(* 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

use"mathengine.sml";

*)

signature MATHENGINE =

  sig

    type nxt_

    (* datatype nxt_ = HElpless | Nexts of CalcHead.calcstate *)

    type NEW

    type lOc_

    (*datatype

      lOc_ =

          ERror of string

        | UNsafe of CalcHead.calcstate'

        | Updated of CalcHead.calcstate' *)

    val CalcTreeTEST :

       fmz list ->

       pos' * NEW * mout * (string * tac) * safe * ptree

    val TESTg_form : ptree * (int list * pos_) -> mout

    val autocalc :

       pos' list ->

       pos' ->

       (ptree * pos') * taci list ->

       auto -> string * pos' list * (ptree * pos')

    val detailstep : ptree -> pos' -> string * ptree * pos'

   (* val e_tac_ : tac_ *)

    val f2str : mout -> cterm'

   (* val get_pblID : ptree * pos' -> pblID option *)

    val initmatch : ptree -> pos' -> ptform

   (* val loc_solve_ :

       string * tac_ -> ptree * (int list * pos_) -> lOc_ *)

   (* val loc_specify_ : tac_ -> ptree * pos' -> lOc_ *)

    val locatetac :     (*tests only*)

       tac ->

       ptree * (posel list * pos_) ->

       string * (taci list * pos' list * (ptree * (posel list * pos_)))

    val me :

       tac'_ ->

       pos' ->

       NEW ->

       ptree -> pos' * NEW * mout * tac'_ * safe * ptree

    val nxt_specify_ : ptree * (int list * pos_) -> calcstate'(*tests only*)

    val set_method : metID -> ptree * pos' -> ptree * ocalhd

    val set_problem : pblID -> ptree * pos' -> ptree * ocalhd

    val set_theory : thyID -> ptree * pos' -> ptree * ocalhd

    val step : pos' -> calcstate -> string * calcstate'

    val trymatch : pblID -> ptree -> pos' -> ptform

    val tryrefine : pblID -> ptree -> pos' -> ptform

  end

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

structure MathEngine : MATHENGINE =

struct

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

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

    let val p' = par_pblobj pt p

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

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

    in if pI <> e_pblID then SOME pI

       else if oI <> e_pblID then SOME oI

       else NONE end;

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

    ((snd3 o (get_obj g_spec pt)) (par_pblobj pt p));*)

(*--vvv--dummies for test*)

val e_tac_ = Tac_ (Pure.thy,"","","");

datatype lOc_ =

  ERror of string         (*after loc_specify, loc_solve*)

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

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

fun loc_specify_ m (pt,pos) =

(* val pos = ip;

   *)

    let val (p,_,f,_,s,pt) = specify m pos [] pt;

(*      val (_,_,_,_,_,pt')= specify m pos [] pt;

   *) 

   in case f of

	   (Error' (Error_ e)) => ERror e

	 | _ => Updated ([], [], (pt,p)) end;

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

(* val (m, pos) = ((mI,m), ip);

   val (m,(pt,pos) ) = ((mI,m), ptp);

   *)  

fun loc_solve_ m (pt,pos) =

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

(* val (tacis,dels,(pt',p')) = cs';

   (tracing o istate2str) (get_istate pt' p');

   (term2str o fst) (get_obj g_result pt' (fst p'));

   *)

    in case msg of

	   "ok" => Updated cs' 

	 | msg => ERror msg 

    end;

datatype nxt_ =

	 HElpless  (**)

       | Nexts of calcstate; (**)

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

(*report applicability of tac in tacis; pt is dropped in setNextTactic*)

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

(* val ptp as (pt, p) = (pt, p);

   val ptp as (pt, p) = (pt, ip);

   *)

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

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

    in case applicable_in p pt m of

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

	 | Appl m =>

(* val Appl m = applicable_in p pt m;

    *) 

	   let val x = if member op = specsteps mI

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

	   in case x of 

		  ERror e => ("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' = ([],Res) then "end-of-calculation" else "ok", 

		   cs')(*for -"-  user to ask ? *)

	   end

    end;

(*------------------------------------------------------------------

fun init_detail ptp = e_calcstate;(*15.8.03.MISSING-->solve.sml!?*)

(*----------------------------------------------------from solve.sml*)

  | nxt_solv (Detail_Set'(thy', rls, t)) (pt, p) =

    let (*val rls = the (assoc(!ruleset',rls'))

	    handle _ => error ("solve: '"^rls'^"' not known");*)

	val thy = assoc_thy thy';

        val (srls, sc, is) = 

	    case rls of

		Rrls {scr=sc as Rfuns {init_state=ii,...},...} => 

		(e_rls, sc, RrlsState (ii t))

	      | Rls {srls=srls,scr=sc as Script s,...} => 

		(srls, sc, ScrState ([(one_scr_arg s,t)], [], 

			       NONE, e_term, Sundef, true));

	val pt = update_tac pt (fst p) (Detail_Set (id_rls rls));

	val (p,cid,_,pt) = generate1 thy (Begin_Trans' t) is p pt;

	val nx = (tac_2tac o fst3) (next_tac (thy',srls) (pt,p) sc is);

	val aopt = applicable_in p pt nx;

    in case aopt of

	   Notappl s => error ("solve Detail_Set: "^s)

	 (* val Appl m = aopt;

	    *)

	 | Appl m => solve ("discardFIXME",m) p pt end

------------------------------------------------------------------*)

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

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

(* val (ptp as (pt, pos as (p,p_))) = ptp;

   val (ptp as (pt, pos as (p,p_))) = (pt,ip);

   *)

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

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

			      probl,spec=(dI,pI,mI),...}) = get_obj I pt p;

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

       then case mI' of

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

       | _ => nxt_specif Model_Problem (pt, (p,Pbl))

       else let val cpI = if pI = e_pblID then pI' else pI;

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

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

		val pre = 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) =

		    nxt_spec p_ pb oris (dI',pI',mI') (probl, meth) 

			     (ppc, (#ppc o get_met) cmI) (dI, pI, mI);

	    in case tac of

		   Apply_Method mI => 

(* val Apply_Method mI = tac;

   *)

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

		 | _ => nxt_specif tac ptp end

    end;

(*.specify a new method;

   WN0512 impl.incomplete, see 'nxt_specif (Specify_Method ' .*)

fun set_method (mI:metID) ptp =

    let val ([(_, Specify_Method' (_, _, mits), _)], [], (pt, pos as (p,_))) = 

	    nxt_specif (Specify_Method mI) ptp

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

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

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

	val PblObj {origin = (_,_,hdf), spec,...} = get_obj I pt p

    in (pt, (complete, Met, hdf, mits, pre, spec):ocalhd) end;

(* val ([(_, Specify_Method' (_, _, mits), _)], [],_) = 

    nxt_specif (Specify_Method mI) ptp;

 *)

(*.specify a new problem;

   WN0512 impl.incomplete, see 'nxt_specif (Specify_Problem ' .*)

(* val (pI, ptp) = (pI, (pt, ip));

   *)

fun set_problem pI (ptp: ptree * pos') =

    let val ([(_, Specify_Problem' (_, (complete, (pits, pre))),_)],

	     _, (pt, pos as (p,_))) = nxt_specif (Specify_Problem pI) ptp

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

	val PblObj {origin = (_,_,hdf), spec,...} = get_obj I pt p

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

fun set_theory (tI:thyID) (ptp: ptree * pos') =

    let val ([(_, Specify_Problem' (_, (complete, (pits, pre))),_)],

	     _, (pt, pos as (p,_))) = nxt_specif (Specify_Theory tI) ptp

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

	val PblObj {origin = (_,_,hdf), spec,...} = get_obj I pt p

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

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

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

arg ip: 

    calcstate

.*)

(* val (ip as (_,p_), (ptp as (pt,p), tacis)) = (get_pos 1 1, get_calc 1);

   val (ip as (_,p_), (ptp as (pt,p), tacis)) = (pos, cs);

   val (ip as (_,p_), (ptp as (pt,p), tacis)) = (p, ((pt, e_pos'),[]));

   val (ip as (_,p_), (ptp as (pt,p), tacis)) = (ip,cs);

   *)

fun step ((ip as (_,p_)):pos') ((ptp as (pt,p), tacis):calcstate) =

    let val pIopt = get_pblID (pt,ip);

    in if (*p = ([],Res) orelse*) ip = ([],Res)

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

       case tacis of

	   (_::_) =>

(* val((tac,_,_)::_) = tacis;

   *) 

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

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

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

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

		       then nxt_specify_ (pt,ip) else nxt_solve_ (pt,ip))

		      handle _ => ([],[],ptp)(*e.g.by Add_Given "equality///"*)

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

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

(* val [] = tacis;

   *) 

	 | _ => (case pIopt of

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

		   | SOME pI =>

(* val SOME pI = pIopt; 

   val cs=(if member op = [Pbl,Met] p_ andalso is_none(get_obj g_env pt (fst p))

	     then nxt_specify_ (pt,ip) else nxt_solve_ (pt,ip))

       handle _ => ([], ptp);

   *)

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

			       andalso is_none (get_obj g_env pt (fst p))

			    (*^^^^^^^^: Apply_Method without init_form*)

			    then nxt_specify_ (pt,ip) else nxt_solve_ (pt,ip) )

			   handle _ => ([],[],ptp)(*e.g.by Add_Giv"equality/"*)

		       of cs as ([],_,_) =>("helpless", cs)(*FIXXMEdel.handle*)

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

    end;

(*  (nxt_solve_ (pt,ip)) handle e => print_exn e ;

   *)

(*.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 !!!*)

(* val (ip, cs as (ptp as (pt,p),tacis)) = (get_pos cI 1, get_calc cI);

   val (ip, cs as (ptp as (pt,p),tacis)) = (pold, get_calc cI);

   val (c, ip, cs as (ptp as (_,p),tacis), Step s) = 

       ([]:pos' list, pold, get_calc cI, auto);

   *) 

fun autocalc c ip (cs as (ptp as (_,p),tacis)) (Step s) =

    if s <= 1

    then let val (str, (_, c', ptp)) = step ip cs;(*1*)

	 (*at least does 1 step, ev.1 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,[]) (Step (s-1))

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

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

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

(* val (c:pos' list, (pos as (_,p_)),((pt,_),_),auto) = 

      ([], pold, get_calc cI, auto);

   *)

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

     then let val ptp = all_modspec (pt, pos);

	  in all_solve auto c ptp end

     else

	 if member op = [Pbl, Met] p_

 	 then if not (is_complete_mod (pt, pos))

	      then let val ptp = complete_mod (pt, pos)

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

		      else 

			  if not (is_complete_spec ptp)

			  then let val ptp = complete_spec ptp

			       in if autoord auto = 3 then ("ok", c, ptp)

				  else all_solve auto c ptp

			       end

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

			  else all_solve auto c ptp 

		   end

	      else 

		  if not (is_complete_spec (pt,pos))

		  then let val ptp = complete_spec (pt, pos)

		       in if autoord auto = 3 then ("ok", c, ptp)

			  else all_solve auto c ptp

		       end

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

		  else all_solve auto c (pt, pos)

	 else complete_solve auto c (pt, pos);

(* val pbl = get_obj g_pbl (fst ptp) [];

   val (oris,_,_) = get_obj g_origin (fst ptp) [];

*)    

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

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

(*fun initmatch pt (pos as (p,_):pos') =

    let val PblObj {probl,origin=(os,(_,pI,_),_),spec=(dI',pI',mI'),...} = 

	    get_obj I pt p

	val pblID = if pI' = e_pblID 

		    then (*TODO.WN051125 (#init o get_pbt) pI          <<<*) 

			takelast (2, pI) (*FIXME.WN051125 a hack, impl.^^^*)

		    else pI'

	val spec = (dI',pblID,mI')

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

	val (model_ok, (pbl, pre)) = 

	    match_itms_oris (assoc_thy "Isac.thy") probl (ppc,where_,prls) os

    in ModSpec (ocalhd_complete pbl pre spec,

		Pbl, e_term, pbl, pre, spec) end;*)

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

    let val PblObj {probl,origin=(os,(_,pI,_),hdl),spec=(dI',pI',mI'),...} = 

	    get_obj I pt p

	val pblID = if pI' = e_pblID 

		    then (*TODO.WN051125 (#init o get_pbt) pI          <<<*) 

			takelast (2, pI) (*FIXME.WN051125 a hack, impl.^^^*)

		    else pI'

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

	val (model_ok, (pbl, pre)) = 

	    match_itms_oris (assoc_thy "Isac.thy") probl (ppc,where_,prls) os

    in (model_ok, pblID, hdl, pbl, pre) end;

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

    let val PblObj {meth,origin=(os,(_,_,mI), _),spec=(_, _, mI'),...} = 

	    get_obj I pt p

	val metID = if mI' = e_metID 

		    then (*TODO.WN051125 (#init o get_pbt) pI          <<<*) 

			takelast (2, mI) (*FIXME.WN051125 a hack, impl.^^^*)

		    else mI'

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

	val (model_ok, (pbl, pre)) = 

	    match_itms_oris (assoc_thy "Isac.thy") 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:pos) =

    let val PblObj {probl,origin=(os,_,hdl),...} = get_obj I pt p

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

	val (model_ok, (pbl, pre)) = 

	    match_itms_oris (assoc_thy "Isac.thy") probl (ppc,where_,prls) os

    in (model_ok, pI, hdl, pbl, pre) end;

fun context_met mI pt (p:pos) =

    let val PblObj {meth,origin=(os,_,hdl),...} = get_obj I pt p

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

	val (model_ok, (pbl, pre)) = 

	    match_itms_oris (assoc_thy "Isac.thy") meth (ppc,pre,prls) os

    in (model_ok, mI, scr, pbl, pre) end

(* val (pI, pt, pos as (p,_)) = (pblID, pt, p);

   *)

fun tryrefine pI pt (pos as (p,_):pos') =

    let val PblObj {probl,origin=(os,_,hdl),...} = get_obj I pt p

    in case refine_pbl (assoc_thy "Isac.thy") pI probl of

	   NONE => (*copy from context_pbl*)

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

	       val (_, (pbl, pre)) = match_itms_oris (assoc_thy "Isac.thy") 

						     probl (ppc,where_,prls) os

	   in (false, pI, hdl, pbl, pre) end

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

	   (true, pI, hdl, pbl, pre) 

    end;

(* val (pt, (pos as (p,p_):pos')) = (pt, ip);

   *)

fun detailstep pt (pos as (p,p_):pos') = 

    let val nd = get_nd pt p

	val cn = children nd

    in if null cn 

       then if (is_rewset o (get_obj g_tac nd)) [(*root of nd*)]

	    then detailrls pt pos

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

       else ("donesteps", pt(*, get_formress [] ((lev_on o lev_dn) p) cn*),

	     (p @ [length (children (get_nd pt p))], Res) ) 

    end;

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

type NEW = int list;

(* val sp = (dI',pI',mI');

   *)

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

 delete as soon as TESTg_form -> _mout_ dropped*)

fun TESTg_form ptp =

(* val ptp = (pt,p);

   *) 

    let val (form,_,_) = pt_extract ptp

    in case form of

	   Form t => Form' (FormKF (~1,EdUndef,0,Nundef,term2str t))

	 | ModSpec (_,p_, head, gfr, pre, _) => 

	   Form' (PpcKF (0,EdUndef,0,Nundef,

			 (case p_ of Pbl => Problem[] | Met => Method[],

			  itms2itemppc (assoc_thy"Isac.thy") gfr pre)))

    end;

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

   compare "fun CalcTree" which DOES decode.*)

fun CalcTreeTEST [(fmz, sp):fmz] = 

(* val [(fmz, sp):fmz] = [(fmz, (dI',pI',mI'))];

   val [(fmz, sp):fmz] = [([], ("e_domID", ["e_pblID"], ["e_metID"]))];

   *)

    let val cs as ((pt,p), tacis) = nxt_specify_init_calc (fmz, sp)

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

	val f = TESTg_form (pt,p)

    in (p, []:NEW, f, (tac2IDstr tac, tac), Sundef, pt) end; 

(*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) *)

(* val ((_,tac), p, _, pt) = (nxt, p, c, pt);

   *)

fun me ((_,tac):tac'_) (p:pos') (_:NEW(*remove*)) (pt:ptree) =

    let val (pt, p) = 

(* val (msg, (tacis, pos's, (pt',p'))) = locatetac tac (pt,p);

   p = ([1, 9], Res);

   (tracing o istate2str) (get_istate 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";

	val (_, ts) = 

(* val (eee, (ts, _, (pt'',_))) = step p ((pt, e_pos'),[]);

   *)

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

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

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

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

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

	    handle _ => error "sys-error";

	val tac = case ts of tacis as (_::_) =>

(* val tacis as (_::_) = ts;

   *)

			     let val (tac,_,_) = last_elem tacis

			     in tac end 

			   | _ => if p = ([],Res) then End_Proof'

				  else Empty_Tac;

      (*form output comes from locatetac*)

    in(p:pos',[]:NEW, TESTg_form (pt, p), 

	(tac2IDstr tac, tac):tac'_, Sundef, pt)  end;

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

fun f2str (Form' (FormKF (_, _, _, _, cterm'))) = cterm';

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

end

open MathEngine;

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