(* the problems and methods as stored in hierarchies

   author Walther Neuper 1998, Mathias Lehnfeld

   (c) due to copyright terms

*)

(*-----------------------------------------vvv-(1) aus modspec.sml 23.3.02*)

val dsc_unknown = (Thm.term_of o the o (parseold @{theory Script})) 

  "unknown::'a => unknow";

(*-----------------------------------------^^^-(1) aus modspec.sml 23.3.02*)

(*-----------------------------------------vvv-(2) aus modspec.sml 23.3.02*)

fun itm_2item thy (Cor ((d,ts),_)) = 

    Correct (term2str (comp_dts (d,ts)))

  | itm_2item _ (Syn c)            = SyntaxE c

  | itm_2item _ (Typ c)            = TypeE c

  | itm_2item thy (Inc ((d,ts),_)) = 

    Incompl (term2str (comp_dts (d,ts)))

  | itm_2item thy (Sup (d,ts))     = 

    Superfl (term2str (comp_dts (d,ts)))

  | itm_2item _ (Mis (d,pid))   =

    Missing (term2str d ^ " " ^ term2str pid);

(* --- 8.3.00

fun get_dsc_in dscppc sel = ((the (assoc (dscppc, sel))):term list)

  handle _ => error ("get_dsc_in not for "^sel);

fun dscs_in dscppc = 

  ((get_dsc_in dscppc "#Given") @

   (get_dsc_in dscppc "#Find") @

   (get_dsc_in dscppc "#Relate")):term list;

   --- 26.1.88

fun get_dsc_of pblID sel = (the (assoc((snd o get_pbt) pblID, sel)));

fun get_dsc pblID = 

  (get_dsc_of pblID "#Given") @

  (get_dsc_of pblID "#Find") @

  (get_dsc_of pblID "#Relate");

 --- *)

fun mappc f ({Given=gi,Where=wh,Find=fi,With=wi,Relate=re}:'a ppc) = 

  {Given=map f gi, Where=map f wh,

   Find=map f fi, With=map f wi, Relate=map f re}:'b ppc;

fun appc f ({Given=gi,Where=wh,Find=fi,With=wi,Relate=re}:'a ppc) = 

  {Given=f gi, Where=f wh,

   Find=f fi, With=f wi, Relate=f re}:'b ppc;

(*for ppc of changing type*)

fun sel_ppc sel ppc =

  case sel of

    "#Given" => #Given (ppc:'a ppc)

  | "#Where" => #Where (ppc:'a ppc)

  | "#Find" => #Find (ppc:'a ppc)

  | "#With" => #With (ppc:'a ppc)

  | "#Relate" => #Relate (ppc:'a ppc)

  | _  => error ("sel_ppc tried to select by '"^sel^"'");

fun repl_sel_ppc sel

  ({Given=gi,Where=wh,Find=fi,With=wi,Relate=re}:'a ppc) x =

  case sel of

    "#Given" => ({Given= x,Where=wh,Find=fi,With=wi,Relate=re}:'a ppc)

  | "#Where" => {Given=gi,Where= x,Find=fi,With=wi,Relate=re}

  | "#Find" => {Given=gi,Where=wh,Find= x,With=wi,Relate=re}

  | "#With" => {Given=gi,Where=wh,Find=fi,With= x,Relate=re}

  | "#Relate" => {Given=gi,Where=wh,Find=fi,With=wi,Relate= x}

  | _  => error ("repl_sel_ppc tried to select by '"^sel^"'");

fun add_sel_ppc thy sel

  ({Given=gi,Where=wh,Find=fi,With=wi,Relate=re}:'a ppc) x =

  case sel of

    "#Given" => ({Given=gi@[x],Where=wh,Find=fi,With=wi,Relate=re}:'a ppc)

  | "#Where" => {Given=gi,Where=wh@[x],Find=fi,With=wi,Relate=re}

  | "#Find"  => {Given=gi,Where=wh,Find=fi@[x],With=wi,Relate=re}

  | "#Relate"=> {Given=gi,Where=wh,Find=fi,With=wi,Relate=re@[x]}

  | "#undef" => {Given=gi@[x],Where=wh,Find=fi,With=wi,Relate=re}(*ori2itmSup*)

  | _  => error ("add_sel_ppc tried to select by '"^sel^"'");

fun add_where ({Given=gi,Find=fi,With=wi,Relate=re,...}:'a ppc) wh =

    ({Given=gi,Where=wh,Find=fi,With=wi,Relate=re}:'a ppc);

(*decompose a problem-type into description and identifier

  FIXME split_dsc: no term list !!! (just for quick redoing prep_ori) *)

fun split_dsc thy t =

  (let val (hd,args) = strip_comb t

   in if is_dsc hd

      then (hd, args)

       else (e_term, [t])    (*??? 9.01 just copied*)

   end)

  handle _ => error ("split_dsc: called with " ^ term2str t);

(*

> val t1 = (Thm.term_of o the o (parse thy)) "errorBound err_";

> split_dsc t1;

(Const ("Descript.errorBound","bool => Tools.nam"),Free ("err_","bool"))

  : term * term

> val t3 = (Thm.term_of o the o (parse thy)) "valuesFor vs_";

> split_dsc t3;

(Const ("Descript.valuesFor","bool List.list => Tools.toreall"),

   Free ("vs_","bool List.list")) : term * term*)

(*. take the first two return-values; for prep_ori .*)

(*WN.13.5.03fun split_dts' thy t =

    let val (d, ts, _) = split_dts thy t

    in (d, ts) end;*)

(*WN.8.12.03 quick for prep_ori'*)

fun split_dsc' t =

  (let val dsc $ var = t

  in var end)

  handle _ => error ("split_dsc': called with "^term2str t);

(*9.3.00*)

(* split a term into description and (id | structured variable)

   for pbt, met.ppc *)

fun split_did t =

  (let val (hd,[arg]) = strip_comb t

  in (hd,arg) end)

  handle _ => 

         error ("split_did: doesn't match (hd,[arg]) for t = " ^term2str t);

(*create output-string for itm_*)

fun itm_out thy (Cor ((d,ts),_)) = term2str (comp_dts (d,ts))

  | itm_out thy (Syn c)      = c

  | itm_out thy (Typ c)      = c

  | itm_out thy (Inc ((d,ts),_)) = term2str (comp_dts (d,ts))

  | itm_out thy (Sup (d,ts)) = term2str (comp_dts (d,ts))

  | itm_out thy (Mis (d,pid)) = term2str d ^ " " ^ term2str pid;

fun boolterm2item (true, term) = Correct (term2str term)

  | boolterm2item (false, term) = False (term2str term);

(* use"ME/modspec.sml";

   *)

fun itms2itemppc thy (itms:itm list) (pre:(bool * term) list) =

  let

    fun coll ppc [] = ppc

      | coll ppc ((_,_,_,field,itm_)::itms) = 

      coll (add_sel_ppc thy field ppc (itm_2item thy itm_)) itms;

    val gfr = coll empty_ppc itms;

  in add_where gfr (map boolterm2item pre) end;

(* 9.3.00

   compare d and dsc in pbt and transfer field to pre-ori *)

fun add_field thy pbt (d,ts) = 

  let fun eq d pt = (d = (fst o snd) pt);

  in case filter (eq d) pbt of

       [(fi,(dsc,_))] => (fi,d,ts)

     | [] => ("#undef",d,ts)   (*may come with met.ppc*)

     | _ => error ("add_field: " ^ term2str d ^ " more than once in pbt")

  end;

(*. take over field from met.ppc at 'Specify_Method' into ori,

   i.e. also removes "#undef" fields                        .*)

(* val (mpc, ori) =  ((#ppc o get_met) mID, oris);

   *)

fun add_field' thy mpc (ori:ori list) =

  let fun eq d pt = (d = (fst o snd) pt);

    fun repl mpc (i,v,_,d,ts) = 

      case filter (eq d) mpc of

	[(fi,(dsc,_))] => [(i,v,fi,d,ts)]

      | [] => [] (*25.2.02: dsc in ori, but not in met -> superfluous*)    

      | _ => error ("add_field': " ^ term2str d ^ " more than once in met");

  in (flat ((map (repl mpc)) ori)):ori list end;

(*.mark an element with the position within a plateau;

   a plateau with length 1 is marked with 0        .*)

fun mark eq [] = error "mark []"

  | mark eq xs =

  let

    fun mar xx eq [x] n = xx @ [(if n=1 then 0 else n,x)]

      | mar xx eq (x::x'::xs) n = 

      if eq(x,x') then mar (xx @ [(n,x)]) eq (x'::xs) (n+1)

      else mar (xx @ [(if n=1 then 0 else n,x)]) eq (x'::xs) 1;

  in mar [] eq xs 1 end;

(*

> val xs = [1,1,1,2,4,4,5];

> mark (op=) xs;

val it = [(1,1),(2,1),(3,1),(0,2),(1,4),(2,4),(0,5)]

*)

(*.assumes equal descriptions to be in adjacent 'plateaus',

   items at a certain position within the plateaus form a variant;

   length = 1 ... marked with 0: covers all variants           .*)

fun add_variants fdts = 

  let 

    fun eq (a,b) = curry op= (snd3 a) (snd3 b);

  in mark eq fdts end;

(* collect equal elements: the model for coll_variants *)

fun coll eq xs =

  let

    fun col xs eq x [] = xs @ [x]

      | col xs eq x (y::ys) = 

      if eq(x,y) then col xs eq x ys

      else col (xs @ [x]) eq y ys;

  in col [] eq (hd xs) xs end;

(* 

> val xs = [1,1,1,2,4,4,4];

> coll (op=) xs;

val it = [1,2,4] : int list

*)

fun max [] = error "max of []"

  | max (y::ys) =

  let fun mx x [] = x

	| mx x (y::ys) = if x < y then mx y ys else mx x ys;

in mx y ys end;

fun gen_max _ [] = error "gen_max of []"

  | gen_max ord (y::ys) =

  let fun mx x [] = x

	| mx x (y::ys) = if ord (x, y) then mx y ys else mx x ys;

in mx y ys end;

(* assumes *)

fun coll_variants (((v,x)::vxs)) =

  let

    fun col xs (vs,x) [] = xs @ [(vs,x)]

      | col xs (vs,x) ((v',x')::vxs') = 

      if x=x' then col xs (vs @ [v'], x') vxs'

      else col (xs @ [(vs,x)]) ([v'], x') vxs';

  in col [] ([v],x) vxs end;

(* val xs = [(1,1),(2,1),(3,1),(0,2),(1,4),(2,4),(0,5)];

> col [] ([(fst o hd) xs],(snd o hd) xs) (tl xs);

val it = [([1,2,3],1),([0],2),([1,2],4),([0],5)]  *)

fun replace_0 vm [0] = intsto vm

  | replace_0 vm vs = vs;

fun add_id [] = error "add_id []"

  | add_id xs =

  let fun add n [] = []

	| add n (x::xs) = (n,x) :: add (n+1) xs;

in add 1 xs end;

(*

> val xs = [([1,2,3],1),([0],2),([1,2],4),([0],5)];

> add_id xs;

val it = [(1,([#,#,#],1)),(2,([#],2)),(3,([#,#],4)),(4,([#],5))]

 *)

fun flattup (a,(b,(c,d,e))) = (a,b,c,d,e);

fun flattup' (a,(b,((c,d),e))) = (a,b,c,d,e);

fun flat3 (a,(b,c)) = (a,b,c);

(*

 val pI = pI';

 !pbts;

*)

(* in root (only!) fmz may be empty: fill with ..,dsc,[]

fun init_ori fmz thy pI =

  if fmz <> [] then prep_ori fmz thy pI (*fmz assumed complete*)

  else

    let 

      val fds = map (cons2 (fst, fst o snd)) (get_pbt pI);

      val vfds = map ((pair [1]) o (rpair [])) fds;

      val ivfds = add_id vfds

    in (map flattup' ivfds):ori list end;   10.3.00---*)

(* val fmz = ctl; val pI=["sqroot-test","univariate","equation"];

   val (thy,pbt) = (assoc_thy dI',(#ppc o get_pbt) pI');

   val (fmz, thy, pbt) = (fmz, thy, ((#ppc o get_pbt) pI));

   *)

fun prep_ori [] _ _ = ([], e_ctxt)

  | prep_ori fmz thy pbt =

      let

        val ctxt = Proof_Context.init_global thy |> fold declare_constraints fmz;

        val ori = map (add_field thy pbt o split_dts o the o parseNEW ctxt) fmz

          |> add_variants;

        val maxv = map fst ori |> max;

        val maxv = if maxv = 0 then 1 else maxv;

        val oris = coll_variants ori

          |> map (replace_0 maxv |> apfst)

          |> add_id

          |> map flattup;

      in (oris, ctxt) end;

val e_errpat = ("e_errpatID", [parse_patt @{theory} "?a = ?b"], [@{thm refl}]): errpat

val e_fillpat = ("e_fillpatID", parse_patt @{theory} "?a = _", "e_errpatID")

(**+ breadth-first search on hierarchy of problem-types +**)

type pblRD = pblID;(*pblID are Reverted _on calling_ the retrieve-funs*)

     (* eg. ["equations","univariate","normalize"] while

	    ["normalize","univariate","equations"] is the related pblID

      WN.24.4.03: also used for metID*)

(*> ptyps:= 

[Ptyp ("1",[("ptyp 1",([],[]))],

	[Ptyp ("11",[("ptyp 11",([],[]))],

		[])

	 ]),

 Ptyp ("2",[("ptyp 2",([],[]))],

	[Ptyp ("21",[("ptyp 21",([],[]))],

		[])

	 ])

 ];

> get_py SqRoot.thy ["1"] ["1"] (!ptyps);

> get_py SqRoot.thy ["2","21"] ["2","21"] (!ptyps);

         _REVERSE_  .......... !!!!!!!!!!*)

(*. apply a fun to a ptyps node .*)

fun app_ptyp x = app_py (get_ptyps ()) x;

(*TODO: search generalized for subthy*)

fun get_pbt (pblID:pblID) = get_py (get_ptyps ()) pblID (rev pblID)

(* get_pbt thy ["1"];

   get_pbt thy ["21","2"];

   *)

(*TODO: throws exn 'get_pbt not found: ' ... confusing !!

  take 'ketype' as an argument !!!!!*)

fun get_met (metID : metID) = get_py (get_mets ()) metID metID;

fun get_met' thy (metID : metID) = get_py (KEStore_Elems.get_mets thy) metID metID;

fun get_the (theID : theID) = get_py (get_thes ()) theID theID;

fun del_eq k ptyps =

let fun del k ptyps [] = ptyps

      | del k ptyps ((Ptyp (k', [p], ps))::pys) =

	if k=k' then del k ptyps pys

	else del k (ptyps @ [Ptyp (k', [p], ps)]) pys;

in del k [] ptyps end;

(*.lookup a guh in hierarchy or methods depending on fst chars in guh.*)

fun guh2kestoreID (guh:guh) =

    case (implode o (take_fromto 1 4) o Symbol.explode) guh of

	"pbl_" =>

	let fun node ids gu (Ptyp (id,[n as {guh,...} : pbt], ns)) =

		if gu = guh 

		then SOME ((ids@[id]) : kestoreID)

		else nodes (ids@[id]) gu ns

	    and nodes _ _ [] = NONE 

	      | nodes ids gu (n::ns) = 

		case node ids gu n of SOME id => SOME id

				    | NONE =>  nodes ids gu ns

	in case nodes [] guh (get_ptyps ()) of

	       SOME id => rev id

	     | NONE => error ("guh2kestoreID: '" ^ guh ^ "' " ^

				    "not found in ptyps")

	end

      | "met_" =>

	let fun node ids gu (Ptyp (id,[n as {guh,...} : met], ns)) =

		if gu = guh 

		then SOME ((ids@[id]) : kestoreID)

		else nodes (ids@[id]) gu ns

	    and nodes _ _ [] = NONE 

	      | nodes ids gu (n::ns) = 

		case node ids gu n of SOME id => SOME id

				    | NONE =>  nodes ids gu ns

	in case nodes [] guh (get_mets ()) of

	       SOME id => id

	     | NONE => error ("guh2kestoreID: '" ^ guh ^ "' " ^

				    "not found in mets") end

      | _ => error ("guh2kestoreID called with '" ^ guh ^ "'");

(*> guh2kestoreID "pbl_equ_univ_lin";

val it = ["linear", "univariate", "equation"] : string list*)

(*. prepare problem-types before storing in pbltypes; 

    dont forget to 'check_guh_unique' before ins.*)

fun prep_pbt thy guh maa init

	     (pblID, dsc_dats: (string * (string list)) list, 

		  ev:rls, ca: string option, metIDs:metID list) =

(* val (thy, (pblID, dsc_dats: (string * (string list)) list, 

		  ev:rls, ca: string option, metIDs:metID list)) =

       ((EqSystem.thy, (["system"],

		       [("#Given" ,["equalities es_", "solveForVars vs_"]),

			("#Find"  ,["solution ss___"](*___ is copy-named*))

			],

		       append_rls "e_rls" e_rls [(*for preds in where_*)], 

		       SOME "solveSystem es_ vs_", 

		       [])));

   *)

    let fun eq f (f', _) = f = f';

	val gi = filter (eq "#Given") dsc_dats;

(*val gi = [("#Given",["equality e_","solveFor v_"])]

  : (string * string list) list*)

	val gi = (case gi of

		     [] => []

		   | ((_,gi')::[]) => 

		     ((map (split_did o Thm.term_of o the o (parse thy)) gi')

		     handle _ => error 

			("prep_pbt: syntax error in '#Given' of "^

			 (strs2str pblID)))

		   | _ =>

		     (error ("prep_pbt: more than one '#Given' in "^

				  (strs2str pblID))));

(*val gi =

  [(Const ("Descript.equality","bool => Tools.una"),Free ("e_","bool")),

   (Const ("Descript.solveFor","RealDef.real => Tools.una"),

    Free ("v_","RealDef.real"))] : (term * term) list  *)

	val gi = map (pair "#Given") gi;

(*val gi =

  [("#Given",

    (Const ("Descript.equality","bool => Tools.una"),Free ("e_","bool"))),

   ("#Given",

    (Const ("Descript.solveFor","RealDef.real => Tools.una"),

     Free ("v_","RealDef.real")))] : (string * (term * term)) list*)

	val fi = filter (eq "#Find") dsc_dats;

	val fi = (case fi of

		     [] => [](*28.8.01: ["tool"] ...// error 

			("prep_pbt: no '#Find' in "^(strs2str pblID))*)

(* val ((_,fi')::[]) = fi;

   *)

		   | ((_,fi')::[]) => 

		     ((map (split_did o Thm.term_of o the o (parse thy)) fi')

		     handle _ => error 

			("prep_pbt: syntax error in '#Find' of "^

			 (strs2str pblID)))

		   | _ =>

		     (error ("prep_pbt: more than one '#Find' in "^

				  (strs2str pblID))));

	val fi = map (pair "#Find") fi;

	val re = filter (eq "#Relate") dsc_dats;

	val re = (case re of

		     [] => []

		   | ((_,re')::[]) => 

		     ((map (split_did o Thm.term_of o the o (parse thy)) re')

		     handle _ => error 

			("prep_pbt: syntax error in '#Relate' of "^

			 (strs2str pblID)))

		   | _ =>

		     (error ("prep_pbt: more than one '#Relate' in "^

				  (strs2str pblID))));

	val re = map (pair "#Relate") re;

	val wh = filter (eq "#Where") dsc_dats;

	val wh = (case wh of

		     [] => []

		   | ((_,wh')::[]) => 

		     ((map (parse_patt thy) wh')

		      handle _ => error 

			("prep_pbt: syntax error in '#Where' of "^

			 (strs2str pblID)))

		   | _ =>

		     (error ("prep_pbt: more than one '#Where' in "^

				  (strs2str pblID))));

    in ({guh=guh,mathauthors=maa,init=init,

	 thy=thy,cas= case ca of NONE => NONE

			       | SOME s => 

				 SOME ((Thm.term_of o the o (parse thy)) s),

	 prls=ev,where_=wh,ppc= gi @ fi @ re,

	 met=metIDs}, pblID):pbt * pblID end;

(* prep_pbt thy (pblID, dsc_dats, metIDs);   

 val it =

  ({met=[],

    ppc=[("#Given",(Const (#,#),Free (#,#))),

         ("#Given",(Const (#,#),Free (#,#))),

         ("#Find",(Const (#,#),Free (#,#)))],

    thy={ProtoPure, ..., Atools, RatArith},

    where_=[Const ("Descript.solutions","bool List.list => Tools.toreall") $

            Free ("v_i_","bool List.list")]},["equation"]) : pbt * pblID    *)

(*. prepare met for storage analogous to pbt .*)

fun prep_met thy guh maa init

	     (metID, ppc: (string * string list) list (*'#Where' -> #pre*),

    {rew_ord'=ro, rls'=rls, srls=srls, prls=prls, 

     calc = scr_isa_fns(*FIXME.040207: del - auto-done*),

     crls=cr, errpats = ep, nrls= nr}, scr) =

    let fun eq f (f', _) = f = f';

	(*val thy = (assoc_thy o fst) metID*)

	val gi = filter (eq "#Given") ppc;

	val gi = (case gi of

		     [] => (writeln ("prep_met: in " ^ guh ^ " #Given is empty ?!?"); [])

		   | ((_,gi')::[]) => 

		     ((map (split_did o Thm.term_of o the o (parse thy)) gi')

		     handle _ => error 

			("prep_pbt: syntax error in '#Given' of "^

			 (strs2str metID)))

		   | _ =>

		     (error ("prep_pbt: more than one '#Given' in "^

				  (strs2str metID))));

	val gi = map (pair "#Given") gi;

	val fi = filter (eq "#Find") ppc;

	val fi = (case fi of

		     [] => (writeln ("prep_met: in " ^ guh ^ " #Find is empty ?!?"); [])

		   | ((_,fi')::[]) => 

		     ((map (split_did o Thm.term_of o the o (parse thy)) fi')

		     handle _ => error 

			("prep_pbt: syntax error in '#Find' of "^

			 (strs2str metID)))

		   | _ =>

		     (error ("prep_pbt: more than one '#Find' in "^

				  (strs2str metID))));

	val fi = map (pair "#Find") fi;

	val re = filter (eq "#Relate") ppc;

	val re = (case re of

		     [] => (writeln ("prep_met: in " ^ guh ^ " #Relate is empty ?!?"); [])

		   | ((_,re')::[]) => 

		     ((map (split_did o Thm.term_of o the o (parse thy)) re')

		     handle _ => error 

			("prep_pbt: syntax error in '#Relate' of "^

			 (strs2str metID)))

		   | _ =>

		     (error ("prep_pbt: more than one '#Relate' in "^

				  (strs2str metID))));

	val re = map (pair "#Relate") re;

	val wh = filter (eq "#Where") ppc;

	val wh = (case wh of

		     [] => (writeln ("prep_met: in " ^ guh ^ " #Where is empty ?!?"); [])

		   | ((_,wh')::[]) => 

		     ((map (parse_patt thy) wh')

		     handle _ => error 

			("prep_pbt: syntax error in '#Where' of "^

			 (strs2str metID)))

		   | _ =>

		     (error ("prep_pbt: more than one '#Where' in "^

				  (strs2str metID))));

	val sc = (((inst_abs thy) o Thm.term_of o the o (parse thy)) scr)

    in ({guh=guh,mathauthors=maa,init=init,

	 ppc=gi@fi@re, pre=wh, rew_ord'=ro, erls=rls, srls=srls, prls=prls,

	 calc = if scr = "empty_script" then []

		else ((assoc_calc' thy |> map) o (map op_of_calc) o 

		      (filter is_calc) o stacpbls) sc, 

	 crls=cr, errpats = ep, nrls= nr, scr = Prog sc}:met,

	metID:metID)

    end;

(**. get pblIDs of all entries in mat3D .**)

fun format_pblID strl = enclose " [" "]" (commas_quote strl);

fun format_pblIDl strll = enclose "[\n" "\n]\n" 

    (space_implode ",\n" (map format_pblID strll));

fun scan _  [] = [] (* no base case, for empty doms only *)

  | scan id ((Ptyp ((i,_,[])))::[]) =      [id@[i]]

  | scan id ((Ptyp ((i,_,pl)))::[]) = scan (id@[i]) pl

  | scan id ((Ptyp ((i,_,[])))::ps) =      [id@[i]]    @(scan id ps)

  | scan id ((Ptyp ((i,_,pl)))::ps) =(scan (id@[i]) pl)@(scan id ps);

fun show_ptyps () = (writeln o format_pblIDl o (scan [])) (get_ptyps ());

(* ptyps:=[];

   show_ptyps();

   *)

fun show_mets () = (writeln o format_pblIDl o (scan [])) (get_mets ());

(*vvvvv---------- preparational work 8.01. UNUSED *)

(**+ instantiate a problem-type +**)

(*+ transform oris +*)

fun coll_vats (vats, ((_,vs,_,_,_):ori)) = union op = vats vs;

(*> coll_vats [11,22] (hd oris);

val it = [22,11,1,2,3] : int list

> foldl coll_vats ([],oris);

val it = [1,2,3] : int list

> val i=1;

> filter ((curry (op mem) i) o #2) oris;

val it =

  [(1,[1,2,3],"#Given",Const (#,#),[# $ #]),

   (2,[1,2,3],"#Find",Const (#,#),[Free #]),

   (3,[1,2,3],"#Find",Const (#,#),[# $ #,# $ #]),

   (4,[1,2],"#Relate",Const (#,#),[# $ #,# $ #]),

   (6,[1],"#undef",Const (#,#),[Free #]),

   (9,[1,2],"#undef",Const (#,#),[# $ #]),

   (11,[1,2,3],"#undef",Const (#,#),[# $ #])] : ori list *)    

local infix mem; (*from Isabelle2002*)

fun x mem [] = false

  | x mem (y :: ys) = x = y orelse x mem ys;

in

fun filter_vat oris i = 

    filter ((curry (op mem) i) o (#2 : ori -> int list)) oris;

end;

(*> map (filter_vat oris) [1,2,3];

val it =

  [[(1,[1,2,3],"#Given",Const (#,#),[# $ #]),

    (2,[1,2,3],"#Find",Const (#,#),[Free #]),

    (3,[1,2,3],"#Find",Const (#,#),[# $ #,# $ #]),

    (4,[1,2],"#Relate",Const (#,#),[# $ #,# $ #]),

    (6,[1],"#undef",Const (#,#),[Free #]),

    (9,[1,2],"#undef",Const (#,#),[# $ #]),

    (11,[1,2,3],"#undef",Const (#,#),[# $ #])],

   [(1,[1,2,3],"#Given",Const (#,#),[# $ #]),

    (2,[1,2,3],"#Find",Const (#,#),[Free #]),

    (3,[1,2,3],"#Find",Const (#,#),[# $ #,# $ #]),

    (4,[1,2],"#Relate",Const (#,#),[# $ #,# $ #]),

    (7,[2],"#undef",Const (#,#),[Free #]),

    (9,[1,2],"#undef",Const (#,#),[# $ #]),

    (11,[1,2,3],"#undef",Const (#,#),[# $ #])],

   [(1,[1,2,3],"#Given",Const (#,#),[# $ #]),

    (2,[1,2,3],"#Find",Const (#,#),[Free #]),

    (3,[1,2,3],"#Find",Const (#,#),[# $ #,# $ #]),

    (5,[3],"#Relate",Const (#,#),[# $ #,# $ #,# $ #]),

    (8,[3],"#undef",Const (#,#),[Free #]),

    (10,[3],"#undef",Const (#,#),[# $ #]),

    (11,[1,2,3],"#undef",Const (#,#),[# $ #])]] : ori list list*)

fun separate_vats oris =

    let val vats = foldl coll_vats ([] : int list, oris);

    in map (filter_vat oris) vats end;

(*^^^ end preparational work 8.01.*)

(**. check a problem (ie. itm list) for matching a problemtype .**)

fun eq1 d (_,(d',_)) = (d = d');

fun itm_id ((i,_,_,_,_):itm) = i;

fun ori_id ((i,_,_,_,_):ori) = i;

fun ori2itmSup ((i,v,_,d,ts):ori) = ((i,v,true,"#Given",Sup(d,ts)):itm);

(*see + add_sel_ppc                             ~~~~~~~*)

fun field_eq f ((_,_,f',_,_):ori) = f = f';

(*. check an item (with arbitrary itm_ from previous matchings) 

    for matching a problemtype; returns true only for itms found in pbt .*)

fun chk_ thy pbt ((i,vats,b,f,Cor ((d,vs),_)):itm) =

    (case find_first (eq1 d) pbt of 

	 SOME (_,(_,id)) => ((i,vats,b,f,Cor ((d,vs),

					      (id, pbl_ids' d vs))):itm)

       | NONE => (i,vats,false,f,Sup (d,vs)))

  | chk_ thy pbt ((i,vats,b,f,Inc ((d,vs),_)):itm) =

    (case find_first (eq1 d) pbt of 

	SOME (_,(_,id)) => ((i,vats,b,f,Cor ((d,vs),

					     (id, pbl_ids' d vs))):itm)

      | NONE => (i,vats,false,f,Sup (d,vs)))

  | chk_ thy pbt (itm as (i,vats,b,f,Syn ct):itm) = itm

  | chk_ thy pbt (itm as (i,vats,b,f,Typ ct):itm) = itm

  | chk_ thy pbt ((i,vats,b,f,Sup (d,vs)):itm) =

    (case find_first (eq1 d) pbt of 

	SOME (_,(_,id)) => ((i,vats,b,f,Cor ((d,vs),

					     (id, pbl_ids' d vs))):itm)

      | NONE => (i,vats,false,f,Sup (d,vs)))

(* val (i,vats,b,f,Mis (d,vs)) = i4;

   *)

  | chk_ thy pbt ((i,vats,b,f,Mis (d,vs)):itm) =

    (case find_first (eq1 d) pbt of

(* val SOME (_,(_,id)) = find_first (eq1 d) pbt;

   *) 

	SOME (_,(_,id)) => error "chk_: ((i,vats,b,f,Cor ((d,vs),\

				   \(id, pbl_ids' d vs))):itm)"

      | NONE => (i,vats,false,f,Sup (d,[vs])));

(* chk_ thy pbt i

    *)

fun eq2 (_,(d,_)) ((_,_,_,_,itm_):itm) = d = d_in itm_;

fun eq2' (_,(d,_)) ((_,_,_,d',_):ori) = d = d';

fun eq0 ((0,_,_,_,_):itm) = true

  | eq0 _ = false;

fun max_i i [] = i

  | max_i i ((id,_,_,_,_)::is) = 

    if i > id then max_i i is else max_i id is;

fun max_id [] = 0

  | max_id ((id,_,_,_,_)::is) = max_i id is;

fun add_idvat itms _ _ [] = itms

  | add_idvat itms i mvat (((_,_,b,f,itm_):itm)::its) =

    add_idvat (itms @ [(i,[(*mvat ...meaningless with pbl-identifier *)

			     ],b,f,itm_):itm]) (i+1) mvat its;

(*. find elements of pbt not contained in itms;

    if such one is untouched, return this one, otherwise create new itm .*)

fun chk_m (itms:itm list) untouched (p as (f,(d,id))) = 

    case find_first (eq2 p) itms of

	SOME _ => []

      | NONE => (case find_first (eq2 p) untouched of

		     SOME itm => [itm]

		   | NONE => [(0,[],false,f,Mis (d,id)):itm]);

(* val itms = itms'';

   *) 

fun chk_mis mvat itms untouched pbt = 

    let val mis = (flat o (map (chk_m itms untouched))) pbt; 

        val mid = max_id itms;

    in add_idvat [] (mid + 1) mvat mis end;

(*. check a problem (ie. itm list) for matching a problemtype, 

    takes the max_vt for concluding completeness (could be another!) .*)

(* val itms = itms'; val (pbt,pre) = (ppc, pre);

   val itms = itms; val (pbt,pre) = (ppc, pre);

   *)

fun match_itms thy itms (pbt,pre,prls) = 

    (let fun okv mvat (_,vats,b,_,_) = member op = vats mvat

				       andalso b;

	val itms' = map (chk_ thy pbt) itms; (*all found are #3 true*)

        val mvat = max_vt itms';

	val itms'' = filter (okv mvat) itms';

	val untouched = filter eq0 itms;(*i.e. dsc only (from init)*)

	val mis = chk_mis mvat itms'' untouched pbt;

	val pre' = check_preconds' prls pre itms'' mvat

	val pb = foldl and_ (true, map fst pre')

    in (length mis = 0 andalso pb, (itms'@ mis, pre')) end);

(*. check a problem pbl (ie. itm list) for matching a problemtype pbt,

    for missing items get data from formalization (ie. ori list); 

    takes the max_vt for concluding completeness (could be another!) .*)

(*  (0) determine the most frequent variant mv in pbl

    ALL pbt. (1) dsc(pbt) notmem dsc(pbls) =>

             (2) filter (dsc(pbt) = dsc(oris)) oris; -> news;

             (3) newitms = filter (mv mem vat(news)) news 

    (4) pbt @ newitms                                           *)

(* val (pbl, pbt, pre) = (met, mtt, pre);

   val (pbl, pbt, pre) = (itms, #ppc pbt, #where_ pbt);

   val (pbl, pbt, pre) = (itms, ppc, where_);

   *)

fun match_itms_oris thy (pbl:itm list) (pbt, pre, prls) oris =

  let 

 (*0*)val mv = max_vt pbl;

      fun eqdsc_pbt_itm ((_,(d,_))) ((_,_,_,_,itm_):itm) = d = d_in itm_;

      fun notmem pbl pbt1 = case find_first (eqdsc_pbt_itm pbt1) pbl of

				SOME _ => false | NONE => true;

 (*1*)val mis = (*(map (cons2 (fst, fst o snd)))o*) (filter (notmem pbl)) pbt;

      fun eqdsc_ori (_,(d,_)) ((_,_,_,d',_):ori) = d = d';

      fun ori2itmMis (f,(d,pid)) ((i,v,_,_,ts):ori) = 

	  (i,v,false,f,Mis (d,pid)):itm;

 (*2*)fun oris2itms oris mis1 = 

	  ((map (ori2itmMis mis1)) o (filter (eqdsc_ori mis1))) oris;

      val news = (flat o (map (oris2itms oris))) mis;

 (*3*)fun mem_vat (_,vats,b,_,_) = member op = vats mv;

      val newitms = filter mem_vat news;

 (*4*)val itms' = pbl @ newitms;

      val pre' = check_preconds' prls pre itms' mv

      val pb = foldl and_ (true, map fst pre')

  in (length mis = 0 andalso pb, (itms', pre')) end;

    (*handle _ => (false,([],[]))*);

(*vvv--- doubled 20.9.01: ... 7.3.02 itms  -->  oris, because oris

  allow for faster access to descriptions and terms *)

(**. check a problem (ie. itm list) for matching a problemtype .**)

(*. check an ori for matching a problemtype by description; 

    returns true only for itms found in pbt .*)

fun chk1_ thy pbt ((i,vats,f,d,vs):ori) =

    case find_first (eq1 d) pbt of 

	SOME (_,(_,id)) => [(i,vats,true,f,

			     Cor ((d,vs), (id, pbl_ids' d vs))):itm]

      | NONE => [];

(* elem 'p' of pbt contained in itms ? *)

fun chk1_m (itms:itm list) p = 

    case find_first (eq2 p) itms of

	SOME _ => true | NONE => false;

fun chk1_m' (oris: ori list) (p as (f,(d,t))) = 

    case find_first (eq2' p) oris of

	SOME _ => []

      | NONE => [(f, Mis (d, t))];

fun pair0vatsfalse (f,itm_) = (0,[],false,f,itm_):itm;

fun chk1_mis mvat itms ppc = foldl and_ (true, map (chk1_m itms) ppc);

fun chk1_mis' oris ppc = 

    map pair0vatsfalse ((flat o (map (chk1_m' oris))) ppc);

(*. check a problem (ie. ori list) for matching a problemtype, 

    takes the max_vt for concluding completeness (FIXME could be another!) .*)

(* val (prls,oris,pbt,pre)=(#prls py, ori, #ppc py, #where_ py);

   *)

fun match_oris thy prls oris (pbt,pre) = 

    let val itms = (flat o (map (chk1_ thy pbt))) oris;

        val mvat = max_vt itms;

	val complete = chk1_mis mvat itms pbt;

	val pre' = check_preconds' prls pre itms mvat

	val pb = foldl and_ (true, map fst pre')

    in if complete andalso pb then true else false end;

(*. check a problem (ie. ori list) for matching a problemtype, 

    returns items for output to math-experts .*)

fun match_oris' thy oris (ppc,pre,prls) =

(* val (thy, oris, (ppc,pre,prls)) = (thy, oris, (ppc, where_, prls));

   *)

    let val itms = (flat o (map (chk1_ thy ppc))) oris;

	val sups = ((map ori2itmSup) o (filter(field_eq "#undef")))oris;

        val mvat = max_vt itms;

	val miss = chk1_mis' oris ppc;

	val pre' = check_preconds' prls pre itms mvat

	val pb = foldl and_ (true, map fst pre')

    in (miss = [] andalso pb, (itms @ miss @ sups, pre')) end;

(* for the user *)

datatype match' = 

  Matches' of item ppc

| NoMatch' of item ppc;

(* match a formalization with a problem type *)

fun match_pbl (fmz:fmz_) ({thy=thy,where_=pre,ppc,prls=er,...}:pbt) =

    let val oris = prep_ori fmz thy ppc |> #1;

	val (bool, (itms, pre')) = match_oris' thy oris (ppc,pre,er);

    in if bool then Matches' (itms2itemppc thy itms pre')

       else NoMatch' (itms2itemppc thy itms pre') end;

(* 

val fmz = ["equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))",

	      "solveFor x","errorBound (eps=0)","solutions L"];

val pbt as {thy = thy, where_ = pre, ppc = ppc,...} =

    get_pbt ["univariate","equation"];

match_pbl fmz pbt;

*)

(*. refine a problem; construct pblRD while scanning .*)

(* val (pblRD,ori)=("xxx",oris);

 val py = get_pbt ["equation"];

 val py = get_pbt ["univariate","equation"];

 val py = get_pbt ["linear","univariate","equation"];

 val py = get_pbt ["root'","univariate","equation"];

 match_oris (#prls py) ori (#ppc py, #where_ py);

  *)

fun refin (pblRD:pblRD) ori 

((Ptyp (pI,[py],[])):pbt ptyp) =

    if match_oris (#thy py) (#prls py) ori (#ppc py, #where_ py) 

    then SOME ((pblRD @ [pI]):pblRD)

    else NONE

  | refin pblRD ori (Ptyp (pI,[py],pys)) =

    if match_oris (#thy py) (#prls py) ori (#ppc py, #where_ py) 

    then (case refins (pblRD @ [pI]) ori pys of

	      SOME pblRD' => SOME pblRD'

	    | NONE => SOME (pblRD @ [pI]))

    else NONE

and refins pblRD ori [] = NONE

  | refins pblRD ori ((p as Ptyp (pI,_,_))::pts) =

    (case refin pblRD ori p of

	 SOME pblRD' => SOME pblRD'

       | NONE => refins pblRD ori pts);

(*. refine a problem; version providing output for math-experts .*)

fun refin' (pblRD: pblRD) fmz pbls ((Ptyp (pI, [py], [])):pbt ptyp) =

    let

      val _ = (tracing o ((curry op ^)"*** pass ") o strs2str) (pblRD @ [pI])

      val {thy, ppc, where_, prls, ...} = py 

      val oris = prep_ori fmz thy ppc |> #1;

      (*8.3.02: itms!: oris ev. are _not_ complete here*)

      val (b, (itms, pre')) = match_oris' thy oris (ppc, where_, prls)

    in if b

      then pbls @ [Matches (rev (pblRD @ [pI]), itms2itemppc thy itms pre')]

      else pbls @ [NoMatch (rev (pblRD @ [pI]), itms2itemppc thy itms pre')]

    end

  | refin' pblRD fmz pbls (Ptyp (pI, [py], pys)) =

    let

      val _ = (tracing o ((curry op ^)"*** pass ") o strs2str) (pblRD @ [pI])

      val {thy, ppc, where_, prls, ...} = py 

      val oris = prep_ori fmz thy ppc |> #1;

      (*8.3.02: itms!: oris ev. are _not_ complete here*)

      val(b, (itms, pre')) = match_oris' thy oris (ppc,where_,prls);

    in if b 

      then let val pbl = Matches (rev (pblRD @ [pI]), itms2itemppc thy itms pre')

	      in refins' (pblRD @ [pI]) fmz (pbls @ [pbl]) pys end

      else (pbls @ [NoMatch (rev (pblRD @ [pI]), itms2itemppc thy itms pre')])

    end

and refins' pblRD fmz pbls [] = pbls

  | refins' pblRD fmz pbls ((p as Ptyp (pI, _, _))::pts) =

    let val pbls' = refin' pblRD fmz pbls p

    in case last_elem pbls' of

        Matches _ => pbls'

      | NoMatch _ => refins' pblRD fmz pbls' pts

    end;

(*. refine a problem; version for tactic Refine_Problem .*)

fun refin'' thy (pblRD:pblRD) itms pbls ((Ptyp (pI,[py],[])):pbt ptyp) =

    let (*val _ = tracing("### refin''1: pI="^pI);*)

	val {thy,ppc,where_,prls,...} = py 

	val (b, (itms', pre')) = match_itms thy itms (ppc,where_,prls);

    in if b then pbls @ [Match_ (rev (pblRD @ [pI]), (itms', pre'))]

       else pbls @ [NoMatch_] 

    end

(* val pblRD = (rev o tl) pblID; val pbls = []; 

   val Ptyp (pI,[py],pys) = app_ptyp I pblID (rev pblID) (!ptyps);

   *)

  | refin'' thy pblRD itms pbls (Ptyp (pI,[py],pys)) =

    let (*val _ = tracing("### refin''2: pI="^pI);*)

	val {thy,ppc,where_,prls,...} = py 

	val(b, (itms', pre')) = match_itms thy itms (ppc,where_,prls);

    in if b 

       then let val pbl = Match_ (rev (pblRD @ [pI]), (itms', pre'))

	    in refins'' thy (pblRD @ [pI]) itms (pbls @ [pbl]) pys end

       else (pbls @ [NoMatch_])

    end

and refins'' thy pblRD itms pbls [] = pbls

  | refins'' thy pblRD itms pbls ((p as Ptyp (pI,_,_))::pts) =

    let val pbls' = refin'' thy pblRD itms pbls p

    in case last_elem pbls' of

	 Match_ _ => pbls'

       | NoMatch_ => refins'' thy pblRD itms pbls' pts end;

(*. for tactic Refine_Tacitly .*)

(*!!! oris are already created wrt. some pbt; pbt contains thy for parsing*)

(* val (thy,pblID) = (assoc_thy dI',pI);

   *)

fun refine_ori oris (pblID:pblID) =

    let val opt = app_ptyp (refin ((rev o tl) pblID) oris) 

			   pblID (rev pblID);

    in case opt of 

	   SOME pblRD => let val (pblID':pblID) =(rev pblRD)

			 in if pblID' = pblID then NONE

			    else SOME pblID' end

	 | NONE => NONE end;

fun refine_ori' oris pI = (the (refine_ori oris pI)) handle _ => pI;

(*. for tactic Refine_Problem .*); 

(* 10.03: returnvalue -> (pIrefined, itm list) would be sufficient *)

(* val pblID = pI; app_ptyp I pblID (rev pblID) (!ptyps);

   *)

fun refine_pbl thy (pblID:pblID) itms =

    case refined_ (app_ptyp (refin'' thy ((rev o tl) pblID) itms []) 

			    pblID (rev pblID)) of

	NONE => NONE

      | SOME (Match_ (rfd as (pI',_))) => 

	if pblID = pI' then NONE else SOME rfd;

(*. for math-experts .*)

(*FIXME.WN021019: needs thy for parsing fmz*)

(* val fmz = fmz1; val pblID = ["pbla"]; val pblRD = (rev o tl) pblID; 

   val pbls = []; val ptys = !ptyps;

   *)

fun refine (fmz:fmz_) (pblID:pblID) =

  app_ptyp (refin' ((rev o tl) pblID) fmz []) pblID (rev pblID);

(*.make a guh from a reference to an element in the kestore;

   EXCEPT theory hierarchy ... compare 'fun keref2xml'.*)

fun pblID2guh (pblID:pblID) =

    (((#guh o get_pbt) pblID)

     handle _ => error ("pblID2guh: not for '"^strs2str' pblID ^ "'"));

fun metID2guh (metID:metID) =

    (((#guh o get_met) metID)

     handle _ => error ("metID2guh: no 'Met_' for '"^

			      strs2str' metID ^ "'"));

fun kestoreID2guh Pbl_ (kestoreID:kestoreID) = pblID2guh kestoreID

  | kestoreID2guh Met_ (kestoreID:kestoreID) = metID2guh kestoreID

  | kestoreID2guh ketype kestoreID =

    error ("kestoreID2guh: '" ^ ketype2str ketype ^ "' not for '" ^

		 strs2str' kestoreID ^ "'");

fun show_pblguhs () =

    (default_print_depth 999; 

     (tracing o strs2str o (map linefeed)) (coll_pblguhs (get_ptyps ())); 

     default_print_depth 3);

fun sort_pblguhs () =

    (default_print_depth 999; 

     (tracing o strs2str o (map linefeed)) 

	 (((sort string_ord) o coll_pblguhs) (get_ptyps ())); 

     default_print_depth 3);

fun show_metguhs () =

    (default_print_depth 999; 

     (tracing o strs2str o (map linefeed)) (coll_metguhs (get_mets ())); 

     default_print_depth 3);

fun sort_metguhs () =

    (default_print_depth 999; 

     (tracing o strs2str o (map linefeed)) 

	 (((sort string_ord) o coll_metguhs) (get_mets ())); 

     default_print_depth 3);