(* The _functional_ mathematics engine, ie. without a state.

    Input and output are Isabelle's formulae as strings.

    authors: Walther Neuper 2000

    (c) due to copyright terms

 *)

 signature MATH_ENGINE =

 sig

   type NEW (* TODO: refactor "fun me" with calcstate and remove *)

   val me : Solve.tac'_ -> Ctree.pos' -> NEW ->

     Ctree.ctree -> Ctree.pos' * NEW * Generate.mout * Solve.tac'_ * Selem.safe * Ctree.ctree

   val autocalc : Ctree.pos' list -> Ctree.pos' -> (Ctree.state) * Generate.taci list ->

     Solve.auto -> string * Ctree.pos' list * (Ctree.state)

   val locatetac :

     Tac.tac -> Ctree.state -> string * (Generate.taci list * Ctree.pos' list * (Ctree.state))

   val step : Ctree.pos' -> Chead.calcstate -> string * Chead.calcstate'

   val detailstep : Ctree.ctree -> Ctree.pos' -> string * Ctree.ctree * Ctree.pos'

   val get_pblID : Ctree.state -> Celem.pblID option

   val initcontext_met : Ctree.ctree -> Ctree.pos' -> bool * string list * Rule.scr * Model.itm list * (bool * term) list

   val initcontext_pbl : Ctree.ctree -> Ctree.pos' -> bool * string list * term * Model.itm list * (bool * term) list

   val context_met : Celem.metID -> Ctree.ctree -> Ctree.pos -> bool * Celem.metID * Rule.scr * Model.itm list * (bool * term) list

   val context_pbl : Celem.pblID -> Ctree.ctree -> Ctree.pos -> bool * Celem.pblID * term * Model.itm list * (bool * term) list

   val set_method : Celem.metID -> Ctree.state -> Ctree.ctree * Ctree.ocalhd

   val set_problem : Celem.pblID -> Ctree.state -> Ctree.ctree * Ctree.ocalhd

   val set_theory : Rule.thyID -> Ctree.state -> Ctree.ctree * Ctree.ocalhd

   val tryrefine : Celem.pblID -> Ctree.ctree -> Ctree.pos' -> bool * Celem.pblID * term * Model.itm list * (bool * term) list

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

   val CalcTreeTEST : Selem.fmz list -> Ctree.pos' * NEW * Generate.mout * (string * Tac.tac) * Selem.safe * Ctree.ctree

   val f2str : Generate.mout -> Rule.cterm'

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

   type nxt_

   datatype lOc_ = ERror of string | UNsafe of Chead.calcstate' | Updated of Chead.calcstate'

   val loc_solve_ : string * Tac.tac_ -> Ctree.ctree *  Ctree.pos' -> lOc_

   val loc_specify_ : Tac.tac_ -> Ctree.state -> lOc_

   val nxt_specify_: Ctree.ctree * Ctree.pos' -> Chead.calcstate'

   val TESTg_form : Ctree.state -> Generate.mout

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

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

   (* NONE *)

 end

 (**)

 structure Math_Engine(**): MATH_ENGINE(**) =

 struct

 (**)

 fun get_pblID (pt, (p, _): Ctree.pos') =

   let val p' = Ctree.par_pblobj pt p

   	val (_, pI, _) = Ctree.get_obj Ctree.g_spec pt p'

   	val (_, (_, oI, _), _) = Ctree.get_obj Ctree.g_origin pt p'

   in

     if pI <> Celem.e_pblID

     then SOME pI

     else

       if oI <> Celem.e_pblID then SOME oI else NONE end;

 datatype lOc_ =

   ERror of string              (*after loc_specify, loc_solve*)

 | UNsafe of Chead.calcstate'   (*after loc_specify, loc_solve*)

 | Updated of Chead.calcstate'  (*after loc_specify, loc_solve*)

 fun loc_specify_ m (pt, pos) =

   let

     val (p, _, f, _, _, pt) = Chead.specify m pos [] pt;

   in

     case f of (Generate.Error' e) => ERror e | _ => Updated ([], [], (pt,p))

   end

 (* TODO push return-value cs' into solve and rename solve->loc_solve?_? *)

 fun loc_solve_ m (pt, pos) =

   let

     val (msg, cs') = Solve.solve m (pt, pos);

   in

     case msg of "ok" => Updated cs' | msg => ERror msg 

   end

 datatype nxt_ =

 	HElpless  (**)

 | Nexts of Chead.calcstate (**)

 (* locate a tactic in a script and apply it if possible;

    report of tacs' applicability in tacis; pt is dropped in setNextTactic*)

 fun locatetac _ (ptp as (_, ([], Ctree.Res))) = ("end-of-calculation", ([], [], ptp))

   | locatetac tac (ptp as (pt, p)) =

     let

       val (mI, m) = Solve.mk_tac'_ tac;

     in

       case Applicable.applicable_in p pt m of

 	      Chead.Notappl _ => ("not-applicable", ([],[],  ptp): Chead.calcstate')

 	    | Chead.Appl m =>

 	      let 

           val x = if member op = Solve.specsteps mI

 		        then loc_specify_ m ptp else loc_solve_ (mI,m) ptp

 	      in 

 	        case x of 

 		        ERror _ => ("failure", ([], [], ptp))

 		        (*FIXXXXXME: loc_specify_, loc_solve_ TOGETHER with dropping meOLD+detail.sml*)

 		      | UNsafe cs' => ("unsafe-ok", cs')

 		      | Updated (cs' as (_, _, (_, p'))) => (*ev.SEVER.tacs like Begin_Trans*)

 		        (if p' = ([], Ctree.Res) then "end-of-calculation" else "ok", cs')

             (*for SEVER.tacs user to ask ? *)

 	      end

     end

 (* iterated by nxt_me; there (the resulting) ptp dropped

    may call nxt_solve Apply_Method --- thus evaluated here after solve.sml *)

 fun nxt_specify_ (ptp as (pt, (p, p_))) =

   let

     val (pblobj, meth, origin, oris, dI', pI', mI', probl, dI, pI, mI) = 

   	  case Ctree.get_obj I pt p of

   	    pblobj as (Ctree.PblObj {meth, origin = origin as (oris, (dI', pI', mI'), _),

   		  probl, spec = (dI, pI, mI), ...}) => (pblobj, meth, origin, oris, dI', pI', mI', probl, dI, pI, mI)

       | Ctree.PrfObj _ => error "nxt_specify_: not on PrfObj"

   in 

     if Ctree.just_created_ pblobj (*by Subproblem*) andalso origin <> Ctree.e_origin

     then 

       case mI' of

         ["no_met"] => Chead.nxt_specif (Tac.Refine_Tacitly pI') (pt, (p, Ctree.Pbl))

       | _ => Chead.nxt_specif Tac.Model_Problem (pt, (p, Ctree.Pbl))

     else 

       let 

         val cpI = if pI = Celem.e_pblID then pI' else pI;

   	    val cmI = if mI = Celem.e_metID then mI' else mI;

   	    val {ppc, prls, where_, ...} = Specify.get_pbt cpI;

   	    val pre = Stool.check_preconds "thy 100820" prls where_ probl;

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

   	    (*FIXME.WN0308:    ~~~~~: just check true in itms of pbl/met?*)

   	    val (_, tac) =

   	      Chead.nxt_spec p_ pb oris (dI', pI', mI') (probl, meth) (ppc, (#ppc o Specify.get_met) cmI) (dI, pI, mI)

       in

         case tac of

   	      Tac.Apply_Method mI => 

   	        LucinNEW.begin_end_prog (Tac.Apply_Method' (mI, NONE, Selem.e_istate, Selem.e_ctxt)) (Selem.e_istate, Selem.e_ctxt) ptp

   	    | _ => Chead.nxt_specif tac ptp

   	  end

   end

 (* specify a new method; WN0512 impl.incomplete, see 'nxt_specif (Specify_Method ' *)

 fun set_method mI ptp =

   let

     val (mits, pt, p) =

       case Chead.nxt_specif (Tac.Specify_Method mI) ptp of

         ([(_, Tac.Specify_Method' (_, _, mits), _)], [], (pt, (p, _))) => (mits, pt, p)

       | _ => error "set_method: case 1 uncovered"

   	val pre = []        (*...from Specify_Method'*)

   	val complete = true (*...from Specify_Method'*)

   	(*from Specify_Method'  ?   vvv,  vvv ?*)

     val (hdf, spec) =

       case Ctree.get_obj I pt p of

         Ctree.PblObj {origin = (_, _, hdf), spec, ...} => (hdf, spec)

       | Ctree.PrfObj _ => error "set_method: case 2 uncovered"

   in

     (pt, (complete, Ctree.Met, hdf, mits, pre, spec) : Ctree.ocalhd)

   end

 (* specify a new problem; WN0512 impl.incomplete, see 'nxt_specif (Specify_Problem ' *)

 fun set_problem pI ptp =

   let

     val (complete, pits, pre, pt, p) =

       case Chead.nxt_specif (Tac.Specify_Problem pI) ptp of

         ([(_, Tac.Specify_Problem' (_, (complete, (pits, pre))),_)], _, (pt, (p,_)))

           => (complete, pits, pre, pt, p)

       | _ => error "set_problem: case 1 uncovered"

     (*from Specify_Problem' ?   vvv,  vvv ?*)

     val (hdf, spec) =

       case Ctree.get_obj I pt p of

         Ctree.PblObj {origin = (_, _, hdf), spec, ...} => (hdf, spec)

       | Ctree.PrfObj _ => error "set_problem: case 2 uncovered"

   in

     (pt, (complete, Ctree.Pbl, hdf, pits, pre, spec) : Ctree.ocalhd)

   end

 fun set_theory tI ptp =

   let

     val (complete, pits, pre, pt, p) =

       case Chead.nxt_specif (Tac.Specify_Theory tI) ptp of  

         ([(_, Tac.Specify_Problem' (_, (complete, (pits, pre))), _)], _, (pt, (p, _)))

           => (complete, pits, pre, pt, p)

       | _ => error "set_theory: case 1 uncovered"

   	(*from Specify_Theory'  ?   vvv,  vvv ?*)

     val (hdf, spec) =

       case Ctree.get_obj I pt p of

         Ctree.PblObj {origin = (_, _, hdf), spec, ...} => (hdf, spec)

       | Ctree.PrfObj _ => error "set_theory: case 2 uncovered"

   in (pt, (complete, Ctree.Pbl, hdf, pits, pre, spec) : Ctree.ocalhd) end;

 (* does a step forward; returns tactic used, ctree updated.

    TODO.WN0512 redesign after specify-phase became more separated from solve-phase *)

 fun step (ip as (_, p_)) (ptp as (pt,p), tacis) =

   let val pIopt = get_pblID (pt,ip);

   in

     if ip = ([], Ctree.Res)

     then ("end-of-calculation", (tacis, [], ptp): Chead.calcstate') 

     else

       case tacis of

         (_::_) => 

           if ip = p (*the request is done where ptp waits for*)

           then 

             let val (pt',c',p') = Generate.generate tacis (pt,[],p)

   	        in ("ok", (tacis, c', (pt', p'))) end

           else (case (if member op = [Ctree.Pbl, Ctree.Met] p_

   	                  then nxt_specify_ (pt, ip) else LucinNEW.do_solve_step (pt, ip))

   	                  handle ERROR msg => (writeln ("*** " ^ msg);

   	                    ([], [], ptp)) (*e.g. Add_Given "equality///"*) of

   	              cs as ([],_,_) => ("helpless", cs)

   	            | cs => ("ok", cs))

       | _ => (case pIopt of

   	            NONE => ("no-fmz-spec", ([], [], ptp))

   	          | SOME _ =>                         (*vvvvvv: Apply_Method without init_form*)

   	            (case if member op = [Ctree.Pbl, Ctree.Met] p_ 

   	                    andalso is_none (Ctree.get_obj Ctree.g_env pt (fst p))

   		                then nxt_specify_ (pt, ip)

                       else (LucinNEW.do_solve_step (pt,ip))

   	                    handle ERROR msg => (writeln ("*** " ^ msg);

   	                      ([],[],ptp)) (*e.g. Add_Given "equality///"*) of

   	               cs as ([],_,_) =>("helpless", cs) (*FIXXME del.handle*)

   		           | cs => ("ok", cs)))

   end

 (* does several steps within one calculation as given by "type auto";

    the steps may arbitrarily go into and leave different phases, 

    i.e. specify-phase and solve-phase

    TODO.WN0512 ? redesign after the phases have been more separated

    at the fron-end in 05: 

    eg. CompleteCalcHead could be done by a separate fun !!!*)

 fun autocalc c ip cs (Solve.Step s) =

     if s <= 1

     then

       let val (str, (_, c', ptp)) = step ip cs;      (* autoord = 1, probably does 1 step too much*)

 	    in (str, c@c', ptp) end

     else

       let val (str, (_, c', ptp as (_, p))) = step ip cs;

       in

         if str = "ok" 

         then autocalc (c@c') p (ptp, []) (Solve.Step (s - 1))

         else (str, c@c', ptp) end

     (* handles autoord <= 3, autoord > 3 handled by all_solve, complete_solve *)

   | autocalc c (pos as (_, p_)) ((pt, _), _(*tacis could help 1x in solve*)) auto =

     if Solve.autoord auto > 3 andalso Ctree.just_created (pt, pos)

     then

       let val ptp = Chead.all_modspec (pt, pos);

       in Solve.all_solve auto c ptp end                    (*... auto = 4 | 5 | 6 *)

     else

       if member op = [Ctree.Pbl, Ctree.Met] p_

       then

         if not (Chead.is_complete_mod (pt, pos))

    	    then

    	      let val ptp = Chead.complete_mod (pt, pos)      (*... auto = 2 | 3 *)

    		    in

    		      if Solve.autoord auto < 3 then ("ok", c, ptp)

    		      else

    		       if not (Chead.is_complete_spec ptp)

    			     then

    			       let val ptp = Chead.complete_spec ptp

    			       in

    			         if Solve.autoord auto = 3 then ("ok", c, ptp) else Solve.all_solve auto c ptp

    			       end

    			     else if Solve.autoord auto = 3 then ("ok", c, ptp) else Solve.all_solve auto c ptp 

    		    end

    	    else 

    		    if not (Chead.is_complete_spec (pt,pos))

    		    then

    		      let val ptp = Chead.complete_spec (pt, pos)

    		      in

    		        if Solve.autoord auto = 3 then ("ok", c, ptp) else Solve.all_solve auto c ptp

    		      end

    		    else

    		      if Solve.autoord auto = 3 then ("ok", c, (pt, pos)) else Solve.all_solve auto c (pt, pos)

    	  else Solve.complete_solve auto c (pt, pos);

 (*.initialiye matching; before 'tryMatch' get the pblID to match with:

    if no pbl has been specified, take the init from origin.*)

 fun initcontext_pbl pt (p, _) =

   let

     val (probl, os, pI, hdl, pI') =

       case Ctree.get_obj I pt p of

         Ctree.PblObj {probl, origin = (os, (_, pI, _), hdl), spec=(_, pI', _), ...}

           => (probl, os, pI, hdl, pI')

       | Ctree.PrfObj _ => error "initcontext_pbl: uncovered case"

   	val pblID =

   	  if pI' = Celem.e_pblID 

   		then (* TODO.WN051125 (#init o get_pbt) pI *) takelast (2, pI)

   		else pI'

   	val {ppc, where_, prls, ...} = Specify.get_pbt pblID

   	val (model_ok, (pbl, pre)) = Specify.match_itms_oris (Celem.assoc_thy "Isac") probl (ppc, where_, prls) os

   in

     (model_ok, pblID, hdl, pbl, pre)

   end

 fun initcontext_met pt (p,_) =

   let

     val (meth, os, mI, mI') =

       case Ctree.get_obj I pt p of

         Ctree.PblObj {meth, origin = (os, (_, _, mI), _), spec=(_, _, mI'), ...} => (meth, os, mI, mI')

       | Ctree.PrfObj _ => error "initcontext_met: uncovered case"

   	val metID = if mI' = Celem.e_metID 

   		    then (*TODO.WN051125 (#init o get_pbt) pI *) takelast (2, mI)

   		    else mI'

   	val {ppc, pre, prls, scr, ...} = Specify.get_met metID

   	val (model_ok, (pbl, pre)) = Specify.match_itms_oris (Celem.assoc_thy "Isac") meth (ppc,pre,prls) os

   in

     (model_ok, metID, scr, pbl, pre)

   end

 (* match the model of a problem at pos p with the model-pattern of the problem with pblID *)

 fun context_pbl pI pt p =

   let

     val (probl, os, hdl) =

       case Ctree.get_obj I pt p of

         Ctree.PblObj {probl,origin = (os, _, hdl),...} => (probl, os, hdl)

       | Ctree.PrfObj _ => error "context_pbl: uncovered case"

   	val {ppc,where_,prls,...} = Specify.get_pbt pI

   	val (model_ok, (pbl, pre)) = Specify.match_itms_oris (Celem.assoc_thy "Isac") probl (ppc,where_,prls) os

   in

     (model_ok, pI, hdl, pbl, pre)

   end

 fun context_met mI pt p =

   let

     val (meth, os) =

       case Ctree.get_obj I pt p of

         Ctree.PblObj {meth, origin = (os, _, _),...} => (meth, os)

       | Ctree.PrfObj _ => error "context_met: uncovered case"

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

   	val (model_ok, (pbl, pre)) = Specify.match_itms_oris (Celem.assoc_thy "Isac") meth (ppc,pre,prls) os

   in

     (model_ok, mI, scr, pbl, pre)

   end

 fun tryrefine pI pt (p,_) =

   let

     val (probl, os, hdl) =

       case Ctree.get_obj I pt p of

         Ctree.PblObj {probl, origin = (os, _, hdl), ...} => (probl, os, hdl)

       | Ctree.PrfObj _ => error "context_met: uncovered case"

   in

     case Specify.refine_pbl (Celem.assoc_thy "Isac") pI probl of

   	  NONE => (*copy from context_pbl*)

   	    let

   	      val {ppc,where_,prls,...} = Specify.get_pbt pI

   	      val (_, (pbl, pre)) = Specify.match_itms_oris (Celem.assoc_thy "Isac") probl (ppc,where_,prls) os

         in

           (false, pI, hdl, pbl, pre)

         end

   	| SOME (pI, (pbl, pre)) => (true, pI, hdl, pbl, pre) 

   end

 fun detailstep pt (pos as (p, _)) = 

   let 

     val nd = Ctree.get_nd pt p

     val cn = Ctree.children nd

   in 

     if null cn 

     then

       if (Tac.is_rewset o (Ctree.get_obj Ctree.g_tac nd)) [(*root of nd*)]

       then Solve.detailrls pt pos

       else ("no-Rewrite_Set...", Ctree.EmptyPtree, Ctree.e_pos')

     else ("donesteps", pt, (p @ [length (Ctree.children (Ctree.get_nd pt p))], Ctree.Res)) 

   end;

 (*** for mathematics authoring on sml-toplevel; no XML ***)

 type NEW = int list;

 (* 15.8.03 for me with loc_specify/solve, nxt_specify/solve

    delete as soon as TESTg_form -> _mout_ dropped           *)

 fun TESTg_form ptp =

   let

     val (form, _, _) = Chead.pt_extract ptp

   in

     case form of

       Ctree.Form t => Generate.FormKF (Rule.term2str t)

     | Ctree.ModSpec (_, p_, _, gfr, pre, _) =>

       Generate.PpcKF (

         (case p_ of Ctree.Pbl => Generate.Problem []

           | Ctree.Met => Generate.Method []

           | _ => error "TESTg_form: uncovered case",

  			Specify.itms2itemppc (Celem.assoc_thy"Isac") gfr pre))

    end

 (* create a calc-tree; for use within sml: thus "^^^" NOT decoded to "^" etc;

    compare "fun CalcTree" which DOES decode                        *)

 fun CalcTreeTEST [(fmz, sp)] = 

   let

     val ((pt, p), tacis) = Chead.nxt_specify_init_calc (fmz, sp)

 	  val tac = case tacis of [] => Tac.Empty_Tac | _ => (#1 o hd) tacis

 	  val f = TESTg_form (pt,p)

   in (p, []:NEW, f, (Tac.tac2IDstr tac, tac), Selem.Sundef, pt) end

 | CalcTreeTEST _ = error "CalcTreeTEST: uncovered case"

 (*for tests > 15.8.03 after separation setnexttactic / nextTac:

   external view: me should be used by math-authors as done so far

   internal view: loc_specify/solve, nxt_specify/solve used

                  i.e. same as in setnexttactic / nextTac*)

 (*ENDE TESTPHASE 08/10.03:

   NEW loeschen, eigene Version von locatetac, step

   meNEW, CalcTreeTEST: tac'_ -replace-> tac, remove [](cid) *)

 fun me (_, tac) p _(*NEW remove*) pt =

   let 

     val (pt, p) = 

 	    (*locatetac is here for testing by me; step would suffice in me*)

 	    case locatetac tac (pt,p) of

 		    ("ok", (_, _, ptp)) => ptp

 	    | ("unsafe-ok", (_, _, ptp)) => ptp

 	    | ("not-applicable",_) => (pt, p)

 	    | ("end-of-calculation", (_, _, ptp)) => ptp

 	    | ("failure", _) => error "sys-error"

 	    | _ => error "me: uncovered case"

 	  val (_, ts) =

 	    (case step p ((pt, Ctree.e_pos'),[]) of

 		    ("ok", (ts as (_, _, _) :: _, _, _)) => ("", ts)

 	    | ("helpless", _) => ("helpless: cannot propose tac", [])

 	    | ("no-fmz-spec", _) => error "no-fmz-spec"

 	    | ("end-of-calculation", (ts, _, _)) => ("", ts)

 	    | _ => error "me: uncovered case")

 	      handle ERROR msg => raise ERROR msg

 	  val tac = 

       case ts of 

         tacis as (_::_) => let val (tac, _, _) = last_elem tacis in tac end 

 		  | _ => if p = ([], Ctree.Res) then Tac.End_Proof' else Tac.Empty_Tac;

   in (p, [] : NEW, TESTg_form (pt, p) (* form output comes from locatetac *), 

 	   (Tac.tac2IDstr tac, tac), Selem.Sundef, pt)

   end

 (* for quick test-print-out, until 'type inout' is removed *)

 fun f2str (Generate.FormKF cterm') = cterm'

   | f2str _ = error "f2str: uncovered case in fun.def.";

 end