(* elements of calculations.

    they are partially held in association lists as ref's for

    switching language levels (meta-string, object-values).

    in order to keep these ref's during re-evaluation of code,

    they are defined here at the beginning of the code.

    author: Walther Neuper

    (c) isac-team 2003

 use"calcelems.sml";

 *)

 val linefeed = (curry op^) "\n";

 type authors = string list;

 type cterm' = string;

 val empty_cterm' = "empty_cterm'";

 type thmID = string;

 type thm' = thmID * cterm';(*WN060610 deprecated in favour of thm''*)

 type thm'' = thmID * term;

 type rls' = string;

 (*.a 'guh'='globally unique handle' is a string unique for each element 

    of isac's KEStore and persistent over time

    (in particular under shifts within the respective hierarchy);

    specialty for thys: 

    # guh NOT resistant agains shifts from one thy to another

    (which is the price for Isabelle's design: thy's overwrite ids of subthy's)

    # requirement for matchTheory: induce guh from tac + current thy

    (see 'fun thy_containing_thm', 'fun thy_containing_rls' etc.)

    TODO: introduce to pbl, met.*) 

 type guh = string;

 val e_guh = "e_guh":guh;

 type xml = string;

 (*. eval function calling sml code during rewriting.*)

 type eval_fn = (string -> term -> theory -> (string * term) option);

 fun e_evalfn (_:'a) (_:term) (_:theory) = NONE:(string * term) option;

 (*. op in isa-term 'Const(op,_)' .*)

 type calID = string;

 type cal = (calID * eval_fn);

 (*. fun calculate_ fetches the evaluation-function via this list. *)

 type calcID = string;

 type calc = (calcID * cal);

 type subs' = (cterm' * cterm') list; (*16.11.00 for FE-KE*)

 type subst = (term * term) list; (*here for ets2str*)

 val e_subst = []:(term * term) list;

 (*TODO.WN060610 make use of "type rew_ord" total*)

 type rew_ord' = string;

 val e_rew_ord' = "e_rew_ord" : rew_ord';

 type rew_ord_ = subst -> Term.term * Term.term -> bool;

 fun dummy_ord (_:subst) (_:term,_:term) = true;

 val e_rew_ord_ = dummy_ord;

 type rew_ord = rew_ord' * rew_ord_;

 val e_rew_ord = dummy_ord; (* TODO.WN071231 clarify identifiers..e_rew_ordX*)

 val e_rew_ordX = (e_rew_ord', e_rew_ord_) : rew_ord;

 datatype rule = 

   Erule                (*.the empty rule                     .*)

 | Thm of (string * thm)(*.a theorem, ie (identifier, Thm.thm).*)

 | Calc of string *     (*.sml-code manipulating a (sub)term  .*)

 	  (string -> term -> theory -> (string * term) option)

 | Cal1 of string *     (*.sml-code applied only to whole term

                           or left/right-hand-side of eqality .*)

 	  (string -> term -> theory -> (string * term) option)

 | Rls_ of rls          (*.ie. rule sets may be nested.*)

 and scr = 

     EmptyScr 

   | Script of term (*for met*)

   | Rfuns of {init_state : term -> 

      (term *          (*the current formula: 

                         goes locate_gen -> next_tac via istate*)

       term *          (*the final formula*)

       rule list       (*of reverse rewrite set (#1#)*)

 	    list *    (*may be serveral, eg. in norm_rational*)

       (rule *         (*Thm (+ Thm generated from Calc) resulting in ...*)

        (term *        (*... rewrite with ...*)

 	term list))   (*... assumptions*)

 	  list),      (*derivation from given term to normalform

 		       in reverse order with sym_thm; 

                        (#1#) could be extracted from here #1*)

 	      normal_form: term -> (term * term list) option,

 	      locate_rule: rule list list -> term -> rule 

 			   -> (rule * (term * term list)) list,

 	      next_rule  : rule list list -> term -> rule option,

 	      attach_form: rule list list -> term -> term 

 			   -> (rule * (term * term list)) list}

 and rls =

     Erls                          (*for init e_rls*)

   | Rls of (*a confluent and terminating ruleset, in general         *)

     {id : string,          (*for trace_rewrite:=true                 *)

      preconds : term list, (*unused WN020820                         *)

      (*WN060616 for efficiency...

       bdvs    : false,       (*set in prep_rls for get_bdvs *)*)

      rew_ord  : rew_ord,   (*for rules*)

      erls     : rls,       (*for the conditions in rules             *)

      srls     : rls,       (*for evaluation of list_fns in script    *)

      calc     : calc list, (*for Calculate in scr, set by prep_rls   *)

      rules    : rule list,

      scr      : scr}       (*Script term: generating intermed.steps  *)

   | Seq of (*a sequence of rules to be tried only once               *)

     {id : string,          (*for trace_rewrite:=true                 *)

      preconds : term list, (*unused 20.8.02                          *)

      (*WN060616 for efficiency...

       bdvs    : false,       (*set in prep_rls for get_bdvs *)*)

      rew_ord  : rew_ord,   (*for rules                               *)

      erls     : rls,       (*for the conditions in rules             *)

      srls     : rls,       (*for evaluation of list_fns in script    *)

      calc     : calc list, (*for Calculate in scr, set by prep_rls   *) 

      rules    : rule list,

      scr      : scr}  (*Script term  (how to restrict type ???)*)

   (*Rrls call SML-code and simulate an rls

     difference: there is always _ONE_ redex rewritten in 1 call,

     thus wrap Rrls by: Rls (Rls_ ...)*)

   | Rrls of (*for 'reverse rewriting' by SML-functions instead Script*)

     {id : string,          (*for trace_rewrite:=true                 *)

      prepat  : (term list *(*preconds, eval with subst from pattern  *)

 		term )     (*pattern matched in subterms             *)

 		   list,   (*meta-conjunction is or                  *)

      rew_ord  : rew_ord,   (*for rules                               *)

      erls     : rls,       (*for the conditions in rules and pat     *)

      (*            '^ because of rewrite in applicable_in

 						compare type met*)

      calc     : calc list, (*for Calculate in scr, set by prep_rls *)

      scr      : scr}; (*Rfuns {...}  (how to restrict type ???)*)

 (*1.8.02 ad (how to restrict type ???): scr should be usable indepentently

   from rls, and then contain both Script _AND_ Rfuns !!!*)

 fun thy2ctxt' thy' = ProofContext.init_global (theory thy');(*FIXXXME thy-ctxt*)

 fun thy2ctxt thy = ProofContext.init_global thy;(*FIXXXME thy-ctxt*)

 (*ctxt for retrieval of all thms in HOL; FIXME make this local?*)

 (*val ctxt_HOL = ProofContext.init_global (theory "Complex_Main");*)

 (*val ctxt_HOL = thy2ctxt' "Complex_Main";*)

 (*lazy ctxt for retrieval of all thms used in isac; FIXME make this local?*)

 (*fun ctxt_Isac _  = thy2ctxt' "Isac";*)

 fun Isac _ = ProofContext.theory_of (thy2ctxt' "Isac");

 val e_rule = 

     Thm ("refl", ProofContext.get_thm (thy2ctxt' "Complex_Main") "refl" );

 fun id_of_thm (Thm (id, _)) = id

   | id_of_thm _ = raise error "id_of_thm";

 fun thm_of_thm (Thm (_, thm)) = thm

   | thm_of_thm _ = raise error "thm_of_thm";

 fun rep_thm_G' (Thm (thmid, thm)) = (thmid, thm);

 fun eq_thmI ((thmid1 : thmID, _ : thm), (thmid2 : thmID, _ : thm)) =

     (strip_thy thmid1) = (strip_thy thmid2);

 val string_of_thm =  Thm.get_name_hint; (*FIXME.2009*)

 (*check for [.] as caused by "fun assoc_thm'"*)

 fun string_of_thmI thm =

     let val ct' = (de_quote o string_of_thm) thm

 	val (a, b) = split_nlast (5, explode ct')

     in case b of 

 	   [" ", " ","[", ".", "]"] => implode a

 	 | _ => ct'

     end;

 (*.id requested for all, Rls,Seq,Rrls.*)

 fun id_rls Erls = "e_rls" (*WN060714 quick and dirty: recursive defs!*)

   | id_rls (Rls {id,...}) = id

   | id_rls (Seq {id,...}) = id

   | id_rls (Rrls {id,...}) = id;

 val rls2str = id_rls;

 fun id_rule (Thm (id, _)) = id

   | id_rule (Calc (id, _)) = id

   | id_rule (Rls_ rls) = id_rls rls;

 fun get_rules (Rls {rules,...}) = rules

   | get_rules (Seq {rules,...}) = rules

   | get_rules (Rrls _) = [];

 fun rule2str Erule = "Erule"

   | rule2str (Thm (str, thm)) = "Thm (\""^str^"\","^(string_of_thmI thm)^")"

   | rule2str (Calc (str,f))  = "Calc (\""^str^"\",fn)"

   | rule2str (Cal1 (str,f))  = "Cal1 (\""^str^"\",fn)"

   | rule2str (Rls_ rls) = "Rls_ (\""^id_rls rls^"\")";

 fun rule2str' Erule = "Erule"

   | rule2str' (Thm (str, thm)) = "Thm (\""^str^"\",\"\")"

   | rule2str' (Calc (str,f))  = "Calc (\""^str^"\",fn)"

   | rule2str' (Cal1 (str,f))  = "Cal1 (\""^str^"\",fn)"

   | rule2str' (Rls_ rls) = "Rls_ (\""^id_rls rls^"\")";

 (*WN080102 compare eq_rule ?!?*)

 fun eqrule (Thm (id1,_), Thm (id2,_)) = id1 = id2

   | eqrule (Calc (id1,_), Calc (id2,_)) = id1 = id2

   | eqrule (Cal1 (id1,_), Cal1 (id2,_)) = id1 = id2

   | eqrule (Rls_ _, Rls_ _) = false (*{id=id1}{id=id2} = id1 = id2 FIXXME*)

   | eqrule _ = false;

 type rrlsstate =      (*state for reverse rewriting*)

      (term *          (*the current formula: 

                         goes locate_gen -> next_tac via istate*)

       term *          (*the final formula*)

       rule list       (*of reverse rewrite set (#1#)*)

 	    list *    (*may be serveral, eg. in norm_rational*)

       (rule *         (*Thm (+ Thm generated from Calc) resulting in ...*)

        (term *        (*... rewrite with ...*)

 	term list))   (*... assumptions*)

 	  list);      (*derivation from given term to normalform

 		       in reverse order with sym_thm; 

                        (#1#) could be extracted from here #1*)

 val e_type = Type("empty",[]);

 val a_type = TFree("'a",[]);

 val e_term = Const("empty",e_type);

 val a_term = Free("empty",a_type);

 val e_rrlsstate = (e_term,e_term,[[e_rule]],[(e_rule,(e_term,[]))]):rrlsstate;

 (*22.2.02: ging auf Linux nicht (Stefan)

 val e_scr = Script ((term_of o the o (parse thy)) "e_script");*)

 val e_term = Const("empty", Type("'a", []));

 val e_scr = Script e_term;

 (*ad thm':

    there are two kinds of theorems ...

    (1) known by isabelle

    (2) not known, eg. calc_thm, instantiated rls

        the latter have a thmid "#..."

    and thus outside isa we ALWAYS transport both (thmid,string_of_thmI)

    and have a special assoc_thm / assoc_rls in this interface      *)

 type theory' = string; (* = domID ^".thy" *)

 type domID = string;   (* domID ^".thy" = theory' TODO.11.03replace by thyID*)

 type thyID = string;    (*WN.3.11.03 TODO: replace domID with thyID*)

 fun string_of_thy thy = Context.theory_name thy: theory';

 val theory2domID = string_of_thy;

 val theory2thyID = (get_thy o string_of_thy) : theory -> thyID;

 val theory2theory' = string_of_thy;

 val theory2str = string_of_thy; (*WN050903 ..most consistent naming*)

 val theory2str' = implode o (drop_last_n 4) o explode o string_of_thy;

 (*> theory2str' Isac.thy;

 al it = "Isac" : string

 *)

 fun thyID2theory' (thyID:thyID) =

     let val ss = explode thyID

 	val ext = implode (takelast (4, ss))

     in if ext = ".thy" then thyID : theory' (*disarm abuse of thyID*)

        else thyID ^ ".thy"

     end;

 (* thyID2theory' "Isac" (*ok*);

 val it = "Isac.thy" : theory'

  > thyID2theory' "Isac.thy" (*abuse, goes ok...*);

 val it = "Isac.thy" : theory'

 *)

 fun theory'2thyID (theory':theory') =

     let val ss = explode theory'

 	val ext = implode (takelast (4, ss))

     in if ext = ".thy" then ((implode o (drop_last_n 4)) ss) : thyID

        else theory' (*disarm abuse of theory'*)

     end;

 (* theory'2thyID "Isac.thy";

 val it = "Isac" : thyID

 > theory'2thyID "Isac";

 val it = "Isac" : thyID*)

 (*. WN0509 discussion:

 #############################################################################

 #   How to manage theorys in subproblems wrt. the requirement,              #

 #   that scripts should be re-usable ?                                      #

 #############################################################################

     eg. 'Script Solve_rat_equation' calls 'SubProblem (RatEq_,..'

     which would not allow to 'solve (y'' = -M_b / EI, M_b)' by this script

     because Biegelinie.thy is subthy of RatEq.thy and thus Biegelinie.M_b 

     is unknown in RatEq.thy and M_b cannot be parsed into the scripts guard

     (see match_ags).

     Preliminary solution:

     # the thy in 'SubProblem (thy_, pbl, arglist)' is not taken automatically,

     # instead the 'maxthy (rootthy pt) thy_' is taken for each subpbl

     # however, a thy specified by the user in the rootpbl may lead to 

       errors in far-off subpbls (which are not yet reported properly !!!) 

       and interactively specifiying thys in subpbl is not very relevant.

     Other solutions possible:

     # always parse and type-check with Isac.thy

       (rejected tue to the vague idea eg. to re-use equations for R in C etc.)

     # regard the subthy-relation in specifying thys of subpbls

     # specifically handle 'SubProblem (undefined_, pbl, arglist)'

     # ???

 .*)

 (*WN0509 TODO "ProtoPure" ... would be more consistent 

   with assoc_thy <--> theory2theory' +FIXME assoc_thy "e_domID" -> Script.thy*)

 val e_domID = "e_domID":domID;

 (*the key into the hierarchy ob theory elements*)

 type theID = string list;

 val e_theID = ["e_theID"];

 val theID2str = strs2str;

 (*theID eg. is ["IsacKnowledge", "Test", "Rulesets", "ac_plus_times"]*)

 fun theID2thyID (theID:theID) =

     if length theID >= 3 then (last_elem o (drop_last_n 2)) theID : thyID

     else raise error ("theID2thyID called with "^ theID2str theID);

 (*the key into the hierarchy ob problems*)

 type pblID = string list; (* domID::...*)

 val e_pblID = ["e_pblID"]:pblID;

 val pblID2str = strs2str;

 (*the key into the hierarchy ob methods*)

 type metID = string list;

 val e_metID = ["e_metID"]:metID;

 val metID2str = strs2str;

 (*either theID or pblID or metID*)

 type kestoreID = string list;

 val e_kestoreID = ["e_kestoreID"];

 val kestoreID2str = strs2str;

 (*for distinction of contexts*)

 datatype ketype = Exp_ | Thy_ | Pbl_ | Met_;

 fun ketype2str Exp_ = "Exp_"

   | ketype2str Thy_ = "Thy_" 

   | ketype2str Pbl_ = "Pbl_" 

   | ketype2str Met_ = "Met_";

 fun ketype2str' Exp_ = "Example"

   | ketype2str' Thy_ = "Theory" 

   | ketype2str' Pbl_ = "Problem" 

   | ketype2str' Met_ = "Method";

 (*see 'How to manage theorys in subproblems' at 'type thyID'*)

 val theory'  = ref ([]:(theory' * theory) list);

 (*.all theories defined for Scripts, recorded in Scripts/Script.ML; 

    in order to distinguish them from general IsacKnowledge defined later on.*)

 val script_thys = ref ([] : (theory' * theory) list);

 (*rewrite orders, also stored in 'type met' and type 'and rls'

   The association list is required for 'rewrite.."rew_ord"..'

   WN0509 tests not well-organized: see smltest/IsacKnowledge/termorder.sml*)

 val rew_ord' = 

     ref ([]:(rew_ord' *        (*the key for the association list         *)

 	     (subst 	       (*the bound variables - they get high order*)

 	      -> (term * term) (*(t1, t2) to be compared                  *)

 	      -> bool))        (*if t1 <= t2 then true else false         *)

 		list);         (*association list                         *)

 rew_ord' := overwritel (!rew_ord', [("e_rew_ord", e_rew_ord),

 				    ("dummy_ord", dummy_ord)]);

 (*WN060120 a hack to get alltogether run again with minimal effort:

   theory' is inserted for creating thy_hierarchy; calls for assoc_rls

   need not be called*)

 val ruleset' = ref ([]:(rls' * (theory' * rls)) list);

 (*FIXME.040207 calclist': used by prep_rls, NOT in met*)

 val calclist'= ref ([]: calc list);

 (*.the hierarchy of thydata.*)

 (*.'a is for pbt | met.*)

 (*WN.24.4.03 -"- ... type parameters; afterwards naming inconsistent*)

 datatype 'a ptyp = 

 	 Ptyp of string *   (*element within pblID*)

 		 'a list *  (*several pbts with different domIDs/thy

 			      TODO: select by subthy (isaref.p.69)

 			      presently only _ONE_ elem*)

 		 ('a ptyp) list;   (*the children nodes*)

 (*.datatype for collecting thydata for hierarchy.*)

 (*WN060720 more consistent naming would be 'type thyelem' or 'thelem'*)

 (*WN0606 Htxt contains html which does not belong to the sml-kernel*)

 datatype thydata = Html of {guh: guh,

 			    coursedesign: authors,

 			    mathauthors: authors,

 			    html: string} (*html; for demos before database*)

 		 | Hthm of {guh: guh,

 			    coursedesign: authors,

 			    mathauthors: authors,

 			    thm: Thm.thm}

 		 | Hrls of {guh: guh,

 			    coursedesign: authors,

 			    mathauthors: authors,

 			    (*like   vvvvvvvvvvvvv val ruleset'

 			     WN060711 redesign together !*)

 			    thy_rls: (thyID * rls)}

 		 | Hcal of {guh: guh,

 			    coursedesign: authors,

 			    mathauthors: authors,

 			    calc: calc}

 		 | Hord of {guh: guh,

 			    coursedesign: authors,

 			    mathauthors: authors,

 			    ord: (subst -> (term * term) -> bool)};

 val e_thydata = Html {guh="e_guh", coursedesign=[], mathauthors=[], html=""};

 type thehier = (thydata ptyp) list;

 val thehier = ref ([] : thehier);

 (*.an association list, gets the value once in Isac.ML.*)

 val isab_thm_thy = ref ([] : (thmID * (thyID * thm)) list);

 type path = string;

 type filename = string;

 (*val xxx = fn: a b => (a,b);   ??? fun-definition ???*)

 local

     fun ii (_:term) = e_rrlsstate;

     fun no (_:term) = SOME (e_term,[e_term]);

     fun lo (_:rule list list) (_:term) (_:rule) = [(e_rule,(e_term,[e_term]))];

     fun ne (_:rule list list) (_:term) = SOME e_rule;

     fun fo (_:rule list list) (_:term) (_:term) = [(e_rule,(e_term,[e_term]))];

 in

 val e_rfuns = Rfuns {init_state=ii,normal_form=no,locate_rule=lo,

 		     next_rule=ne,attach_form=fo};

 end;

 val e_rls = 

   Rls{id = "e_rls",

       preconds = [], 

       rew_ord = ("dummy_ord", dummy_ord),

       erls = Erls,srls = Erls,

       calc = [],

       rules = [], scr = EmptyScr}:rls;

 val e_rrls = Rrls {id = "e_rrls",

 		   prepat = [],

 		   rew_ord = ("dummy_ord", dummy_ord),

 		   erls = Erls,

 		   calc = [],

 		   (*asm_thm=[],*)

 		   scr=e_rfuns}:rls;

 ruleset' := overwritel (!ruleset', [("e_rls",("Tools",e_rls)),

 				    ("e_rrls",("Tools",e_rrls))

 				    ]);

 fun rep_rls (Rls {id,preconds,rew_ord,erls,srls,calc,(*asm_thm,*)rules,scr}) =

   {id=id,preconds=preconds,rew_ord=rew_ord,erls=erls,srls=srls,calc=calc,

    (*asm_thm=asm_thm,*)rules=rules,scr=scr}

   | rep_rls (Seq {id,preconds,rew_ord,erls,srls,calc,(*asm_thm,*)rules,scr}) =

   {id=id,preconds=preconds,rew_ord=rew_ord,erls=erls,srls=srls,calc=calc,

    (*asm_thm=asm_thm,*)rules=rules,scr=scr}

   | rep_rls Erls = rep_rls e_rls

   | rep_rls (Rrls {id,...})  = rep_rls e_rls

     (*raise error("rep_rls doesn't take apart reverse-rewrite-rule-sets: "^id)*);

 (*| rep_rls (Seq {id,...})  = 

     raise error("rep_rls doesn't take apart reverse-rewrite-rule-sets: "^id);

 --1.7.03*)

 fun rep_rrls 

 	(Rrls {id,(*asm_thm,*) calc, erls, prepat, rew_ord, 

 	       scr=Rfuns

 		       {attach_form,init_state,locate_rule,

 			next_rule,normal_form}}) =

     {id=id,(*asm_thm=asm_thm,*) calc=calc, erls=erls, prepat=prepat, 

      rew_ord=rew_ord, attach_form=attach_form, init_state=init_state, 

      locate_rule=locate_rule, next_rule=next_rule, normal_form=normal_form}

   | rep_rrls (Rls {id,...}) = 

     raise error ("rep_rrls doesn't take apart (normal) rule-sets: "^id)

   | rep_rrls (Seq {id,...}) = 

     raise error ("rep_rrls doesn't take apart (normal) rule-sets: "^id);

 fun append_rls id (Rls {id=_,preconds=pc,rew_ord=ro,erls=er,srls=sr,calc=ca,

 			rules =rs,scr=sc}) r =

     (Rls{id=id,preconds=pc,rew_ord=ro,erls=er,srls=sr,calc=ca,

 	 rules = rs @ r,scr=sc}:rls)

   | append_rls id (Seq {id=_,preconds=pc,rew_ord=ro,erls=er,srls=sr,calc=ca,

 			rules =rs,scr=sc}) r =

     (Seq{id=id,preconds=pc,rew_ord=ro,erls=er,srls=sr,calc=ca,

 	 rules = rs @ r,scr=sc}:rls)

   | append_rls id (Rrls _) _ = 

     raise error ("append_rls: not for reverse-rewrite-rule-set "^id);

 (*. are _atomic_ rules equal ?.*)

 (*WN080102 compare eqrule ?!?*)

 fun eq_rule (Thm (thm1,_), Thm (thm2,_)) = thm1 = thm2

   | eq_rule (Calc (id1,_), Calc (id2,_)) = id1 = id2

   | eq_rule (Rls_ rls1, Rls_ rls2) = id_rls rls1 = id_rls rls2

   (*id_rls checks for Rls, Seq, Rrls*)

   | eq_rule _ = false;

 fun merge_rls _ Erls rls = rls

   | merge_rls _ rls Erls = rls

   | merge_rls id

 	(Rls {id=id1,preconds=pc1,rew_ord=ro1,erls=er1,srls=sr1,calc=ca1,

 	      (*asm_thm=at1,*)rules =rs1,scr=sc1}) 

 	(r2 as Rls {id=id2,preconds=pc2,rew_ord=ro2,erls=er2,srls=sr2,calc=ca2,

 	      (*asm_thm=at2,*)rules =rs2,scr=sc2}) =

 	(Rls {id=id,preconds=pc1 @ ((#preconds o rep_rls) r2),

 	      rew_ord=ro1,erls=merge_rls "" er1 er2(*er1*),

 	      srls=merge_rls ("merged_"^id1^"_"^((#id o rep_rls) r2)) sr1 

 			     ((#srls o rep_rls) r2),

 	      calc=ca1 @ ((#calc o rep_rls) r2),

 	      (*asm_thm=at1 @ ((#asm_thm o rep_rls) r2),*)

 	      rules = gen_union eq_rule rule2str (rs1, (#rules o rep_rls) r2),

 	      scr=sc1}:rls)

   | merge_rls id

 	(Seq {id=id1,preconds=pc1,rew_ord=ro1,erls=er1,srls=sr1,calc=ca1,

 	      (*asm_thm=at1,*)rules =rs1,scr=sc1}) 

 	(r2 as Seq {id=id2,preconds=pc2,rew_ord=ro2,erls=er2,srls=sr2,calc=ca2,

 	      (*asm_thm=at2,*)rules =rs2,scr=sc2}) =

 	(Seq {id=id,preconds=pc1 @ ((#preconds o rep_rls) r2),

 	      rew_ord=ro1,erls=merge_rls "" er1 er2(*er1*),

 	      srls=merge_rls ("merged_"^id1^"_"^((#id o rep_rls) r2)) sr1 

 			     ((#srls o rep_rls) r2),

 	      calc=ca1 @ ((#calc o rep_rls) r2),

 	      (*asm_thm=at1 @ ((#asm_thm o rep_rls) r2),*)

 	      rules = gen_union eq_rule rule2str (rs1, (#rules o rep_rls) r2),

 	      scr=sc1}:rls)

   | merge_rls _ _ _ = 

     raise error "merge_rls: not for reverse-rewrite-rule-sets\

 		\and not for mixed Rls -- Seq";

 fun remove_rls id (Rls {id=_,preconds=pc,rew_ord=ro,erls=er,srls=sr,calc=ca,

 		     (*asm_thm=at,*)rules =rs,scr=sc}) r =

     (Rls{id=id,preconds=pc,rew_ord=ro,erls=er,srls=sr,calc=ca,

 	 (*asm_thm=at,*)rules = gen_rems eq_rule (rs, r),

 	 scr=sc}:rls)

   | remove_rls id (Seq {id=_,preconds=pc,rew_ord=ro,erls=er,srls=sr,calc=ca,

 		     (*asm_thm=at,*)rules =rs,scr=sc}) r =

     (Seq{id=id,preconds=pc,rew_ord=ro,erls=er,srls=sr,calc=ca,

 	 (*asm_thm=at,*)rules = gen_rems eq_rule (rs, r),

 	 scr=sc}:rls)

   | remove_rls id (Rrls _) _ = raise error 

                    ("remove_rls: not for reverse-rewrite-rule-set "^id);

 (*!!!> gen_rems (op=) ([1,2,3,4], [3,4,5]);

 val it = [1, 2] : int list*)

 (*elder version: migrated 3 calls in smtest to memrls

 fun mem_rls id rls = 

     case find_first ((curry op=) id) (map id_rule ((#rules o rep_rls) rls)) of

 	SOME _ => true | NONE => false;*)

 fun memrls r (Rls {rules,...}) = gen_mem eqrule (r, rules)

   | memrls r (Seq {rules,...}) = gen_mem eqrule (r, rules)

   | memrls r _ = raise error ("memrls: incomplete impl. r= "^(rule2str r));

 fun rls_get_thm rls (id: xstring) =

     case find_first (curry eq_rule e_rule) 

 		    ((#rules o rep_rls) rls) of

 	SOME thm => SOME thm | NONE => NONE;

 fun assoc' ([], key) = raise error ("ME_Isa: '"^key^"' not known")

   | assoc' ((keyi, xi) :: pairs, key) =

       if key = keyi then SOME xi else assoc' (pairs, key);

 (*100818 fun assoc_thy (thy:theory') = ((the o assoc')(!theory',thy))

   handle _ => raise error ("ME_Isa: thy '"^thy^"' not in system");*)

 fun assoc_thy (thy:theory') = (*FIXME100818 abolish*)

     (theory ((implode o (curry takelast 4) o explode) thy))

     handle _ => raise error ("ME_Isa: thy '" ^ thy ^ "' not in system");

 (*.associate an rls-identifier with an rls; related to 'fun assoc_rls';

    these are NOT compatible to "fun assoc_thm'" in that they do NOT handle

    overlays by re-using an identifier in different thys.*)

 fun assoc_rls (rls:rls') = ((#2 o the o assoc')(!ruleset',rls))

   handle _ => raise error ("ME_Isa: '"^rls^"' not in system");

 (*fun assoc_rls (rls:rls') = ((the o assoc')(!ruleset',rls))

   handle _ => raise error ("ME_Isa: '"^rls^"' not in system");*)

 (*.overwrite an element in an association list and pair it with a thyID

    in order to create the thy_hierarchy;

    overwrites existing rls' even if they are defined in a different thy;

    this is related to assoc_rls, TODO.WN060120: assoc_rew_ord, assoc_calc;.*)

 (*WN060120 ...these are NOT compatible to "fun assoc_thm'" in that 

    they do NOT handle overlays by re-using an identifier in different thys;

    "thyID.rlsID" would be a good solution, if the "." would be possible

    in scripts...

    actually a hack to get alltogether run again with minimal effort*)

 fun insthy thy' (rls', rls) = (rls', (thy', rls));

 fun overwritelthy thy (al, bl:(rls' * rls) list) =

     let val bl' = map (insthy ((get_thy o theory2theory') thy)) bl

     in overwritel (al, bl') end;

 fun assoc_rew_ord ro = ((the o assoc') (!rew_ord',ro))

   handle _ => raise error ("ME_Isa: rew_ord '"^ro^"' not in system");

 (*get the string for stac from rule*)

 fun assoc_calc ([], key) = raise error ("assoc_calc: '"^ key ^"' not found")

   | assoc_calc ((calc, (keyi, xi)) :: pairs, key) =

       if key = keyi then calc else assoc_calc (pairs, key);

 (*only used for !calclist'...*)

 fun assoc1 ([], key) = raise error ("assoc1 (for met.calc=): '"^ key 

 				    ^"' not found")

   | assoc1 ((all as (keyi, _)) :: pairs, key) =

       if key = keyi then all else assoc1 (pairs, key);

 (*TODO.WN080102 clarify usage of type cal and type calc..*)

 fun calID2calcID (calID : calID) = 

     let fun ass [] = raise error ("calID2calcID: "^calID^"not in calclist'")

 	  | ass ((calci, (cali, eval_fn))::ids) =

 	    if calID = cali then calci

 	    else ass ids

     in ass (!calclist') : calcID end;

 fun termopt2str (SOME t) = 

     "SOME " ^ (Syntax.string_of_term (thy2ctxt' "Isac") t)

   | termopt2str NONE = "NONE";

 fun term2str t = Syntax.string_of_term (thy2ctxt' "Isac") t;

 fun terms2str ts= (strs2str o (map (Syntax.string_of_term 

 					(thy2ctxt' "Isac")))) ts;

 fun type2str typ = Syntax.string_of_typ (thy2ctxt' "Isac") typ;

 val string_of_typ = type2str;

 fun subst2str (s:subst) = 

     (strs2str o 

      (map (linefeed o pair2str o

 	   (apsnd term2str) o 

 	   (apfst term2str)))) s;

 fun subst2str' (s:subst) = 

     (strs2str' o 

      (map (pair2str o

 	   (apsnd term2str) o 

 	   (apfst term2str)))) s;

 (*> subst2str' [(str2term "bdv", str2term "x"),

 		(str2term "bdv_2", str2term "y")];

 val it = "[(bdv, x)]" : string

 *)

 val env2str = subst2str;

 (*recursive defs:*)

 fun scr2str (Script s) = "Script "^(term2str s)

   | scr2str (Rfuns _)  = "Rfuns";

 fun maxthy thy1 thy2 = if Theory.subthy (thy1, thy2) then thy2 else thy1;

 (*.trace internal steps of isac's rewriter*)

 val trace_rewrite = ref false;

 (*.depth of recursion in traces of the rewriter, if trace_rewrite:=true.*)

 val depth = ref 99999;

 (*.no of rewrites exceeding this int -> NO rewrite.*)

 (*WN060829 still unused...*)

 val lim_rewrite = ref 99999;

 (*.no of derivation-elements exceeding this int -> SOME derivation-elements.*)

 val lim_deriv = ref 100;

 (*.switch for checking guhs unique before storing a pbl or met;

    set true at startup (done at begin of ROOT.ML)

    set false for editing IsacKnowledge (done at end of ROOT.ML).*)

 val check_guhs_unique = ref false;

 datatype lrd = (*elements of a path (=loc_) into an Isabelle term*)

 	 L     (*go left at $*) 

        | R     (*go right at $*)

        | D;     (*go down at Abs*)

 type loc_ = lrd list;

 fun ldr2str L = "L"

   | ldr2str R = "R"

   | ldr2str D = "D";

 fun loc_2str (k:loc_) = (strs2str' o (map ldr2str)) k;