TFL/rules.ML
author wenzelm
Fri Sep 15 22:56:13 2006 +0200 (2006-09-15)
changeset 20548 8ef25fe585a8
parent 20243 8b64a1ea9b1b
child 20951 868120282837
permissions -rw-r--r--
renamed Term.map_term_types to Term.map_types (cf. Term.fold_types);
     1 (*  Title:      TFL/rules.ML
     2     ID:         $Id$
     3     Author:     Konrad Slind, Cambridge University Computer Laboratory
     4     Copyright   1997  University of Cambridge
     5 
     6 Emulation of HOL inference rules for TFL
     7 *)
     8 
     9 signature RULES =
    10 sig
    11   val dest_thm: thm -> term list * term
    12 
    13   (* Inference rules *)
    14   val REFL: cterm -> thm
    15   val ASSUME: cterm -> thm
    16   val MP: thm -> thm -> thm
    17   val MATCH_MP: thm -> thm -> thm
    18   val CONJUNCT1: thm -> thm
    19   val CONJUNCT2: thm -> thm
    20   val CONJUNCTS: thm -> thm list
    21   val DISCH: cterm -> thm -> thm
    22   val UNDISCH: thm  -> thm
    23   val SPEC: cterm -> thm -> thm
    24   val ISPEC: cterm -> thm -> thm
    25   val ISPECL: cterm list -> thm -> thm
    26   val GEN: cterm -> thm -> thm
    27   val GENL: cterm list -> thm -> thm
    28   val LIST_CONJ: thm list -> thm
    29 
    30   val SYM: thm -> thm
    31   val DISCH_ALL: thm -> thm
    32   val FILTER_DISCH_ALL: (term -> bool) -> thm -> thm
    33   val SPEC_ALL: thm -> thm
    34   val GEN_ALL: thm -> thm
    35   val IMP_TRANS: thm -> thm -> thm
    36   val PROVE_HYP: thm -> thm -> thm
    37 
    38   val CHOOSE: cterm * thm -> thm -> thm
    39   val EXISTS: cterm * cterm -> thm -> thm
    40   val EXISTL: cterm list -> thm -> thm
    41   val IT_EXISTS: (cterm*cterm) list -> thm -> thm
    42 
    43   val EVEN_ORS: thm list -> thm list
    44   val DISJ_CASESL: thm -> thm list -> thm
    45 
    46   val list_beta_conv: cterm -> cterm list -> thm
    47   val SUBS: thm list -> thm -> thm
    48   val simpl_conv: simpset -> thm list -> cterm -> thm
    49 
    50   val rbeta: thm -> thm
    51 (* For debugging my isabelle solver in the conditional rewriter *)
    52   val term_ref: term list ref
    53   val thm_ref: thm list ref
    54   val ss_ref: simpset list ref
    55   val tracing: bool ref
    56   val CONTEXT_REWRITE_RULE: term * term list * thm * thm list
    57                              -> thm -> thm * term list
    58   val RIGHT_ASSOC: thm -> thm
    59 
    60   val prove: bool -> cterm * tactic -> thm
    61 end;
    62 
    63 structure Rules: RULES =
    64 struct
    65 
    66 structure S = USyntax;
    67 structure U = Utils;
    68 structure D = Dcterm;
    69 
    70 
    71 fun RULES_ERR func mesg = U.ERR {module = "Rules", func = func, mesg = mesg};
    72 
    73 
    74 fun cconcl thm = D.drop_prop (#prop (Thm.crep_thm thm));
    75 fun chyps thm = map D.drop_prop (#hyps (Thm.crep_thm thm));
    76 
    77 fun dest_thm thm =
    78   let val {prop,hyps,...} = Thm.rep_thm thm
    79   in (map HOLogic.dest_Trueprop hyps, HOLogic.dest_Trueprop prop) end
    80   handle TERM _ => raise RULES_ERR "dest_thm" "missing Trueprop";
    81 
    82 
    83 (* Inference rules *)
    84 
    85 (*---------------------------------------------------------------------------
    86  *        Equality (one step)
    87  *---------------------------------------------------------------------------*)
    88 
    89 fun REFL tm = Thm.reflexive tm RS meta_eq_to_obj_eq
    90   handle THM (msg, _, _) => raise RULES_ERR "REFL" msg;
    91 
    92 fun SYM thm = thm RS sym
    93   handle THM (msg, _, _) => raise RULES_ERR "SYM" msg;
    94 
    95 fun ALPHA thm ctm1 =
    96   let
    97     val ctm2 = Thm.cprop_of thm;
    98     val ctm2_eq = Thm.reflexive ctm2;
    99     val ctm1_eq = Thm.reflexive ctm1;
   100   in Thm.equal_elim (Thm.transitive ctm2_eq ctm1_eq) thm end
   101   handle THM (msg, _, _) => raise RULES_ERR "ALPHA" msg;
   102 
   103 fun rbeta th =
   104   (case D.strip_comb (cconcl th) of
   105     (_, [l, r]) => Thm.transitive th (Thm.beta_conversion false r)
   106   | _ => raise RULES_ERR "rbeta" "");
   107 
   108 
   109 (*----------------------------------------------------------------------------
   110  *        Implication and the assumption list
   111  *
   112  * Assumptions get stuck on the meta-language assumption list. Implications
   113  * are in the object language, so discharging an assumption "A" from theorem
   114  * "B" results in something that looks like "A --> B".
   115  *---------------------------------------------------------------------------*)
   116 
   117 fun ASSUME ctm = Thm.assume (D.mk_prop ctm);
   118 
   119 
   120 (*---------------------------------------------------------------------------
   121  * Implication in TFL is -->. Meta-language implication (==>) is only used
   122  * in the implementation of some of the inference rules below.
   123  *---------------------------------------------------------------------------*)
   124 fun MP th1 th2 = th2 RS (th1 RS mp)
   125   handle THM (msg, _, _) => raise RULES_ERR "MP" msg;
   126 
   127 (*forces the first argument to be a proposition if necessary*)
   128 fun DISCH tm thm = Thm.implies_intr (D.mk_prop tm) thm COMP impI
   129   handle THM (msg, _, _) => raise RULES_ERR "DISCH" msg;
   130 
   131 fun DISCH_ALL thm = fold_rev DISCH (#hyps (Thm.crep_thm thm)) thm;
   132 
   133 
   134 fun FILTER_DISCH_ALL P thm =
   135  let fun check tm = P (#t (Thm.rep_cterm tm))
   136  in  foldr (fn (tm,th) => if check tm then DISCH tm th else th)
   137               thm (chyps thm)
   138  end;
   139 
   140 (* freezeT expensive! *)
   141 fun UNDISCH thm =
   142    let val tm = D.mk_prop (#1 (D.dest_imp (cconcl (Thm.freezeT thm))))
   143    in Thm.implies_elim (thm RS mp) (ASSUME tm) end
   144    handle U.ERR _ => raise RULES_ERR "UNDISCH" ""
   145      | THM _ => raise RULES_ERR "UNDISCH" "";
   146 
   147 fun PROVE_HYP ath bth = MP (DISCH (cconcl ath) bth) ath;
   148 
   149 fun IMP_TRANS th1 th2 = th2 RS (th1 RS Thms.imp_trans)
   150   handle THM (msg, _, _) => raise RULES_ERR "IMP_TRANS" msg;
   151 
   152 
   153 (*----------------------------------------------------------------------------
   154  *        Conjunction
   155  *---------------------------------------------------------------------------*)
   156 
   157 fun CONJUNCT1 thm = thm RS conjunct1
   158   handle THM (msg, _, _) => raise RULES_ERR "CONJUNCT1" msg;
   159 
   160 fun CONJUNCT2 thm = thm RS conjunct2
   161   handle THM (msg, _, _) => raise RULES_ERR "CONJUNCT2" msg;
   162 
   163 fun CONJUNCTS th = CONJUNCTS (CONJUNCT1 th) @ CONJUNCTS (CONJUNCT2 th) handle U.ERR _ => [th];
   164 
   165 fun LIST_CONJ [] = raise RULES_ERR "LIST_CONJ" "empty list"
   166   | LIST_CONJ [th] = th
   167   | LIST_CONJ (th :: rst) = MP (MP (conjI COMP (impI RS impI)) th) (LIST_CONJ rst)
   168       handle THM (msg, _, _) => raise RULES_ERR "LIST_CONJ" msg;
   169 
   170 
   171 (*----------------------------------------------------------------------------
   172  *        Disjunction
   173  *---------------------------------------------------------------------------*)
   174 local val {prop,sign,...} = rep_thm disjI1
   175       val [P,Q] = term_vars prop
   176       val disj1 = Thm.forall_intr (Thm.cterm_of sign Q) disjI1
   177 in
   178 fun DISJ1 thm tm = thm RS (forall_elim (D.drop_prop tm) disj1)
   179   handle THM (msg, _, _) => raise RULES_ERR "DISJ1" msg;
   180 end;
   181 
   182 local val {prop,sign,...} = rep_thm disjI2
   183       val [P,Q] = term_vars prop
   184       val disj2 = Thm.forall_intr (Thm.cterm_of sign P) disjI2
   185 in
   186 fun DISJ2 tm thm = thm RS (forall_elim (D.drop_prop tm) disj2)
   187   handle THM (msg, _, _) => raise RULES_ERR "DISJ2" msg;
   188 end;
   189 
   190 
   191 (*----------------------------------------------------------------------------
   192  *
   193  *                   A1 |- M1, ..., An |- Mn
   194  *     ---------------------------------------------------
   195  *     [A1 |- M1 \/ ... \/ Mn, ..., An |- M1 \/ ... \/ Mn]
   196  *
   197  *---------------------------------------------------------------------------*)
   198 
   199 
   200 fun EVEN_ORS thms =
   201   let fun blue ldisjs [] _ = []
   202         | blue ldisjs (th::rst) rdisjs =
   203             let val tail = tl rdisjs
   204                 val rdisj_tl = D.list_mk_disj tail
   205             in fold_rev DISJ2 ldisjs (DISJ1 th rdisj_tl)
   206                :: blue (ldisjs @ [cconcl th]) rst tail
   207             end handle U.ERR _ => [fold_rev DISJ2 ldisjs th]
   208    in blue [] thms (map cconcl thms) end;
   209 
   210 
   211 (*----------------------------------------------------------------------------
   212  *
   213  *         A |- P \/ Q   B,P |- R    C,Q |- R
   214  *     ---------------------------------------------------
   215  *                     A U B U C |- R
   216  *
   217  *---------------------------------------------------------------------------*)
   218 
   219 fun DISJ_CASES th1 th2 th3 =
   220   let
   221     val c = D.drop_prop (cconcl th1);
   222     val (disj1, disj2) = D.dest_disj c;
   223     val th2' = DISCH disj1 th2;
   224     val th3' = DISCH disj2 th3;
   225   in
   226     th3' RS (th2' RS (th1 RS Thms.tfl_disjE))
   227       handle THM (msg, _, _) => raise RULES_ERR "DISJ_CASES" msg
   228   end;
   229 
   230 
   231 (*-----------------------------------------------------------------------------
   232  *
   233  *       |- A1 \/ ... \/ An     [A1 |- M, ..., An |- M]
   234  *     ---------------------------------------------------
   235  *                           |- M
   236  *
   237  * Note. The list of theorems may be all jumbled up, so we have to
   238  * first organize it to align with the first argument (the disjunctive
   239  * theorem).
   240  *---------------------------------------------------------------------------*)
   241 
   242 fun organize eq =    (* a bit slow - analogous to insertion sort *)
   243  let fun extract a alist =
   244      let fun ex (_,[]) = raise RULES_ERR "organize" "not a permutation.1"
   245            | ex(left,h::t) = if (eq h a) then (h,rev left@t) else ex(h::left,t)
   246      in ex ([],alist)
   247      end
   248      fun place [] [] = []
   249        | place (a::rst) alist =
   250            let val (item,next) = extract a alist
   251            in item::place rst next
   252            end
   253        | place _ _ = raise RULES_ERR "organize" "not a permutation.2"
   254  in place
   255  end;
   256 (* freezeT expensive! *)
   257 fun DISJ_CASESL disjth thl =
   258    let val c = cconcl disjth
   259        fun eq th atm = exists (fn t => HOLogic.dest_Trueprop t
   260                                        aconv term_of atm)
   261                               (#hyps(rep_thm th))
   262        val tml = D.strip_disj c
   263        fun DL th [] = raise RULES_ERR "DISJ_CASESL" "no cases"
   264          | DL th [th1] = PROVE_HYP th th1
   265          | DL th [th1,th2] = DISJ_CASES th th1 th2
   266          | DL th (th1::rst) =
   267             let val tm = #2(D.dest_disj(D.drop_prop(cconcl th)))
   268              in DISJ_CASES th th1 (DL (ASSUME tm) rst) end
   269    in DL (Thm.freezeT disjth) (organize eq tml thl)
   270    end;
   271 
   272 
   273 (*----------------------------------------------------------------------------
   274  *        Universals
   275  *---------------------------------------------------------------------------*)
   276 local (* this is fragile *)
   277       val {prop,sign,...} = rep_thm spec
   278       val x = hd (tl (term_vars prop))
   279       val cTV = ctyp_of sign (type_of x)
   280       val gspec = forall_intr (cterm_of sign x) spec
   281 in
   282 fun SPEC tm thm =
   283    let val {sign,T,...} = rep_cterm tm
   284        val gspec' = instantiate ([(cTV, ctyp_of sign T)], []) gspec
   285    in
   286       thm RS (forall_elim tm gspec')
   287    end
   288 end;
   289 
   290 fun SPEC_ALL thm = fold SPEC (#1(D.strip_forall(cconcl thm))) thm;
   291 
   292 val ISPEC = SPEC
   293 val ISPECL = fold ISPEC;
   294 
   295 (* Not optimized! Too complicated. *)
   296 local val {prop,sign,...} = rep_thm allI
   297       val [P] = add_term_vars (prop, [])
   298       fun cty_theta s = map (fn (i, (S, ty)) => (ctyp_of s (TVar (i, S)), ctyp_of s ty))
   299       fun ctm_theta s = map (fn (i, (_, tm2)) =>
   300                              let val ctm2 = cterm_of s tm2
   301                              in (cterm_of s (Var(i,#T(rep_cterm ctm2))), ctm2)
   302                              end)
   303       fun certify s (ty_theta,tm_theta) =
   304         (cty_theta s (Vartab.dest ty_theta),
   305          ctm_theta s (Vartab.dest tm_theta))
   306 in
   307 fun GEN v th =
   308    let val gth = forall_intr v th
   309        val {prop=Const("all",_)$Abs(x,ty,rst),sign,...} = rep_thm gth
   310        val P' = Abs(x,ty, HOLogic.dest_Trueprop rst)  (* get rid of trueprop *)
   311        val theta = Pattern.match sign (P,P') (Vartab.empty, Vartab.empty);
   312        val allI2 = instantiate (certify sign theta) allI
   313        val thm = Thm.implies_elim allI2 gth
   314        val {prop = tp $ (A $ Abs(_,_,M)),sign,...} = rep_thm thm
   315        val prop' = tp $ (A $ Abs(x,ty,M))
   316    in ALPHA thm (cterm_of sign prop')
   317    end
   318 end;
   319 
   320 val GENL = fold_rev GEN;
   321 
   322 fun GEN_ALL thm =
   323    let val {prop,sign,...} = rep_thm thm
   324        val tycheck = cterm_of sign
   325        val vlist = map tycheck (add_term_vars (prop, []))
   326   in GENL vlist thm
   327   end;
   328 
   329 
   330 fun MATCH_MP th1 th2 =
   331    if (D.is_forall (D.drop_prop(cconcl th1)))
   332    then MATCH_MP (th1 RS spec) th2
   333    else MP th1 th2;
   334 
   335 
   336 (*----------------------------------------------------------------------------
   337  *        Existentials
   338  *---------------------------------------------------------------------------*)
   339 
   340 
   341 
   342 (*---------------------------------------------------------------------------
   343  * Existential elimination
   344  *
   345  *      A1 |- ?x.t[x]   ,   A2, "t[v]" |- t'
   346  *      ------------------------------------     (variable v occurs nowhere)
   347  *                A1 u A2 |- t'
   348  *
   349  *---------------------------------------------------------------------------*)
   350 
   351 fun CHOOSE (fvar, exth) fact =
   352   let
   353     val lam = #2 (D.dest_comb (D.drop_prop (cconcl exth)))
   354     val redex = D.capply lam fvar
   355     val {sign, t = t$u,...} = Thm.rep_cterm redex
   356     val residue = Thm.cterm_of sign (Term.betapply (t, u))
   357   in
   358     GEN fvar (DISCH residue fact) RS (exth RS Thms.choose_thm)
   359       handle THM (msg, _, _) => raise RULES_ERR "CHOOSE" msg
   360   end;
   361 
   362 local val {prop,sign,...} = rep_thm exI
   363       val [P,x] = term_vars prop
   364 in
   365 fun EXISTS (template,witness) thm =
   366    let val {prop,sign,...} = rep_thm thm
   367        val P' = cterm_of sign P
   368        val x' = cterm_of sign x
   369        val abstr = #2 (D.dest_comb template)
   370    in
   371    thm RS (cterm_instantiate[(P',abstr), (x',witness)] exI)
   372      handle THM (msg, _, _) => raise RULES_ERR "EXISTS" msg
   373    end
   374 end;
   375 
   376 (*----------------------------------------------------------------------------
   377  *
   378  *         A |- M
   379  *   -------------------   [v_1,...,v_n]
   380  *    A |- ?v1...v_n. M
   381  *
   382  *---------------------------------------------------------------------------*)
   383 
   384 fun EXISTL vlist th =
   385   fold_rev (fn v => fn thm => EXISTS(D.mk_exists(v,cconcl thm), v) thm)
   386            vlist th;
   387 
   388 
   389 (*----------------------------------------------------------------------------
   390  *
   391  *       A |- M[x_1,...,x_n]
   392  *   ----------------------------   [(x |-> y)_1,...,(x |-> y)_n]
   393  *       A |- ?y_1...y_n. M
   394  *
   395  *---------------------------------------------------------------------------*)
   396 (* Could be improved, but needs "subst_free" for certified terms *)
   397 
   398 fun IT_EXISTS blist th =
   399    let val {sign,...} = rep_thm th
   400        val tych = cterm_of sign
   401        val detype = #t o rep_cterm
   402        val blist' = map (fn (x,y) => (detype x, detype y)) blist
   403        fun ex v M  = cterm_of sign (S.mk_exists{Bvar=v,Body = M})
   404 
   405   in
   406   fold_rev (fn (b as (r1,r2)) => fn thm =>
   407         EXISTS(ex r2 (subst_free [b]
   408                    (HOLogic.dest_Trueprop(#prop(rep_thm thm)))), tych r1)
   409               thm)
   410        blist' th
   411   end;
   412 
   413 (*---------------------------------------------------------------------------
   414  *  Faster version, that fails for some as yet unknown reason
   415  * fun IT_EXISTS blist th =
   416  *    let val {sign,...} = rep_thm th
   417  *        val tych = cterm_of sign
   418  *        fun detype (x,y) = ((#t o rep_cterm) x, (#t o rep_cterm) y)
   419  *   in
   420  *  fold (fn (b as (r1,r2), thm) =>
   421  *  EXISTS(D.mk_exists(r2, tych(subst_free[detype b](#t(rep_cterm(cconcl thm))))),
   422  *           r1) thm)  blist th
   423  *   end;
   424  *---------------------------------------------------------------------------*)
   425 
   426 (*----------------------------------------------------------------------------
   427  *        Rewriting
   428  *---------------------------------------------------------------------------*)
   429 
   430 fun SUBS thl =
   431   rewrite_rule (map (fn th => th RS eq_reflection handle THM _ => th) thl);
   432 
   433 val rew_conv = MetaSimplifier.rewrite_cterm (true, false, false) (K (K NONE));
   434 
   435 fun simpl_conv ss thl ctm =
   436  rew_conv (ss addsimps thl) ctm RS meta_eq_to_obj_eq;
   437 
   438 
   439 val RIGHT_ASSOC = rewrite_rule [Thms.disj_assoc];
   440 
   441 
   442 
   443 (*---------------------------------------------------------------------------
   444  *                  TERMINATION CONDITION EXTRACTION
   445  *---------------------------------------------------------------------------*)
   446 
   447 
   448 (* Object language quantifier, i.e., "!" *)
   449 fun Forall v M = S.mk_forall{Bvar=v, Body=M};
   450 
   451 
   452 (* Fragile: it's a cong if it is not "R y x ==> cut f R x y = f y" *)
   453 fun is_cong thm =
   454   let val {prop, ...} = rep_thm thm
   455   in case prop
   456      of (Const("==>",_)$(Const("Trueprop",_)$ _) $
   457          (Const("==",_) $ (Const ("Wellfounded_Recursion.cut",_) $ f $ R $ a $ x) $ _)) => false
   458       | _ => true
   459   end;
   460 
   461 
   462 
   463 fun dest_equal(Const ("==",_) $
   464                (Const ("Trueprop",_) $ lhs)
   465                $ (Const ("Trueprop",_) $ rhs)) = {lhs=lhs, rhs=rhs}
   466   | dest_equal(Const ("==",_) $ lhs $ rhs)  = {lhs=lhs, rhs=rhs}
   467   | dest_equal tm = S.dest_eq tm;
   468 
   469 fun get_lhs tm = #lhs(dest_equal (HOLogic.dest_Trueprop tm));
   470 
   471 fun dest_all used (Const("all",_) $ (a as Abs _)) = S.dest_abs used a
   472   | dest_all _ _ = raise RULES_ERR "dest_all" "not a !!";
   473 
   474 val is_all = can (dest_all []);
   475 
   476 fun strip_all used fm =
   477    if (is_all fm)
   478    then let val ({Bvar, Body}, used') = dest_all used fm
   479             val (bvs, core, used'') = strip_all used' Body
   480         in ((Bvar::bvs), core, used'')
   481         end
   482    else ([], fm, used);
   483 
   484 fun break_all(Const("all",_) $ Abs (_,_,body)) = body
   485   | break_all _ = raise RULES_ERR "break_all" "not a !!";
   486 
   487 fun list_break_all(Const("all",_) $ Abs (s,ty,body)) =
   488      let val (L,core) = list_break_all body
   489      in ((s,ty)::L, core)
   490      end
   491   | list_break_all tm = ([],tm);
   492 
   493 (*---------------------------------------------------------------------------
   494  * Rename a term of the form
   495  *
   496  *      !!x1 ...xn. x1=M1 ==> ... ==> xn=Mn
   497  *                  ==> ((%v1...vn. Q) x1 ... xn = g x1 ... xn.
   498  * to one of
   499  *
   500  *      !!v1 ... vn. v1=M1 ==> ... ==> vn=Mn
   501  *      ==> ((%v1...vn. Q) v1 ... vn = g v1 ... vn.
   502  *
   503  * This prevents name problems in extraction, and helps the result to read
   504  * better. There is a problem with varstructs, since they can introduce more
   505  * than n variables, and some extra reasoning needs to be done.
   506  *---------------------------------------------------------------------------*)
   507 
   508 fun get ([],_,L) = rev L
   509   | get (ant::rst,n,L) =
   510       case (list_break_all ant)
   511         of ([],_) => get (rst, n+1,L)
   512          | (vlist,body) =>
   513             let val eq = Logic.strip_imp_concl body
   514                 val (f,args) = S.strip_comb (get_lhs eq)
   515                 val (vstrl,_) = S.strip_abs f
   516                 val names  =
   517                   Name.variant_list (add_term_names(body, [])) (map (#1 o dest_Free) vstrl)
   518             in get (rst, n+1, (names,n)::L) end
   519             handle TERM _ => get (rst, n+1, L)
   520               | U.ERR _ => get (rst, n+1, L);
   521 
   522 (* Note: rename_params_rule counts from 1, not 0 *)
   523 fun rename thm =
   524   let val {prop,sign,...} = rep_thm thm
   525       val tych = cterm_of sign
   526       val ants = Logic.strip_imp_prems prop
   527       val news = get (ants,1,[])
   528   in
   529   fold rename_params_rule news thm
   530   end;
   531 
   532 
   533 (*---------------------------------------------------------------------------
   534  * Beta-conversion to the rhs of an equation (taken from hol90/drule.sml)
   535  *---------------------------------------------------------------------------*)
   536 
   537 fun list_beta_conv tm =
   538   let fun rbeta th = Thm.transitive th (beta_conversion false (#2(D.dest_eq(cconcl th))))
   539       fun iter [] = Thm.reflexive tm
   540         | iter (v::rst) = rbeta (combination(iter rst) (Thm.reflexive v))
   541   in iter  end;
   542 
   543 
   544 (*---------------------------------------------------------------------------
   545  * Trace information for the rewriter
   546  *---------------------------------------------------------------------------*)
   547 val term_ref = ref[] : term list ref
   548 val ss_ref = ref [] : simpset list ref;
   549 val thm_ref = ref [] : thm list ref;
   550 val tracing = ref false;
   551 
   552 fun say s = if !tracing then writeln s else ();
   553 
   554 fun print_thms s L =
   555   say (cat_lines (s :: map string_of_thm L));
   556 
   557 fun print_cterms s L =
   558   say (cat_lines (s :: map string_of_cterm L));
   559 
   560 
   561 (*---------------------------------------------------------------------------
   562  * General abstraction handlers, should probably go in USyntax.
   563  *---------------------------------------------------------------------------*)
   564 fun mk_aabs (vstr, body) =
   565   S.mk_abs {Bvar = vstr, Body = body}
   566   handle U.ERR _ => S.mk_pabs {varstruct = vstr, body = body};
   567 
   568 fun list_mk_aabs (vstrl,tm) =
   569     fold_rev (fn vstr => fn tm => mk_aabs(vstr,tm)) vstrl tm;
   570 
   571 fun dest_aabs used tm =
   572    let val ({Bvar,Body}, used') = S.dest_abs used tm
   573    in (Bvar, Body, used') end
   574    handle U.ERR _ =>
   575      let val {varstruct, body, used} = S.dest_pabs used tm
   576      in (varstruct, body, used) end;
   577 
   578 fun strip_aabs used tm =
   579    let val (vstr, body, used') = dest_aabs used tm
   580        val (bvs, core, used'') = strip_aabs used' body
   581    in (vstr::bvs, core, used'') end
   582    handle U.ERR _ => ([], tm, used);
   583 
   584 fun dest_combn tm 0 = (tm,[])
   585   | dest_combn tm n =
   586      let val {Rator,Rand} = S.dest_comb tm
   587          val (f,rands) = dest_combn Rator (n-1)
   588      in (f,Rand::rands)
   589      end;
   590 
   591 
   592 
   593 
   594 local fun dest_pair M = let val {fst,snd} = S.dest_pair M in (fst,snd) end
   595       fun mk_fst tm =
   596           let val ty as Type("*", [fty,sty]) = type_of tm
   597           in  Const ("fst", ty --> fty) $ tm  end
   598       fun mk_snd tm =
   599           let val ty as Type("*", [fty,sty]) = type_of tm
   600           in  Const ("snd", ty --> sty) $ tm  end
   601 in
   602 fun XFILL tych x vstruct =
   603   let fun traverse p xocc L =
   604         if (is_Free p)
   605         then tych xocc::L
   606         else let val (p1,p2) = dest_pair p
   607              in traverse p1 (mk_fst xocc) (traverse p2  (mk_snd xocc) L)
   608              end
   609   in
   610   traverse vstruct x []
   611 end end;
   612 
   613 (*---------------------------------------------------------------------------
   614  * Replace a free tuple (vstr) by a universally quantified variable (a).
   615  * Note that the notion of "freeness" for a tuple is different than for a
   616  * variable: if variables in the tuple also occur in any other place than
   617  * an occurrences of the tuple, they aren't "free" (which is thus probably
   618  *  the wrong word to use).
   619  *---------------------------------------------------------------------------*)
   620 
   621 fun VSTRUCT_ELIM tych a vstr th =
   622   let val L = S.free_vars_lr vstr
   623       val bind1 = tych (HOLogic.mk_Trueprop (HOLogic.mk_eq(a,vstr)))
   624       val thm1 = implies_intr bind1 (SUBS [SYM(assume bind1)] th)
   625       val thm2 = forall_intr_list (map tych L) thm1
   626       val thm3 = forall_elim_list (XFILL tych a vstr) thm2
   627   in refl RS
   628      rewrite_rule [Thm.symmetric (surjective_pairing RS eq_reflection)] thm3
   629   end;
   630 
   631 fun PGEN tych a vstr th =
   632   let val a1 = tych a
   633       val vstr1 = tych vstr
   634   in
   635   forall_intr a1
   636      (if (is_Free vstr)
   637       then cterm_instantiate [(vstr1,a1)] th
   638       else VSTRUCT_ELIM tych a vstr th)
   639   end;
   640 
   641 
   642 (*---------------------------------------------------------------------------
   643  * Takes apart a paired beta-redex, looking like "(\(x,y).N) vstr", into
   644  *
   645  *     (([x,y],N),vstr)
   646  *---------------------------------------------------------------------------*)
   647 fun dest_pbeta_redex used M n =
   648   let val (f,args) = dest_combn M n
   649       val dummy = dest_aabs used f
   650   in (strip_aabs used f,args)
   651   end;
   652 
   653 fun pbeta_redex M n = can (U.C (dest_pbeta_redex []) n) M;
   654 
   655 fun dest_impl tm =
   656   let val ants = Logic.strip_imp_prems tm
   657       val eq = Logic.strip_imp_concl tm
   658   in (ants,get_lhs eq)
   659   end;
   660 
   661 fun restricted t = isSome (S.find_term
   662                             (fn (Const("Wellfounded_Recursion.cut",_)) =>true | _ => false)
   663                             t)
   664 
   665 fun CONTEXT_REWRITE_RULE (func, G, cut_lemma, congs) th =
   666  let val globals = func::G
   667      val ss0 = Simplifier.theory_context (Thm.theory_of_thm th) empty_ss
   668      val pbeta_reduce = simpl_conv ss0 [split_conv RS eq_reflection];
   669      val tc_list = ref[]: term list ref
   670      val dummy = term_ref := []
   671      val dummy = thm_ref  := []
   672      val dummy = ss_ref  := []
   673      val cut_lemma' = cut_lemma RS eq_reflection
   674      fun prover used ss thm =
   675      let fun cong_prover ss thm =
   676          let val dummy = say "cong_prover:"
   677              val cntxt = MetaSimplifier.prems_of_ss ss
   678              val dummy = print_thms "cntxt:" cntxt
   679              val dummy = say "cong rule:"
   680              val dummy = say (string_of_thm thm)
   681              val dummy = thm_ref := (thm :: !thm_ref)
   682              val dummy = ss_ref := (ss :: !ss_ref)
   683              (* Unquantified eliminate *)
   684              fun uq_eliminate (thm,imp,sign) =
   685                  let val tych = cterm_of sign
   686                      val dummy = print_cterms "To eliminate:" [tych imp]
   687                      val ants = map tych (Logic.strip_imp_prems imp)
   688                      val eq = Logic.strip_imp_concl imp
   689                      val lhs = tych(get_lhs eq)
   690                      val ss' = MetaSimplifier.add_prems (map ASSUME ants) ss
   691                      val lhs_eq_lhs1 = MetaSimplifier.rewrite_cterm (false,true,false) (prover used) ss' lhs
   692                        handle U.ERR _ => Thm.reflexive lhs
   693                      val dummy = print_thms "proven:" [lhs_eq_lhs1]
   694                      val lhs_eq_lhs2 = implies_intr_list ants lhs_eq_lhs1
   695                      val lhs_eeq_lhs2 = lhs_eq_lhs2 RS meta_eq_to_obj_eq
   696                   in
   697                   lhs_eeq_lhs2 COMP thm
   698                   end
   699              fun pq_eliminate (thm,sign,vlist,imp_body,lhs_eq) =
   700               let val ((vstrl, _, used'), args) = dest_pbeta_redex used lhs_eq (length vlist)
   701                   val dummy = assert (forall (op aconv)
   702                                       (ListPair.zip (vlist, args)))
   703                                "assertion failed in CONTEXT_REWRITE_RULE"
   704                   val imp_body1 = subst_free (ListPair.zip (args, vstrl))
   705                                              imp_body
   706                   val tych = cterm_of sign
   707                   val ants1 = map tych (Logic.strip_imp_prems imp_body1)
   708                   val eq1 = Logic.strip_imp_concl imp_body1
   709                   val Q = get_lhs eq1
   710                   val QeqQ1 = pbeta_reduce (tych Q)
   711                   val Q1 = #2(D.dest_eq(cconcl QeqQ1))
   712                   val ss' = MetaSimplifier.add_prems (map ASSUME ants1) ss
   713                   val Q1eeqQ2 = MetaSimplifier.rewrite_cterm (false,true,false) (prover used') ss' Q1
   714                                 handle U.ERR _ => Thm.reflexive Q1
   715                   val Q2 = #2 (Logic.dest_equals (Thm.prop_of Q1eeqQ2))
   716                   val Q3 = tych(list_comb(list_mk_aabs(vstrl,Q2),vstrl))
   717                   val Q2eeqQ3 = Thm.symmetric(pbeta_reduce Q3 RS eq_reflection)
   718                   val thA = Thm.transitive(QeqQ1 RS eq_reflection) Q1eeqQ2
   719                   val QeeqQ3 = Thm.transitive thA Q2eeqQ3 handle THM _ =>
   720                                ((Q2eeqQ3 RS meta_eq_to_obj_eq)
   721                                 RS ((thA RS meta_eq_to_obj_eq) RS trans))
   722                                 RS eq_reflection
   723                   val impth = implies_intr_list ants1 QeeqQ3
   724                   val impth1 = impth RS meta_eq_to_obj_eq
   725                   (* Need to abstract *)
   726                   val ant_th = U.itlist2 (PGEN tych) args vstrl impth1
   727               in ant_th COMP thm
   728               end
   729              fun q_eliminate (thm,imp,sign) =
   730               let val (vlist, imp_body, used') = strip_all used imp
   731                   val (ants,Q) = dest_impl imp_body
   732               in if (pbeta_redex Q) (length vlist)
   733                  then pq_eliminate (thm,sign,vlist,imp_body,Q)
   734                  else
   735                  let val tych = cterm_of sign
   736                      val ants1 = map tych ants
   737                      val ss' = MetaSimplifier.add_prems (map ASSUME ants1) ss
   738                      val Q_eeq_Q1 = MetaSimplifier.rewrite_cterm
   739                         (false,true,false) (prover used') ss' (tych Q)
   740                       handle U.ERR _ => Thm.reflexive (tych Q)
   741                      val lhs_eeq_lhs2 = implies_intr_list ants1 Q_eeq_Q1
   742                      val lhs_eq_lhs2 = lhs_eeq_lhs2 RS meta_eq_to_obj_eq
   743                      val ant_th = forall_intr_list(map tych vlist)lhs_eq_lhs2
   744                  in
   745                  ant_th COMP thm
   746               end end
   747 
   748              fun eliminate thm =
   749                case (rep_thm thm)
   750                of {prop = (Const("==>",_) $ imp $ _), sign, ...} =>
   751                    eliminate
   752                     (if not(is_all imp)
   753                      then uq_eliminate (thm,imp,sign)
   754                      else q_eliminate (thm,imp,sign))
   755                             (* Assume that the leading constant is ==,   *)
   756                 | _ => thm  (* if it is not a ==>                        *)
   757          in SOME(eliminate (rename thm)) end
   758          handle U.ERR _ => NONE    (* FIXME handle THM as well?? *)
   759 
   760         fun restrict_prover ss thm =
   761           let val dummy = say "restrict_prover:"
   762               val cntxt = rev(MetaSimplifier.prems_of_ss ss)
   763               val dummy = print_thms "cntxt:" cntxt
   764               val {prop = Const("==>",_) $ (Const("Trueprop",_) $ A) $ _,
   765                    sign,...} = rep_thm thm
   766               fun genl tm = let val vlist = gen_rems (op aconv)
   767                                            (add_term_frees(tm,[]), globals)
   768                             in fold_rev Forall vlist tm
   769                             end
   770               (*--------------------------------------------------------------
   771                * This actually isn't quite right, since it will think that
   772                * not-fully applied occs. of "f" in the context mean that the
   773                * current call is nested. The real solution is to pass in a
   774                * term "f v1..vn" which is a pattern that any full application
   775                * of "f" will match.
   776                *-------------------------------------------------------------*)
   777               val func_name = #1(dest_Const func)
   778               fun is_func (Const (name,_)) = (name = func_name)
   779                 | is_func _                = false
   780               val rcontext = rev cntxt
   781               val cncl = HOLogic.dest_Trueprop o Thm.prop_of
   782               val antl = case rcontext of [] => []
   783                          | _   => [S.list_mk_conj(map cncl rcontext)]
   784               val TC = genl(S.list_mk_imp(antl, A))
   785               val dummy = print_cterms "func:" [cterm_of sign func]
   786               val dummy = print_cterms "TC:"
   787                               [cterm_of sign (HOLogic.mk_Trueprop TC)]
   788               val dummy = tc_list := (TC :: !tc_list)
   789               val nestedp = isSome (S.find_term is_func TC)
   790               val dummy = if nestedp then say "nested" else say "not_nested"
   791               val dummy = term_ref := ([func,TC]@(!term_ref))
   792               val th' = if nestedp then raise RULES_ERR "solver" "nested function"
   793                         else let val cTC = cterm_of sign
   794                                               (HOLogic.mk_Trueprop TC)
   795                              in case rcontext of
   796                                 [] => SPEC_ALL(ASSUME cTC)
   797                                | _ => MP (SPEC_ALL (ASSUME cTC))
   798                                          (LIST_CONJ rcontext)
   799                              end
   800               val th'' = th' RS thm
   801           in SOME (th'')
   802           end handle U.ERR _ => NONE    (* FIXME handle THM as well?? *)
   803     in
   804     (if (is_cong thm) then cong_prover else restrict_prover) ss thm
   805     end
   806     val ctm = cprop_of th
   807     val names = add_term_names (term_of ctm, [])
   808     val th1 = MetaSimplifier.rewrite_cterm(false,true,false)
   809       (prover names) (ss0 addsimps [cut_lemma'] addeqcongs congs) ctm
   810     val th2 = equal_elim th1 th
   811  in
   812  (th2, List.filter (not o restricted) (!tc_list))
   813  end;
   814 
   815 
   816 fun prove strict (ptm, tac) =
   817   let
   818     val {thy, t, ...} = Thm.rep_cterm ptm;
   819     val ctxt = ProofContext.init thy |> Variable.fix_frees t;
   820   in
   821     if strict then Goal.prove ctxt [] [] t (K tac)
   822     else Goal.prove ctxt [] [] t (K tac)
   823       handle ERROR msg => (warning msg; raise RULES_ERR "prove" msg)
   824   end;
   825 
   826 end;