(* isac's rewriter

   (c) Walther Neuper 2000

use"ProgLang/rewrite.sml"; 

use"rewrite.sml";

*)

exception NO_REWRITE;

exception STOP_REW_SUB; (*WN050820 quick and dirty*)

(*17.6.00: rewrite by going down the term with rew_sub*)

(* val (thy, i, bdv, tless, rls, put_asm, thm, ct) =

       (thy, 1, []:(Term.term * Term.term) list, rew_ord, erls, bool,thm,term);

   *)

fun rewrite__ thy i bdv tless rls put_asm thm ct =

  (let

    val (t',asms,lrd,rew) = 

	rew_sub thy i bdv tless rls put_asm [(*root of the term*)]

		(((inst_bdv bdv) o norm o #prop o rep_thm) thm) ct;

  in if rew then SOME (t', distinct asms)

     else NONE end)

(* one rewrite (possibly conditional, ordered) EXOR exn EXOR go into subterms *)

and rew_sub thy i bdv tless rls put_asm lrd r t = 

  ((*tracing ("@@@ rew_sub begin: t = "^(term2str t));*)

    let                  (* copy from Pure/thm.ML: fun rewritec *)

     val (lhs, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop

                       o Logic.strip_imp_concl) r;

     val r' = Envir.subst_term (Pattern.match thy (lhs, t) 

					      (Vartab.empty, Vartab.empty)) r;

     val p' = map HOLogic.dest_Trueprop ((fst o Logic.strip_prems) 

                                             (Logic.count_prems r', [], r'));

     val t' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop 

               o Logic.strip_imp_concl) r';

     (*val _= tracing("@@@ rew_sub match: t'= "^(term2str t'));*)

     val _= if ! trace_rewrite andalso i < ! depth andalso p' <> []

	    then tracing((idt"#"(i+1))^" eval asms: "^(term2str r')) else();

     val (t'',p'') =                                   (*conditional rewriting*)

	 let val (simpl_p', nofalse) = eval__true thy (i+1) p' bdv rls 	     

	 in if nofalse

	    then (if ! trace_rewrite andalso i < ! depth andalso p' <> []

		  then tracing((idt"#"(i+1))^" asms accepted: "^(terms2str p')^

			       "   stored: "^(terms2str simpl_p'))

		  else(); (t',simpl_p'))             (* uncond.rew. from above*)

	    else 

		(if ! trace_rewrite andalso i < ! depth 

		 then tracing((idt"#"(i+1))^" asms false: "^(terms2str p')) 

		 else(); raise STOP_REW_SUB (*dont go into subterms of cond*))

	 end

   in if perm lhs rhs andalso not (tless bdv (t',t))       (*ordered rewriting*)

	then (if ! trace_rewrite andalso i < ! depth 

	      then tracing((idt"#"i)^" not: \""^

	      (term2str t)^"\" > \""^

	      (term2str t')^"\"") else (); 

	      raise NO_REWRITE )

	else ((*tracing("##@ rew_sub: (t''= "^(term2str t'')^

		      ", p'' ="^(terms2str p'')^", true)");*)

	      (t'',p'',[],true))

   end

   ) handle _ (*NO_REWRITE WN050820 causes diff.behav. in tests + MATCH!*) => 

     ((*tracing ("@@@ rew_sub gosub: t = "^(term2str t));*)

      case t of

	Const(s,T) => (Const(s,T),[],lrd,false)

      | Free(s,T) => (Free(s,T),[],lrd,false)

      | Var(n,T) => (Var(n,T),[],lrd,false)

      | Bound i => (Bound i,[],lrd,false)

      | Abs(s,T,body) => 

	  let val (t', asms, lrd, rew) = 

		  rew_sub thy i bdv tless rls put_asm (lrd@[D]) r body

	  in (Abs(s,T,t'), asms, [], rew) end

      | t1 $ t2 => 

	  let val (t2', asm2, lrd, rew2) = 

		  rew_sub thy i bdv tless rls put_asm (lrd@[R]) r t2

	  in if rew2 then (t1 $ t2', asm2, lrd, true)

	     else let val (t1', asm1, lrd, rew1) = 

	       rew_sub thy i bdv tless rls put_asm (lrd@[L]) r t1

		  in if rew1 then (t1' $ t2, asm1, lrd, true)

		     else (t1 $ t2,[], lrd, false) end

	  end)

(* simplify asumptions until one evaluates to false, store intermined's (x~=0)*)

and eval__true thy i asms bdv rls =

  if asms = [HOLogic.true_const] orelse asms = [] then ([], true)

  (* this allows to check Rrls with prepat = ([HOLogic.true_const], pat) *)

  else if asms = [HOLogic.false_const] then ([], false)

  else let                            

      fun chk indets [] = (indets, true)(*return asms<>True until false*)

	| chk indets (a::asms) =

	  (case rewrite__set_ thy (i+1) false bdv rls a of

	      NONE => (chk (indets @ [a]) asms)

	    | SOME (t, a') =>

	      if t = HOLogic.true_const 

	      then (chk (indets @ a') asms)

	      else if t = HOLogic.false_const then ([], false)

	      (*asm false .. thm not applied ^^^; continue until False vvv*)

	      else chk (indets @ [t] @ a') asms);

  in chk [] asms end

(* rewrite with a rule set, which must not be the empty Erls *)

and rewrite__set_ _ _ __ Erls t = 

    error("rewrite__set_ called with 'Erls' for '"^term2str t^"'")

  (* rewrite with a 'reverse rule set' implemented by ML code *)

  | rewrite__set_ thy i _ _ (rrls as Rrls _) t =

    let val _= if ! trace_rewrite andalso i < ! depth 

	       then tracing ((idt"#"i)^" rls: "^(id_rls rrls)^" on: "^

			     (term2str t)) else ()

	val (t', asm, rew) = app_rev thy (i+1) rrls t

    in if rew then SOME (t', distinct asm)

       else NONE end

  (* rewrite with a rule set containing Thms or Calculations *)

  | rewrite__set_ thy i put_asm bdv rls ct =

(* val (thy, i, put_asm, bdv, rls, ct) = (thy, 1, bool, [], rls, term);

   *)

  let

    datatype switch = Appl | Noap;

    fun rew_once ruls asm ct Noap [] = (ct,asm)

      | rew_once ruls asm ct Appl [] = 

	(case rls of Rls _ => rew_once ruls asm ct Noap ruls

		   | Seq _ => (ct,asm))

      | rew_once ruls asm ct apno (rul::thms) =

(* val (ruls, asm, ct, apno, (rul::thms)) = (ruls, [], ct, Noap, ruls);

   val Thm (thmid, thm) = rul;

   *)

      case rul of

	Thm (thmid, thm) =>

	  (if !trace_rewrite andalso i < ! depth 

	   then tracing((idt"#"(i+1))^" try thm: "^thmid) else ();

	   case rewrite__ thy (i+1) bdv ((snd o #rew_ord o rep_rls) rls)

	     ((#erls o rep_rls) rls) put_asm thm ct of

	     NONE => rew_once ruls asm ct apno thms

	   | SOME (ct',asm') => (if ! trace_rewrite andalso i < ! depth 

	     then tracing((idt"="(i+1))^" rewrites to: "^

			  (term2str ct')) else ();

	       rew_once ruls (union (op =) asm asm') ct' Appl (rul::thms)))

      | Calc (cc as (op_,_)) => 

	  (let val _= if !trace_rewrite andalso i < ! depth then

		      tracing((idt"#"(i+1))^" try calc: "^op_^"'") else ();

	     val ct = uminus_to_string ct

	   in case get_calculation_ thy cc ct of

	     NONE => rew_once ruls asm ct apno thms

	   | SOME (thmid, thm') => 

	       let 

		 val pairopt = 

		   rewrite__ thy (i+1) bdv ((snd o #rew_ord o rep_rls) rls)

		   ((#erls o rep_rls) rls) put_asm thm' ct;

		 val _ = if pairopt <> NONE then () 

			 else error("rewrite_set_, rewrite_ \""^

			 (string_of_thmI thm')^"\" "^(term2str ct)^" = NONE")

		 val _ = if ! trace_rewrite andalso i < ! depth 

			   then tracing((idt"="(i+1))^" calc. to: "^

					(term2str ((fst o the) pairopt)))

			 else()

	       in rew_once ruls asm ((fst o the) pairopt) Appl (rul::thms) end

	   end)

      | Cal1 (cc as (op_,_)) => 

	  (let val _= if !trace_rewrite andalso i < ! depth then

		      tracing((idt"#"(i+1))^" try cal1: "^op_^"'") else ();

	     val ct = uminus_to_string ct

	   in case get_calculation1_ thy cc ct of

	     NONE => (ct, asm)

	   | SOME (thmid, thm') =>

	       let 

		 val pairopt = 

		   rewrite__ thy (i+1) bdv ((snd o #rew_ord o rep_rls) rls)

		   ((#erls o rep_rls) rls) put_asm thm' ct;

		 val _ = if pairopt <> NONE then () 

			 else error("rewrite_set_, rewrite_ \""^

			 (string_of_thmI thm')^"\" "^(term2str ct)^" = NONE")

		 val _ = if ! trace_rewrite andalso i < ! depth 

			   then tracing((idt"="(i+1))^" cal1. to: "^

					(term2str ((fst o the) pairopt)))

			 else()

	       in the pairopt end

	   end)

      | Rls_ rls' => 

	(case rewrite__set_ thy (i+1) put_asm bdv rls' ct of

	     SOME (t',asm') => rew_once ruls (union (op =) asm asm') t' Appl thms

	   | NONE => rew_once ruls asm ct apno thms);

    val ruls = (#rules o rep_rls) rls;

    val _= if ! trace_rewrite andalso i < ! depth 

	   then tracing ((idt"#"i)^" rls: "^(id_rls rls)^" on: "^

			 (term2str ct)) else ()

    val (ct',asm') = rew_once ruls [] ct Noap ruls;

  in if ct = ct' then NONE else SOME (ct', distinct asm') end

and app_rev thy i rrls t = 

    let (* check a (precond, pattern) of a rev-set; stops with 1st true *)

	fun chk_prepat thy erls [] t = true

	  | chk_prepat thy erls prepat t =

	    let fun chk (pres, pat) =

		    (let val subst: Type.tyenv * Envir.tenv = 

			     Pattern.match thy (pat, t)

					    (Vartab.empty, Vartab.empty)

			 val _ = tracing ("app_rev: pres=------------------");

			 val _ = tracing ("app_rev: pres=" ^ terms2str pres);

			 val _ = tracing ("app_rev: pat =" ^ term2str pat);

			 val _ = tracing ("app_rev: t   =" ^ term2str t);

		     in snd (eval__true thy (i+1) 

					(map (Envir.subst_term subst) pres)

					[] erls)

		     end)

		    handle _ => false

		fun scan_ f [] = false (*scan_ NEVER called by []*)

		  | scan_ f (pp::pps) = if f pp then true

					else scan_ f pps;

	    in scan_ chk prepat end;

	(* apply the normal_form of a rev-set *)

	fun app_rev' thy (Rrls{erls,prepat,scr=Rfuns{normal_form,...},...}) t =

	    if chk_prepat thy erls prepat t

	    then ((*tracing("### app_rev': t = "^(term2str t));*)

                  normal_form t)

	    else NONE;

	val opt = app_rev' thy rrls t

    in case opt of

	   SOME (t', asm) => (t', asm, true)

	 | NONE => app_sub thy i rrls t

    end

and app_sub thy i rrls t =

     ((*tracing("### app_sub: subterm = "^(term2str t));*)

      case t of

	Const (s, T) => (Const(s, T), [], false)

      | Free (s, T) => (Free(s, T), [], false)

      | Var (n, T) => (Var(n, T), [], false)

      | Bound i => (Bound i, [], false)

      | Abs (s, T, body) => 

	  let val (t', asm, rew) = app_rev thy i rrls body

	  in (Abs(s, T, t'), asm, rew) end

      | t1 $ t2 => 

	let val (t2', asm2, rew2) = app_rev thy i rrls t2

	in if rew2 then (t1 $ t2', asm2, true)

	   else let val (t1', asm1, rew1) = app_rev thy i rrls t1

		in if rew1 then (t1' $ t2, asm1, true)

		   else (t1 $ t2, [], false) end

	end);

(*.rewriting without argument [] for rew_ord.*)

(*WN.11.6.03: shouldnt asm<>[] lead to false ????*)

fun eval_true thy terms rls = (snd o (eval__true thy 1 terms [])) rls;

(*.rewriting without internal argument [] for rew_ord.*)

(* val (thy, rew_ord, erls, bool, thm, term) =

       (thy, (assoc_rew_ord ro), rls', false, (assoc_thm' thy thm'), f);

   val (thy, rew_ord, erls, bool, thm, term) =

       (thy, rew_ord, erls, false, thm, t'');

   *)

fun rewrite_ thy rew_ord erls bool thm term = 

    rewrite__ thy 1 [] rew_ord erls bool thm term;

fun rewrite_set_ thy bool rls term =

(* val (thy, bool, rls, term) = (thy, false, srls, t);

   *)

    rewrite__set_ thy 1 bool [] rls term;

fun subs'2subst thy (s:subs') = 

    (((map (apfst (term_of o the o (parse thy)))) 

     o (map (apsnd (term_of o the o (parse thy))))) s):subst;

(*.variants of rewrite.*)

(*FIXME 12.8.02: put_asm = true <==> rewrite_inst,

  thus the argument put_asm  IS NOT NECESSARY -- FIXME*)

(* val (rew_ord,rls,put_asm,thm,ct)=

       (e_rew_ord,poly_erls,false,num_str d1_isolate_add2,t);

   *)

fun rewrite_inst_ (thy:theory) rew_ord (rls:rls) (put_asm:bool) 

		  (subst:(term * term) list) (thm:thm) (ct:term) =

    rewrite__ thy 1 subst rew_ord rls put_asm thm ct;

fun rewrite_set_inst_ (thy:theory) 

  (put_asm:bool) (subst:(term * term) list) (rls:rls) (ct:term) =

  (*let 

    val subst = subs'2subst thy subs';

    val subrls = instantiate_rls subs' rls

  in*) rewrite__set_ thy 1 put_asm subst (*sub*)rls ct

  (*end*);

(* given a list of equalities (lhs = rhs) and a term, 

   replace all occurrences of lhs in the term with rhs;

   thus the order or equalities matters: put variables in lhs first. *)

fun rewrite_terms_ thy ord erls equs t =

    let (*val _=tracing("### rewrite_terms_ equs= '"^terms2str equs^"' ..."^

		      term_detail2str (hd equs)^

		      "### rewrite_terms_ t= '"^term2str t^"' ..."^

		      term_detail2str t);*)

	fun rew_ (t', asm') [] _ = (t', asm')

	  (* 1st val (t', asm', rules as r::rs, t) = (e_term, [], equs, t);

	     2nd val (t', asm', rules as r::rs, t) = (t'', [], rules, t'');

	     rew_ (t', asm') (r::rs) t;

	     *)

	  | rew_ (t', asm') (rules as r::rs) t =

	    let val _ = tracing("rew_ "^term2str t);

		val (t'', asm'', lrd, rew) = 

		    rew_sub thy 1 [] ord erls false [] (Trueprop $ r) t

	    in if rew 

	       then (tracing ("true  rew_ " ^ term2str t'');

		   rew_ (t'', asm' @ asm'') rules t'')

	       else (tracing ("false rew_ " ^ term2str t'');

		   rew_ (t', asm') rs t')

	    end

	val (t'', asm'') = rew_ (e_term, []) equs t

    in if t'' = e_term 

       then NONE else SOME (t'', asm'')

    end;

(*. search ct for adjacent numerals and calculate them by operator isa_fn .*)

fun calculate_ thy isa_fn ct =

  let val ct = uminus_to_string ct

    in case get_calculation_ thy isa_fn ct of

	   NONE => NONE

	 | SOME (thmID, thm) => 

	   (let val SOME (rew,_) = rewrite_ thy dummy_ord e_rls false thm ct

    in SOME (rew,(thmID, thm)) end)

	   handle _ => error ("calculate_: "^thmID^" does not rewrite")

  end;

(*

> val thy = InsSort.thy;

> val op_ = "le";      (* < *)

> val ct = (the o (parse thy)) 

   "foldr ins [#2] (if #1 < #3 then #1 # ins [] #3 else [#3, #1])";

> calculate_ thy op_ ct;

  SOME

    ("foldr ins [#2] (if True then #1 # ins [] #3 else [#3, #1])",

     "(#1 < #3) = True") : (cterm * thm) option  *)

(* for test-printouts:

val _ = tracing("in rew_sub  : "^( Syntax.string_of_term (thy2ctxt thy) t))

val _ = tracing("in eval_true: prems= "^(commas (map (Syntax.string_of_term (thy2ctxt thy)) prems')))

*)

fun get_rls_scr rs' = ((#scr o rep_rls o #2 o the o assoc') (!ruleset',rs'))

  handle _ => error ("get_rls_scr: no script for "^rs');

(*make_thm added to Pure/thm.ML*)

fun mk_thm thy str = 

    let val t = (term_of o the o (parse thy)) str

	val t' = case t of

		     Const ("==>",_) $ _ $ _ => t

		   | _ => Trueprop $ t

    in make_thm (cterm_of thy t') end;

(*

  val str = "?r ^^^ 2 = ?r * ?r";

  val thm = realpow_twoI;

  val t1 = (#prop o rep_thm) (num_str thm);

  val t2 = Trueprop $ ((term_of o the o (parse thy)) str);

  t1 = t2;

val it = true : bool      ... !!!

  val th1 = (num_str thm);

  val th2 = ((*num_str*) (mk_thm thy str)) handle e => print_exn e;

  th1 = th2;

ML> val it = false : bool ... HIDDEN DIFFERENCES IRRELEVANT FOR ISAC ?!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  val str = "k ~= 0 ==> m * k / (n * k) = m / n";

  val thm = real_mult_div_cancel2;

  val t1 = (#prop o rep_thm) (num_str thm);

  val t2 = ((term_of o the o (parse thy)) str);

  t1 = t2;

val it = false : bool     ... Var .. Free

  val th1 = (num_str thm);

  val th2 = ((*num_str*) (mk_thm thy str)) handle e => print_exn e;

  th1 = th2;

ML> val it = false : bool ... PLUS HIDDEN DIFFERENCES IRRELEVANT FOR ISAC ?!

*)

(*prints subgoal etc. 

((goal thy);(topthm()) o ) str;                      *)

(*assume rejects scheme variables 

  assume ((cterm_of thy) (Trueprop $ 

		(term_of o the o (parse thy)) str)); *)

(* outcommented 18.11.xx, xx < 02 -------

fun rul2rul' (Thm (thmid, thm)) = Thm'(thmid, string_of_thmI thm)

  | rul2rul' (Calc op_)         = Calc' op_;

fun rul'2rul thy (Thm'(thmid, ct')) = 

       Thm (thmid, mk_thm thy ct')

  | rul'2rul thy' (Calc' op_)        = Calc op_;

fun rls2rls' (Rls{preconds=preconds,rew_ord=rew_ord,rules=rules}:rls) =

  Rls'{preconds'= map string_of_cterm preconds,

       rew_ord' = fst rew_ord,

       rules'   = map rul2rul' rules}:rlsdat';

fun rls'2rls thy' (Rls'{preconds'=preconds,rew_ord'=rew_ord,

		   rules'=rules}:rlsdat') =

  let val thy = the (assoc' (theory',thy'))

  in Rls{preconds = map (the o (parse thy)) preconds,

	 rew_ord  = (rew_ord, the (assoc'(rew_ord',rew_ord))),

	 rules    = map (rul'2rul thy) rules}:rls end;

------- *)

(*.get the theorem associated with the xstring-identifier;

   if the identifier starts with "sym_" then swap lhs = rhs around =

   (ATTENTION: "RS sym" attaches a [.] -- remove it with string_of_thmI);

   identifiers starting with "#" come from Calc and

   get a hand-made theorem (containing numerals only).*)

fun assoc_thm' (thy:theory) ((thmid, ct'):thm') =

    (case explode thmid of

	"s"::"y"::"m"::"_"::id => 

	if hd id = "#" 

	then mk_thm thy ct'

	else ((num_str o (PureThy.get_thm thy)) (implode id)) RS sym

      | id => 

	if hd id = "#" 

	then mk_thm thy ct'

	else (num_str o (PureThy.get_thm thy)) thmid

	     ) handle _ => 

		      error ("assoc_thm': '"^thmid^"' not in '"^

				   (theory2domID thy)^"' (and parents)");

(*> assoc_thm' Isac.thy ("sym_#mult_2_3","6 = 2 * 3");

val it = "6 = 2 * 3" : thm          

> assoc_thm' Isac.thy ("add_0_left","");

val it = "0 + ?z = ?z" : thm

> assoc_thm' Isac.thy ("sym_real_add_zero_left","");

val it = "?t = 0 + ?t"  [.] : thm

> assoc_thm' HOL.thy ("sym_real_add_zero_left","");

*** Unknown theorem(s) "add_0_left"

*** assoc_thm': 'sym_real_add_zero_left' not in 'HOL.thy' (and parents)

 uncaught exception ERROR*)

fun parse' (thy:theory') (ct:cterm') =

    case parse ((the o assoc')(!theory',thy)) ct of

	NONE => NONE

      | SOME ct => SOME ((term2str (term_of ct)):cterm');

(*FIXME 12.8.02: put_asm = true <==> rewrite_inst, rewrite_set_inst

  thus the argument put_asm  IS NOT NECESSARY -- FIXME        ~~~~~*)

fun rewrite (thy':theory') (rew_ord:rew_ord') (rls:rls') 

    (put_asm:bool) (thm:thm') (ct:cterm') =

(* val (rew_ord, rls, thm, ct) = (rew_ord', id_rls rls', thm', f);

   *)

    let val thy = (the o assoc')(!theory',thy');

    in

    case rewrite_ thy

	((the o assoc')(!rew_ord',rew_ord))((#2 o the o assoc')(!ruleset',rls))

	put_asm ((assoc_thm' thy) thm)

	((term_of o the o (parse thy)) ct) of

	NONE => NONE

      | SOME (t, ts) => SOME (term2str t, terms2str ts)

    end;

(*

val thy     = "RatArith.thy";

val rew_ord = "dummy_ord"; 

> val rls     = "eval_rls";

val put_asm = true; 

val thm     = ("square_equation_left","");

val ct      = "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";

val Zthy     = ((the o assoc')(!theory',thy));

val Zrew_ord = ((the o assoc')(!rew_ord',rew_ord)); 

val Zrls     = ((the o assoc')(!ruleset',rls));

val Zput_asm = put_asm; 

val Zthm     = ((the o (assoc'_thm' thy)) thm);

val Zct      = ((the o (parse ((the o assoc')(!theory',thy)))) ct);

rewrite_ Zthy Zrew_ord Zrls Zput_asm Zthm Zct;

 use"Isa99/interface_ME_ISA.sml";

*)

(*FIXME 12.8.02: put_asm = true <==> rewrite_inst, rewrite_set_inst

  thus the argument put_asm  IS NOT NECESSARY -- FIXME        ~~~~~*)

fun rewrite_set (thy':theory') (put_asm:bool)

    (rls:rls') (ct:cterm') =

    let val thy = (the o assoc')(!theory',thy');

    in

    case rewrite_set_ thy put_asm ((#2 o the o assoc')(!ruleset',rls))

    ((term_of o the o (parse thy)) ct) of

	NONE => NONE

      | SOME (t, ts) => SOME (term2str t, terms2str ts)

    end;

(*evaluate list-expressions

  should work on term, and stand in Isa99/rewrite-parse.sml, 

  but there list_rls <- eval_binop is not yet defined*)

(*fun eval_listexpr' ct = 

    let val rew = rewrite_set "ListC.thy" false "list_rls" ct;

    in case rew of 

	   SOME (res,_) => res

	 | NONE => ct end;-----------------30.9.02---*)

fun eval_listexpr_ thy srls t =

(* val (thy,            srls, t) = 

       ((assoc_thy th), sr,  (subst_atomic (upd_env_opt E (a,v)) t));

   *) 

    let val rew = rewrite_set_ thy false srls t;

    in case rew of 

	   SOME (res,_) => res

	 | NONE => t end;

fun get_calculation' (thy:theory') op_ (ct:cterm') =

   case get_calculation_ ((the o assoc')(!theory',thy)) op_

    ((uminus_to_string o term_of o the o 

      (parse ((the o assoc')(!theory',thy)))) ct) of

	NONE => NONE

      | SOME (thmid, thm) => 

	    SOME ((thmid, string_of_thmI thm):thm');

fun calculate (thy':theory') op_ (ct:cterm') =

    let val thy = (the o assoc')(!theory',thy');

    in

	case calculate_ thy op_

			((term_of o the o (parse thy)) ct) of

	    NONE => NONE

	  | SOME (ct,(thmID,thm)) => 

	    SOME (term2str ct, 

		  (thmID, string_of_thmI thm):thm')

    end;

(*

fun instantiate'' thy' subs ((thmid,ct'):thm') = 

  let val thmid_ = implode ("#"::(explode thmid))  (*see type thm'*)

  in (thmid_, (string_of_thmI o (read_instantiate subs)) 

      ((the o (assoc_thm' thy')) (thmid_,ct'))):thm' end;

fun instantiate_rls' thy' subs (rls:rls') = 

    rls2rls' (instantiate_rls subs ((the o (assoc_rls thy')) rls)):rlsdat';

... problem with these functions: 

> val thm = mk_thm thy "(bdv + a = b) = (bdv = b - a)";

val thm = "(bdv + a = b) = (bdv = b - a)" : thm

> show_types:=true; thm;    

val it = "((bdv::'a) + (a::'a) = (b::'a)) = (bdv = b - a)" : thm

... and this doesn't match because of too general typing (?!)

    and read_insitantiate doesn't instantiate the types (?!)

=== solutions:

(1) hard-coded type-instantiation ("'a", "RatArith.rat")

(2) instantiate', instantiate ... no help by isabelle-users@ !!!

=== conclusion:

    rewrite_inst, rewrite_set_inst circumvent the problem,

    according functions out-commented with 'instantiate''

*)

(* instantiate''

fun instantiate'' thy' subs ((thmid,ct'):thm') = 

  let 

    val thmid_ = implode ("#"::(explode thmid));  (*see type thm'*)

    val thy = (the o assoc')(!theory',thy');

    val typs = map (#T o rep_cterm o the o (parse thy)) 

      ((snd o split_list) subs);

    val ctyps = map 

      ((ctyp_of (sign_of thy)) o #T o rep_cterm o the o (parse thy)) 

      ((snd o split_list) subs);

> val thy' = "RatArith.thy";

> val subs = [("bdv","x::rat"),("zzz","z::nat")];

> (the o (parse ((the o assoc')(!theory',thy')))) "x::rat";

> (#T o rep_cterm o the o (parse ((the o assoc')(!theory',thy'))));

> val ctyp = ((ctyp_of (sign_of thy)) o #T o rep_cterm o the o 

	      (parse ((the o assoc')(!theory',thy')))) "x::rat";

> val bdv = (the o (parse thy)) "bdv";

> val x   = (the o (parse thy)) "x";

> (instantiate ([(("'a",0),ctyp)],[(bdv,x)]) isolate_bdv_add)

      handle e => print_exn e;

uncaught exception THM

  raised at: thm.ML:1085.18-1085.69

             thm.ML:1092.34

             goals.ML:536.61

> val bdv = (the o (parse thy)) "bdv::nat";

> val x   = (the o (parse thy)) "x::nat";

> (instantiate ([(("'a",0),ctyp)],[(bdv,x)]) isolate_bdv_add)

      handle e => print_exn e;

uncaught exception THM

  raised at: thm.ML:1085.18-1085.69

             thm.ML:1092.34

             goals.ML:536.61

> (instantiate' [SOME ctyp] [] isolate_bdv_add)

      handle e => print_exn e;      

uncaught exception TYPE

  raised at: drule.ML:613.13-615.44

             goals.ML:536.61

> val repct = (rep_cterm o the o (parse ((the o assoc')(!theory',thy')))) "x::rat";

*)

(*FIXME 12.8.02: put_asm = true <==> rewrite_inst, rewrite_set_inst

  thus the argument put_asm  IS NOT NECESSARY -- FIXME        ~~~~~*)

fun rewrite_inst (thy':theory') (rew_ord:rew_ord') (rls:rls') 

  (put_asm:bool) subs (thm:thm') (ct:cterm') =

  let

    val thy = (the o assoc')(!theory',thy');

    val thm = assoc_thm' thy thm; (*28.10.02*)

    (*val subthm = read_instantiate subs ((assoc_thm' thy) thm)*)

  in

    case rewrite_ thy

      ((the o assoc')(!rew_ord',rew_ord)) ((#2 o the o assoc')(!ruleset',rls))

      put_asm (*sub*)thm ((term_of o the o (parse thy)) ct) of

      NONE => NONE

    | SOME (ctm, ctms) => 

      SOME ((term2str ctm):cterm', (map term2str ctms):cterm' list)

  end;

(*FIXME 12.8.02: put_asm = true <==> rewrite_inst, rewrite_set_inst

  thus the argument put_asm  IS NOT NECESSARY -- FIXME        ~~~~~*)

fun rewrite_set_inst (thy':theory') (put_asm:bool)

  subs' (rls:rls') (ct:cterm') =

  let

    val thy = (the o assoc')(!theory',thy');

    val rls = assoc_rls rls

    val subst = subs'2subst thy subs'

    (*val subrls = instantiate_rls subs ((the o assoc')(!ruleset',rls))*)

  in case rewrite_set_inst_ thy put_asm subst (*sub*)rls

			    ((term_of o the o (parse thy)) ct) of

	 NONE => NONE

       | SOME (t, ts) => SOME (term2str t, terms2str ts)

  end;

(*vor check_elementwise: SqRoot_eval_rls .. wie *_simplify ?! TODO *)

fun eval_true' (thy':theory') (rls':rls') (Const ("True",_)) = true

  | eval_true' (thy':theory') (rls':rls') (t:term) =

(* val thy'="Isac.thy"; val rls'="eval_rls"; val t=hd pres';

   *)

    let val ct' = term2str t;

    in case rewrite_set thy' false rls' ct' of

	   SOME ("True",_) => true

	 | _ => false 

    end;

fun eval_true_ _ _ (Const ("True",_)) = true

  | eval_true_ (thy':theory') rls t =

    case rewrite_set_ (assoc_thy thy') false rls t of

	   SOME (Const ("True",_),_) => true

	 | _ => false;

(*

val test_rls = 

  Rls{preconds = [], rew_ord = ("sqrt_right",sqrt_right), 

      rules = [Calc ("matches",eval_matches "")

	       ],

      scr = Script ((term_of o the o (parse thy)) 

      "empty_script")

      }:rls;      

  rewrite_set_ Isac.thy eval_rls false test_rls 

        ((the o (parse thy)) "matches (?a = ?b) (x = #0)");

  val xxx = (term_of o the o (parse thy)) 

	       "matches (?a = ?b) (x = #0)";

  eval_matches """" xxx thy;

SOME ("matches (?a = ?b) (x + #1 + #-1 * #2 = #0) = True",

     Const ("Trueprop","bool => prop") $ (Const # $ (# $ #) $ Const (#,#)))

  rewrite_set_ Isac.thy eval_rls false eval_rls 

        ((the o (parse thy)) "contains_root (sqrt #0)");

val it = SOME ("True",[]) : (cterm * cterm list) option

*)

(*----------WN:16.5.03 stuff below considered illdesigned, thus coded from scratch in appl.sml fun check_elementwise

datatype det = TRUE  | FALSE | INDET;(*FIXXME.WN:16.5.03

				     introduced with quick-and-dirty code*)

fun determine dts =

    let val false_indet = 

	    filter_out ((curry op= TRUE) o (#1:det * term -> det)) dts

        val ts = map (#2: det * term -> term) dts

    in if nil = false_indet then (TRUE, ts)

       else if nil = filter ((curry op= FALSE) o (#1:det * term -> det))

			    false_indet

       then (INDET, ts)

       else (FALSE, ts) end;

(* val dts = [(INDET,e_term), (FALSE,HOLogic.false_const), 

	      (INDET,e_term), (TRUE,HOLogic.true_const)];

  determine dts;

val it =

  (FALSE,

   [Const ("empty","'a"),Const ("False","bool"),Const ("empty","'a"),

    Const ("True","bool")]) : det * term list*)

fun eval__indet_ thy cs rls = (*FIXXME.WN:16.5.03 pull into eval__true_, update check (check_elementwise), and regard eval_true_ + eval_true*)

if cs = [HOLogic.true_const] orelse cs = [] then (TRUE, [])

    else if cs = [HOLogic.false_const] then (FALSE, cs)

    else

	let fun eval t = 

		let val taopt = rewrite__set_ thy 1 false [] rls t

		in case taopt of

		       SOME (t,_) =>

		       if t = HOLogic.true_const then (TRUE, t)

		       else if t = HOLogic.false_const then (FALSE, t)

		       else (INDET, t)

		     | NONE => (INDET, t) end

	in (determine o (map eval)) cs end;

WN.16.5.0-------------------------------------------------------------*)