(* 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 2003

   (c) copyright due to lincense terms

*)

(*

structure CalcElems =

struct

*)

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

type authors = string list;

type cterm' = string;

val empty_cterm' = "empty_cterm'";

type thmID = string;    (* identifier for a thm (the shortest possible identifier)       *)

type thmDeriv = string; (* WN120524 deprecated

  thyID ^"."^ xxx ^"."^ thmID, see fun thmID_of_derivation_name 

  WN120524: dont use Thm.derivation_name, this is destroyed by num_str;

  Thm.get_name_hint survives num_str and seems perfectly reliable *)

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.

Unifying "type cal" and "type calc" would make Lucas-Interpretation more efficient,

  see "fun rule2stac": instead of 

    Calc: calID * eval_fn -> rule

  would be better

    Calc: prog_calcID * (calID * eval_fn)) -> rule*)

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 prog_calcID = string;

type calc = (prog_calcID * cal);

type calc_elem =

  prog_calcID *   (* a simple identifier used in programs *)

  (calID *        (* a long identifier used in Const *)

    eval_fn)      (* an ML function *)

fun calc_eq ((pi1, (ci1, _)) : calc_elem, (pi2, (ci2, _)) : calc_elem) =

  if pi1 = pi2

  then if ci1 = ci2 then true else error ("calc_eq: " ^ ci1 ^ " <> " ^ ci2)

  else false

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;

(* error patterns and fill patterns *)

type errpatID = string

type errpat =

  errpatID    (* one identifier for a list of patterns                       

                 DESIGN ?TODO: errpatID list for hierarchy of errpats ?      *)

  * term list (* error patterns                                              *)

  * thm list  (* thms related to error patterns; note that respective lhs 

                 do not match (which reflects student's error).

                 fillpatterns are stored with these thms.                    *)

(* for (at least) 2 kinds of access:

  (1) given an errpatID, find the respective fillpats (e.g. in fun find_fill_pats)

  (2) given a thm, find respective fillpats *)

type fillpatID = string

type fillpat =

  fillpatID   (* DESIGN ?TODO: give an order w.r.t difficulty ? *)

  * term      (* the pattern with fill-in gaps                  *)

  * errpatID; (* which the fillpat would be a help for          

                 DESIGN ?TODO: list for several patterns ?      *)

datatype rule =

  Erule                (*.the empty rule                     .*)

| Thm of (string * Basic_Thm.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

  | Prog of term (* for met *)

  | Rfuns of     (* for Rrls, usage see rational.sml ----- reverse rewrite -----      *)

    {init_state : (* initialise for reverse rewriting by the Interpreter              *)

      term ->         (* for this the rrlsstate is initialised:                       *)

      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:  (* the function which drives the Rrls ##############################*)

	    term -> (term * term list) option,

	  locate_rule:  (* checks a rule R for being a cancel-rule, and if it is,

                     then return the list of rules (+ the terms they are rewriting to)

                     which need to be applied before R should be applied.

                     precondition: the rule is applicable to the argument-term.       *)

	    rule list list -> (* the reverse rule list                                      *)

	    term ->         (* ... to which the rule shall be applied                       *)

	    rule ->         (* ... to be applied to term                                    *)

	    ( rule *        (* value: a rule rewriting to ...                               *)

	      (term *       (*   ... the resulting term ...                                 *)

	      term list))   (*   ... with the assumptions ( //#0)                           *)

	    list,           (*   there may be several such rules; the list is empty,          

                           if the rule has nothing to do with e.g. cancelation        *)

	  next_rule:    (* for a given term return the next rules to be done for cancelling *)

	    rule list list->(* the reverse rule list                                        *)

	    term ->         (* the term for which ...                                       *)

	    rule option,    (* ... this rule is appropriate for cancellation;

		                     there may be no such rule (if the term is eg.canceled already*)

	  attach_form:  (* checks an input term TI, if it may belong to e.g. a current 

                     cancellation, by trying to derive it from the given term TG.     

                     NOT IMPLEMENTED                                                 *)

	    rule list list->(**)

	    term ->         (* TG, the last one agreed upon by user + math-eng              *)

	    term ->         (* TI, the next one input by the user                           *)

	    ( rule *        (* the rule to be applied in order to reach TI                  *) 

	      (term *       (* ... obtained by applying the rule ...                        *)

	      term list))   (* ... and the respective assumptions                           *) 

	    list}           (* there may be several such rules; the list is empty, if the 

                         users term does not belong to e.g. a cancellation of the term 

                         last agreed upon.                                            *)

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,

     errpatts : errpatID list,(*dialog-authoring in Build_Thydata.thy*)

     scr      : scr}       (*Prog 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,

     errpatts : errpatID list,(*dialog-authoring in Build_Thydata.thy*)

     scr      : scr}  (*Prog 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 (* SML-functions within rewriting; step-wise execution provided;   

               Rrls simulate an rls

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

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

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

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

                              if [@{term True}], match decides alone          *)

		            term )     (* pattern matched with current (sub)term          *)

		   list,               (* meta-conjunction is or                          *)

     rew_ord  : rew_ord,   (* for rules                                       *)

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

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

     errpatts : errpatID list,(*dialog-authoring in Build_Thydata.thy*)

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

fun thy2ctxt' thy' = Proof_Context.init_global (Thy_Info.get_theory thy');(*FIXXXME thy-ctxt*)

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

fun Isac _ = Proof_Context.theory_of (thy2ctxt' "Isac"); (*@{theory "Isac"}*)

val e_rule = Thm ("refl", @{thm refl});

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

  | id_of_thm _ = error "error id_of_thm";

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

  | thm_of_thm _ = error "error thm_of_thm";

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

fun thmID_of_derivation_name dn = last_elem (space_explode "." dn);

fun thyID_of_derivation_name dn = hd (space_explode "." dn);

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

    (strip_thy thmid1) = (strip_thy thmid2);

(*WN120201 weakened*)

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

(*version typed weaker WN100910*)

fun eq_thmI' ((thmid1, _), (thmid2, _)) =

    (thmID_of_derivation_name thmid1) = (thmID_of_derivation_name thmid2);

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

fun thm'_of_thm thm =

  ((thmID_of_derivation_name o Thm.get_name_hint) thm, ""): thm'

(*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, Symbol.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, comments see type rule and scr | Rfuns *)

  (term * term * rule list list * (rule * (term * term list)) list);

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;

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

val e_scr = Prog 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" WN.101011 ABOLISH !*)

type domID = string;   (* domID ^".thy" = theory' WN.101011 replace 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 Symbol.explode o string_of_thy;

(* fun theory'2theory = fun thyID2thy ... see fun assoc_thy (...Thy_Info.get_theory string);

al it = "Isac" : string

*)

fun thyID2theory' (thyID:thyID) = thyID;

(*

    let val ss = Symbol.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" : theory'

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

val it = "Isac" : theory'

*)

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

(*

    let val ss = Symbol.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";

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 Thy_Info.get_theory "Isac"

      (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 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;

type spec = 

     domID * (*WN.12.03: is replaced by thy from get_met ?FIXME? in:

	      specify (Init_Proof..), nxt_specify_init_calc,

	      assod (.SubProblem...), stac2tac (.SubProblem...)*)

     pblID * 

     metID;

fun spec2str ((dom,pbl,met)(*:spec*)) = 

  "(" ^ (quote dom) ^ ", " ^ (strs2str pbl) ^ 

  ", " ^ (strs2str met) ^ ")";

(*> spec2str empty_spec;

val it = "(\"\", [], (\"\", \"\"))" : string *)

val empty_spec = (e_domID,e_pblID,e_metID):spec;

val e_spec = empty_spec;

(*.association list with cas-commands, for generating a complete calc-head.*)

type generate_fn = 

  (term list ->    (* the arguments of the cas-command, eg. (x+1=2, x) *)

    (term *        (* description of an element                        *)

      term list)   (* value of the element (always put into a list)    *)

  list)            (* of elements in the formalization                 *)

type cas_elem = 

  (term *          (* cas-command, eg. 'solve'                         *)

    (spec *        (* theory, problem, method                          *)

    generate_fn))

fun cas_eq ((t1, (_, _)) : cas_elem, (t2, (_, _)) : cas_elem) = t1 = t2

(*either theID or pblID or metID*)

type kestoreID = string list;

val e_kestoreID = ["e_kestoreID"];

val kestoreID2str = strs2str;

(*for distinction of contexts WN130621: disambiguate with Isabelle's Context !*)

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

(* theories for html representation: Isabelle, Knowledge, ProgLang *)

val isabthys = Unsynchronized.ref ([] : theory list);

val knowthys = Unsynchronized.ref ([] : theory list);

val progthys = Unsynchronized.ref ([] : 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/Knowledge/termorder.sml*)

val rew_ord' =

    Unsynchronized.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)]);

(* A tree for storing data defined in different theories 

  for access from the Interpreter and from dialogue authoring 

  using a string list as key.

  'a is for pbt | met | thydata; after WN030424 naming became inappropriate *)

datatype 'a ptyp =

	Ptyp of string * (* element of the key *)

		'a list *      (* several pbts with different domIDs/thy TODO: select by subthy (isaref.p.69)

			                presently only _ONE_ elem FOR ALL KINDS OF CONTENT pbt | met | thydata *)

		('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,

			    fillpats: fillpat list,

			    thm: term}

		 | Hrls of {guh: guh,

			    coursedesign: authors,

			    mathauthors: authors,

			    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 = Unsynchronized.ref ([] : thehier); (*WN101011 make argument, del*)

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

   stores Isabelle's thms as terms for compatibility with Theory.axioms_of.

   WN1-1-28 make this data arguments and del ref ?*)

val isab_thm_thy = Unsynchronized.ref ([] : (thmDeriv * term) list);

val isabthys = Unsynchronized.ref ([] : theory list);

val first_ProgLang_thy = Unsynchronized.ref (@{theory Pure});

val first_Knowledge_thy = Unsynchronized.ref (@{theory Pure});

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

val e_rrls =

  Rrls {id = "e_rrls", prepat = [], rew_ord = ("dummy_ord", dummy_ord), erls = Erls,

    calc = [], errpatts = [], scr=e_rfuns}:rls;

fun rep_rls (Rls {id,preconds,rew_ord,erls,srls,calc,errpatts,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,errpatts,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

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

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

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

--1.7.03*)

fun rep_rrls (Rrls {id, calc, erls, prepat, rew_ord, errpatts,

	      scr = Rfuns {attach_form, init_state, locate_rule, next_rule, normal_form}}) =

  {id=id, calc=calc, erls=erls, prepat=prepat,

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

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

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

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

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

    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, errpatts=errpatts, scr=sc}) r =

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

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

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

			rules =rs, errpatts=errpatts, scr=sc}) r =

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

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

  | append_rls id (Rrls _) _ =

    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_ids rls1 rls2 =

  let 

    val id1 = (#id o rep_rls) rls1

    val id2 = (#id o rep_rls) rls2

  in

    if id1 = id2 then id1

    else "merged_" ^ id1 ^ "_" ^ id2

  end

fun merge_rls _ Erls rls = rls

  | merge_rls _ rls Erls = rls

  | merge_rls _ (Rrls x) _ = Rrls x (* required for merging Theory_Data *)

  | merge_rls _ _ (Rrls x) = Rrls x

  | merge_rls id

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

	    rules = rs1, errpatts = eps1, scr = sc1, ...})

	  (Rls {preconds = pc2, erls = er2, srls = sr2, calc = ca2,

	    rules = rs2, errpatts = eps2, ...})

    =

	  (Rls {id = id, rew_ord = ro1, scr = sc1,

	    preconds = union (op =) pc1 pc2,	    

	    erls = merge_rls (merge_ids er1 er2) er1 er2,

	    srls = merge_rls (merge_ids sr1 sr2) sr1 sr2,

	    calc = union calc_eq ca1 ca2,

		  rules = union eq_rule rs1 rs2,

      errpatts = union (op =) eps1 eps2} : rls)

  | merge_rls id

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

	    rules = rs1, errpatts = eps1, scr = sc1, ...})

	  (Seq {preconds = pc2, erls = er2, srls = sr2, calc = ca2,

	    rules = rs2, errpatts = eps2, ...})

    =

	  (Seq {id = id, rew_ord = ro1, scr = sc1,

	    preconds = union (op =) pc1 pc2,	    

	    erls = merge_rls (merge_ids er1 er2) er1 er2,

	    srls = merge_rls (merge_ids sr1 sr2) sr1 sr2,

	    calc = union calc_eq ca1 ca2,

		  rules = union eq_rule rs1 rs2,

      errpatts = union (op =) eps1 eps2} : rls)

  | merge_rls id _ _ = error ("merge_rls: \"" ^ id ^ 

    "\"; 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,

		     rules=rs, errpatts=eps, scr=sc}) r =

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

	   rules = gen_rems eq_rule (rs, r),

	   errpatts = eps(*gen_rems op= (eps, TODO)*),

	 scr=sc}:rls)

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

		     rules =rs, errpatts=eps, scr=sc}) r =

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

	   rules = gen_rems eq_rule (rs, r),

	   errpatts = eps(*gen_rems op= (eps, TODO)*),

	 scr=sc}:rls)

  | remove_rls id (Rrls _) _ = error

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

(* datastructure for KEStore_Elems, intermediate for thehier *)

type rlss_elem = 

  (rls' *     (* identifier unique within Isac *)

  (theory' *  (* just for assignment in thehier, not appropriate for parsing etc *)

    rls))     (* ((#id o rep_rls) rls) = rls'   by coding discipline *)

fun rls_eq ((id1, (_, _)), (id2, (_, _))) = id1 = id2

fun insert_merge_rls (re as (id, (thyID, r1)) : rlss_elem) ys = 

  case get_index (fn y => if curry rls_eq re y then SOME y else NONE) ys of

    NONE => re :: ys

  | SOME (i, (_, (_, r2))) => 

      let

        val r12 = merge_rls id r1 r2

      in list_update ys i (id, (thyID, r12)) end

fun merge_rlss (s1, s2) = fold insert_merge_rls s1 s2;

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

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

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

fun assoc' ([], key) = 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 _ => error ("ME_Isa: thy '"^thy^"' not in system");*)

fun assoc_thy (thy:theory') =

    if thy = "e_domID" then (Thy_Info.get_theory "Script") (*lower bound of Knowledge*)

    else (Thy_Info.get_theory thy)

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

(*get the string for stac from rule*)

fun term_to_string' ctxt t =

  let

    val ctxt' = Config.put show_markup false ctxt

  in Print_Mode.setmp [] (Syntax.string_of_term ctxt') t end;

fun term_to_string'' (thyID : thyID) t =

  let

    val ctxt' = Config.put show_markup false (Proof_Context.init_global (Thy_Info.get_theory thyID))

  in Print_Mode.setmp [] (Syntax.string_of_term ctxt') t end;

fun term_to_string''' thy t =

  let

    val ctxt' = Config.put show_markup false (Proof_Context.init_global thy)

  in Print_Mode.setmp [] (Syntax.string_of_term ctxt') t end;

fun term_to_string t = term_to_string'' "Isac" t;

fun term2str t = term_to_string'' "Isac" t; (*legacy*)

fun terms2str ts = (strs2str o (map term2str )) ts;

(*terms2str [t1,t2] = "[\"1 + 2\",\"abc\"]";*)

fun terms2str' ts = (strs2str' o (map term2str )) ts;

(*terms2str' [t1,t2] = "[1 + 2,abc]";*)

fun terms2strs ts = (map term2str) ts;

(*terms2strs [t1,t2] = ["1 + 2", "abc"];*)

fun termopt2str (SOME t) = "SOME " ^ term2str t

  | termopt2str NONE = "NONE";

fun type_to_string' ctxt t =

  let

    val ctxt' = Config.put show_markup false ctxt

  in Print_Mode.setmp [] (Syntax.string_of_typ ctxt') t end;

fun type_to_string'' (thyID : thyID) t =

  let

    val ctxt' = Config.put show_markup false (Proof_Context.init_global (Thy_Info.get_theory thyID))

  in Print_Mode.setmp [] (Syntax.string_of_typ ctxt') t end;

fun type_to_string''' thy t =

  let

    val ctxt' = Config.put show_markup false (Proof_Context.init_global thy)

  in Print_Mode.setmp [] (Syntax.string_of_typ ctxt') t end;

fun type2str typ = type_to_string'' "Isac" typ; (*legacy*)

val string_of_typ = type2str; (*legacy*)

fun string_of_typ_thy thy typ = type_to_string'' thy typ; (*legacy*)

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 (Prog s) = "Prog " ^ 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 = Unsynchronized.ref false;

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

val depth = Unsynchronized.ref 99999;

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

(*WN060829 still unused...*)

val lim_rewrite = Unsynchronized.ref 99999;

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

val lim_deriv = Unsynchronized.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 = Unsynchronized.ref true;

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;

(* the pattern for an item of a problems model or a methods guard *)

type pat =

  (string *     (* field               *)

	  (term *     (* description         *)

	     term))   (* id | arbitrary term *);

fun pat2str ((field, (dsc, id)) : pat) = 

  pair2str (field, pair2str (term2str dsc, term2str id))

fun pats2str pats = (strs2str o (map pat2str)) pats

(* types for problems models *)

type pbt_ =

  (string *   (* field "#Given",..*)(*deprecated due to 'type pat'*)

    (term *   (* description      *)

      term)); (* id | struct-var  *)

val e_pbt_ = ("#Undef", (e_term, e_term)) : pbt_

type pbt = 

  {guh : guh,         (* unique within this isac-knowledge *)

  mathauthors : string list, (* copyright *)

  init : pblID,       (* to start refinement with *)

  thy  : theory,      (* which allows to compile that pbt

                      TODO: search generalized for subthy (ref.p.69*)

                      (*^^^ WN050912 NOT used during application of the problem,

                      because applied terms may be from 'subthy' as well as from super;

                      thus we take 'maxthy'; see match_ags !*)

  cas : term option,  (* 'CAS-command'*)

  prls : rls,         (* for preds in where_*)

  where_ : term list, (* where - predicates*)

  ppc : pat list,     (* this is the model-pattern; 

                       it contains "#Given","#Where","#Find","#Relate"-patterns

                       for constraints on identifiers see "fun cpy_nam" *)

  met : metID list}   (* methods solving the pbt*)

val e_pbt = {guh = "pbl_empty", mathauthors = [], init = e_pblID, thy = Thy_Info.get_theory "Pure",

  cas = NONE, prls = Erls, where_ = [], ppc = [], met = []} : pbt

fun pbt2str

        ({cas = cas', guh = guh', init = init', mathauthors = ma', met = met', ppc = ppc',

          prls = prls', thy = thy', where_ = where'} : pbt) =

      "{cas = " ^ (termopt2str cas') ^  ", guh = \"" ^ guh'  ^ "\", init = "

      ^ (strs2str init') ^ ", mathauthors = \"" ^ (strs2str ma') ^ "\", met = "

      ^ (strslist2strs met') ^ ", ppc = " ^ pats2str ppc' ^ ", prls = \""

      ^ (rls2str prls') ^ "\", thy = {" ^ Context.theory_name thy'

      ^ "}, where_ = " ^ (terms2str where') ^ "}" |> linefeed;

fun pbts2str pbts = map pbt2str pbts |> strs2str;

val e_Ptyp = Ptyp ("e_pblID",[e_pbt],[])

type ptyps = (pbt ptyp) list

val ptyps = Unsynchronized.ref ([e_Ptyp] : ptyps);

fun insrt _ pbt [k] [] = [Ptyp (k, [pbt],[])]

  | insrt d pbt [k] ((Ptyp (k', [p], ps))::pys) =

((*tracing("### insert 1: ks = "^(strs2str [k])^"    k'= "^k');*)

     if k=k'

     then ((Ptyp (k', [pbt], ps))::pys)

     else (*ev.newly added pbt is free _only_ with 'last_elem pblID'*)

	 ((Ptyp (k', [p], ps))::(insrt d pbt [k] pys))

)			 

  | insrt d pbt (k::ks) ((Ptyp (k', [p], ps))::pys) =

((*tracing("### insert 2: ks = "^(strs2str (k::ks))^"    k'= "^k');*)

     if k=k'

     then ((Ptyp (k', [p], insrt d pbt ks ps))::pys)

     else 

	 if length pys = 0

	 then error ("insert: not found "^(strs2str (d:pblID)))

	 else ((Ptyp (k', [p], ps))::(insrt d pbt (k::ks) pys))

);

(* this function only works wrt. the way Isabelle evaluates Theories and is not a general merge

  function for trees / ptyps *)

fun merge_ptyps ([], pt) = pt

  | merge_ptyps (pt, []) = pt

  | merge_ptyps ((Ptyp (k, x, ps)::xs), (ys' as Ptyp (k', y, ps')::ys)) =

      if k = k' then

        (Ptyp (k, y, merge_ptyps (ps, ps')) :: merge_ptyps (xs, ys)) else

        (Ptyp (k, x, ps) :: merge_ptyps (xs, ys'));

(* types for methods *)

(*

end (*struct*)

*)