(* Title:  Interpret/li-tool.sml

    Author: Walther Neuper 2000

    (c) due to copyright terms

 Tools for Lucas_Interpreter

 *)

 signature LUCAS_INTERPRETER_TOOL =

 sig

   datatype ass =

     Associated of Tactic.T * term (*..result*) * Proof.context

   | Ass_Weak of Tactic.T * term (*..result*) * Proof.context

   | Not_Associated;

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

   val parent_node: Ctree.ctree -> Pos.pos' -> bool * Pos.pos * Rule_Set.T * Proof.context

   val init_pstate: Proof.context -> I_Model.T_TEST -> MethodC.id ->

     Istate.T * Proof.context * Program.T

   val resume_prog: Pos.pos' -> Ctree.ctree -> 

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

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

       Program.leaf * term option

   val implicit_take: Proof.context -> Program.T -> Env.T -> term option

   val get_simplifier: Calc.T -> Rule_Set.T

   val tac_from_prog: Ctree.state -> term -> Tactic.input

 (*from isac_test for Minisubpbl*)

   val arguments_from_model : Proof.context -> MethodC.id -> I_Model.T -> term list

   val errmsg: string

   val error_msg_2: Proof.context -> term -> I_Model.T -> string

   val error_msg_2_TEST: Proof.context -> term -> I_Model.T_TEST -> string

   val error_msg_1: string

   val relate_args: Env.T -> term list -> term list -> Proof.context -> Program.term ->

     MethodC.id -> term list -> term list -> (term * term) list

 \<^isac_test>\<open>

   val trace_init: Proof.context -> string list -> unit

 (**)

 \<close>

 end 

 (* traces the leaves (ie. non-tactical nodes) of Prog found by find_next_step *)   

 val LI_trace = Attrib.setup_config_bool \<^binding>\<open>LI_trace\<close> (K false);

 (**)

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

 struct

 (**)

 open Ctree

 open Pos

 (* find the formal argument of a tactic in case there is only one (e.g. in simplification) *)

 fun implicit_take _ (Rule.Prog prog) env =

     Option.map (subst_atomic env) (Prog_Tac.get_first_argument prog)

   | implicit_take _ _ _ = raise ERROR "implicit_take: no match";

 val error_msg_1 = "ERROR: the guard is missing (#model in 'type met' added in prep_met)."

 fun error_msg_2 ctxt d itms =

   ("arguments_from_model: '" ^ UnparseC.term ctxt d ^ "' not in itms:\n" ^

   "itms:\n" ^ I_Model.to_string @{context} itms)

 fun error_msg_2_TEST ctxt d itms =

   ("arguments_from_model: '" ^ UnparseC.term ctxt d ^ "' not in itms:\n" ^

   "itms:\n" ^ I_Model.to_string_TEST @{context} itms)

 (* turn Model-items into arguments for a program *)

 fun arguments_from_model ctxt mI itms =

   let

     val mvat = Pre_Conds.max_variant itms

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

     val itms = filter (okv mvat) itms

     fun itm2arg _ (_, (_, _)) = [](*this limits errors to init_pstate,

       while changing I_Model.penvval_in triggers much more errors*)

     val pats = (#model o MethodC.from_store ctxt) mI

     val _ = if pats = [] then raise ERROR error_msg_1 else ()

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

 (*

   convert a Prog_Tac to Tactic.input;

   argument Ctree.state is specifically for "Prog_Tac.SubProblem" (requires Pos),

 *)

 fun tac_from_prog (pt, pos) intac =

   let

     val pos = Pos.back_from_new pos

     val ctxt = Ctree.get_ctxt pt pos

     val thy = Proof_Context.theory_of ctxt

   in

     case intac of

       (Const (\<^const_name>\<open>Prog_Tac.Rewrite\<close>, _) $ thmID $ _) =>

         let

           val tid = HOLogic.dest_string thmID

         in (Tactic.Rewrite (tid, ThmC.thm_from_thy thy tid)) end

       | (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Inst\<close>, _) $ sub $ thmID $ _) =>

         let

           val tid = HOLogic.dest_string thmID

           val sub' = Subst.program_to_input ctxt sub

         in (Tactic.Rewrite_Inst (sub', (tid, ThmC.thm_from_thy thy tid))) end

       | (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Set\<close>,_) $ rls $ _) =>

          (Tactic.Rewrite_Set (HOLogic.dest_string rls))

       | (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Set_Inst\<close>, _) $ sub $ rls $ _) =>

         let

           val sub' = Subst.program_to_input ctxt sub

         in (Tactic.Rewrite_Set_Inst (sub', HOLogic.dest_string rls)) end

       | (Const (\<^const_name>\<open>Prog_Tac.Calculate\<close>, _) $ op_ $ _) =>

           (Tactic.Calculate (HOLogic.dest_string op_))

       | (Const (\<^const_name>\<open>Prog_Tac.Take\<close>, _) $ t) =>

            (Tactic.Take (UnparseC.term ctxt t))

       | (Const (\<^const_name>\<open>Prog_Tac.Substitute\<close>, _) $ isasub $ _) =>

           Tactic.Substitute (Prog_Tac.Substitute_adapt_to_type thy isasub)

       | (Const (\<^const_name>\<open>Prog_Tac.Check_elementwise\<close>, _) $ _ $ 

         (Const (\<^const_name>\<open>Collect\<close>, _) $ Abs (_, _, pred))) =>

           (Tactic.Check_elementwise (UnparseC.term ctxt pred))

       | (Const (\<^const_name>\<open>Prog_Tac.Or_to_List\<close>, _) $ _ ) => Tactic.Or_to_List

       | (ptac as Const (\<^const_name>\<open>Prog_Tac.SubProblem\<close>, _) $ _ $ _) =>

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

       | t =>

           raise ERROR ("stac2tac_ TODO: no match for " ^ UnparseC.term ctxt t)

   end

 datatype ass =

     Associated of

       Tactic.T         (* Subproblem' gets args instantiated in associate *)

       * term           (* resulting from application of Tactic.T          *)

       * Proof.context  (* updated by assumptioons from Rewrite*           *)

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

   | Not_Associated;

 (*

   associate is the ONLY code within by_tactic, which handles Tactic.T individually;

   thus it does ContextC.insert_assumptions in case of Rewrite*.

   The argument Ctree.ctree is required only for Subproblem'.

 *)

 fun trace_msg_3 ctxt tac =

   if Config.get ctxt LI_trace then

     tracing("@@@ the \"tac_\" proposed to apply does NOT match the leaf found in the program:\n" ^

       "@@@ tac_ = \"" ^ Tactic.string_of ctxt tac ^ "\"")

   else ();

 fun associate _ ctxt (m as Tactic.Rewrite_Inst'

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

       (case stac of

   	    (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Inst\<close>, _) $ _ $ thmID_ $ f_) =>

   	      if thmID = HOLogic.dest_string thmID_ then

   	        if f = f_ then 

               Associated (m, f', ContextC.insert_assumptions asms' ctxt)

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

   	      else Not_Associated

       | (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Set_Inst\<close>,_) $ _ $ rls_ $ f_) =>

   	      if Rule_Set.contains (Rule.Thm thm'') (get_rls ctxt (HOLogic.dest_string rls_)) then

             if f = f_ then

               Associated (m, f', ContextC.insert_assumptions asms' ctxt)

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

   	      else Not_Associated

       | _ => Not_Associated)

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

       (case stac of

   	    (Const (\<^const_name>\<open>Prog_Tac.Rewrite\<close>, _) $ thmID_ $ f_) =>

   	      if thmID = HOLogic.dest_string thmID_ then

   	        if f = f_ then

               Associated (m, f', ContextC.insert_assumptions asms' ctxt)

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

   	      else Not_Associated

       | (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Set\<close>, _) $ rls_ $ f_) =>

   	       if Rule_Set.contains (Rule.Thm thm'') (get_rls ctxt (HOLogic.dest_string rls_)) then

              if f = f_ then

                Associated (m, f', ContextC.insert_assumptions asms' ctxt)

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

   	       else Not_Associated

       | _ => Not_Associated)

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

         (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Set_Inst\<close>, _) $ _ $ rls_ $ f_)) = 

       if Rule_Set.id rls = HOLogic.dest_string rls_ then

         if f = f_ then

           Associated (m, f', ContextC.insert_assumptions asms' ctxt)

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

       else Not_Associated

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

         (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Set\<close>, _) $ rls_ $ f_)) = 

       if Rule_Set.id rls = HOLogic.dest_string rls_ then

         if f = f_ then

           Associated (m, f', ContextC.insert_assumptions asms' ctxt)

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

       else Not_Associated

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

       (case stac of

   	    (Const (\<^const_name>\<open>Prog_Tac.Calculate\<close>,_) $ op__ $ f_) =>

   	      if op_ = HOLogic.dest_string op__ then

             if f = f_ then Associated (m, f', ctxt) else Ass_Weak (m ,f', ctxt)

   	      else Not_Associated

       | (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Set_Inst\<close>, _) $ _ $ rls_ $ f_)  =>

           if Rule_Set.contains (Rule.Eval (get_calc ctxt

             op_ |> snd)) (get_rls ctxt (HOLogic.dest_string rls_)) then

             if f = f_ then Associated (m, f', ctxt) else Ass_Weak (m ,f', ctxt)

           else Not_Associated

       | (Const (\<^const_name>\<open>Prog_Tac.Rewrite_Set\<close>,_) $ rls_ $ f_) =>

           if Rule_Set.contains (Rule.Eval (get_calc ctxt

             op_ |> snd)) (get_rls ctxt (HOLogic.dest_string rls_)) then

             if f = f_ then Associated (m, f', ctxt) else Ass_Weak (m ,f', ctxt)

           else Not_Associated

       | _ => Not_Associated)

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

         (Const (\<^const_name>\<open>Prog_Tac.Check_elementwise\<close>,_) $ consts' $ _)) =

       if consts = consts' then Associated (m, consts_chkd, ctxt) else Not_Associated

   | associate _ ctxt (m as Tactic.Or_to_List' (_, list), (Const (\<^const_name>\<open>Prog_Tac.Or_to_List\<close>, _) $ _)) =

       Associated (m, list, ctxt)

   | associate _ ctxt (m as Tactic.Take' term, (Const (\<^const_name>\<open>Prog_Tac.Take\<close>, _) $ _)) =

       Associated (m, term, ctxt)

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

         (Const (\<^const_name>\<open>Prog_Tac.Substitute\<close>, _) $ _ $ t)) =

   	  if f = t then

   	   Associated (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) t

   		    in

   		      if t = t' then raise ERROR "associate: Substitute' not applicable to val of Expr"

   		      else Associated (Tactic.Substitute' (ro, asm_rls, subte, t, t'), t', ctxt)

   		    end

   		  else

   		    (case Rewrite.rewrite_terms_ ctxt ro asm_rls subte t of

   		      SOME (t', _) =>  Associated (Tactic.Substitute' (ro, asm_rls, subte, t, t'), t', ctxt)

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

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

         (stac as Const (\<^const_name>\<open>Prog_Tac.SubProblem\<close>, _) $ _ $ _)) =

       (case Sub_Problem.tac_from_prog pt stac of

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

           if domID = dI andalso pblID = pI then Associated (tac, f, ctxt) else Not_Associated

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

   | associate _ ctxt (tac, _) = 

     (trace_msg_3 ctxt tac; Not_Associated);

 (* in detail step find the next parent, which is either a PblObj xor a PrfObj *)

 fun parent_node _ ([], _) = (true, [], Rule_Set.Empty, ContextC.empty)

   | parent_node pt (pos as (p, _)) =

     let

       fun par _ [] = (true, [], Rule_Set.Empty, ContextC.empty)

         | par pt p =

             if Ctree.is_pblobj (Ctree.get_obj I pt p)

             then (true, p, Rule_Set.Empty, ContextC.empty)

   		      else 

               let

                 val ctxt = Ctree.get_ctxt pt pos

               in

                 case Ctree.get_obj Ctree.g_tac pt p of

       				    Tactic.Rewrite_Set rls' => (false, p, get_rls ctxt rls', ctxt)

       			    | Tactic.Rewrite_Set_Inst (_, rls') => (false, p, get_rls ctxt rls', ctxt)

       			    | _ => par pt (Pos.lev_up p)

               end

     in par pt (Pos.lev_up p) end; 

 (* create the initial interpreter state

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

 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 O_Model.T as a prerequisite for efficient interactive modelling

   (c) modelling creates an I_Model.T from O_Model.T + possible user input

   (d) specifying a theory might add some items to I_Model.T and create a guard for the program

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

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

   * Since the arguments of the partial_function have no description (see Input_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 programs.

 *)

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

 (** )local( ** ) open for tests*)

 fun msg_miss ctxt 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 \"" ^ MethodC.id_to_string metID ^ "\" by \"" ^ caller ^ "\":\n" ^

 	"formal arg \"" ^ UnparseC.term ctxt f ^ "\" doesn't match any actual arg.\n" ^

 	"with:\n" ^

 	(string_of_int o length) formals ^ " formal args: " ^ UnparseC.terms ctxt formals ^ "\n" ^

 	(string_of_int o length) actuals ^ " actual args: " ^ UnparseC.terms ctxt actuals

 fun msg_miss_type ctxt 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 \"" ^ MethodC.id_to_string metID ^ "\" by \"assoc_by_type\":\n" ^

 	"formal arg \"" ^ UnparseC.term ctxt f ^ "\" of type \"" ^ UnparseC.typ ctxt (type_of f) ^

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

 	(string_of_int o length) formals ^ " formal args: " ^ UnparseC.terms ctxt formals ^ "\n" ^

 	(string_of_int o length) actuals ^ " actual args: " ^ UnparseC.terms ctxt actuals ^ "\n" ^

   "   with types: " ^ (strs2str o (map ((UnparseC.typ ctxt) o type_of))) actuals

 fun msg_ambiguous ctxt 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 \"" ^ MethodC.id_to_string metID ^ "\" by \"assoc_by_type\":\n" ^

   "formal arg. \"" ^ UnparseC.term ctxt f ^ "\" type-matches with several..."  ^

   "actual args. \"" ^ UnparseC.terms ctxt aas ^ "\"\n" ^

   "selected \"" ^ UnparseC.term ctxt (hd aas) ^ "\"\n" ^

 	"with\n" ^

 	"formals: " ^ UnparseC.terms ctxt formals ^ "\n" ^

 	"actuals: " ^ UnparseC.terms ctxt actuals

 (*for isac_test*)

 fun trace_init ctxt metID =

   if Config.get ctxt LI_trace

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

   else ();

 fun assoc_by_type ctxt f aa prog met_id formals actuals =

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

     [] => raise ERROR (msg_miss_type ctxt prog met_id f formals actuals)

   | [a] => (f, a)

   | aas as (a :: _) => (writeln (msg_ambiguous ctxt prog met_id f aas formals actuals); (f, a));

 (*

   The sequence of \<open>formals\<close> and \<open>actuals\<close> must be the same:

   the sequence of \<open>formals\<close> is given by the program,

   the sequence of \<open>actuals\<close> is given by the by theMethodC#model

   In case of equal sequence the \<open>fun relate\<close> could be simpler ...

 *)

 fun relate_args _ (f::_) [] ctxt prog met_id formals actuals =

     raise ERROR (msg_miss ctxt prog met_id "relate_args" f formals actuals)

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

   | relate_args env (f::ff) (aas as (a::aa)) ctxt prog met_id formals actuals = 

     if type_of f = type_of a 

     then

       relate_args (env @ [(f, a)]) ff aa ctxt prog met_id formals actuals

     else

       let

         val (f, a) = assoc_by_type ctxt f aas prog met_id formals actuals

       in

         relate_args (env @ [(f, a)]) ff (remove op = a aas) ctxt prog met_id formals actuals

       end

 (** )in( **)

 fun init_pstate ctxt i_model met_id =

   let

     val (model_patt, program, prog, prog_rls, where_, where_rls) =

       case MethodC.from_store ctxt met_id of

         {model = model_patt, program = program as Rule.Prog prog, prog_rls, where_, where_rls,...} =>

           (model_patt, program, prog, prog_rls, where_, where_rls)

       | _ => raise ERROR ("init_pstate with " ^ MethodC.id_to_string met_id)

     val (env_model, (env_subst, env_eval)) = Pre_Conds.make_environments model_patt i_model;

     val actuals = map snd env_model

     val formals = Program.formal_args prog    

     val preconds = Pre_Conds.check_envs ctxt where_rls where_ (env_model, (env_subst, env_eval))

     val ctxt = ctxt |> ContextC.insert_assumptions (map snd (snd preconds));

     val ist = Istate.e_pstate

       |> Istate.set_eval prog_rls

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

   in

     (Istate.Pstate ist, ctxt, program)

   end

 (** )end( ** )local*)

 (*DEL single call +tests, get the simplifier of the current method *)

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

   let

     val p' = Ctree.par_pblobj pt p

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

 	  val ctxt = Ctree.get_ctxt pt pos

 	  val {prog_rls, ...} = MethodC.from_store ctxt metID

   in prog_rls end

 (* resume program interpretation at the beginning of a step *)

 fun resume_prog pos pt =

   let

     val (is_problem, p', rls', ctxt) = parent_node pt pos (*is Ctree.PrfObj in case of detail step*)

   in

     if is_problem then

       let

 	      val metID = get_obj g_metID pt p'

 	      val {prog_rls, ...} = MethodC.from_store ctxt metID

 	      val (is, ctxt) =

 	        case get_loc pt pos of

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

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

 	    in

 	      ((is, ctxt), (#program o MethodC.from_store ctxt) metID)

 	    end

     else

       (get_loc pt pos,

       Rule.Prog (Auto_Prog.gen (Proof_Context.theory_of ctxt) (get_last_formula (pt, pos)) rls'))

   end

 fun trace_msg_1 ctxt call t stac =

   if Config.get ctxt LI_trace then

 	  tracing ("@@@ " ^ call ^ " leaf \"" ^ UnparseC.term ctxt t ^ "\" \<longrightarrow> Tac \"" ^

 	    UnparseC.term ctxt stac ^ "\"")

 	else ();

 fun trace_msg_2 ctxt call t lexpr' =

   if Config.get ctxt LI_trace then

 	  tracing("@@@ " ^ call ^ " leaf '" ^ UnparseC.term ctxt t ^ "' \<longrightarrow> Expr \"" ^

 	    UnparseC.term ctxt lexpr' ^ "\"")

 	else ();

 (*

   check a leaf at the end of recursive descent; a leaf is either a Prog_Tac or a Prog_Expr.

   snd of return value are the formal arguments in case of currying.

 *)

 fun check_leaf call ctxt prog_rls (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 ctxt prog_rls 

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

 	      in

           (trace_msg_1 ctxt call t stac; (Program.Tac stac', a'))

 	      end

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

 	      let

 	        val lexpr' = Rewrite.eval_prog_expr ctxt prog_rls

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

 	      in

           (trace_msg_2 ctxt call t lexpr'; (Program.Expr lexpr', a'))

 	      end;

 (**)end(**)