(* ~~/src/Tools/isac/calcelems.sml

   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 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 authors

    type guh

    val env2str: Rule.subst -> string

    val subst2str: Rule.subst -> string

    val subst2str': Rule.subst -> string

    type fillpat

    datatype thydata

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

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

      | Hrls of {coursedesign: authors, guh: guh, mathauthors: authors, thy_rls: Rule.thyID * Rule.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 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 part2guh: theID -> guh

    val spec2str: string * string list * string list -> 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 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 assoc_thy: Rule.theory' -> theory

    type loc_

    val loc_2str: loc_ -> string

    type thm''

    val metID2str: string list -> string

    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 pats2str: pat list -> string

    val maxthy: theory -> theory -> theory

    eqtype filename

    val lim_deriv: int Unsynchronized.ref

    val id_of_thm: Rule.rule -> string

    val isabthys: unit -> theory list

    val thyID_of_derivation_name: string -> string

    val partID': Rule.theory' -> string

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

    val thmID_of_derivation_name: string -> string

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

    val theID2guh: theID -> guh

    eqtype fillpatID

    type pbt_ = string * (term * term)

    eqtype xml

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

    val ketype2str': ketype -> string

    val str2ketype': string -> ketype

    val thmID_of_derivation_name': thm -> string

    eqtype path

    val theID2thyID: theID -> Rule.thyID

    val thy2guh: theID -> guh

    val thypart2guh: theID -> guh

    val ord2guh: string * Rule.theory' -> string -> string

    val update_hrls: thydata -> Rule.errpatID list -> thydata

    eqtype iterID

    eqtype calcID

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

    val thm_of_thm: Rule.rule -> thm

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

    val thm2str: thm -> string

    val pats2str' : pat list -> string

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

      thydata ptyp list

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

    val knowthys: unit -> theory list

    val e_pbt: pbt

    val e_met: met

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

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

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

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

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

struct

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

type authors = string list;

type iterID = int;

type calcID = int;

(* TODO CLEANUP Thm:

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 * Rule.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 Rule.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 *)

(*.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 *)

(* 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                  *)

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

                 DESIGN ?TODO: list for several patterns ?      *)

(*  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 id_of_thm (Rule.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 (Rule.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''

(*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 = Rule.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 = (Rule.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)

(* 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: (Rule.thyID * Rule.rls)}

| Hcal of {guh: guh, coursedesign: authors, mathauthors: authors, calc: Rule.calc}

| Hord of {guh: guh, coursedesign: authors, mathauthors: authors,

    ord: (Rule.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_" ^ Rule.theory'2thyID thyID ^ "-thm-" ^ strip_thy thmID : guh

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

  | "IsacScripts" => "thy_scri_" ^ Rule.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_" ^ Rule.theory'2thyID thyID ^ "-rls-" ^ rls' : guh

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

  | "IsacScripts" => "thy_scri_" ^ Rule.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_" ^ Rule.theory'2thyID thyID ^ "-cal-" ^ calID : guh

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

  | "IsacScripts" => "thy_scri_" ^ Rule.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_" ^ Rule.theory'2thyID thyID ^ "-ord-" ^ rew_ord' : guh

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

  | "IsacScripts" => "thy_scri_" ^ Rule.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;

(* datastructure for KEStore_Elems, intermediate for thehier *)

type rlss_elem = 

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

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

    Rule.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 = Rule.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_thy thy =

    if thy = "e_domID"

    then (Rule.Thy_Info_get_theory "Script") (*lower bound of Knowledge*)

    else (Rule.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: (Rule.rls' * Rule.rls) list) =

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

    in overwritel (al, bl') end;

fun subst2str s =

    (strs2str o

      (map (

        linefeed o pair2str o (apsnd Rule.term2str) o (apfst Rule.term2str)))) s;

fun subst2str' s =

    (strs2str' o

     (map (

       pair2str o (apsnd Rule.term2str) o (apfst Rule.term2str)))) s;

val env2str = subst2str;

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 (Rule.term2str dsc, Rule.term2str id))

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

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

  pair2str (field, pair2str (Rule.term2str dsc, Rule.term2str id)) ^ "\n"

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 : Rule.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 = Rule.Erls, where_ = [], ppc = [], met = []} : pbt

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

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

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

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

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

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

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

fun pbts2str pbts = map pbt2str pbts |> list2str;

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

type ptyps = (pbt ptyp) list

fun coll_pblguhs pbls =

  let

    fun node coll (Ptyp (_, [n], ns)) = [(#guh : pbt -> guh) n] @ (nodes coll ns)

      | node _ _ = raise ERROR "coll_pblguhs - node"

	  and nodes coll [] = coll

      | nodes coll (n :: ns) = (node coll n) @ (nodes coll ns);

  in nodes [] pbls end;

fun check_pblguh_unique guh pbls =

  if member op = (coll_pblguhs pbls) guh

  then error ("check_guh_unique failed with \""^ guh ^"\";\n"^

	      "use \"sort_pblguhs()\" for a list of guhs;\n"^

	      "consider setting \"check_guhs_unique := false\"")

  else ();

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

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

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

    if k = k'

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

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

    )			 

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

    ((*writeln ("### 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))

    )

  | insrt _ _ _ _ = raise ERROR "";

fun update_ptyps ID _ _ [] =

    error ("update_ptyps: " ^ strs2str' ID ^ " does not exist")

  | update_ptyps ID [i] data ((py as Ptyp (key, _, pys)) :: pyss) =

    if i = key

    then 

      if length pys = 0

      then ((Ptyp (key, [data], [])) :: pyss)

      else error ("update_ptyps: " ^ strs2str' ID ^ " has descendants")

    else py :: update_ptyps ID [i] data pyss

  | update_ptyps ID (i :: is) data ((py as Ptyp (key, d, pys)) :: pyss) =

    if i = key

    then ((Ptyp (key,  d, update_ptyps ID is data pys)) :: pyss)

    else (py :: (update_ptyps ID (i :: is) data pyss))

  | update_ptyps _ _ _ _ = raise ERROR "update_ptyps called with undef pattern.";

(* 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 ((x' as Ptyp (k, _, ps)) :: xs, (xs' as Ptyp (k', y, ps') :: ys)) =

      if k = k'

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

      else x' :: merge_ptyps (xs, xs');

(* data for methods stored in 'methods'-database*)

type met = 

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

      mathauthors: string list,     (* copyright                                     *)

      init       : pblID,           (* WN060721 introduced mistakenly--TODO.REMOVE!  *)

      rew_ord'   : Rule.rew_ord',   (* for rules in Detail                           

			                                 TODO.WN0509 store fun itself, see 'type pbt'  *)

      erls       : Rule.rls,        (* the eval_rls for cond. in rules FIXME "rls'   

				                               instead erls in "fun prep_met"                *)

      srls       : Rule.rls,        (* for evaluating list expressions in scr        *)

      prls       : Rule.rls,        (* for evaluating predicates in modelpattern     *)

      crls       : Rule.rls,        (* for check_elementwise, ie. formulae in calc.  *)

      nrls       : Rule.rls,        (* canonical simplifier specific for this met    *)

      errpats    : Rule.errpat list,(* error patterns expected in this method        *)

      calc       : Rule.calc list,  (* Theory_Data in fun prep_met                   *)

      (*branch   : TransitiveB set in append_problem at generation ob pblobj         *)

      ppc        : pat list,        (* items in given, find, relate;

	      items (in "#Find") which need not occur in the arg-list of a SubProblem

        are 'copy-named' with an identifier "*'.'".

        copy-named items are 'generating' if they are NOT "*'''" ?WN120516??

        see ME/calchead.sml 'fun is_copy_named'.                                     *)

      pre        : term list,       (* preconditions in where                        *)

      scr        : Rule.scr         (* progam, empty as @{thm refl} or Rfuns         *)

	   };

val e_met = {guh = "met_empty", mathauthors = [], init = e_metID, rew_ord' = "e_rew_ord'",

	erls = Rule.e_rls, srls = Rule.e_rls, prls = Rule.e_rls, calc = [], crls = Rule.e_rls,

	errpats = [], nrls = Rule.e_rls, ppc = [], pre = [], scr = Rule.EmptyScr};

val e_Mets = Ptyp ("e_metID", [e_met],[]);

type mets = (met ptyp) list;

fun coll_metguhs mets =

  let

    fun node coll (Ptyp (_, [n], ns)) = [(#guh : met -> guh) n] @ (nodes coll ns)

      | node _ _ = raise ERROR "coll_pblguhs - node"

  	and nodes coll [] = coll

  	  | nodes coll (n :: ns) = (node coll n) @ (nodes coll ns);

    in nodes [] mets end;

fun check_metguh_unique (guh:guh) (mets: (met ptyp) list) =

    if member op = (coll_metguhs mets) guh

    then raise ERROR ("check_guh_unique failed with \"" ^ guh ^"\";\n"^

		(*"use \"sort_metguhs()\" for a list of guhs;\n" ^        ...evaluates to [] ?!?*)

		  "consider setting \"check_guhs_unique := false\"")

    else ();

fun Html_default exist = (Html {guh = theID2guh exist, 

  coursedesign = ["isac team 2006"], mathauthors = [], html = ""})

fun fill_parents (_, [i]) thydata = Ptyp (i, [thydata], [])

  | fill_parents (exist, i :: is) thydata =

    Ptyp (i, [Html_default (exist @ [i])], [fill_parents (exist @ [i], is) thydata])

  | fill_parents _ _ = raise ERROR "Html_default: avoid ML warning: Matches are not exhaustive"

fun add_thydata (exist, is) thydata [] = [fill_parents (exist, is) thydata]

  | add_thydata (exist, [i]) data (pys as (py as Ptyp (key, _, _)) :: pyss) = 

    if i = key

    then pys (* preserve existing thydata *) 

    else py :: add_thydata (exist, [i]) data pyss

  | add_thydata (exist, iss as (i :: is)) data ((py as Ptyp (key, d, pys)) :: pyss) = 

    if i = key

    then       

      if length pys = 0

      then Ptyp (key, d, [fill_parents (exist @ [i], is) data]) :: pyss

      else Ptyp (key, d, add_thydata (exist @ [i], is) data pys) :: pyss

    else py :: add_thydata (exist, iss) data pyss

  | add_thydata _ _ _ = raise ERROR "add_thydata: avoid ML warning: Matches are not exhaustive"

fun update_hthm (Hthm {guh, coursedesign, mathauthors, thm, ...}) fillpats' =

  Hthm {guh = guh, coursedesign = coursedesign, mathauthors = mathauthors,

    fillpats = fillpats', thm = thm}

  | update_hthm _ _ = raise ERROR "update_hthm: wrong arguments";

(* for dialog-authoring *)

fun update_hrls (Hrls {guh, coursedesign, mathauthors, thy_rls = (thyID, rls)}) errpatIDs =

    let

      val rls' = 

        case rls of

          Rule.Rls {id, preconds, rew_ord, erls, srls, calc, rules, scr, ...}

          => Rule.Rls {id = id, preconds = preconds, rew_ord = rew_ord, erls = erls, srls = srls,

               calc = calc, rules = rules, scr = scr, errpatts = errpatIDs}

        | Rule.Seq {id, preconds, rew_ord, erls, srls, calc, rules, scr, ...}

          => Rule.Seq {id = id, preconds = preconds, rew_ord = rew_ord, erls = erls, srls = srls,

               calc = calc, rules = rules, scr = scr, errpatts = errpatIDs}

        | Rule.Rrls {id, prepat, rew_ord, erls, calc, scr, ...}

          => Rule.Rrls {id = id, prepat = prepat, rew_ord = rew_ord, erls = erls, calc = calc,

               scr = scr, errpatts = errpatIDs}

        | Erls => Erls

    in

      Hrls {guh = guh, coursedesign = coursedesign, mathauthors = mathauthors,

        thy_rls = (thyID, rls')}

    end

  | update_hrls _ _ = raise ERROR "update_hrls: wrong arguments";

fun app_py p f (d:pblID) (k(*:pblRD*)) =

  let

    fun py_err _ = raise ERROR ("app_py: not found: " ^ strs2str d);

    fun app_py' _ [] = py_err ()

      | app_py' [] _ = py_err ()

      | app_py' [k0] ((p' as Ptyp (k', _, _  )) :: ps) =

        if k0 = k' then f p' else app_py' [k0] ps

      | app_py' (k' as (k0 :: ks)) (Ptyp (k'', _, ps) :: ps') =

        if k0 = k'' then app_py' ks ps else app_py' k' ps';

  in app_py' k p end;

fun get_py p =

  let

    fun extract_py (Ptyp (_, [py], _)) = py

      | extract_py _ = raise ERROR ("extract_py: Ptyp has wrong format.");

  in app_py p extract_py end;

fun (*KEStore_Elems.*)insert_fillpats th fis = (* for tests bypassing setup KEStore_Elems *)

  let

    fun update_elem th (theID, fillpats) =

      let

        val hthm = get_py th theID theID

        val hthm' = update_hthm hthm fillpats

          handle ERROR _ => error ("insert_fillpats: " ^ strs2str theID ^ "must address a theorem")

      in update_ptyps theID theID hthm' end

  in fold (update_elem th) fis end

(* group the theories defined in Isac, compare Build_Thydata:

  section "Get and group the theories defined in Isac" *) 

fun isabthys () = (*["Complex_Main", "Taylor", .., "Pure"]*)

  let

    val allthys = Theory.ancestors_of (Rule.Thy_Info_get_theory "Build_Thydata")

  in

    drop ((find_index (curry Context.eq_thy (Thy_Info.get_theory "Complex_Main")) allthys), allthys)

  end

fun knowthys () = (*["Isac", .., "Descript", "Delete"]*)

  let

    fun isacthys () = (* ["Isac", .., "KEStore"] without Build_Isac thys: "Interpret" etc *)

      let

        val allthys = filter_out (member Context.eq_thy

          [(*Thy_Info_get_theory "ProgLang",*) Rule.Thy_Info_get_theory "Interpret", 

            Rule.Thy_Info_get_theory "xmlsrc", Rule.Thy_Info_get_theory "Frontend"]) 

          (Theory.ancestors_of (Rule.Thy_Info_get_theory "Build_Thydata"))

      in

        take ((find_index (curry Context.eq_thy (Thy_Info.get_theory "Complex_Main")) allthys), 

        allthys)

      end

    val isacthys' = isacthys ()

    val proglang_parent = Rule.Thy_Info_get_theory "ProgLang"

  in

    take ((find_index (curry Context.eq_thy proglang_parent) isacthys'), isacthys')

  end

fun progthys () = (*["Isac", .., "Descript", "Delete"]*)

  let

    fun isacthys () = (* ["Isac", .., "KEStore"] without Build_Isac thys: "Interpret" etc *)

      let                                                        

        val allthys = filter_out (member Context.eq_thy

          [(*Thy_Info_get_theory "ProgLang",*) Rule.Thy_Info_get_theory "Interpret", 

            Rule.Thy_Info_get_theory "xmlsrc", Rule.Thy_Info_get_theory "Frontend"]) 

          (Theory.ancestors_of (Rule.Thy_Info_get_theory "Build_Thydata"))

      in

        take ((find_index (curry Context.eq_thy (Thy_Info.get_theory "Complex_Main")) allthys), 

        allthys)

      end

    val isacthys' = isacthys ()

    val proglang_parent = Rule.Thy_Info_get_theory "ProgLang"

  in

    drop ((find_index (curry Context.eq_thy proglang_parent) isacthys') + 1(*ProgLang*), isacthys')

  end

fun partID thy = 

  if member Context.eq_thy (knowthys ()) thy then "IsacKnowledge"

  else if member Context.eq_thy (progthys ()) thy then "IsacScripts"

  else if member Context.eq_thy (isabthys ()) thy then "Isabelle"

  else error ("closure of thys in Isac is broken by " ^ Rule.string_of_thy thy)

fun partID' thy' = partID (Rule.Thy_Info_get_theory thy')

end (*struct*)