(* 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

*)

signature CALC_ELEMENT =

  sig

    type eval_fn

    type rew_ord

    eqtype errpatID

    type calc

        datatype rule = Cal1 of string * eval_fn | Calc of string * eval_fn | Erule | Rls_ of rls 

      | Thm of string * thm

    and scr

      = EmptyScr

      | Prog of term

      | Rfuns of

          {attach_form: rule list list -> term -> term -> (rule * (term * term list)) list,

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

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

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

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

    and rls =

        Erls

      | Rls of {calc: calc list, erls: rls, errpatts: errpatID list, id: string, preconds: term list, 

        rew_ord: rew_ord, rules: rule list, scr: scr, srls: rls}

      | Seq of {calc: calc list, erls: rls, errpatts: errpatID list, id: string, preconds: term list,

        rew_ord: rew_ord, rules: rule list, scr: scr, srls: rls}

      | Rrls of {calc: calc list, erls: rls, errpatts: errpatID list, 

        id: string, prepat: (term list * term) list, rew_ord: rew_ord, scr: scr}

    eqtype rls'

    eqtype theory'

    eqtype prog_calcID

    eqtype calID

    type cas_elem

    type pbt

    type ptyps

    type metID

    type pblID

    type mets

    type met

    datatype 'a ptyp = Ptyp of string * 'a list * 'a ptyp list

    type cal = calID * eval_fn

    type authors

    type guh

    type subst

    val env2str: subst -> string

    val subst2str: subst -> string

    val subst2str': subst -> string

    eqtype thyID

    type fillpat

    datatype thydata

      = Hcal of {calc: calc, coursedesign: authors, guh: guh, mathauthors: authors}

      | Hord of {coursedesign: authors, guh: guh, mathauthors: authors, ord: subst -> term * term -> bool}

      | Hrls of {coursedesign: authors, guh: guh, mathauthors: authors, thy_rls: thyID * rls}

      | Hthm of {coursedesign: authors, fillpats: fillpat list, guh: guh, mathauthors: authors, thm: thm}

      | Html of {coursedesign: authors, guh: guh, html: string, mathauthors: authors}

    type theID

    type rlss_elem

    val merge_rlss: rlss_elem list * rlss_elem list -> rlss_elem list

    val rls_eq: (''a * ('b * 'c)) * (''a * ('d * 'e)) -> bool

    type calc_elem

    val calc_eq: calc_elem * calc_elem -> bool

    type spec

    val cas_eq: cas_elem * cas_elem -> bool

    val e_Ptyp: pbt ptyp

    val merge_ptyps: 'a ptyp list * 'a ptyp list -> 'a ptyp list

    val check_guhs_unique: bool Unsynchronized.ref

    val check_pblguh_unique: guh -> pbt ptyp list -> unit

    val insrt: pblID -> 'a -> string list -> 'a ptyp list -> 'a ptyp list

    val e_Mets: met ptyp

    val check_metguh_unique: guh -> met ptyp list -> unit

    val add_thydata: string list * string list -> thydata -> thydata ptyp list -> thydata ptyp list

    val get_py: 'a ptyp list -> pblID -> string list -> 'a

    val update_hthm: thydata -> fillpat list -> thydata

    val update_ptyps: string list -> string list -> 'a -> 'a ptyp list -> 'a ptyp list

    val e_rls: rls

    val e_rrls: rls

    val part2guh: theID -> guh

    val spec2str: string * string list * string list -> string

    val term_to_string''': theory -> term -> string

    val linefeed: string -> string

    val pbts2str: pbt list -> string

    val thes2str: thydata list -> string

    val theID2str: string list -> string

    val the2str: thydata -> string

    val Thy_Info_get_theory: string -> theory

    val string_of_typ: typ -> string

    val string_of_typ_thy: thyID -> typ -> string

    val term2str: term -> string

    val thy2ctxt: theory -> Proof.context

    val trace_calc: bool Unsynchronized.ref

    eqtype thmID

    type thm'

    datatype lrd = D | L | R

    val trace_rewrite: bool Unsynchronized.ref

    val depth: int Unsynchronized.ref

    val t2str: theory -> term -> string

    val ts2str: theory -> term list -> string

    val terms2str: term list -> string

    val id_rls: rls -> string

    val rls2str: rls -> string

    type errpat

    val rep_rls: rls -> {calc: calc list, erls: rls, errpats: errpatID list, id: string,

      preconds: term list, rew_ord: rew_ord, rules: rule list, scr: scr, srls: rls}

    val string_of_thmI: thm -> string

    val rule2str: rule -> string

    val e_term: term

    val dummy_ord: subst -> term * term -> bool

    val theory2domID: theory -> theory'

    val assoc_thy: theory' -> theory

    val append_rls: string -> rls -> rule list -> rls

    eqtype domID

    val get_rules: rls -> rule list

    val id_rule: rule -> string

    eqtype cterm'

    val term_to_string': Proof.context -> term -> string

    val thy2ctxt': string -> Proof.context

    type rrlsstate = term * term * rule list list * (rule * (term * term list)) list

    type loc_

    val loc_2str: loc_ -> string

    val termopt2str: term option -> string

    eqtype rew_ord'

    type thm''

    type rew_ord_

    val metID2str: string list -> string

    val e_domID: domID

    val e_pblID: pblID

    val e_metID: metID

    val empty_spec: spec

    val e_spec: spec

    datatype ketype = Exp_ | Met_ | Pbl_ | Thy_

    type kestoreID

    val app_py: 'a ptyp list -> ('a ptyp -> 'b) -> pblID -> string list -> 'b

    val ketype2str: ketype -> string

    val coll_pblguhs: pbt ptyp list -> guh list

    val coll_metguhs: met ptyp list -> guh list

    type pat

    val e_type: typ

    val theory2str: theory -> theory'

    val pats2str: pat list -> string

    val string_of_thy: theory -> theory'

    val theory2theory': theory -> theory'

    val maxthy: theory -> theory -> theory

    val e_evalfn: 'a -> term -> theory -> (string * term) option

    val assoc_rew_ord: string -> subst -> term * term -> bool

    eqtype filename

    val rule2str': rule -> string

    val lim_deriv: int Unsynchronized.ref

    val id_of_thm: rule -> string

    val isabthys: unit -> theory list

    val thyID_of_derivation_name: string -> string

    val partID': theory' -> string

    val Isac: 'a -> theory

    val theory'2thyID: theory' -> theory'

    val thm2guh: string * thyID -> thmID -> guh

    val thmID_of_derivation_name: string -> string

    val rls2guh: string * thyID -> rls' -> guh

    val eq_rule: rule * rule -> bool

    val e_rew_ordX: rew_ord

    val theID2guh: theID -> guh

    val thyID2theory': thyID -> thyID

    val e_rule: rule

    val scr2str: scr -> string

    val type2str: typ -> string

    eqtype fillpatID

    type pbt_ = string * (term * term)

    val e_rew_ord: subst -> term * term -> bool

    eqtype xml

    val cal2guh: string * thyID -> string -> guh

    val ketype2str': ketype -> string

    val str2ketype': string -> ketype

    val thmID_of_derivation_name': thm -> string

    eqtype path

    val theID2thyID: theID -> thyID

    val thy2guh: theID -> guh

    val theory2thyID: theory -> thyID

    val thypart2guh: theID -> guh

    val ord2guh: string * thyID -> rew_ord' -> guh

    val update_hrls: thydata -> errpatID list -> thydata

    eqtype iterID

    eqtype calcID

    val thm''_of_thm: thm -> thm''

    val rew_ord': (rew_ord' * (subst -> term * term -> bool)) list Unsynchronized.ref

    val merge_rls: string -> rls -> rls -> rls

    val e_rrlsstate: rrlsstate

    val thm_of_thm: rule -> thm

    val remove_rls: string -> rls -> rule list -> rls

(* ---- for tests only: shifted from below to remove the Warning "unused" at fun.def. --------- *)

    val thm2str: thm -> string

    val term_to_string'': thyID -> term -> string

    val terms2str': term list -> string

    val insert_fillpats: thydata ptyp list -> (pblID * fillpat list) list -> thydata ptyp list ->

      thydata ptyp list

(*/-------------------------------------------------------- ! aktivate for Test_Isac BEGIN ---\* )

    val terms2strs: term list -> string list

    val string_of_thm': theory -> thm -> string

    val string_of_thm: thm -> string

    val knowthys: unit -> theory list

    val e_pbt: pbt

( *\--- ! aktivate for Test_Isac END ----------------------------------------------------------/*)

(*----- unused code, kept as hints to design ideas ---------------------------------------------*)

val overwritelthy: theory -> (rls' * (string * rls)) list * (rls' * rls) list ->

  (rls' * (string * rls)) list  end

(**)

structure Celem(**): CALC_ELEMENT(**) =

struct

(**)

val linefeed = (curry op^) "\n"; (* ?\<longrightarrow> libraryC ?*)

type authors = string list;

type cterm' = string;

type iterID = int;

type calcID = int;

(* TODO CLEANUP Thm:

type rule = 

Thm (string, thm): (a) needs string to identify sym_thmID for handling in front-end;

                   (b) investigate if ""RS sym" attaches a [.]" still occurs: string_of_thmI

thmID            : type for data from user input + program

thmDeriv         : type for thy_hierarchy ONLY

obsolete types   : thm' (SEE "ad thm'"), thm''. 

revise funs      : id_of_thm, thm_of_thm, rep_thm_G', eq_thmI, eq_thmI', thm''_of_thm thm.

activate         : thmID_of_derivation_name'

*)

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''; WN180324: used in TODO review:

val thm'2xml : int -> Celem.thm' -> Celem.xml

val assoc_thm': theory -> Celem.thm' -> thm

| Calculate' of Celem.theory' * string * term * (term * Celem.thm')

*)

(* tricky combination of (string, term) for theorems in Isac:

  * case 1 general: frontend + lucin, e.g. applicable_in..Rewrite: (thmID, _) --> (thmID, thm)

    by Global_Theory.get_thm, special cases ("add_commute",..) see convert_metaview_to_thmid.

  * case 2 "sym_..": Global_Theory.get_thm..RS sym

  * case 3 ad-hoc thm "#..." mk_thm from ad-hoc term (numerals only) in calculate_:

    from applicable_in..Calculate: opstr --calculate_/adhoc_thm--> (thmID, thm)

*)

type thm'' = thmID * thm; (* only for transport via libisabelle isac-java <--- ME *)

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;

type xml = string; (* rm together with old code replaced by XML.tree *)

(* 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;

type prog_calcID = string;

type calc = (prog_calcID * cal);

type calc_elem =  (* fun calculate_ fetches the evaluation-function via this list *)

  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, _)), (pi2, (ci2, _))) =

  if pi1 = pi2

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

  else false

(*WN180324 TODO clean types subst, *)

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

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

(*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) (* see TODO CLEANUP Thm     *)

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

	  eval_fn

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

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

	  eval_fn

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

and scr =

    EmptyScr

  | Prog of term (* a leaf is either a tactic or an 'exp' in 'let v = expr' 

                    where 'exp' does not contain a tactic. *)

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

  | 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 (Cal1 (id, _)) = id

  | id_rule (Rls_ rls) = id_rls rls

  | id_rule Erule = "Erule";

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

  | eq_rule _ = false;

(*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*)

val e_domID = "e_domID" : domID;

(* Since Isabelle2017 sessions in theory identifiers are enforced.

  However, we leave theory identifiers short, in particular in use as keys into KEStore. *)

fun Thy_Info_get_theory thyID = Thy_Info.get_theory ("Isac." ^ thyID)

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"}*)

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*)

fun thyID2theory' (thyID:thyID) = thyID;

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

(*  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 due 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)'

    # ???

*)

fun thm2str thm =

  let

    val t = Thm.prop_of thm

    val ctxt = Proof_Context.init_global (Thy_Info.get_theory ("Isac.Isac"))

    val ctxt' = Config.put show_markup false ctxt

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

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 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 term2str t = term_to_string' (thy2ctxt' "Isac") t;

fun t2str thy t = term_to_string' (thy2ctxt thy) t;

fun ts2str thy ts = ts |> map (t2str thy) |> strs2str';

fun terms2strs ts = map term2str ts;     (* terms2strs [t1,t2] = ["1 + 2", "abc"];      *)

val terms2str = strs2str o terms2strs;   (* terms2str  [t1,t2] = "[\"1 + 2\",\"abc\"]"; *)

val terms2str' = strs2str' o terms2strs; (* terms2str' [t1,t2] = "[1 + 2,abc]";         *)

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

  | termopt2str NONE = "NONE";

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

val string_of_typ = type2str; (*legacy*)

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

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

fun id_of_thm (Thm (id, _)) = id  (* TODO re-arrange code for rule2str *)

  | id_of_thm _ = raise ERROR ("id_of_thm: uncovered case " (* ^ rule2str r *))

fun thm_of_thm (Thm (_, thm)) = thm  (* TODO re-arrange code for rule2str *)

  | thm_of_thm _ = raise ERROR ("thm_of_thm: uncovered case " (* ^ rule2str r *))

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

fun thmID_of_derivation_name' thm = (thmID_of_derivation_name o Thm.get_name_hint) thm

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

fun thm''_of_thm thm = (thmID_of_derivation_name' thm, thm) : thm''

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

fun string_of_thm thm = term_to_string' (thy2ctxt' "Isac") (Thm.prop_of thm)

fun string_of_thm' thy thm = term_to_string' (thy2ctxt thy) (Thm.prop_of thm)

fun string_of_thmI thm =

  let 

    val str = (de_quote o string_of_thm) thm

    val (a, b) = split_nlast (5, Symbol.explode str)

  in 

    case b of

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

    | _ => str

  end

fun get_rules Erls = []

  | 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, _)) = "Calc (\""^str^"\",fn)"

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

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

fun rule2str' Erule = "Erule"

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

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

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

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

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 e_term = Const ("empty", e_type);

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

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

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

type theID = string list;

val theID2str = strs2str; (*theID eg. is ["IsacKnowledge", "Test", "Rulesets", "ac_plus_times"]*)

fun theID2thyID theID =

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

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

(*the key into the hierarchy ob problems*)

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

val e_pblID = ["e_pblID"];

(*the key into the hierarchy ob methods*)

type metID = string list;

type spec = domID * pblID * metID;

fun spec2str (dom, pbl, met) = 

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

val e_metID = ["e_metID"];

val metID2str = strs2str;

val empty_spec = (e_domID, e_pblID, e_metID);

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;

(* 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";

(* for conversion from XML *)

fun str2ketype' "exp" = Exp_

  | str2ketype' "thy" = Thy_

  | str2ketype' "pbl" = Pbl_

  | str2ketype' "met" = Met_

  | str2ketype' str = raise ERROR ("str2ketype': WRONG arg = " ^ str)

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

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

val rew_ord' = Unsynchronized.ref

  ([("e_rew_ord", e_rew_ord), ("dummy_ord", dummy_ord)]

	: (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                         *)

(* 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 "pbt" 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'*)

datatype thydata =

  Html of {guh: guh, coursedesign: authors, mathauthors: authors, html: string}

| Hthm of {guh: guh, coursedesign: authors, mathauthors: authors, fillpats: fillpat list,

   thm: thm} (* here no sym_thm, thus no thmID required *)

| 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)};

fun the2str (Html {guh, ...}) = guh

  | the2str (Hthm {guh, ...}) = guh

  | the2str (Hrls {guh, ...}) = guh

  | the2str (Hcal {guh, ...}) = guh

  | the2str (Hord {guh, ...}) = guh

fun thes2str thes = map the2str thes |> list2str;

(* notes on thehier concerning sym_thmID theorems (created in derivations, reverse rewriting)

     (a): thehier does not contain sym_thmID theorems

     (b): lookup for sym_thmID directly from Isabelle using sym_thm

          (within math-engine NO lookup in thehier -- within java in *.xml only!)

TODO (c): export from thehier to xml

TODO (c1)   creates one entry for "thmID" (and NONE for "sym_thmID") in the hierarchy

TODO (c2)   creates 2 files "thy_*-thm-thmID.xml" and "thy_*-thm-sym_thmID.xml"

TODO (d): 1 entry in the MiniBrowser's hierarchy (generated from xml)

          stands for both, "thmID" and "sym_thmID" 

TODO (d1)   lookup from calctxt          

TODO (d1)   lookup from from rule set in MiniBrowser *)

type thehier = (thydata ptyp) list;

(* required to determine sequence of main nodes of thehier in KEStore.thy *)

fun part2guh [str] = (case str of

	  "Isabelle" => "thy_isab_" ^ str ^ "-part" : guh

      | "IsacScripts" => "thy_scri_" ^ str ^ "-part"

      | "IsacKnowledge" => "thy_isac_" ^ str ^ "-part"

      | str => raise ERROR ("thy2guh: called with \""^ str ^"\""))

  | part2guh theID = raise ERROR ("part2guh called with theID = \"" ^ theID2str theID ^ "'");

fun thy2guh [part, thyID] = (case part of

      "Isabelle" => "thy_isab_" ^ thyID

    | "IsacScripts" => "thy_scri_" ^ thyID

    | "IsacKnowledge" => "thy_isac_" ^ thyID

    | str => raise ERROR ("thy2guh: called with \"" ^ str ^ "\""))

  | thy2guh theID = raise ERROR ("thy2guh called with \"" ^ strs2str' theID ^ "\"");

fun thypart2guh ([part, thyID, thypart] : theID) = (case part of

      "Isabelle" => "thy_isab_" ^ thyID ^ "-" ^ thypart : guh

    | "IsacScripts" => "thy_scri_" ^ thyID ^ "-" ^ thypart

    | "IsacKnowledge" => "thy_isac_" ^ thyID ^ "-" ^ thypart

    | str => raise ERROR ("thypart2guh: called with '" ^ str ^ "'"))

  | thypart2guh strs = raise ERROR ("thypart2guh called with \"" ^ strs2str' strs ^ "\"");

(* convert the data got via contextToThy to a globally unique handle.

   there is another way to get the guh: get out of the 'theID' in the hierarchy *)

fun thm2guh (isa, thyID) thmID = case isa of

    "Isabelle" => "thy_isab_" ^ theory'2thyID thyID ^ "-thm-" ^ strip_thy thmID : guh

  | "IsacKnowledge" => "thy_isac_" ^ theory'2thyID thyID ^ "-thm-" ^ strip_thy thmID

  | "IsacScripts" => "thy_scri_" ^ theory'2thyID thyID ^ "-thm-" ^ strip_thy thmID

  | _ => raise ERROR

    ("thm2guh called with (isa, thyID) = (" ^ isa ^ ", " ^ thyID ^ ") for thm = \"" ^ thmID ^ "\"");

fun rls2guh (isa, thyID) rls' = case isa of

    "Isabelle" => "thy_isab_" ^ theory'2thyID thyID ^ "-rls-" ^ rls' : guh

  | "IsacKnowledge" => "thy_isac_" ^ theory'2thyID thyID ^ "-rls-" ^ rls'

  | "IsacScripts" => "thy_scri_" ^ theory'2thyID thyID ^ "-rls-" ^ rls'

  | _ => raise ERROR

    ("rls2guh called with (isa, thyID) = (" ^ isa ^ ", " ^ thyID ^ ") for rls = \"" ^ rls' ^ "\"");

fun cal2guh (isa, thyID) calID = case isa of

    "Isabelle" => "thy_isab_" ^ theory'2thyID thyID ^ "-cal-" ^ calID : guh

  | "IsacKnowledge" => "thy_isac_" ^ theory'2thyID thyID ^ "-cal-" ^ calID

  | "IsacScripts" => "thy_scri_" ^ theory'2thyID thyID ^ "-cal-" ^ calID

  | _ => raise ERROR

    ("cal2guh called with (isa, thyID) = (" ^ isa ^ ", " ^ thyID ^ ") for cal = \"" ^ calID ^ "\"");

fun ord2guh (isa, thyID) rew_ord' = case isa of

    "Isabelle" => "thy_isab_" ^ theory'2thyID thyID ^ "-ord-" ^ rew_ord' : guh

  | "IsacKnowledge" => "thy_isac_" ^ theory'2thyID thyID ^ "-ord-" ^ rew_ord'

  | "IsacScripts" => "thy_scri_" ^ theory'2thyID thyID ^ "-ord-" ^ rew_ord'

  | _ => raise ERROR

    ("ord2guh called with (isa, thyID) = (" ^ isa ^ ", " ^ thyID ^ ") for ord = \"" ^ rew_ord' ^ "\"");

(* not only for thydata, but also for thy's etc *)

(* TODO

fun theID2guh theID = case length theID of

    0 => error ("theID2guh: called with theID = " ^ strs2str' theID)

  | 1 => part2guh theID

  | 2 => thy2guh theID

  | 3 => thypart2guh theID

  | 4 => 

    let val [isa, thyID, typ, elemID] = theID

    in case typ of

        "Theorems" => thm2guh (isa, thyID) elemID

      | "Rulesets" => rls2guh (isa, thyID) elemID

      | "Calculations" => cal2guh (isa, thyID) elemID

      | "Orders" => ord2guh (isa, thyID) elemID

      | "Theorems" => thy2guh [isa, thyID]

      | str => raise ERROR ("theID2guh: called with theID = " ^ strs2str' theID)

    end

  | n => raise ERROR ("theID2guh called with theID = " ^ strs2str' theID);

*)

(* not only for thydata, but also for thy's etc *)

fun theID2guh [] = raise ERROR ("theID2guh: called with []")

  | theID2guh [str] = part2guh [str]

  | theID2guh [s1, s2] = thy2guh [s1, s2]

  | theID2guh [s1, s2, s3] = thypart2guh [s1, s2, s3]

  | theID2guh (strs as [isa, thyID, typ, elemID]) = (case typ of

      "Theorems" => thm2guh (isa, thyID) elemID

    | "Rulesets" => rls2guh (isa, thyID) elemID

    | "Calculations" => cal2guh (isa, thyID) elemID

    | "Orders" => ord2guh (isa, thyID) elemID

    | _ => raise ERROR ("theID2guh: called with theID = " ^ strs2str' strs))

  | theID2guh strs = raise ERROR ("theID2guh called with theID = " ^ strs2str' strs);

type path = string;

type filename = string;

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 Erls = rep_rls e_rls

  | 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, errpats = errpatts,

      calc = calc, 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, errpats = errpatts,

      calc = calc, rules = rules, scr = scr}

  | rep_rls (Rrls _)  = rep_rls e_rls

fun append_rls id Erls _ = raise ERROR ("append_rls: with \"" ^ id ^ "\" not for Erls")

  | 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}

  | 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}

  | append_rls id (Rrls _) _ = raise ERROR ("append_rls: not for reverse-rewrite-rule-set " ^ id);

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}

  | 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}

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

    "\"; not for reverse-rewrite-rule-sets and not for mixed Rls -- Seq");

(* used only for one hack TODO remove *)

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,

	    scr = sc}

  | 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,

	    scr = sc}

  | remove_rls id (Rrls _) _ = raise ERROR ("remove_rls: not for reverse-rewrite-rule-set "^id)

  | remove_rls _ rls _ = raise ERROR ("remove_rls called with " ^ rls2str rls);

(* 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 assoc' ([], key) = raise ERROR ("ME_Isa: \"" ^ key ^ "\" not known")

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

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

fun assoc_thy thy =

    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");

fun subst2str s =

    (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;

val env2str = subst2str;

fun scr2str EmptyScr = "EmptyScr"

  | scr2str (Prog s) = "Prog " ^ term2str s

  | scr2str (Rfuns _)  = "Rfuns";

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

(* trace internal steps of isac's numeral calculations *)

val trace_calc = Unsynchronized.ref false;

(* 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 *)

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 "type 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 = (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 (TODO rename to specification models) *)

type pbt_ =

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

    (term *   (* description      *)

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

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 = []}

fun pbt2str ({cas = cas', guh = guh', init = init', mathauthors = ma', met = met', ppc = ppc',

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

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

      ^ (strs2str init') ^ ", mathauthors = " ^ (strs2str ma' |> quote) ^ ", met = "

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

      ^ (rls2str prls' |> quote) ^ ", thy = {" ^ (theory2str thy') ^ "}, where_ = "

      ^ (terms2str w') ^ "}" |> linefeed;

fun pbts2str pbts = map pbt2str pbts |> list2str;