(* 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.ctree -> 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: Rule_Set.T -> Proof.context -> I_Model.T -> 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: Program.T -> Env.T -> term option

   val get_simplifier: Calc.T -> Rule_Set.T

   val tac_from_prog: Ctree.ctree -> theory (*..for lookup in Know_Store*) -> term -> Tactic.input

 \<^isac_test>\<open>

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

 \<close>

 end 

 (**)

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

 struct

 (**)

 open Ctree

 open Pos

 (* 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);

 (* 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 (#ppc in 'type met' added in prep_met)."

 fun error_msg_2 d itms = ("arguments_from_model: '" ^ UnparseC.term d ^ "' not in itms:\n" ^

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

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

 fun arguments_from_model ctxt mI itms =

   let

     val mvat = I_Model.max_variant itms

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

     val itms = filter (okv mvat) itms

     fun test_dsc d (_, _, _, _, itm_) = (d = I_Model.descriptor itm_)

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

       case find_first (test_dsc d) itms of

         NONE => raise ERROR (error_msg_2 d itms)

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

     val pats = (#ppc 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; specific for "Prog_Tac.SubProblem" *)

 fun tac_from_prog _ thy (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

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

     let

       val tid = HOLogic.dest_string thmID

       val sub' = (**)Subst.program_to_input(** )Prog_Tac.Rewrite_Inst_adapt_to_type thy( **) sub

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

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

      (Tactic.Rewrite_Set (HOLogic.dest_string rls))

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

     let

       val sub' = (**)Subst.program_to_input(** )Prog_Tac.Rewrite_Inst_adapt_to_type thy( **) sub

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

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

       (Tactic.Calculate (HOLogic.dest_string op_))

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

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

       Tactic.Substitute (Prog_Tac.Substitute_adapt_to_type thy isasub)

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

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

       (Tactic.Check_elementwise (UnparseC.term_in_thy thy pred))

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

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

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

   | tac_from_prog _ thy t = raise ERROR ("stac2tac_ TODO: no match for " ^ UnparseC.term_in_thy thy t);

 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 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, erls, 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, erls, subte, t, t'), t', ctxt)

   		    end

   		  else

   		    (case Rewrite.rewrite_terms_ (Proof_Context.init_global (ThyC.Isac ())) ro erls subte t of

   		      SOME (t', _) =>  Associated (Tactic.Substitute' (ro, erls, 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);

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

 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 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 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.

   *)

 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 \"" ^ MethodC.id_to_string metID ^ "\" by \"" ^ caller ^ "\":\n" ^

 	"formal arg \"" ^ UnparseC.term f ^ "\" doesn't mach an actual arg.\n" ^

 	"with:\n" ^

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

 	(string_of_int o length) actuals ^ " actual args: " ^ UnparseC.terms 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 \"" ^ MethodC.id_to_string metID ^ "\" by \"assoc_by_type\":\n" ^

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

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

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

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

   "   with types: " ^ (strs2str o (map (UnparseC.typ 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 \"" ^ MethodC.id_to_string metID ^ "\" by \"assoc_by_type\":\n" ^

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

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

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

 	"with\n" ^

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

 	"actuals: " ^ UnparseC.terms actuals

 fun trace_init ctxt metID =

   if Config.get ctxt LI_trace

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

   else ();

 in

 fun init_pstate (srls: Rule_Def.rule_set) (ctxt: Proof.context) (itms) (metID) =

   let

     val actuals = arguments_from_model ctxt metID itms

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

     val (scr, sc) = (case (#scr o MethodC.from_store ctxt) metID of

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

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

         [] => raise 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::_)  [] = raise 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, ...} = MethodC.from_store ctxt metID;

     val pres = Pre_Conds.check prls pre itms 0 |> snd |> 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*)

 (* 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 {srls, ...} = MethodC.from_store ctxt metID

   in srls 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 {srls, ...} = MethodC.from_store ctxt metID

 	      val (is, ctxt) =

 	        case get_loc pt pos 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 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 t ^ "\" \<longrightarrow> Tac \"" ^ UnparseC.term stac ^ "\"")

 	else ();

 fun trace_msg_2 ctxt call t lexpr' =

   if Config.get ctxt LI_trace then

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

               (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 srls

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

 	      in

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

 	      end;

 (**)end(**)