(* Title:  Interpret/lucas-interpreter.sml

    Author: Walther Neuper 2019

    (c) due to copyright terms

 *)

 signature LUCAS_INTERPRETER =

 sig

   datatype input_tactic_result =

       Safe_Step of Istate.T * Proof.context * Tactic.T

     | Unsafe_Step of Istate.T * Proof.context * Tactic.T

     | Not_Locatable of string

   val locate_input_tactic: Rule.program -> Ctree.state -> Istate.T -> Proof.context -> Tactic.T

     -> input_tactic_result

   datatype next_tactic_result =

       Next_Step of Istate.T * Proof.context * Tactic.T

     | Helpless | End_Program of Istate.T * Tactic.T

   val find_next_tactic: Rule.program -> Ctree.state -> Istate.T -> Proof.context

     -> next_tactic_result

 (*TODO      input_formula_result = Found_Step of  Ctree.state | Not_Derivable *)

   datatype input_formula_result =

     Found_Step of Ctree.state * Istate.T * Proof.context

   | Not_Derivable of Chead.calcstate'

 (*TODOlocate_input_formula: Ctree.state -> term -> input_formula_result *)

   val locate_input_formula: Rule.program -> Ctree.state -> Istate.T -> Proof.context -> term

     -> input_formula_result

   (* must reside here:

      find_next_tactic calls do_next and is called by by_tactic;

      by_tactic and do_next are mutually recursive via by_tactic Apply_Method'

    *)

   val by_tactic: Tactic.T -> Istate.T * Proof.context -> Ctree.state -> string * Chead.calcstate'

   val do_next: Ctree.state -> string * Chead.calcstate'

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

   datatype expr_val1 =

       Accept_Tac1 of Istate.pstate * Proof.context * Tactic.T

     | Reject_Tac1 of Istate.pstate * Proof.context * Tactic.T

     | Term_Val1 of term;

   val assoc2str: expr_val1 -> string

 (* ---- for paper on Lucas-Interpretation ------------------------------------------- --------- *)

   val at_location: TermC.path -> term -> term

   val check_Seq_up: Istate.pstate -> term -> term

   datatype expr_val2 = Accept_Tac2 of Tactic.T * Istate.pstate * Proof.context

     | Reject_Tac2 | Term_Val2 of term

   val scan_dn2: Ctree.state * Proof.context -> Istate.pstate -> term -> expr_val2

   val scan_up2: term * (Ctree.state * Proof.context) -> Istate.pstate -> term -> expr_val2

   val go_scan_up2: term * (Ctree.state * Proof.context) -> Istate.pstate -> expr_val2

   val scan_to_tactic2: term * (Ctree.state * Proof.context) -> Istate.T -> expr_val2

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

   val go_up: TermC.path -> term -> term

   val check_Let_up: Istate.pstate -> term -> term * term

   val compare_step: Generate.taci list * Ctree.pos' list * (Ctree.state) -> term -> string * Chead.calcstate'

   val scan_dn1: (Ctree.state * Proof.context * Tactic.T) -> Istate.pstate -> term -> expr_val1

   val scan_up1: term * (Ctree.state * Proof.context * Tactic.T) -> Istate.pstate -> term -> expr_val1;

   val go_scan_up1: term * (Ctree.state * Proof.context * Tactic.T) -> Istate.pstate -> expr_val1;

   val scan_to_tactic1: term * (Ctree.state * Proof.context * Tactic.T) -> Istate.T -> expr_val1

   val interpret_tac1: Ctree.state * Proof.context * Tactic.T -> Istate.pstate -> term option * term -> expr_val1

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

 end

 (**)

 structure LucinNEW(**): LUCAS_INTERPRETER(**) = (*LucinNEW \<rightarrow> Lucin after code re-arrangement*)

 struct

 (**)

 open Ctree

 open Pos

 open TermC

 open Istate

 (*** auxiliary functions ***)

 (*go to a location in a program and fetch the resective sub-term*)

 fun at_location [] t = t

   | at_location (D :: p) (Abs(_, _, body)) = at_location (p : TermC.path) body

   | at_location (L :: p) (t1 $ _) = at_location p t1

   | at_location (R :: p) (_ $ t2) = at_location p t2

   | at_location l _ = error ("at_location: no " ^ TermC.path2str l);

 fun go_up l t =

   if length l > 1 then at_location (drop_last l) t else raise ERROR ("go_up [] " ^ Rule.term2str t)

 fun check_Let_up ({path, ...}: pstate) prog =

   case at_location (drop_last path) prog of

     Const ("HOL.Let",_) $ _ $ (Abs (i, T, body)) => (TermC.mk_Free (i, T), body)

   | t => raise ERROR ("scan_up1..\"HOL.Let $ _\" with: \"" ^ Rule.term2str t ^ "\"")

 fun check_Seq_up  ({path, ...}: pstate) prog =

   case at_location (drop_last path) prog of

     Const ("Tactical.Chain",_) $ _ $ e2=> e2

   | t => raise ERROR ("scan_up1..\"Tactical.Chain $ _\" with: \"" ^ Rule.term2str t ^ "\"")

 (*** locate an input tactic within a program ***)

 datatype input_tactic_result =

     Safe_Step of Istate.T * Proof.context * Tactic.T

   | Unsafe_Step of Istate.T * Proof.context * Tactic.T

   | Not_Locatable of string

 datatype expr_val1 = (* "ExprVal" in the sense of denotational semantics        *)

   Reject_Tac1 of     (* tactic is found but NOT acknowledged, scan is continued *)

     Istate.pstate * Proof.context * Tactic.T (*TODO: revise Pstate {or,...},no args as Reject_Tac2*)

 | Accept_Tac1 of       (* tactic is found and acknowledged, scan is stalled       *)

     Istate.pstate *  (* the current state, returned for resuming execution      *)

     Proof.context *  (* updated according to evaluation of Prog_Tac             *)

     Tactic.T         (* Prog_Tac is associated to Tactic.input                  *)

 | Term_Val1 of       (* Prog_Expr is found and evaluated, scan is continued     *)

 	  term             (* value of Prog_Expr, for updating environment            *)

 fun assoc2str (Accept_Tac1 _) = "Accept_Tac1"                                         

   | assoc2str (Term_Val1 _) = "Term_Val1"

   | assoc2str (Reject_Tac1 _) = "Reject_Tac1";

 (** interpret a Prog_Tac: is it associated to Tactic ? **)

 fun interpret_tac1 ((pt, p), ctxt, tac) (ist as {act_arg, or, ...}) (form_arg, prog_tac) =

   case Lucin.associate pt ctxt (tac, prog_tac) of

      (* HERE ----------------vvvv ContextC.insert_assumptions asm ctxt DONE -- 2nd in gen//*)

       Lucin.Ass      (m, v', ctxt) => Accept_Tac1 (ist |> set_subst_true  (form_arg, v'), ctxt, m)

     | Lucin.Ass_Weak (m, v', ctxt) => Accept_Tac1 (ist |> set_subst_false (form_arg, v'), ctxt, m)

     | Lucin.NotAss =>

       (case or of (* switch for Tactical.Or: 1st AssOnly, 2nd AssGen *)

          AssOnly => Term_Val1 act_arg

        | _(*ORundef*) =>

           case Applicable.applicable_in p pt (Lucin.stac2tac pt (Celem.assoc_thy "Isac_Knowledge") prog_tac) of

              Applicable.Appl m' => Reject_Tac1 (ist |> set_subst_false (form_arg, Tactic.result m'), ctxt, tac)

            | Applicable.Notappl _ => Term_Val1 act_arg)

 (** scan to a Prog_Tac **)

 fun scan_dn1 cct ist (Const ("Tactical.Try"(*1*), _) $ e $ a) =

     (case scan_dn1 cct (ist |> path_down_form ([L, R], a)) e of goback => goback) 

   | scan_dn1 cct ist (Const ("Tactical.Try"(*2*), _) $ e) =

     (case scan_dn1 cct (ist |> path_down [R]) e of goback => goback)

   | scan_dn1 cct ist (Const ("Tactical.Repeat"(*1*), _) $ e $ a) =

     scan_dn1 cct (ist |> path_down_form ([L, R], a)) e

   | scan_dn1 cct ist (Const ("Tactical.Repeat"(*2*), _) $ e) =

     scan_dn1 cct (ist |> path_down [R]) e

   | scan_dn1 (cct as (cstate, _, _)) ist (Const ("Tactical.Chain"(*1*), _) $ e1 $ e2 $ a) =

     (case scan_dn1 cct (ist |> path_down_form ([L, L, R], a)) e1 of

 	     Term_Val1 v => scan_dn1 cct (ist |> path_down [L, R] |> set_subst' (a, v)) e2

      | Reject_Tac1 (ist', ctxt', tac') => scan_dn1 (cstate, ctxt', tac') (ist

         |> path_down_form ([L, R], a) |> trans_env_act ist') e2

      | goback => goback)

   | scan_dn1 (cct as (cstate, _, _)) ist (Const ("Tactical.Chain"(*2*), _) $e1 $ e2) =

     (case scan_dn1 cct (ist |> path_down [L, R]) e1 of

 	     Term_Val1 v => scan_dn1 cct (ist |> path_down [R] |> set_act v) e2

      | Reject_Tac1 (ist', ctxt', tac') =>

         scan_dn1 (cstate, ctxt', tac') (ist |> path_down [R] |> trans_env_act ist') e2

      | goback => goback)

   | scan_dn1 cct ist (Const ("HOL.Let", _) $ e $ (Abs (id, T, b))) =

     (case scan_dn1 cct (ist |> path_down [L, R]) e of

        Reject_Tac1 (ist', _, _) =>

          scan_dn1 cct (ist' |> path_down [R, D] |> upd_env (TermC.mk_Free (id, T)) |> trans_ass ist) b

      | Term_Val1 v =>

          scan_dn1 cct (ist |> path_down [R, D] |> upd_env'' (TermC.mk_Free (id, T), v)) b

      | goback => goback)

   | scan_dn1 (cct as (_, ctxt, _)) (ist as {eval, act_arg, ...})

       (Const ("Tactical.While"(*1*), _) $ c $ e $ a) =

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval

       (subst_atomic (ist |> get_act_env |> Env.update' a) c)

     then scan_dn1 cct (ist |> path_down_form ([L, R], a)) e

     else Term_Val1 act_arg

   | scan_dn1 (cct as (_, ctxt, _)) (ist as {eval, act_arg, ...})

       (Const ("Tactical.While"(*2*),_) $ c $ e) =

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval (subst_atomic (Env.update_opt' (get_subst ist)) c) 

     then scan_dn1 cct (ist |> path_down [R]) e

     else Term_Val1 act_arg

   | scan_dn1 cct (ist as {or = ORundef, ...}) (Const ("Tactical.Or"(*1*), _) $e1 $ e2 $ a) =

     (case scan_dn1 cct (ist |> path_down_form ([L, L, R], a) |> set_or AssOnly) e1 of

 	     Term_Val1 v =>

 	       (case scan_dn1 cct (ist |> path_down [L, R] |> set_subst' (a, v) |> set_or AssOnly) e2 of

 	          Term_Val1 v => 

 	            (case scan_dn1 cct (ist |> path_down [L, L, R] |> upd_env'' (a, v) |> set_or AssGen) e1 of

 	               Term_Val1 v => 

 	                 scan_dn1 cct (ist |> path_down [L, R] |> upd_env'' (a, v) |> set_or AssGen) e2

 	             | goback => goback)

 	        | goback => goback)

      | Reject_Tac1 _ => raise ERROR ("scan_dn1 Tactical.Or(*1*): must not return Reject_Tac1")

      | goback => goback)

   | scan_dn1 cct ist (Const ("Tactical.Or"(*2*), _) $e1 $ e2) =

     (case scan_dn1 cct (ist |> path_down [L, R]) e1 of

 	     Term_Val1 v => scan_dn1 cct (ist |> path_down [R] |> set_act v) e2

      | goback => goback)

   | scan_dn1 (cct as (_, ctxt, _)) (ist as {eval, ...}) (Const ("Tactical.If", _) $ c $ e1 $ e2) =

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval (subst_atomic (Env.update_opt' (get_subst ist)) c)

     then scan_dn1 cct (ist |> path_down [L, R]) e1

     else scan_dn1 cct (ist |> path_down [R]) e2

   | scan_dn1 (cct as (_, ctxt, _)) (ist as {eval, ...}) t =

     if Tactical.contained_in t then raise TERM ("scan_dn1 expects Prog_Tac or Prog_Expr", [t])

     else

       case Lucin.interpret_leaf "locate" ctxt eval (get_subst ist) t of

   	    (Program.Expr _, form_arg) => 

   	      Term_Val1 (Rewrite.eval_prog_expr (Proof_Context.theory_of ctxt) eval

   		      (subst_atomic (Env.update_opt'' (get_act_env ist, form_arg)) t))

       | (Program.Tac prog_tac, form_arg) =>

           interpret_tac1 cct ist (form_arg, prog_tac)

 fun go_scan_up1 (pcct as (prog, _)) (ist as {path, act_arg, ...}) =

     if 1 < length path

     then scan_up1 pcct (ist |> path_up) (at_location (path_up' path) prog)

     else Term_Val1 act_arg

 and scan_up1 pcct ist (Const ("Tactical.Try"(*1*), _) $ _ $ _) = go_scan_up1 pcct ist

   | scan_up1 pcct ist (Const ("Tactical.Try"(*2*), _) $ _) = go_scan_up1 pcct ist

   | scan_up1 (pcct as (prog, cct as (cstate, _, _))) ist (t as Const ("Tactical.Repeat"(*1*), _) $ e $ a) =

     (case scan_dn1 cct (ist |> path_down_form ([L, R], a) |> set_or ORundef) e of 

       Term_Val1 v => go_scan_up1 pcct (ist |> set_act v |> set_form a)

     | Reject_Tac1 (ist', ctxt', tac') => scan_up1 (prog, (cstate, ctxt', tac')) ist' t

     | goback => goback)

   | scan_up1 (pcct as (prog, cct as (cstate, _, _))) ist (t as Const ("Tactical.Repeat"(*2*), _) $ e) =

     (case scan_dn1 cct (ist |> path_down [R] |> set_or ORundef) e of

        Term_Val1 v' => go_scan_up1 pcct (ist |> set_act v')

      | Reject_Tac1 (ist', ctxt', tac') => scan_up1 (prog, (cstate, ctxt', tac')) ist' t

      | goback => goback)

     (*all has been done in (*2*) below*)

   | scan_up1 pcct ist (Const ("Tactical.Chain"(*1*), _) $ _ $ _ $ _) = go_scan_up1 pcct ist

   | scan_up1 pcct ist (Const ("Tactical.Chain"(*2*), _) $ _ $ _) = go_scan_up1 pcct ist (*comes from e2*)    

   | scan_up1 (pcct as (prog, cct as (cstate, _, _))) ist (Const ("Tactical.Chain"(*3*), _) $ _ ) =

      let 

        val e2 = check_Seq_up ist prog (*comes from e1, goes to e2*)

      in

        case scan_dn1 cct (ist |> path_up_down [R] |> set_or ORundef) e2 of

          Term_Val1 v => go_scan_up1 pcct (ist |> path_up |> set_act v)

        | Reject_Tac1 (ist', ctxt', tac') => go_scan_up1 (prog, (cstate, ctxt', tac')) ist'

        | goback => goback 

      end

   | scan_up1 (pcct as (prog, cct as (cstate, _, _))) ist (Const ("HOL.Let"(*1*), _) $ _) =

     let 

       val (i, body) = check_Let_up ist prog

     in case scan_dn1 cct (ist |> path_up_down [R, D] |> upd_env i |> set_or ORundef) body of

 	       Accept_Tac1 iss => Accept_Tac1 iss

 	     | Reject_Tac1 (ist', ctxt', tac') => go_scan_up1 (prog, (cstate, ctxt', tac')) ist'

 	     | Term_Val1 v => go_scan_up1 pcct (ist |> path_up |> set_act v) 

 	  end

   | scan_up1 pcct ist (Abs(*2*) _) = go_scan_up1 pcct ist

   | scan_up1 pcct ist (Const ("HOL.Let"(*3*), _) $ _ $ (Abs _)) = go_scan_up1 pcct ist

   | scan_up1 (pcct as (prog, cct as (cstate, ctxt, _))) (ist as {eval, ...})

       (t as Const ("Tactical.While"(*1*),_) $ c $ e $ a) =

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval (subst_atomic (Env.update' a (get_act_env ist)) c)

     then

       case scan_dn1 cct (ist |> path_down_form ([L, R], a) |> set_or ORundef) e of 

         Term_Val1 v => go_scan_up1 pcct (ist |> set_act v |> set_form a)

       | Reject_Tac1 (ist', ctxt', tac') => scan_up1 (prog, (cstate, ctxt', tac')) ist' t

       | goback => goback

     else go_scan_up1 pcct (ist |> set_form a)

   | scan_up1 (pcct as (prog, cct as (cstate, ctxt, _))) (ist as {eval, ...})

       (t as Const ("Tactical.While"(*2*), _) $ c $ e) =

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval (subst_atomic (Env.update_opt' (get_subst ist)) c)

     then

       case scan_dn1 cct (ist |> path_down [R] |> set_or ORundef) e of 

         Term_Val1 v => go_scan_up1 pcct (ist |> set_act v)

        | Reject_Tac1 (ist', ctxt', tac') => scan_up1 (prog, (cstate, ctxt', tac')) ist' t

        | goback => goback

     else go_scan_up1 pcct ist

   | scan_up1 pcct ist (Const ("If", _) $ _ $ _ $ _) = go_scan_up1 pcct ist

   | scan_up1 pcct ist (Const ("Tactical.Or"(*1*), _) $ _ $ _ $ _) = go_scan_up1 pcct ist

   | scan_up1 pcct ist (Const ("Tactical.Or"(*2*), _) $ _ $ _) = go_scan_up1 pcct ist

   | scan_up1 pcct ist (Const ("Tactical.Or"(*3*), _) $ _ ) = go_scan_up1 pcct (ist |> path_up)

   | scan_up1 pcct ist (Const ("Tactical.If",_) $ _ $ _ $ _) = go_scan_up1 pcct ist

   | scan_up1 _ _ t = error ("scan_up1 not impl for t= " ^ Rule.term2str t)

 fun scan_to_tactic1 (prog, (cctt as ((_, p), _, _))) (Istate.Pstate (ist as {path, ...})) =

     if path = [] orelse Pos.at_first_tactic(*RM prog path RM WITH find_next_tactic IN solve*)p

     then scan_dn1 cctt (ist |> set_path [R] |> set_or ORundef) (Program.body_of prog)

     else go_scan_up1 (prog, cctt) ist

   | scan_to_tactic1 _ _ = raise ERROR "scan_to_tactic1: uncovered pattern in fun.def"

 (*locate an input tactic within a program*)

 fun locate_input_tactic (Rule.Prog prog) cstate istate ctxt tac =

     (case scan_to_tactic1 (prog, (cstate, ctxt, tac)) istate of

          Accept_Tac1 ((ist as {assoc, ...}), ctxt, tac') =>

           if assoc

           then Safe_Step (Istate.Pstate ist, ctxt, tac')

  	        else Unsafe_Step (Istate.Pstate ist, ctxt, tac')

       | Reject_Tac1 _ => Not_Locatable (Tactic.string_of tac ^ " not locatable")

       | err => raise ERROR ("not-found-in-script: NotLocatable from " ^ @{make_string} err))

   | locate_input_tactic _ _ _ _ _ = raise ERROR "locate_input_tactic: uncovered case in definition"

 (*** determine a next tactic by executing the program ***)

   datatype next_tactic_result = Next_Step of Istate.T * Proof.context * Tactic.T

     | Helpless | End_Program of Istate.T * Tactic.T (*contains prog_result, without asms*)

 (** scan to a Prog_Tac **)

 datatype expr_val2 = (* "ExprVal" in the sense of denotational semantics           *)

   Reject_Tac2        (* tactic is found but NOT acknowledged, scan is continued    *)

 | Accept_Tac2 of     (* tactic is found and acknowledged, scan is stalled          *)

     Tactic.T *       (* Prog_Tac is applicable_in cstate                           *)

     Istate.pstate *  (* created by application of Tactic.T, for resuming execution *)

     Proof.context    (* created by application of Tactic.T                         *)

 | Term_Val2 of       (* Prog_Expr is found and evaluated, scan is continued        *)

     term;            (* value of Prog_Expr, for updating environment               *)

 (*

   scan_dn2, go_scan_up2, scan_up2 scan for find_next_tactic.

   (1) scan_dn2 is recursive descent;

   (2) go_scan_up2 goes to the parent node and calls (3);

   (3) scan_up2 resumes according to the interpreter-state.

   Call of (2) means that there was an applicable Prog_Tac below

 *)

 fun scan_dn2 cc (ist as {act_arg, ...}) (Const ("Tactical.Try"(*1*), _) $ e $ a) =

     (case scan_dn2 cc (ist|> path_down_form ([L, R], a)) e of

       Reject_Tac2 => Term_Val2 act_arg

     | (*Accept_Tac2*) goback => goback)

   | scan_dn2 cc (ist as {act_arg, ...}) (Const ("Tactical.Try"(*2*), _) $ e) =

     (case scan_dn2 cc (ist |> path_down [R]) e of

       Reject_Tac2 => Term_Val2 act_arg

     | (*Accept_Tac2*) goback => goback)

   | scan_dn2 cc ist (Const ("Tactical.Repeat"(*1*), _) $ e $ a) = 

     scan_dn2 cc (ist |> path_down_form ([L, R], a)) e

   | scan_dn2 cc ist (Const ("Tactical.Repeat"(*2*), _) $ e) =

     scan_dn2 cc (ist |> path_down [R]) e

   | scan_dn2 cc ist (Const ("Tactical.Chain"(*1*), _) $ e1 $ e2 $ a) =

     (case scan_dn2 cc (ist |> path_down_form ([L, L, R], a)) e1 of

 	    Term_Val2 v => scan_dn2 cc (ist |> path_down_form ([L, R], a) |> set_act v) e2 (*UPD*)

     | (*Accept_Tac2*) goback => goback)

   | scan_dn2 cc ist (Const ("Tactical.Chain"(*2*), _) $ e1 $ e2) =

     (case scan_dn2 cc (ist |> path_down [L, R]) e1 of

 	    Term_Val2 v => scan_dn2 cc (ist |> path_down [R] |> set_act v) e2

     | (*Accept_Tac2*) goback => goback)

   | scan_dn2 cc ist (Const ("HOL.Let"(*1*), _) $ e $ (Abs (i, T, b))) =

      (case scan_dn2 cc (ist |> path_down [L, R]) e of

        Term_Val2 res => scan_dn2 cc (ist |> path_down [R, D] |> upd_env'' (Free (i, T), res)) b

     | (*Accept_Tac2*) goback => goback)

   | scan_dn2 (cc as (_, ctxt)) (ist as {eval, act_arg, ...}) (Const ("Tactical.While"(*1*), _) $ c $ e $ a) =

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval (subst_atomic (ist |> get_act_env |> Env.update' a) c)

     then scan_dn2 cc (ist |> path_down_form ([L, R], a)) e

     else Term_Val2 act_arg

   | scan_dn2 (cc as (_, ctxt)) (ist as {eval, act_arg, ...}) (Const ("Tactical.While"(*2*), _) $ c $ e) =

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval (subst_atomic (Env.update_opt' (get_subst ist)) c)

     then scan_dn2 cc (ist |> path_down [R]) e

     else Term_Val2 act_arg

   |scan_dn2 cc ist (Const ("Tactical.Or"(*1*), _) $e1 $ e2 $ a) =

     (case scan_dn2 cc (ist |> path_down_form ([L, L, R], a)) e1 of

 	    Accept_Tac2 lme => Accept_Tac2 lme

     | _ => scan_dn2 cc (ist |> path_down_form ([L, R], a)) e2)

   | scan_dn2 cc ist (Const ("Tactical.Or"(*2*), _) $e1 $ e2) =

     (case scan_dn2 cc (ist |> path_down [L, R]) e1 of

 	    Accept_Tac2 lme => Accept_Tac2 lme

     | _ => scan_dn2 cc (ist |> path_down [R]) e2)

   |  scan_dn2 (cc as (_, ctxt)) (ist as {eval, ...}) (Const ("Tactical.If"(*1*), _) $ c $ e1 $ e2) =

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval (subst_atomic (Env.update_opt' (get_subst ist)) c)

     then scan_dn2 cc (ist |> path_down [L, R]) e1

     else scan_dn2 cc (ist |> path_down [R]) e2

   | scan_dn2 ((pt, p), ctxt) (ist as {eval, ...}) t =

     if Tactical.contained_in t then raise TERM ("scan_dn2 expects Prog_Tac or Prog_Expr", [t])

     else

       case Lucin.interpret_leaf "next  " ctxt eval (get_subst ist) t of

   	    (Program.Expr s, _) => Term_Val2 s

       | (Program.Tac stac, a') =>

   	    let

   	      val (m, m') = Lucin.stac2tac_ pt (Proof_Context.theory_of ctxt) stac

         in

           case m of (*TODO?: make applicable_in..Subproblem analogous to other tacs ?refine problem?*)

     	      Tactic.Subproblem _ =>

     	        Accept_Tac2 (m', ist |> set_subst_reset (a', Tactic.result m'), ctxt)

     	    | _ =>

             (case Applicable.applicable_in p pt m of

     		      Applicable.Appl m' => Accept_Tac2 (m',

     		        ist |> set_subst_reset (a', Tactic.result m'), Tactic.insert_assumptions m' ctxt)

     		    | _ => Reject_Tac2)

   	    end

     (*makes Reject_Tac2 to Term_Val2*)

 fun go_scan_up2 (pcc as (sc, _)) (ist as {path, act_arg, finish, ...}) = 

     if 1 < length path

     then 

       scan_up2 pcc (ist |> path_up) (go_up path sc)

     else (*interpreted to end*)

       if finish = Skip_ then Term_Val2 act_arg else Reject_Tac2

 and scan_up2 pcc ist (Const ("Tactical.Try"(*1*), _) $ _ $ _) = go_scan_up2 pcc (ist |> set_appy Skip_)

   | scan_up2 pcc ist (Const ("Tactical.Try"(*2*), _) $ _) = go_scan_up2 pcc (ist |> set_appy Skip_)

   | scan_up2 (pcc as (_, cc)) ist (Const ("Tactical.Repeat"(*1*), _) $ e $ _) =

     (case scan_dn2 cc (ist |> path_down [L, R]) e of (* no appy_: there was already a stac below *)

       Accept_Tac2 lr => Accept_Tac2 lr

     | Reject_Tac2 =>  go_scan_up2 pcc (ist |> set_appy Skip_)

     | Term_Val2 v =>  go_scan_up2 pcc (ist |> set_act v |> set_appy Skip_))

     (*no appy_: there was already a stac below*)

   | scan_up2 (pcc as (_, cc)) ist (Const ("Tactical.Repeat"(*2*), _) $ e) =

     (case scan_dn2 cc (ist |> path_down [R]) e of

       Accept_Tac2 lr => Accept_Tac2 lr

     | Reject_Tac2 => go_scan_up2 pcc (ist |> set_appy Skip_)

     | Term_Val2 v => go_scan_up2 pcc (ist |> set_act v |> set_appy Skip_))

   | scan_up2 pcc ist (Const ("Tactical.Chain"(*1*), _) $ _ $ _ $ _) = go_scan_up2 pcc ist

   | scan_up2 pcc ist (Const ("Tactical.Chain"(*2*), _) $ _ $ _) = go_scan_up2 pcc ist

   | scan_up2 (pcc as (sc, cc)) (ist as {finish, ...}) (Const ("Tactical.Chain"(*3*), _) $ _) =

     if finish = Napp_

     then go_scan_up2 pcc (ist |> path_up)

     else (*Skip_*)

       let 

         val e2 = check_Seq_up ist sc

       in

         case scan_dn2 cc (ist |> path_up_down [R]) e2 of

           Accept_Tac2 lr => Accept_Tac2 lr

         | Reject_Tac2 => go_scan_up2 pcc (ist |> path_up)

         | Term_Val2 v => go_scan_up2 pcc (ist |> path_up |> set_act v |> set_appy Skip_)

       end

   | scan_up2 (pcc as (sc, cc)) (ist as {finish, ...}) (Const ("HOL.Let"(*1*), _) $ _) =

     if finish = Napp_

     then go_scan_up2 pcc (ist |> path_up)

     else (*Skip_*)

 	    let

         val (i, body) = check_Let_up ist sc

       in

         case scan_dn2 cc (ist |> path_up_down [R, D] |> upd_env i) body of

 	        Accept_Tac2 lre => Accept_Tac2 lre

 	      | Reject_Tac2 => go_scan_up2 pcc (ist |> path_up)

 	      | Term_Val2 v => go_scan_up2 pcc (ist |> path_up |> set_act v |> set_appy Skip_)

 	    end

   | scan_up2 pcc ist (Abs _(*2*)) =  go_scan_up2 pcc ist

   | scan_up2 pcc ist (Const ("HOL.Let"(*3*),_) $ _ $ (Abs _)) =

     go_scan_up2 pcc ist

     (*no appy_: never causes Reject_Tac2 -> Helpless*)

   | scan_up2 (pcc as (_, cc as (_, ctxt)))  (ist as {eval, ...}) (Const ("Tactical.While"(*1*), _) $ c $ e $ _) = 

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval (subst_atomic (Env.update_opt' (get_subst ist)) c) 

     then

       case scan_dn2 cc (ist |> path_down [L, R]) e of

   	     Accept_Tac2 lr => Accept_Tac2 lr

   	  | Reject_Tac2 => go_scan_up2 pcc (ist |> set_appy Skip_)

   	  | Term_Val2 v => go_scan_up2 pcc (ist |> set_act v |> set_appy Skip_)

     else

       go_scan_up2 pcc (ist |> set_appy Skip_)

     (*no appy_: never causes Reject_Tac2 - Helpless*)

   | scan_up2  (pcc as (_, cc as (_, ctxt))) (ist as {eval, ...}) (Const ("Tactical.While"(*2*), _) $ c $ e) = 

     if Rewrite.eval_true_ (Proof_Context.theory_of ctxt) eval (subst_atomic (Env.update_opt' (get_subst ist)) c) 

     then

       case scan_dn2 cc (ist |> path_down [R]) e of

   	    Accept_Tac2 lr => Accept_Tac2 lr

   	  | Reject_Tac2 => go_scan_up2 pcc (ist |> set_appy Skip_)

   	  | Term_Val2 v => go_scan_up2 pcc (ist |> set_act v |> set_appy Skip_)

     else

       go_scan_up2 pcc (ist |> set_appy Skip_)

   | scan_up2 pcc ist (Const ("Tactical.Or"(*1*), _) $ _ $ _ $ _) = go_scan_up2 pcc ist

   | scan_up2 pcc ist (Const ("Tactical.Or"(*2*), _) $ _ $ _) = go_scan_up2 pcc ist

   | scan_up2 pcc ist (Const ("Tactical.Or"(*3*), _) $ _ ) = go_scan_up2 pcc ist

   | scan_up2 pcc ist (Const ("Tactical.If"(*1*), _) $ _ $ _ $ _) = go_scan_up2 pcc ist

   | scan_up2 _ _ t = error ("scan_up2 not impl for " ^ Rule.term2str t)

 (* scan program until an applicable tactic is found *)

 fun scan_to_tactic2 (prog, cc) (Istate.Pstate (ist as {path, ...})) =

   if path = []

   then scan_dn2 cc (trans_scan_down2 ist) (Program.body_of prog)

   else go_scan_up2 (prog, cc) (trans_scan_up2 ist |> set_appy Skip_)

 | scan_to_tactic2 _ _ = raise ERROR "scan_to_tactic2: uncovered pattern";

 (* decide for the next applicable Prog_Tac *)

 fun find_next_tactic (Rule.Prog prog) (ptp as(pt, (p, _))) (Istate.Pstate ist) ctxt =

    (case scan_to_tactic2 (prog, (ptp, ctxt)) (Istate.Pstate ist) of

       Accept_Tac2 (tac, ist, ctxt) =>

         Next_Step (Istate.Pstate ist, Tactic.insert_assumptions tac ctxt, tac)

     | Term_Val2 prog_result =>

         (case par_pbl_det pt p of

           (true, p', _) => 

             let

               val (_, pblID, _) = get_obj g_spec pt p';

             in

               End_Program (Istate.Pstate ist, Tactic.Check_Postcond' (pblID, (prog_result, [(*???*)])))

             end

         | _ => End_Program (Istate.Pstate ist, Tactic.End_Detail' (Rule.e_term,[])))

     | Reject_Tac2 => Helpless)

   | find_next_tactic _ _ is _ =

     raise ERROR ("find_next_tactic: not impl for " ^ Istate.istate2str is);

 (*** locate an input formula in the program ***)

 datatype input_formula_result =

     Found_Step of Ctree.state * Istate.T * Proof.context

   | Not_Derivable of Chead.calcstate'

 fun by_tactic (Tactic.Apply_Method' (mI, _, _, _)) (_, ctxt) (pt, pos as (p, _)) =

     let

       val (itms, (*l..*)oris, probl(*..l*)) = case get_obj I pt p of

         PblObj {meth = itms, origin = (oris, _, _), probl, ...} => (itms, oris, probl)

       | _ => error "LucinNEW.by_tactic Apply_Method': uncovered case get_obj"

 (*l*) val {ppc, ...} = Specify.get_met mI;

 (*l*) val itms = if itms <> [] then itms else Chead.complete_metitms oris probl [] ppc

 (*l*) val itms = Specify.hack_until_review_Specify_1 mI itms

       val thy = Celem.assoc_thy (get_obj g_domID pt p);

       val srls = Lucin.get_simplifier (pt, pos)

       val (is, env, ctxt, scr) = case Lucin.init_pstate srls ctxt itms mI of

         (is as Istate.Pstate {env, ...}, ctxt, scr) => (is, env, ctxt, scr)

       | _ => error "LucinNEW.by_tactic Apply_Method': uncovered case init_pstate"

      val ini = Lucin.init_form thy scr env;

    in 

      case ini of

        SOME t =>

        let

          val pos = start_new_level pos

 	       val tac_ = Tactic.Apply_Method' (mI, SOME t, is, ctxt);

 	       val (pos, c, _, pt) = Generate.generate1 thy tac_ (is, ctxt) pos pt (* implicit Take *)

        in

         ("ok", ([(Tactic.Apply_Method mI, tac_, (pos, (is, ctxt)))], c, (pt, pos)))

        end

      | NONE =>

        let

          val pt = update_env pt (fst pos) (SOME (is, ctxt))

 	       val (_, (tacis, c, ptp)) = do_next (pt, pos)

        in ("ok", (tacis @ [(Tactic.Apply_Method mI,

             Tactic.Apply_Method' (mI, NONE, Istate.e_istate, ctxt), (pos, (is, ctxt)))], c, ptp))

        end

     end

   | by_tactic (Tactic.Check_Postcond' (pI, (prog_res, _))) _ (pt, pos as (p, _))  =

     let

       val pp = par_pblobj pt p

       val thy = Celem.assoc_thy (get_obj g_domID pt pp);

       val (ist, ctxt) = get_loc pt pos

       val asm = (case get_obj g_tac pt p of (*collects and instantiates asms*)

         Tactic.Check_elementwise _ => (snd o (get_obj g_result pt)) p

       | _ => get_assumptions_ pt pos)

 	    val tac = Tactic.Check_Postcond' (pI, (prog_res, asm))

     in

       if pp = []

       then 

 	      let

           val is = Istate.Pstate (ist |> the_pstate

             |> Istate.set_act prog_res |> Istate.set_appy Istate.Skip_)

 	        val ((p, p_), ps, _, pt) = Generate.generate1 thy tac (is, ctxt) (pp, Res) pt;

 	      in ("ok", ([(Tactic.Check_Postcond pI, tac, ((pp, Res), (is, ctxt)))], ps, (pt, (p, p_)))) end

       else

         let (*resume script of parent PblObj, transfer value of subpbl-script*)

           val thy = Celem.assoc_thy (get_obj g_domID pt (par_pblobj pt (lev_up p)));

           val (pst', ctxt') = case get_loc pt (pp, Frm) of

             (Istate.Pstate pst', ctxt') => (pst', ctxt')

           | _ => error "by_tactic Check_Postcond' script of parpbl: uncovered case get_loc"

 	        val ctxt'' = ContextC.from_subpbl_to_caller ctxt prog_res ctxt'

 	        val is = Istate.Pstate (pst' |> Istate.set_act prog_res |> Istate.set_appy Istate.Skip_)

           val ((p, p_), ps, _, pt) = Generate.generate1 thy tac (is, ctxt'') (pp, Res) pt;

         in ("ok", ([(Tactic.Check_Postcond pI, tac, ((pp, Res), (is, ctxt'')))], ps, (pt, (p, p_)))) end

     end

   | by_tactic (Tactic.End_Proof'') _ ptp = ("end-of-calculation", ([], [], ptp))

   | by_tactic tac_ is (pt, pos) =

     let

       val pos = next_in_prog' pos

  	    val (pos', c, _, pt) = Generate.generate1 (Celem.assoc_thy "Isac_Knowledge") tac_ is pos pt;

     in

       ("ok", ([(Tactic.input_from_T tac_, tac_, (pos, is))], c, (pt, pos')))

     end

 (*find_next_tactic from program, by_tactic will update Ctree*)

 and do_next (ptp as (pt, pos as (p, p_))) =

     if Celem.e_metID = get_obj g_metID pt (par_pblobj pt p)

     then ("helpless", ([], [], (pt, (p, p_))))

     else 

       let 

         val thy' = get_obj g_domID pt (par_pblobj pt p);

 	      val (_, (ist, ctxt), sc) = Lucin.from_pblobj_or_detail' thy' (p,p_) pt;

       in

         case find_next_tactic sc (pt, pos) ist ctxt of

            Next_Step (ist, ctxt, tac) =>

              by_tactic tac (ist, Tactic.insert_assumptions tac ctxt) ptp

          | End_Program (ist, tac) =>

              (case tac of

                Tactic.End_Detail' res =>

                  ("ok", ([(Tactic.End_Detail, 

                    Tactic.End_Detail' res, (pos, (ist, ctxt)))], [], ptp))

              | _ => by_tactic tac (ist, ctxt) ptp

              )

          | Helpless => ("helpless", Chead.e_calcstate')

       end;

 (*

   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.

   Code's structure is 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_))): Chead.calcstate') ifo =

   let

     val fo =

       case p_ of

         Pos.Frm => Ctree.get_obj Ctree.g_form pt p

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

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

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

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

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

   in

     if found

     then

        let

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

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

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

      else 

 	     if pos = ([], Pos.Res) (*TODO: we should stop earlier with trying subproblems *)

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

 	     else

          let

            val msg_cs' as (_, (tacis, c', ptp)) = do_next ptp; (*<---------------------*)

 		       val (_, (tacis, c'', ptp)) = case tacis of

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

 			         let

                  val ptp as (pt, (p,_)) = Chead.all_modspec ptp (*<--------------------*)

 				         val mI = Ctree.get_obj Ctree.g_metID pt p

 			         in

 			           by_tactic (Tactic.Apply_Method' (mI, NONE, Istate.e_istate, ContextC.e_ctxt)) (Istate.e_istate, ContextC.e_ctxt) ptp

                end

 			     | _ => msg_cs';

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

   end

 (*

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

  * CAS-command: create a calchead, and do 1 step

  * formula, which is no CAS-command:

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

    collect all the Prog_Tac applied by the way; ...???TODO?

    If "no derivation found" then check_error_patterns.

    ALTERNATIVE: check_error_patterns _within_ compare_step: seems too expensive

 *)

 (*                       vvvv           vvvvvv vvvv    NEW args for compare_step *)

 fun locate_input_formula (Rule.Prog _)  ((pt, pos) : Ctree.state) (_ : Istate.T) (_ : Proof.context) tm =

      let                                                          

    		val pos_pred = Pos.lev_back' pos (*f_pred ---"step pos cs"---> f_succ in appendFormula*)

    		val _(*f_pred*) = Ctree.get_curr_formula (pt, pos_pred)

      in

        (*TODO: use prog, istate, ctxt in compare_step ...*)

    		case compare_step ([], [], (pt, pos_pred)) tm of

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

        | ("ok", (_, _, cstate as (pt', pos'))) => 

            Found_Step (cstate, get_istate pt' pos', get_ctxt pt' pos')

        | _ => raise ERROR "compare_step: uncovered case"

      end

   | locate_input_formula _ _ _ _ _ = error ""

 (**)end(**)