(* Title:  interpreter for scripts

    Author: Walther Neuper 2000

    (c) due to copyright terms

 *)

 signature LUCAS_INTERPRETER_TOOL =

 sig

   datatype ass =

     Ass of Tactic.T * term * Proof.context

   | Ass_Weak of Tactic.T * term * Proof.context

   | NotAss;

   val associate: Ctree.ctree -> Proof.context -> (Tactic.T * term) -> ass

   val init_form : 'a -> Program.T -> (term * term) list -> term option

   val init_pstate : Rule.rls -> Proof.context -> Model.itm list -> Celem.metID ->

     Istate.T * Proof.context * Program.T

   val get_simplifier : Calc.T -> Rule.rls

 (*vvv initialise : Rule.theory'(*?!?*) -> Calc.T -> (Istate.T * Proof.context) * Program.T*)

   val resume_prog : Rule.theory' -> Ctree.pos' -> Ctree.ctree -> 

     (Istate.T * Proof.context) * Program.T

   val tac_from_prog : Ctree.ctree -> theory -> term -> Tactic.input

   val check_leaf : string -> Proof.context -> Rule.rls -> (Env.T * (term option * term)) -> term -> 

       Program.leaf * term option

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

   (*NONE*)

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

   val itms2args : 'a -> Celem.metID -> Model.itm list -> term list

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

 end 

 (* traces the leaves (ie. non-tactical nodes) of Prog found by find_next_step, see "and scr" *)   

 val trace_script = Unsynchronized.ref false; (* TODO: how are traces done in Isabelle? *)

 (**)

 structure LItool(**): LUCAS_INTERPRETER_TOOL(**) =

 struct

 (**)

 open Ctree

 open Pos

 (* determine the first tactic in case of a program with one argument (like simplification)

   and without an initial Tactic.Take *)

 fun init_form thy (Rule.Prog prog) env =

     (case Prog_Tac.get_first thy prog of

       NONE => NONE 

     | SOME prog_tac => SOME (subst_atomic env prog_tac))

   | init_form _ _ _ = error "init_form: no match";

 type dsc = typ; (* <-> nam..unknow in Descript.thy *)

 (*.create the actual parameters (args) of script: their order 

   is given by the order in met.pat .*)

 (*WN.5.5.03: ?: does this allow for different descriptions ???

              ?: why not taken from formal args of script ???

 !: FIXXXME penv: push it here in itms2args into script-evaluation*)

 val errmsg = "ERROR: the guard is missing (#ppc in 'type met' added in prep_met)."

 fun errmsg2 d itms = ("itms2args: '" ^ Rule.term2str d ^ "' not in itms:\n" ^

 "itms:\n" ^ Model.itms2str_ @{context} itms)

 fun itms2args _ mI itms =

   let

     val mvat = Model.max_vt itms

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

     val itms = filter (okv mvat) itms

     fun test_dsc d (_, _, _, _, itm_) = (d = Model.d_in itm_)

     fun itm2arg itms (_,(d,_)) =

         case find_first (test_dsc d) itms of

           NONE => raise ERROR (errmsg2 d itms)

         | SOME (_, _, _, _, itm_) => Model.penvval_in itm_

       (*| SOME (_,_,_,_,itm_) => mk_arg thy (Model.d_in itm_) (ts_in itm_);

             penv postponed; presently penv holds already Env.update for script*)

     val pats = (#ppc o Specify.get_met) mI

     val _ = if pats = [] then raise ERROR errmsg else ()

   in (flat o (map (itm2arg itms))) pats end;

 (* convert a Prog_Tac to Tactic.input *)

 fun tac_from_prog _ thy (Const ("Prog_Tac.Rewrite", _) $ thmID $ _) =

     let

       val tid = HOLogic.dest_string thmID

     in (Tactic.Rewrite (tid, Rewrite.assoc_thm'' thy tid)) end

   | tac_from_prog _ thy (Const ("Prog_Tac.Rewrite'_Inst", _) $ sub $ thmID $ _) =

     let

       val tid = HOLogic.dest_string thmID

     in (Tactic.Rewrite_Inst (Selem.subst'_to_sube sub, (tid, Rewrite.assoc_thm'' thy tid))) end

   | tac_from_prog _ _ (Const ("Prog_Tac.Rewrite'_Set",_) $ rls $ _) =

      (Tactic.Rewrite_Set (HOLogic.dest_string rls))

   | tac_from_prog _ _ (Const ("Prog_Tac.Rewrite'_Set'_Inst", _) $ sub $ rls $ _) =

       (Tactic.Rewrite_Set_Inst (Selem.subst'_to_sube sub, HOLogic.dest_string rls))

   | tac_from_prog _ _ (Const ("Prog_Tac.Calculate", _) $ op_ $ _) =

       (Tactic.Calculate (HOLogic.dest_string op_))

   | tac_from_prog _ _ (Const ("Prog_Tac.Take", _) $ t) = (Tactic.Take (Rule.term2str t))

   | tac_from_prog _ _ (Const ("Prog_Tac.Substitute", _) $ isasub $ _) =

     (Tactic.Substitute ((Selem.subte2sube o TermC.isalist2list) isasub))

   | tac_from_prog _ thy (Const("Prog_Tac.Check'_elementwise", _) $ _ $ 

     (Const ("Set.Collect", _) $ Abs (_, _, pred))) =

       (Tactic.Check_elementwise (Rule.term_to_string''' thy pred))

   | tac_from_prog _ _ (Const("Prog_Tac.Or'_to'_List", _) $ _ ) = Tactic.Or_to_List

   | tac_from_prog pt _ (ptac as Const ("Prog_Tac.SubProblem", _) $ _ $ _) =

     fst (Sub_Problem.tac_from_prog pt ptac) (*might involve problem refinement etc*)

   | tac_from_prog _ thy t = error ("stac2tac_ TODO: no match for " ^ Rule.term_to_string''' thy t);

 datatype ass =

     Ass of

       Tactic.T        (* SubProblem gets args instantiated in associate     *)

       * term          (* for itr_arg, result in ets                         *)

       * Proof.context (* separate from Tactic.T like in locate_input_tactic *)

   | Ass_Weak of Tactic.T * term * Proof.context

   | NotAss;

 (* check if tac_ is associated with stac.

    Note: this is the only fun in "fun locate_input_tactic", which handles tactics individually.

    Additional tasks: 

   (1) to "Subproblem'" add "pors, hdl, fmz_, ctxt, f" TODO: ctxt <-?-> sig locate_input_tac

   (2) check if term t (the result has been calculated from) in tac_

    has been changed (see "datatype tac_"); if yes, recalculate result

    TODO.WN120106 recalculate impl.only for Substitute'

 args

   pt     : ctree for pushing the thy specified in rootpbl into subpbls

   d      : unused (planned for data for comparison)

   tac_   : from user (via applicable_in); to be compared with ...

   stac   : found in program

 returns

   Ass    : associated: e.g. thmID in stac = thmID in m

                        +++ arg   in stac = arg   in m

   Ass_Weak: weakly ass.:e.g. thmID in stac = thmID in m, //arg//

   NotAss :             e.g. thmID in stac/=/thmID in m (not =)

 *)

 fun associate _ ctxt (m as Tactic.Rewrite_Inst'

       (_, _, _, _, _, thm'' as (thmID, _), f, (f', asms')), stac) =

     (case stac of

 	    (Const ("Prog_Tac.Rewrite'_Inst", _) $ _ $ thmID_ $ f_) =>

 	      if thmID = HOLogic.dest_string thmID_

         then 

 	        if f = f_ 

           then Ass (m, f', ContextC.insert_assumptions asms' ctxt)

 	        else Ass_Weak (m, f', ContextC.insert_assumptions asms' ctxt)

 	      else ((*tracing"3### associate ..NotAss";*) NotAss)

     | (Const ("Prog_Tac.Rewrite'_Set'_Inst",_) $ _ $ rls_ $ f_) =>

 	      if Rtools.contains_rule (Rule.Thm thm'') (assoc_rls (HOLogic.dest_string rls_))

         then if f = f_ then Ass (m, f', ContextC.insert_assumptions asms' ctxt)

         else Ass_Weak (m, f', ContextC.insert_assumptions asms' ctxt)

 	      else NotAss

     | _ => NotAss)

   | associate _ ctxt (m as Tactic.Rewrite' (_, _, _, _, thm'' as (thmID, _), f, (f', asms')), stac) =

     (case stac of

 	    (Const ("Prog_Tac.Rewrite", _) $ thmID_ $ f_) =>

 	      if thmID = HOLogic.dest_string thmID_

         then 

 	        if f = f_

           then Ass (m, f', ContextC.insert_assumptions asms' ctxt)

 	        else Ass_Weak (m, f', ContextC.insert_assumptions asms' ctxt)

 	      else NotAss

     | (Const ("Prog_Tac.Rewrite'_Set", _) $ rls_ $ f_) =>

 	       if Rtools.contains_rule (Rule.Thm thm'') (assoc_rls (HOLogic.dest_string rls_))

          then

            if f = f_

            then Ass (m, f', ContextC.insert_assumptions asms' ctxt)

 	         else Ass_Weak (m, f', ContextC.insert_assumptions asms' ctxt)

 	       else NotAss

     | _ => NotAss)

   | associate _ ctxt (m as Tactic.Rewrite_Set_Inst' (_, _, _, rls, f, (f', asms')),

       (Const ("Prog_Tac.Rewrite'_Set'_Inst", _) $ _ $ rls_ $ f_)) = 

     if Rule.id_rls rls = HOLogic.dest_string rls_ 

     then

       if f = f_

       then Ass (m, f', ContextC.insert_assumptions asms' ctxt)

       else Ass_Weak (m ,f', ContextC.insert_assumptions asms' ctxt)

     else NotAss

   | associate _ ctxt (m as Tactic.Detail_Set_Inst' (_, _, _, rls, f, (f', asms')),

       (Const ("Prog_Tac.Rewrite'_Set'_Inst", _) $ _ $ rls_ $ f_)) = 

     if Rule.id_rls rls = HOLogic.dest_string rls_

     then

       if f = f_

       then Ass (m, f', ContextC.insert_assumptions asms' ctxt)

       else Ass_Weak (m ,f', ContextC.insert_assumptions asms' ctxt)

     else NotAss

   | associate _ ctxt (m as Tactic.Rewrite_Set' (_, _, rls, f, (f', asms')),

       (Const ("Prog_Tac.Rewrite'_Set", _) $ rls_ $ f_)) = 

     if Rule.id_rls rls = HOLogic.dest_string rls_

     then

       if f = f_

       then Ass (m, f', ContextC.insert_assumptions asms' ctxt)

       else Ass_Weak (m ,f', ContextC.insert_assumptions asms' ctxt)

     else NotAss

   | associate _ ctxt (m as Tactic.Detail_Set' (_, _, rls, f, (f', asms')),

       (Const ("Prog_Tac.Rewrite'_Set", _) $ rls_ $ f_)) = 

     if Rule.id_rls rls = HOLogic.dest_string rls_

     then 

       if f = f_

       then Ass (m, f', ContextC.insert_assumptions asms' ctxt)

       else Ass_Weak (m ,f', ContextC.insert_assumptions asms' ctxt)

     else NotAss

   | associate _ ctxt (m as Tactic.Calculate' (_, op_, f, (f', _)), stac) =

     (case stac of

 	    (Const ("Prog_Tac.Calculate",_) $ op__ $ f_) =>

 	      if op_ = HOLogic.dest_string op__

         then

           if f = f_

           then Ass (m, f', ctxt)

           else Ass_Weak (m ,f', ctxt)

 	      else NotAss

     | (Const ("Prog_Tac.Rewrite'_Set'_Inst", _) $ _ $ rls_ $ f_)  =>

         let val thy = Celem.assoc_thy "Isac_Knowledge";

         in

           if Rtools.contains_rule (Rule.Num_Calc (assoc_calc' thy op_ |> snd)) 

             (assoc_rls (HOLogic.dest_string rls_))

           then

             if f = f_

             then Ass (m, f', ctxt)

             else Ass_Weak (m ,f', ctxt)

           else NotAss

         end

     | (Const ("Prog_Tac.Rewrite'_Set",_) $ rls_ $ f_) =>

         let val thy = Celem.assoc_thy "Isac_Knowledge";

         in

           if Rtools.contains_rule (Rule.Num_Calc (assoc_calc' thy op_ |> snd))

             (assoc_rls (HOLogic.dest_string rls_))

           then

             if f = f_

             then Ass (m, f', ctxt)

             else Ass_Weak (m ,f', ctxt)

           else NotAss

         end

     | _ => NotAss)

   | associate _ ctxt (m as Tactic.Check_elementwise' (consts, _, (consts_chkd, _)),

       (Const ("Prog_Tac.Check'_elementwise",_) $ consts' $ _)) =

     if consts = consts'

     then Ass (m, consts_chkd, ctxt)

     else NotAss

   | associate _ ctxt (m as Tactic.Or_to_List' (_, list), (Const ("Prog_Tac.Or'_to'_List", _) $ _)) =

     Ass (m, list, ctxt)

   | associate _ ctxt (m as Tactic.Take' term, (Const ("Prog_Tac.Take", _) $ _)) = Ass (m, term, ctxt)

   | associate _ ctxt (m as Tactic.Substitute' (ro, erls, subte, f, f'),

       (Const ("Prog_Tac.Substitute", _) $ _ $ t)) =

 	  if f = t then Ass (m, f', ctxt)

 	  else (*compare | applicable_in (p,p_) pt (m as Substitute sube)*)

 		  if foldl and_ (true, map TermC.contains_Var subte)

 		  then

 		    let val t' = subst_atomic (map HOLogic.dest_eq subte (*TODO subte2subst*)) t

 		    in if t = t' then error "associate: Substitute' not applicable to val of Expr"

 		       else Ass (Tactic.Substitute' (ro, erls, subte, t, t'), t', ctxt)

 		    end

 		  else (case Rewrite.rewrite_terms_ (Rule.Isac ()) ro erls subte t of

 		         SOME (t', _) =>  Ass (Tactic.Substitute' (ro, erls, subte, t, t'), t', ctxt)

 		       | NONE => error "associate: Substitute' not applicable to val of Expr")

   | associate pt ctxt (Tactic.Subproblem' ((domID, pblID, _), _, _, _, _, _),

       (stac as Const ("Prog_Tac.SubProblem", _) $ _ $ _)) =

     (case Sub_Problem.tac_from_prog pt stac of

       (_, tac as Tactic.Subproblem' ((dI, pI, _), _, _, _, _, f)) =>

         if domID = dI andalso pblID = pI

         then Ass (tac, f, ctxt)

         else NotAss

     | _ => raise ERROR ("associate: uncovered case"))

   | associate _ _ (m, _) = 

     (if (!trace_script) 

      then tracing("@@@ the 'tac_' proposed to apply does NOT match the leaf found in the script:\n"

 		   ^ "@@@ tac_ = " ^ Tactic.string_of m)

      else ();

     NotAss);

 (* create the initial interpreter state

   from the items of the guard and the formal arguments of the partial_function.

 Note on progression from (a) type fmz_ \<longrightarrow> (e) arguments of the partial_function:

   (a) fmz is given by a math author

   (b) fmz_ is transformed to ori list as a prerequisite for efficient interactive modelling

   (c) modelling creates an itm list from ori list + possible user input

   (d) specifying a theory might add some items and create a guard for the partial_function

   (e) fun relate_args creates an environment for evaluating the partial_function.

 Note on sequence-relation (a) -- (e), i.e. the (formal) arguments of the partial_function:

   * Since the arguments of the partial_function have no description (see Descript.thy),

     (e) depends on the sequence in fmz_ and on the types of the formal arguments.

   * pairing formal arguments with itm's follows the sequence

   * Thus the resulting sequence-relation can be ambiguous.

   * Ambiguities are done by rearranging fmz_ or the formal arguments.

   * The latter is easier, albeit not optimal: a fmz_ can be used by different partial_functions.

   *)

 local

 val errmsg = "ERROR: found no actual arguments for prog. of "

 fun msg_miss sc metID caller f formals actuals =

   "ERROR in creating the environment from formal args. of partial_function \"" ^ fst (Program.get_fun_id sc) ^ "\"\n" ^

 	"and the actual args., ie. items of the guard of \"" ^ Celem.metID2str metID ^ "\" by \"" ^ caller ^ "\":\n" ^

 	"formal arg \"" ^ Rule.term2str f ^ "\" doesn't mach an actual arg.\n" ^

 	"with:\n" ^

 	(string_of_int o length) formals ^ " formal args: " ^ Rule.terms2str formals ^ "\n" ^

 	(string_of_int o length) actuals ^ " actual args: " ^ Rule.terms2str actuals

 fun msg_miss_type sc metID f formals actuals =

   "ERROR in creating the environment from formal args. of partial_function \"" ^ fst (Program.get_fun_id sc) ^ "\"\n" ^

 	"and the actual args., ie. items of the guard of \"" ^ Celem.metID2str metID ^ "\" by \"assoc_by_type\":\n" ^

 	"formal arg \"" ^ Rule.term2str f ^ "\" of type \"" ^ Rule.type2str (type_of f) ^

   "\" doesn't mach an actual arg.\nwith:\n" ^

 	(string_of_int o length) formals ^ " formal args: " ^ Rule.terms2str formals ^ "\n" ^

 	(string_of_int o length) actuals ^ " actual args: " ^ Rule.terms2str actuals ^ "\n" ^

   "   with types: " ^ (strs2str o (map (Rule.type2str o type_of))) actuals

 fun msg_ambiguous sc metID f aas formals actuals =

   "AMBIGUITY in creating the environment from formal args. of partial_function \"" ^ fst (Program.get_fun_id sc) ^ "\"\n" ^

 	"and the actual args., ie. items of the guard of \"" ^ Celem.metID2str metID ^ "\" by \"assoc_by_type\":\n" ^

   "formal arg. \"" ^ Rule.term2str f ^ "\" type-matches with several..."  ^

   "actual args. \"" ^ Rule.terms2str aas ^ "\"\n" ^

   "selected \"" ^ Rule.term2str (hd aas) ^ "\"\n" ^

 	"with\n" ^

 	"formals: " ^ Rule.terms2str formals ^ "\n" ^

 	"actuals: " ^ Rule.terms2str actuals

 fun trace_init metID =

   if (!trace_script) 

   then tracing("@@@ program " ^ strs2str metID)

   else ();

 in

 fun init_pstate srls ctxt itms metID =

   let

     val itms = Specify.hack_until_review_Specify_2 metID itms

     val actuals = itms2args (Proof_Context.theory_of ctxt) metID itms

     val _ = if actuals <> [] then () else raise ERROR (errmsg ^ strs2str' metID)

     val (scr, sc) = (case (#scr o Specify.get_met) metID of

            scr as Rule.Prog sc => (trace_init metID; (scr, sc))

        | _ => raise ERROR ("init_pstate with " ^ Celem.metID2str metID))

     val formals = Program.formal_args sc    

     fun assoc_by_type f aa =

       case filter (curry (fn (f, a) => type_of f = type_of a) f) aa of

         [] => error (msg_miss_type sc metID f formals actuals)

       | [a] => (f, a)

       | aas as (a :: _) => (writeln (msg_ambiguous sc metID f aas formals actuals); (f, a));

 	  fun relate_args _ (f::_)  [] = error (msg_miss sc metID "relate_args" f formals actuals)

 	    | relate_args env [] _ = env (*may drop Find?*)

 	    | relate_args env (f::ff) (aas as (a::aa)) = 

 	      if type_of f = type_of a 

 	      then relate_args (env @ [(f, a)]) ff aa

         else

           let val (f, a) = assoc_by_type f aas

           in relate_args (env @ [(f, a)]) ff (remove op = a aas) end

     val {pre, prls, ...} = Specify.get_met metID;

     val pres = Stool.check_preconds (Proof_Context.theory_of ctxt) prls pre itms |> map snd;

     val ctxt = ctxt |> ContextC.insert_assumptions pres;

     val ist = Istate.e_pstate

       |> Istate.set_eval srls

       |> Istate.set_env_true (relate_args [] formals actuals)

   in

     (Istate.Pstate ist, ctxt, scr)

   end;

 end (*local*)

 fun get_simplifier (pt, (p, _)) =

   let

     val p' = Ctree.par_pblobj pt p

 	  val metID = Ctree.get_obj Ctree.g_metID pt p'

 	  val {srls, ...} = Specify.get_met metID

   in srls end

 fun resume_prog thy (p, p_) pt =

   let

     val (is_problem, p', rls') = parent_node pt p

   in

     if is_problem

     then

       let

 	      val metID = get_obj g_metID pt p'

 	      val {srls, ...} = Specify.get_met metID

 	      val (is, ctxt) =

 	        case get_loc pt (p, p_) of

 	           (Istate.Pstate ist, ctxt) => (Istate.Pstate (Istate.set_eval srls ist), ctxt)

 	        | _ => raise ERROR "resume_prog: unexpected result from get_loc"

 	    in ((is, ctxt), (#scr o Specify.get_met) metID) end

     else                                                                                (* 3 *)

       (get_loc pt (p, p_),

       Rule.Prog (Auto_Prog.gen (Celem.assoc_thy thy) (get_last_formula (pt, (p, p_))) rls'))

   end

 (* handle a leaf at the end of recursive descent; a leaf is either a Prog_Tac or a Prog_Expr.

   TODO: what is a' ??? *)

 fun check_leaf call ctxt srls (E, (a, v)) t =

     case Prog_Tac.eval_leaf E a v t of

 	    (Program.Tac stac, a') =>

 	      let val stac' =

             Rewrite.eval_prog_expr (Proof_Context.theory_of ctxt) srls 

               (subst_atomic (Env.update_opt E (a, v)) stac)

 	      in

           (if (! trace_script) 

 	         then tracing ("@@@ " ^ call ^ " leaf '" ^ Rule.term2str t ^ "' ---> Tac '" ^ Rule.term2str stac ^ "'")

 	         else ();

 	         (Program.Tac stac', a'))

 	      end

     | (Program.Expr lexpr, a') =>

 	      let val lexpr' =

             Rewrite.eval_prog_expr (Proof_Context.theory_of ctxt) srls

               (subst_atomic (Env.update_opt E (a, v)) lexpr)

 	      in

           (if (! trace_script) 

 	         then tracing("@@@ " ^ call ^ " leaf '" ^ Rule.term2str t ^ "' ---> Expr '" ^ Rule.term2str lexpr' ^ "'")

 	         else ();

 	         (Program.Expr lexpr', a'))

 	      end;

 (**)end(**)