(* Handle user-input during the specify- and the solve-phase. 

    author: Walther Neuper

    0603

    (c) due to copyright terms

 use"ME/inform.sml";

 use"inform.sml";

 *)

 signature INFORM =

   sig 

     type castab

     type icalhd

    (* type iitem *)

     datatype

       iitem =

           Find of cterm' list

         | Given of cterm' list

         | Relate of cterm' list

     type imodel

     val imodel2fstr : iitem list -> (string * cterm') list

     val Isac : 'a -> theory

     val appl_add' :

        theory' ->

        SpecifyTools.ori list ->

        SpecifyTools.itm list ->

        ('a * (Term.term * Term.term)) list ->

        string * cterm' -> SpecifyTools.itm

   (*  val appl_adds :

        theory' ->

        SpecifyTools.ori list ->

        SpecifyTools.itm list ->

        (string * (Term.term * Term.term)) list ->

        (string * string) list -> SpecifyTools.itm list *)

    (* val cas_input : string -> ptree * ocalhd *)

    (* val cas_input_ :

        spec ->

        (Term.term * Term.term list) list ->

        pblID * SpecifyTools.itm list * metID * SpecifyTools.itm list *

        (bool * Term.term) list  *)

     val castab : castab Unsynchronized.ref

     val compare_step :

        calcstate' -> Term.term -> string * calcstate'

    (* val concat_deriv :

        'a * ((Term.term * Term.term) list -> Term.term * Term.term -> bool)

        ->

        rls ->

        rule list ->

        Term.term ->

        Term.term ->

        bool * (Term.term * rule * (Term.term * Term.term list)) list *)

     val dropwhile' :   (* systest/auto-inform.sml *)

        ('a -> 'b -> bool) -> 'a list -> 'b list -> 'a list * 'b list

    (* val dtss2itm_ :

        pbt_ list ->

        Term.term * Term.term list ->

        int list * bool * string * SpecifyTools.itm_ *)

    (* val e_icalhd : icalhd *)

     val eq7 : ''a * ''b -> ''a * (''b * 'c) -> bool

     val equal : ''a -> ''a -> bool

    (* val filter_dsc :

        SpecifyTools.ori list -> SpecifyTools.itm -> SpecifyTools.ori list *)

    (* val filter_sep : ('a -> bool) -> 'a list -> 'a list * 'a list *)

    (* val flattup2 : 'a * ('b * 'c * 'd * 'e) -> 'a * 'b * 'c * 'd * 'e *)

    (* val fstr2itm_ :

        theory ->

        (''a * (Term.term * Term.term)) list ->

        ''a * string -> int list * bool * ''a * SpecifyTools.itm_ *)

     val inform :

        calcstate' -> cterm' -> string * calcstate'   

     val input_icalhd : ptree -> icalhd -> ptree * ocalhd

    (* val is_Par : SpecifyTools.itm -> bool *)

    (* val is_casinput : cterm' -> fmz -> bool *)

    (* val is_e_ts : Term.term list -> bool *)

    (* val itms2fstr : SpecifyTools.itm -> string * string *)

    (* val mk_tacis :

        rew_ord' * 'a ->

        rls ->

        Term.term * rule * (Term.term * Term.term list) ->

        tac * tac_ * (pos' * istate)      *)

     val oris2itms :

        'a -> int -> SpecifyTools.ori list -> SpecifyTools.itm list

    (* val par2fstr : SpecifyTools.itm -> string * cterm' *)

    (* val parsitm : theory -> SpecifyTools.itm -> SpecifyTools.itm *)

     val rev_deriv' : 'a * rule * ('b * 'c) -> 'b * rule * ('a * 'c)

    (* val unknown_expl :

        theory' ->

        (string * (Term.term * Term.term)) list ->

        (string * string) list -> SpecifyTools.itm list *)

   end

 (***. handle an input calc-head .***)

 (*------------------------------------------------------------------(**)

 structure inform :INFORM =

 struct

 (**)------------------------------------------------------------------*)

 datatype iitem = 

   Given of cterm' list

 (*Where is never input*) 

 | Find  of cterm' list

 | Relate  of cterm' list;

 type imodel = iitem list;

 (*calc-head as input*)

 type icalhd =

      pos' *     (*the position of the calc-head in the calc-tree

 		 pos' as (p,p_) where p_ is neglected due to pos_ below*) 

      cterm' *   (*the headline*)

      imodel *   (*the model (without Find) of the calc-head*)

      pos_ *     (*model belongs to Pbl or Met*)

      spec;      (*specification: domID, pblID, metID*)

 val e_icalhd = (e_pos', "", [Given [""]], Pbl, e_spec): icalhd;

 fun is_casinput (hdf: cterm') ((fmz_, spec): fmz) =

     hdf <> "" andalso fmz_ = [] andalso spec = e_spec;

 (*.handle an input as into an algebra system.*)

 fun dtss2itm_ ppc (d, ts) =

     let val (f, (d, id)) = the (find_first ((curry op= d) o 

 					    (#1: (term * term) -> term) o

 					    (#2: pbt_ -> (term * term))) ppc)

     in ([1], true, f, Cor ((d, ts), (id, ts))) end;

 fun flattup2 (a,(b,c,d,e)) = (a,b,c,d,e);

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

 type castab = 

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

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

        		     (*the function generating a kind of formalization*)

        (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*)

 	 list;       (*of cas-entries in the association list*)

 val castab = Unsynchronized.ref ([]: castab);

 fun cas_input_ ((dI,pI,mI): spec) dtss = (*WN110515 reconsider thy..ctxt*)

   let

     val thy = assoc_thy dI

 	  val {ppc, ...} = get_pbt pI

 	  val its_ = map (dtss2itm_ ppc) dtss (*([1],true,"#Given",Cor (...))*)

 	  val its = add_id its_

 	  val pits = map flattup2 its

 	  val (pI, mI) =

       if mI <> ["no_met"]

       then (pI, mI)

 		  else

         case refine_pbl thy pI pits of

 			    SOME (pI,_) => (pI, (hd o #met o get_pbt) pI)

 			  | NONE => (pI, (hd o #met o get_pbt) pI)

 	  val {ppc, pre, prls, ...} = get_met mI

 	  val its_ = map (dtss2itm_ ppc) dtss (*([1],true,"#Given",Cor (...))*)

 	  val its = add_id its_

 	  val mits = map flattup2 its

 	  val pre = check_preconds thy prls pre mits

     val ctxt = e_ctxt (*WN110515 cas_input_ DOESNT WORK*)

   in (pI, pits: itm list, mI, mits: itm list, pre, ctxt) end;

 (* check if the input term is a CAScmd and return a ptree with a _complete_ calchead *)

 fun cas_input hdt =

   let val (h,argl) = strip_comb hdt

   in

     case assoc (!castab, h) of

      NONE => NONE

    | SOME (spec as (dI,_,_), argl2dtss) =>

 	      let

           val dtss = argl2dtss argl

 	        val (pI, pits, mI, mits, pre, ctxt) = cas_input_ spec dtss

 	        val spec = (dI, pI, mI)

 	        val (pt,_) = 

 		        cappend_problem e_ptree [] (e_istate, e_ctxt) ([], e_spec) ([], e_spec, hdt)

 	        val pt = update_spec pt [] spec

 	        val pt = update_pbl pt [] pits

 	        val pt = update_met pt [] mits

 	        val pt = update_ctxt pt [] ctxt

 	      in SOME (pt, (true, Met, hdt, mits, pre, spec) : ocalhd) end

   end;

 (*lazy evaluation for (Thy_Info.get_theory "Isac")*)

 fun Isac _  = assoc_thy "Isac";

 (*re-parse itms with a new thy and prepare for checking with ori list*)

 fun parsitm dI (itm as (i,v,b,f, Cor ((d,ts),_)):itm) =

 (* val itm as (i,v,b,f, Cor ((d,ts),_)) = hd probl;

    *)

     (let val t = comp_dts (d,ts);

 	 val s = Print_Mode.setmp [] (Syntax.string_of_term (thy2ctxt dI)) t;

      (*this    ^ should raise the exn on unability of re-parsing dts*)

      in itm end handle _ => ((i,v,false,f, Syn (term2str t)):itm))

   | parsitm dI (itm as (i,v,b,f, Syn str)) =

     (let val t = (term_of o the o (parse dI)) str

      in (i,v,b,f, Par str) end handle _ => (i,v,b,f, Syn str))

   | parsitm dI (itm as (i,v,b,f, Typ str)) =

     (let val t = (term_of o the o (parse dI)) str

      in (i,v,b,f, Par str) end handle _ => (i,v,b,f, Syn str))

   | parsitm dI (itm as (i,v,_,f, Inc ((d,ts),_))) =

     (let val t = comp_dts (d,ts);

 	 val s = Print_Mode.setmp [] (Syntax.string_of_term (thy2ctxt dI)) t;

      (*this    ^ should raise the exn on unability of re-parsing dts*)

      in itm end handle _ => ((i,v,false,f, Syn (term2str t)):itm))

   | parsitm dI (itm as (i,v,_,f, Sup (d,ts))) =

     (let val t = comp_dts (d,ts);

 	 val s = Print_Mode.setmp [] (Syntax.string_of_term (thy2ctxt dI)) t;

      (*this    ^ should raise the exn on unability of re-parsing dts*)

      in itm end handle _ => ((i,v,false,f, Syn (term2str t)):itm))

   | parsitm dI (itm as (i,v,_,f, Mis (d,t'))) =

     (let val t = d $ t';

 	 val s = Print_Mode.setmp [] (Syntax.string_of_term (thy2ctxt dI)) t;

      (*this    ^ should raise the exn on unability of re-parsing dts*)

      in itm end handle _ => ((i,v,false,f, Syn (term2str t)):itm))

   | parsitm dI (itm as (i,v,_,f, Par _)) = 

     error ("parsitm (" ^ itm2str_ (thy2ctxt dI) itm^

 		 "): Par should be internal");

 (*separate a list to a pair of elements that do NOT satisfy the predicate,

  and of elements that satisfy the predicate, i.e. (false, true)*)

 fun filter_sep pred xs =

   let fun filt ab [] = ab

         | filt (a,b) (x :: xs) = if pred x 

 				 then filt (a,b@[x]) xs 

 				 else filt (a@[x],b) xs

   in filt ([],[]) xs end;

 fun is_Par ((_,_,_,_,Par _):itm) = true

   | is_Par _ = false;

 fun is_e_ts [] = true

   | is_e_ts [Const ("List.list.Nil", _)] = true

   | is_e_ts _ = false;

 (*WN.9.11.03 copied from fun appl_add (in modspec.sml)*)

 (* val (sel,ct) = selct;

    val (dI, oris, ppc, pbt, (sel, ct))=

        (#1 (some_spec ospec spec), oris, []:itm list,

 	((#ppc o get_pbt) (#2 (some_spec ospec spec))),

 	hd (imodel2fstr imodel));

    *)

 fun appl_add' dI oris ppc pbt (sel, ct) = 

     let 

       val ctxt = assoc_thy dI |> thy2ctxt;

     in case parseNEW ctxt ct of

 	   NONE => (0,[],false,sel, Syn ct):itm

 	 | SOME t => (case is_known ctxt sel oris t of

          ("", ori', all) =>

            (case is_notyet_input ctxt ppc all ori' pbt of

 	         ("",itm)  => itm

 	       | (msg,_) => error ("appl_add': " ^ msg))

      | (_, (i, v, _, d, ts), _) => if is_e_ts ts then

          (i, v, false, sel, Inc ((d, ts), (e_term, []))) else

          (i, v, false, sel, Sup (d, ts)))

     end;

 (*.generate preliminary itm_ from a strin (with field "#Given" etc.).*)

 (* val (f, str) = hd selcts;

    *)

 fun eq7 (f, d) (f', (d', _)) = f=f' andalso d=d';

 fun fstr2itm_ thy pbt (f, str) =

     let val topt = parse thy str

     in case topt of

 	   NONE => ([], false, f, Syn str)

 	 | SOME ct => 

 (* val SOME ct = parse thy str;

    *)

 	   let val (d,ts) = (split_dts o term_of) ct

 	       val popt = find_first (eq7 (f,d)) pbt

 	   in case popt of

 		  NONE => ([1](*??*), true(*??*), f, Sup (d,ts))

 		| SOME (f, (d, id)) => ([1], true, f, Cor ((d,ts), (id, ts))) 

 	   end

     end; 

 (*.input into empty PblObj, i.e. empty fmz+origin (unknown example).*)

 fun unknown_expl dI pbt selcts =

   let

     val thy = assoc_thy dI

     val its_ = map (fstr2itm_ thy pbt) selcts (*([1],true,"#Given",Cor (...))*)

     val its = add_id its_ 

 in (map flattup2 its): itm list end;

 (*WN.11.03 for input_icalhd, ~ specify_additem for Add_Given/_Find/_Relation

  appl_add': generate 1 item 

  appl_add' . is_known: parse, get data from oris (vats, all (elems if list)..)

  appl_add' . is_notyet_input: compare with items in model already input

  insert_ppc': insert this 1 item*)

 (* val (dI,oris,ppc,pbt,selcts) =((#1 (some_spec ospec spec)),oris,[(*!!*)],

 			       ((#ppc o get_pbt) (#2 (some_spec ospec spec))),

 			       (imodel2fstr imodel));

    *)

 fun appl_adds dI [] _ pbt selcts = unknown_expl dI pbt selcts

   (*already present itms in model are being overwritten*)

   | appl_adds dI oris ppc pbt [] = ppc

   | appl_adds dI oris ppc pbt (selct::ss) =

     (* val selct = (sel, string_of_cterm ct);

        *)

     let val itm = appl_add' dI oris ppc pbt selct;

     in appl_adds dI oris (insert_ppc' itm ppc) pbt ss end;

 (* val (dI, oris, ppc, pbt, selct::ss) = 

        (dI, pors, probl, ppc, map itms2fstr probl);

    ...vvv

    *)

 (* val (dI, oris, ppc, pbt, (selct::ss))=

        (#1 (some_spec ospec spec), oris, []:itm list,

 	((#ppc o get_pbt) (#2 (some_spec ospec spec))),(imodel2fstr imodel));

    val iii = appl_adds dI oris ppc pbt (selct::ss); 

    tracing(itms2str_ thy iii);

  val itm = appl_add' dI oris ppc pbt selct;

  val ppc = insert_ppc' itm ppc;

  val _::selct::ss = (selct::ss);

  val itm = appl_add' dI oris ppc pbt selct;

  val ppc = insert_ppc' itm ppc;

  val _::selct::ss = (selct::ss);

  val itm = appl_add' dI oris ppc pbt selct;

  val ppc = insert_ppc' itm ppc;

  tracing(itms2str_ thy ppc);

  val _::selct::ss = (selct::ss);

  val itm = appl_add' dI oris ppc pbt selct;

  val ppc = insert_ppc' itm ppc;

    *)

 fun oris2itms _ _ ([]:ori list) = ([]:itm list)

   | oris2itms pbt vat ((i,v,f,d,ts)::(os: ori list)) =

     if member op = vat v 

     then (i,v,true,f,Cor ((d,ts),(e_term,[])))::(oris2itms pbt vat os)

     else oris2itms pbt vat os;

 fun filter_dsc oris itm = 

     filter_out ((curry op= ((d_in o #5) (itm:itm))) o 

 		(#4:ori -> term)) oris;

 fun par2fstr ((_,_,_,f, Par s):itm) = (f, s)

   | par2fstr itm = error ("par2fstr: called with " ^

 			      itm2str_ (thy2ctxt' "Isac") itm);

 fun itms2fstr ((_,_,_,f, Cor ((d,ts),_)):itm) = (f, comp_dts'' (d,ts))

   | itms2fstr (_,_,_,f, Syn str) = (f, str)

   | itms2fstr (_,_,_,f, Typ str) = (f, str)

   | itms2fstr (_,_,_,f, Inc ((d,ts),_)) = (f, comp_dts'' (d,ts))

   | itms2fstr (_,_,_,f, Sup (d,ts)) = (f, comp_dts'' (d,ts))

   | itms2fstr (_,_,_,f, Mis (d,t)) = (f, term2str (d $ t))

   | itms2fstr (itm as (_,_,_,f, Par _)) = 

     error ("parsitm ("^itm2str_ (thy2ctxt' "Isac") itm ^

 		 "): Par should be internal");

 fun imodel2fstr iitems = 

   let 

     fun xxx is [] = is

 	    | xxx is ((Given strs)::iis) = xxx (is @ (map (pair "#Given") strs)) iis

 	    | xxx is ((Find strs)::iis) = xxx (is @ (map (pair "#Find") strs)) iis

 	    | xxx is ((Relate strs)::iis) = xxx (is @ (map (pair "#Relate") strs)) iis

   in xxx [] iitems end;

 (* input a calchead, WN110505 "prep_oris -> (_, ctxt)" not handled properly *)

 fun input_icalhd pt (((p,_), hdf, imodel, Pbl, spec as (dI,pI,mI)):icalhd) =

     let val PblObj {fmz = fmz as (fmz_,_), origin = (oris, ospec, hdf'), 

 		      spec = sspec as (sdI,spI,smI), probl, meth, ...} = get_obj I pt p;

     in if is_casinput hdf fmz then the (cas_input (str2term hdf)) 

        else        (*hacked WN0602 ~~~            ~~~~~~~~~,   ..dropped !*)

          let val (pos_, pits, mits) = 

 	         if dI <> sdI

 	         then let val its = map (parsitm (assoc_thy dI)) probl;

 			            val (its, trms) = filter_sep is_Par its;

 			            val pbt = (#ppc o get_pbt) (#2(some_spec ospec sspec));

 		            in (Pbl, appl_adds dI oris its pbt  (map par2fstr trms), meth) end 

            else if pI <> spI 

 	              then if pI = snd3 ospec then (Pbl, probl, meth) 

                      else

 		                   let val pbt = (#ppc o get_pbt) pI

 			                   val dI' = #1 (some_spec ospec spec)

 			                   val oris = if pI = #2 ospec then oris 

 				                            else prep_ori fmz_(assoc_thy"Isac") pbt |> #1;

 		                   in (Pbl, appl_adds dI' oris probl pbt 

 				                 (map itms2fstr probl), meth) end 

                 else if mI <> smI (*FIXME.WN0311: what if probl is incomplete?!*)

 	                   then let val met = (#ppc o get_met) mI

 		                        val mits = complete_metitms oris probl meth met

 		                      in if foldl and_ (true, map #3 mits)

 		                         then (Pbl, probl, mits) else (Met, probl, mits) 

 		                      end 

                      else (Pbl, appl_adds (#1 (some_spec ospec spec)) oris [(*!!!*)]

 			                     ((#ppc o get_pbt) (#2 (some_spec ospec spec)))

 			                     (imodel2fstr imodel), meth);

 	         val pt = update_spec pt p spec;

          in if pos_ = Pbl

 	          then let val {prls,where_,...} = get_pbt (#2 (some_spec ospec spec))

 		               val pre =check_preconds(assoc_thy"Isac")prls where_ pits

 	               in (update_pbl pt p pits,

 		                 (ocalhd_complete pits pre spec, Pbl, hdf', pits, pre, spec):ocalhd) 

                  end

 	           else let val {prls,pre,...} = get_met (#3 (some_spec ospec spec))

 		                val pre = check_preconds (assoc_thy"Isac") prls pre mits

 	                in (update_met pt p mits,

 		                  (ocalhd_complete mits pre spec, Met, hdf', mits, pre, spec):ocalhd)

                   end

          end 

     end

   | input_icalhd pt ((p,_), hdf, imodel, _(*Met*), spec as (dI,pI,mI)) =

     error "input_icalhd Met not impl.";

 (***. handle an input formula .***)

 (*

 Untersuchung zur Formeleingabe (appendFormula, replaceFormla) zu einer Anregung von Alan Krempler:

 Welche RICHTIGEN Formeln koennen NICHT abgeleitet werden, 

 wenn Abteilungen nur auf gleichem Level gesucht werden ?

 WN.040216 

 Beispiele zum Equationsolver von Richard Lang aus /src/sml/kbtest/rlang.sml

 ------------------------------------------------------------------------------

 "Schalk I s.87 Bsp 52a ((5*x)/(x - 2) - x/(x+2)=4)";

 ------------------------------------------------------------------------------

 1. "5 * x / (x - 2) - x / (x + 2) = 4"

 ...

 4. "12 * x + 4 * x ^^^ 2 = 4 * (-4 + x ^^^ 2)",Subproblem["normalize", "poly"..

 ...

 4.3. "16 + 12 * x = 0", Subproblem["degree_1", "polynomial", "univariate"..

 ...

 4.3.3. "[x = -4 / 3]")), Check_elementwise "Assumptions"

 ...

 "[x = -4 / 3]"

 ------------------------------------------------------------------------------

 (1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]

 (4.1)..(4.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 4.3.n]

 ------------------------------------------------------------------------------

 ------------------------------------------------------------------------------

 "Schalk I s.87 Bsp 55b (x/(x^^^2 - 6*x+9) - 1/(x^^^2 - 3*x) =1/x)";

 ------------------------------------------------------------------------------

 1. "x / (x ^^^ 2 - 6 * x + 9) - 1 / (x ^^^ 2 - 3 * x) = 1 / x"

 ...

 4. "(3 + (-1 * x + x ^^^ 2)) * x = 1 * (9 * x + (x ^^^ 3 + -6 * x ^^^ 2))"

                          Subproblem["normalize", "polynomial", "univariate"..

 ...

 4.4. "-6 * x + 5 * x ^^^ 2 = 0", Subproblem["bdv_only", "degree_2", "poly"..

 ...

 4.4.4. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"

 4.4.5. "[x = 0, x = 6 / 5]"

 ...

 5. "[x = 0, x = 6 / 5]", Check_elementwise "Assumptions"

    "[x = 6 / 5]"

 ------------------------------------------------------------------------------

 (1)..(4): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite schiebt [Ableitung waere in 4.4.x]

 (4.1)..(4.4.5): keine 'richtige' Eingabe kann abgeleitet werden, die dem Ergebnis "[x = 6 / 5]" aequivalent ist [Ableitung waere in 5.]

 ------------------------------------------------------------------------------

 ------------------------------------------------------------------------------

 "Schalk II s.56 Bsp 73b (sqrt(x+1)+sqrt(4*x+4)=sqrt(9*x+9))";

 ------------------------------------------------------------------------------

 1. "sqrt (x + 1) + sqrt (4 * x + 4) = sqrt (9 * x + 9)"

 ...

 6. "13 + 13 * x + -2 * sqrt ((4 + 4 * x) * (9 + 9 * x)) = 1 + x"

                              Subproblem["sq", "root'", "univariate", "equation"]

 ...

 6.6. "144 + 288 * x + 144 * x ^^^ 2 = 144 + x ^^^ 2 + 288 * x + 143 * x ^^^ 2"

                 Subproblem["normalize", "polynomial", "univariate", "equation"]

 ...

 6.6.3 "0 = 0"    Subproblem["degree_0", "polynomial", "univariate", "equation"]

 ...                                       Or_to_List

 6.6.3.2 "UniversalList"

 ------------------------------------------------------------------------------

 (1)..(6): keine 'richtige' Eingabe kann abgeleitet werden, die eine der Wurzeln auf die andere Seite verschieb [Ableitung ware in 6.6.n]

 (6.1)..(6.3): keine 'richtige' Eingabe kann abgeleitet werden, die einen Summanden auf die andere Seite verschiebt [Ableitung ware in 6.6.n]

 ------------------------------------------------------------------------------

 *)

 (*sh. comments auf 498*)

 fun equal a b = a=b;

 (*the lists contain eq-al elem-pairs at the beginning;

   return first list reverted (again) - ie. in order as required subsequently*)

 fun dropwhile' equal (f1::f2::fs) (i1::i2::is) =

     if equal f1 i1 then

 	 if equal f2 i2 then dropwhile' equal (f2::fs) (i2::is)

 	 else (rev (f1::f2::fs), i1::i2::is)

     else error "dropwhile': did not start with equal elements"

   | dropwhile' equal (f::fs) [i] =

     if equal f i then (rev (f::fs), [i])

     else error "dropwhile': did not start with equal elements"

   | dropwhile' equal [f] (i::is) =

     if equal f i then ([f], i::is)

     else error "dropwhile': did not start with equal elements";

 (*

  fun equal a b = a=b;

  val foder = [0,1,2,3,4,5]; val ifoder = [11,12,3,4,5];

  val r_foder = rev foder;  val r_ifoder = rev ifoder;

  dropwhile' equal r_foder r_ifoder;

 > vval it = ([0, 1, 2, 3], [3, 12, 11]) : int list * int list

  val foder = [3,4,5]; val ifoder = [11,12,3,4,5];

  val r_foder = rev foder;  val r_ifoder = rev ifoder;

  dropwhile' equal r_foder r_ifoder;

 > val it = ([3], [3, 12, 11]) : int list * int list

  val foder = [5]; val ifoder = [11,12,3,4,5];

  val r_foder = rev foder;  val r_ifoder = rev ifoder;

  dropwhile' equal r_foder r_ifoder;

 > val it = ([5], [5, 4, 3, 12, 11]) : int list * int list

  val foder = [10,11,12,13,14,15]; val ifoder = [11,12,3,4,5];

  val r_foder = rev foder;  val r_ifoder = rev ifoder;

  dropwhile' equal r_foder r_ifoder;

 > *** dropwhile': did not start with equal elements*)

 (*040214: version for concat_deriv*)

 fun rev_deriv' (t, r, (t', a)) = (t', sym_Thm r, (t, a));

 fun mk_tacis ro erls (t, r as Thm _, (t', a)) = 

       (Rewrite (rule2thm' r), 

          Rewrite' ("Isac", fst ro, erls, false, rule2thm' r, t, (t', a)),

        (e_pos'(*to be updated before generate tacis!!!*), (Uistate, e_ctxt)))

   | mk_tacis ro erls (t, r as Rls_ rls, (t', a)) = 

       (Rewrite_Set (rule2rls' r), 

          Rewrite_Set' ("Isac", false, rls, t, (t', a)),

        (e_pos'(*to be updated before generate tacis!!!*), (Uistate, e_ctxt)));

 (*fo = ifo excluded already in inform*)

 fun concat_deriv rew_ord erls rules fo ifo =

     let fun derivat ([]:(term * rule * (term * term list)) list) = e_term

 	  | derivat dt = (#1 o #3 o last_elem) dt

         fun equal (_,_,(t1, _)) (_,_,(t2, _)) = t1=t2

 	val  fod = make_deriv (Isac"") erls rules (snd rew_ord) NONE  fo

 	val ifod = make_deriv (Isac"") erls rules (snd rew_ord) NONE ifo

     in case (fod, ifod) of

 	   ([], []) => if fo = ifo then (true, [])

 		       else (false, [])

 	 | (fod, []) => if derivat fod = ifo 

 			then (true, fod) (*ifo is normal form*)

 			else (false, [])

 	 | ([], ifod) => if fo = derivat ifod 

 			 then (true, ((map rev_deriv') o rev) ifod)

 			 else (false, [])

 	 | (fod, ifod) =>

 	   if derivat fod = derivat ifod (*common normal form found*)

 	   then let val (fod', rifod') = 

 			dropwhile' equal (rev fod) (rev ifod)

 		in (true, fod' @ (map rev_deriv' rifod')) end

 	   else (false, [])

     end;

 (*

  val ({rew_ord, erls, rules,...}, fo, ifo) = 

      (rep_rls Test_simplify, str2term "x+1+ -1*2=0", str2term "-2*1+(x+1)=0");

  (tracing o trtas2str) fod';

 > ["

 (x + 1 + -1 * 2 = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (x + 1) = 0, []))","

 (-1 * 2 + (x + 1) = 0, Thm ("radd_commute","?m + ?n = ?n + ?m"), (-1 * 2 + (1 + x) = 0, []))","

 (-1 * 2 + (1 + x) = 0, Thm ("radd_left_commute","?x + (?y + ?z) = ?y + (?x + ?z)"), (1 + (-1 * 2 + x) = 0, []))","

 (1 + (-1 * 2 + x) = 0, Thm ("#mult_Float ((~1,0), (0,0)) __ ((2,0), (0,0))","-1 * 2 = -2"), (1 + (-2 + x) = 0, []))"]

 val it = () : unit

  (tracing o trtas2str) (map rev_deriv' rifod');

 > ["

 (1 + (-2 + x) = 0, Thm ("sym_#mult_Float ((~2,0), (0,0)) __ ((1,0), (0,0))","-2 = -2 * 1"), (1 + (-2 * 1 + x) = 0, []))","

 (1 + (-2 * 1 + x) = 0, Thm ("sym_radd_left_commute","?y + (?x + ?z) = ?x + (?y + ?z)"), (-2 * 1 + (1 + x) = 0, []))","

 (-2 * 1 + (1 + x) = 0, Thm ("sym_radd_commute","?n + ?m = ?m + ?n"), (-2 * 1 + (x + 1) = 0, []))"]

 val it = () : unit

 *)

 (* compare inform with ctree.form at current pos by nrls;

    if found, embed the derivation generated during comparison

    if not, let the mat-engine compute the next ctree.form *)

 (*structure copied from complete_solve

   CAUTION: tacis in returned calcstate' do NOT construct resulting ptp --

            all_modspec etc. has to be inserted at Subproblem'*)

 fun compare_step ((tacis, c, ptp as (pt, pos as (p,p_))): calcstate') ifo =

   let

     val fo =

       case p_ of

         Frm => get_obj g_form pt p

 			| Res => (fst o (get_obj g_result pt)) p

 			| _ => e_term (*on PblObj is fo <> ifo*);

 	  val {nrls, ...} = get_met (get_obj g_metID pt (par_pblobj pt p))

 	  val {rew_ord, erls, rules, ...} = rep_rls nrls

 	  val (found, der) = concat_deriv rew_ord erls rules fo ifo; (*<---------------*)

   in

     if found

     then

        let

          val tacis' = map (mk_tacis rew_ord erls) der;

 		     val (c', ptp) = embed_deriv tacis' ptp;

 	     in ("ok", (tacis (*@ tacis'?WN050408*), c @ c', ptp)) end

      else 

 	     if pos = ([], Res) 

 	     then ("no derivation found", (tacis, c, ptp): calcstate') 

 	     else

          let

            val cs' as (tacis, c', ptp) = nxt_solve_ ptp; (*<---------------------*)

 		       val cs' as (tacis, c'', ptp) = 

 			       case tacis of

 			         ((Subproblem _, _, _)::_) => 

 			           let

                    val ptp as (pt, (p,_)) = all_modspec ptp

 				           val mI = get_obj g_metID pt p

 			           in

 			             nxt_solv (Apply_Method' (mI, NONE, e_istate, e_ctxt)) (e_istate, e_ctxt) ptp

                  end

 			       | _ => cs';

 		     in compare_step (tacis, c @ c' @ c'', ptp) ifo end

   end;

 (* check if (agreed result, input formula) matches the error pattern "pat" modulo simplifier rls *)

 fun check_err_patt (res, inf) (subst: subst) (errpatID: errpatID, pat) rls =

   let 

     val (res', _, _, rewritten) =

       rew_sub (Isac()) 1 subst e_rew_ord e_rls false [] (Trueprop $ pat) res;

   in

     if rewritten

     then 

       let

         val norm_res = case rewrite_set_inst_ (Isac()) false subst rls  res' of

           NONE => res'

         | SOME (norm_res, _) => norm_res

         val norm_inf = case rewrite_set_inst_ (Isac()) false subst rls inf of

           NONE => inf

         | SOME (norm_inf, _) => norm_inf

       in if norm_res = norm_inf then SOME errpatID else NONE

       end

     else NONE

   end;

 (* check if (agreed result, input formula) matches SOME error pattern modulo simplifier rls;

    (prog, env) for retrieval of casual substitution for bdv in the pattern. *)

 fun check_error_patterns (res, inf) (prog, env) (errpats, rls) =

   let

     val (_, subst) = get_bdv_subst prog env

     fun scan (_, [], _) = NONE

       | scan (errpatID, errpat :: errpats, _) =

           case check_err_patt (res, inf) (subst: subst) (errpatID, errpat) rls of

             NONE => scan (errpatID, errpats, [])

           | SOME errpatID => SOME errpatID

     fun scans [] = NONE

       | scans (group :: groups) =

           case scan group of

             NONE => scans groups

           | SOME errpatID => SOME errpatID

   in scans errpats end;

 (*.handle a user-input formula, which may be a CAS-command, too.

 CAS-command:

    create a calchead, and do 1 step

    TOOODO.WN0602 works only for the root-problem !!!

 formula, which is no CAS-command:

    compare iform with calc-tree.form at pos by equ_nrls and all subsequent pos;

    collect all the tacs applied by the way;

    if "no derivation found" then check_error_patterns.

    ALTERNATIVE: check_error_patterns _within_ compare_step seems too expensive.*)

 fun inform (cs as (_, _, ptp as (pt, pos as (p, p_))): calcstate') istr =

   case parse (assoc_thy "Isac") istr of

 	  SOME f_in =>

 	    let

 	      val f_in = term_of f_in

 	      val f_succ = get_curr_formula (pt, pos);

 			in

 			  if f_succ = f_in

 			  then ("same-formula", cs) (* ctree not cut with replaceFormula *)

 			  else

 			    case cas_input f_in of

 			      SOME (pt, _) => ("ok",([], [], (pt, (p, Met))))

 			    | NONE =>

 			        let

 			          val pos_pred = lev_back' pos

 			          (* f_pred ---"step pos cs"---> f_succ in appendFormula *)

 			          val f_pred = get_curr_formula (pt, pos_pred)

 			          val msg_calcstate' = compare_step ([], [], (pt, pos_pred)) f_in (*<<=====*)

 			          (*last step re-calc in compare_step TODO before WN09*)

 			        in

 			          case msg_calcstate' of

 			            ("no derivation found", calcstate') => 

 			               let

 			                 val pp = par_pblobj pt p

 			                 val {errpats, nrls, scr = Script prog, ...} = get_met (get_obj g_metID pt pp)

 			                 val ScrState (env, _, _, _, _, _) = get_istate pt pos

 			               in

 			                 case check_error_patterns (f_pred, f_in) (prog, env) (errpats, nrls) of

 			                   SOME errpatID => ("error pattern #" ^ errpatID ^ "#", calcstate')

 			                 | NONE => msg_calcstate'

 			               end

 			          | _ => msg_calcstate'

 			        end

 			end

     | NONE => ("syntax error in '" ^ istr ^ "'", e_calcstate');

 (* fill-in patterns an forms.

   returns thm required by "fun in_fillform *)

 fun get_fillform (subs_opt, subst) (thm, form) errpatID ((fillpatID, pat, erpaID): fillpat) =

   let

     val (form', _, _, rewritten) =

       rew_sub (Isac()) 1 subst e_rew_ord e_rls false [] (Trueprop $ pat) form;

   in (*the fillpat of the thm must be dedicated to errpatID*)

     if errpatID = erpaID andalso rewritten

     then SOME (fillpatID, HOLogic.mk_eq (form, form'), thm, subs_opt) else NONE end;

 fun get_fillpats subst form errpatID thm =

       let

         val thmDeriv = Thm.get_name_hint thm

         val (part, thyID) = thy_containing_thm thmDeriv

         val theID = [part, thyID, "Theorems", thmID_of_derivation_name thmDeriv]

         val Hthm {fillpats, ...} = get_the theID

         val some = map (get_fillform subst (thm, form) errpatID) fillpats

       in some |> filter is_some |> map the end;

 fun find_fillpatterns (pt, pos as (p, _): pos') errpatID =

   let 

     val f_curr = get_curr_formula (pt, pos); (* = "d_d x (x ^^^ 2) + d_d x (sin (x ^^^ 4))"*)

     val pp = par_pblobj pt p

 			    val {errpats, scr = Script prog, ...} = get_met (get_obj g_metID pt pp)

     val ScrState (env, _, _, _, _, _) = get_istate pt pos

     val subst = get_bdv_subst prog env

     val errpatthms = errpats

       |> filter ((curry op = errpatID) o (#1: errpat -> errpatID))

       |> map (#3: errpat -> thm list)

       |> flat

   in map (get_fillpats subst f_curr errpatID) errpatthms |> flat end;

 (*------------------------------------------------------------------(**)

 end

 open inform; 

 (**)------------------------------------------------------------------*)