(* 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))

  | 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 =>

	           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 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, 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 => 

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

(*.specify a new problem;

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

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 *)

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

	      (_::_) => 

          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. Add_Given "equality///"*) of

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

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

	    | _ => (case pIopt of

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

		          | SOME pI =>

		            (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;

(*.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 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 =

     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") 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") 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") 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") 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") 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") 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") 

						     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") 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] = 

  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) *)

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

  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";

	  val (_, ts) = (*WN101102 TODO: locatetac + step create _same_ (pt,p) ?*)

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

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

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

	   (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;

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