ------------------------------------------------------------------------- %
let LIST_MK_PFORALL = itlist PFORALL_EQ ;;
% ------------------------------------------------------------------------- %
% A |- t = u %
% ---------------------------------------- LIST_MK_PEXISTS [p1;...pn] %
% A |- (?p1 ... pn. t) = (?p1 ... pn. u) %
% ------------------------------------------------------------------------- %
let LIST_MK_PEXISTS = itlist PEXISTS_EQ ;;
% ------------------------------------------------------------------------- %
% A |- P ==> Q %
% -------------------------- EXISTS_IMP "p" %
% A |- (?p. P) ==> (?p. Q) %
% ------------------------------------------------------------------------- %
let PEXISTS_IMP p th =
(let (a,c) = dest_imp (concl th) in
let th1 = PEXISTS (mk_pexists(p,c),p) (UNDISCH th) in
let asm = mk_pexists(p,a) in
let th2 = DISCH asm (PCHOOSE (p, ASSUME asm) th1) in
(CONV_RULE (RAND_CONV (GEN_PALPHA_CONV p))) th2
) ? failwith `PEXISTS_IMP`;;
% ------------------------------------------------------------------------- %
% SWAP_PFORALL_CONV "!p q. t" = (|- (!p q. t) = (!q p. t)) %
% ------------------------------------------------------------------------- %
let SWAP_PFORALL_CONV pqt =
(let (p,qt) = dest_pforall pqt in
let (q,t) = dest_pforall qt in
let p' = genlike p in
let q' = genlike q in
let th1 = GEN_PALPHA_CONV p' pqt in
let th2 = CONV_RULE
(RAND_CONV (RAND_CONV (PABS_CONV (GEN_PALPHA_CONV q')))) th1 in
let th3 = CONV_RULE (RAND_CONV (GEN_PALPHA_CONV q)) th2 in
CONV_RULE
(RAND_CONV (RAND_CONV (PABS_CONV (GEN_PALPHA_CONV p)))) th3
) ? failwith `SWAP_PFORALL_CONV`;;
% ------------------------------------------------------------------------- %
% SWAP_PEXISTS_CONV "?p q. t" = (|- (?p q. t) = (?q p. t)) %
% ------------------------------------------------------------------------- %
let SWAP_PEXISTS_CONV pqt =
(let (p,qt) = dest_pexists pqt in
let (q,t) = dest_pexists qt in
let p' = genlike p in
let q' = genlike q in
let th1 = GEN_PALPHA_CONV p' pqt in
let th2 = CONV_RULE
(RAND_CONV (RAND_CONV (PABS_CONV (GEN_PALPHA_CONV q')))) th1 in
let th3 = CONV_RULE (RAND_CONV (GEN_PALPHA_CONV q)) th2 in
CONV_RULE
(RAND_CONV (RAND_CONV (PABS_CONV (GEN_PALPHA_CONV p)))) th3
) ? failwith `SWAP_PEXISTS_CONV`;;
% --------------------------------------------------------------------- %
% PART_PMATCH : just like PART_MATCH but doesn't mind leading paird q.s %
% --------------------------------------------------------------------- %
let PART_PMATCH partfn th =
let pth = GPSPEC (GSPEC (GEN_ALL th)) in
let pat = partfn (concl pth) in
let matchfn = match pat in
\tm. INST_TY_TERM (matchfn tm) pth;;
% --------------------------------------------------------------------- %
% A ?- !v1...vi. t' %
% ================== MATCH_MP_TAC (A' |- !x1...xn. s ==> !y1...tm. t) %
% A ?- ?z1...zp. s' %
% where z1, ..., zp are (type instances of) those variables among %
% x1, ..., xn that do not occur free in t. %
% --------------------------------------------------------------------- %
let PMATCH_MP_TAC : thm_tactic =
let efn p (tm,th) = let ntm = mk_pexists(p,tm) in
(ntm, PCHOOSE (p, ASSUME ntm) th)
in
\thm.
let (tps,(ant,(cps,con))) =
((I # ((I # strip_forall) o dest_imp)) o strip_pforall o concl) thm
? failwith `MATCH_MP_TAC: not an implication` in
let th1 = PSPECL cps (UNDISCH (PSPECL tps thm)) in
let eps = filter (\p. not (occs_in p con)) tps in
let th2 = uncurry DISCH (itlist efn eps (ant,th1)) in
\(A,g).
let (gps,gl) = strip_pforall g in
let ins = match con gl ? failwith `PMATCH_MP_TAC: no match` in
let ith = INST_TY_TERM ins th2 in
let newg = fst(dest_imp(concl ith)) in
let gth = PGENL gps (UNDISCH ith) ?
failwith `PMATCH_MP_TAC: generalized pair(s)` in
([(A,newg)], \[th]. PROVE_HYP th gth);;
% --------------------------------------------------------------------- %
% A1 |- !x1..xn. t1 ==> t2 A2 |- t1' %
% -------------------------------------- PMATCH_MP %
% A1 u A2 |- !xa..xk. t2' %
% --------------------------------------------------------------------- %
let PMATCH_MP =
letrec variants as vs =
if null vs then
[]
else
let (h.t) = vs in
let h' = variant (as@(filter (\e. not (e = h)) t)) h in
(h',h).(variants (h'.as) t) in
let frev_assoc e2 l = (fst (rev_assoc e2 l)) ? e2
in
\ith.
let t = (fst o dest_imp o snd o strip_pforall o concl) ith
? failwith `PMATCH_MP: not an implication` in
\th.
(let (B,t') = dest_thm th in
let ty_inst = snd (match t t') in
let ith_ = INST_TYPE ty_inst ith in
let (A_, forall_ps_t_imp_u_) = dest_thm ith_ in
let (ps_,t_imp_u_) = strip_pforall forall_ps_t_imp_u_ in
let (t_,u_) = dest_imp (t_imp_u_) in
let pvs = freesl ps_ in
let A_vs = freesl A_ in
let B_vs = freesl B in
let tm_inst = fst (match t_ t') in
let (match_vs, unmatch_vs) = partition (C free_in t_) (frees u_) in
let rename = subtract unmatch_vs (subtract A_vs pvs) in
let new_vs = freesl (map (C frev_assoc tm_inst) match_vs) in
let renaming = variants (new_vs@A_vs@B_vs) rename in
let (specs,insts) = partition (C mem (freesl pvs) o snd)
(renaming@tm_inst) in
let spec_list = map (subst specs) ps_ in
let mp_th = MP (PSPECL spec_list (INST insts ith_)) th in
let gen_ps = (filter (\p. null (subtract (rip_pair p) rename)) ps_) in
let qs = map (subst renaming) gen_ps
in
PGENL qs mp_th
) ? failwith `PMATCH_MP: can't instantiate theorem`;;
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