(*  Title:      Tools/nbe.ML

     Authors:    Klaus Aehlig, LMU Muenchen; Tobias Nipkow, Florian Haftmann, TU Muenchen

 Normalization by evaluation, based on generic code generator.

 *)

 signature NBE =

 sig

   val norm_conv: cterm -> thm

   val norm: theory -> term -> term

   datatype Univ =

       Const of int * Univ list               (*named (uninterpreted) constants*)

     | DFree of string * int                  (*free (uninterpreted) dictionary parameters*)

     | BVar of int * Univ list

     | Abs of (int * (Univ list -> Univ)) * Univ list

   val apps: Univ -> Univ list -> Univ        (*explicit applications*)

   val abss: int -> (Univ list -> Univ) -> Univ

                                              (*abstractions as closures*)

   val same: Univ -> Univ -> bool

   val univs_ref: (unit -> Univ list -> Univ list) option Unsynchronized.ref

   val trace: bool Unsynchronized.ref

   val setup: theory -> theory

   val add_const_alias: thm -> theory -> theory

 end;

 structure Nbe: NBE =

 struct

 (* generic non-sense *)

 val trace = Unsynchronized.ref false;

 fun traced f x = if !trace then (tracing (f x); x) else x;

 (** certificates and oracle for "trivial type classes" **)

 structure Triv_Class_Data = Theory_Data

 (

   type T = (class * thm) list;

   val empty = [];

   val extend = I;

   fun merge data : T = AList.merge (op =) (K true) data;

 );

 fun add_const_alias thm thy =

   let

     val (ofclass, eqn) = case try Logic.dest_equals (Thm.prop_of thm)

      of SOME ofclass_eq => ofclass_eq

       | _ => error ("Bad certificate: " ^ Display.string_of_thm_global thy thm);

     val (T, class) = case try Logic.dest_of_class ofclass

      of SOME T_class => T_class

       | _ => error ("Bad certificate: " ^ Display.string_of_thm_global thy thm);

     val tvar = case try Term.dest_TVar T

      of SOME (tvar as (_, sort)) => if null (filter (can (AxClass.get_info thy)) sort)

           then tvar

           else error ("Bad sort: " ^ Display.string_of_thm_global thy thm)

       | _ => error ("Bad type: " ^ Display.string_of_thm_global thy thm);

     val _ = if Term.add_tvars eqn [] = [tvar] then ()

       else error ("Inconsistent type: " ^ Display.string_of_thm_global thy thm);

     val lhs_rhs = case try Logic.dest_equals eqn

      of SOME lhs_rhs => lhs_rhs

       | _ => error ("Not an equation: " ^ Syntax.string_of_term_global thy eqn);

     val c_c' = case try (pairself (Code.check_const thy)) lhs_rhs

      of SOME c_c' => c_c'

       | _ => error ("Not an equation with two constants: "

           ^ Syntax.string_of_term_global thy eqn);

     val _ = if the_list (AxClass.class_of_param thy (snd c_c')) = [class] then ()

       else error ("Inconsistent class: " ^ Display.string_of_thm_global thy thm);

   in Triv_Class_Data.map (AList.update (op =) (class, thm)) thy end;

 local

 val get_triv_classes = map fst o Triv_Class_Data.get;

 val (_, triv_of_class) = Context.>>> (Context.map_theory_result

   (Thm.add_oracle (Binding.name "triv_of_class", fn (thy, T, class) =>

     Thm.cterm_of thy (Logic.mk_of_class (T, class)))));

 in

 fun lift_triv_classes_conv thy conv ct =

   let

     val algebra = Sign.classes_of thy;

     val certT = Thm.ctyp_of thy;

     val triv_classes = get_triv_classes thy;

     fun additional_classes sort = filter_out (fn class => Sorts.sort_le algebra (sort, [class])) triv_classes;

     fun mk_entry (v, sort) =

       let

         val T = TFree (v, sort);

         val cT = certT T;

         val triv_sort = additional_classes sort;

       in

         (v, (Sorts.inter_sort algebra (sort, triv_sort),

           (cT, AList.make (fn class => Thm.of_class (cT, class)) sort

             @ AList.make (fn class => triv_of_class (thy, T, class)) triv_sort)))

       end;

     val vs_tab = map mk_entry (Term.add_tfrees (Thm.term_of ct) []);

     fun instantiate thm =

       let

         val cert_tvars = map (certT o TVar) (Term.add_tvars

           ((fst o Logic.dest_equals o Logic.strip_imp_concl o Thm.prop_of) thm) []);

         val instantiation =

           map2 (fn cert_tvar => fn (_, (_, (cT, _))) => (cert_tvar, cT)) cert_tvars vs_tab;

       in Thm.instantiate (instantiation, []) thm end;

     fun of_class (TFree (v, _), class) =

           the (AList.lookup (op =) ((snd o snd o the o AList.lookup (op =) vs_tab) v) class)

       | of_class (T, _) = error ("Bad type " ^ Syntax.string_of_typ_global thy T);

     fun strip_of_class thm =

       let

         val prems_of_class = Thm.prop_of thm

           |> Logic.strip_imp_prems

           |> map (Logic.dest_of_class #> of_class);

       in fold Thm.elim_implies prems_of_class thm end;

   in

     ct

     |> (Drule.cterm_fun o map_types o map_type_tfree)

         (fn (v, sort) => TFree (v, (fst o the o AList.lookup (op =) vs_tab) v))

     |> conv

     |> Thm.strip_shyps

     |> Thm.varifyT_global

     |> Thm.unconstrainT

     |> instantiate

     |> strip_of_class

   end;

 fun lift_triv_classes_rew thy rew t =

   let

     val algebra = Sign.classes_of thy;

     val triv_classes = get_triv_classes thy;

     val vs = Term.add_tfrees t [];

   in t

     |> (map_types o map_type_tfree)

         (fn (v, sort) => TFree (v, Sorts.inter_sort algebra (sort, triv_classes)))

     |> rew

     |> (map_types o map_type_tfree)

         (fn (v, _) => TFree (v, the (AList.lookup (op =) vs v)))

   end;

 end;

 (** the semantic universe **)

 (*

    Functions are given by their semantical function value. To avoid

    trouble with the ML-type system, these functions have the most

    generic type, that is "Univ list -> Univ". The calling convention is

    that the arguments come as a list, the last argument first. In

    other words, a function call that usually would look like

    f x_1 x_2 ... x_n   or   f(x_1,x_2, ..., x_n)

    would be in our convention called as

               f [x_n,..,x_2,x_1]

    Moreover, to handle functions that are still waiting for some

    arguments we have additionally a list of arguments collected to far

    and the number of arguments we're still waiting for.

 *)

 datatype Univ =

     Const of int * Univ list           (*named (uninterpreted) constants*)

   | DFree of string * int              (*free (uninterpreted) dictionary parameters*)

   | BVar of int * Univ list            (*bound variables, named*)

   | Abs of (int * (Univ list -> Univ)) * Univ list

                                        (*abstractions as closures*);

 fun same (Const (k, xs)) (Const (l, ys)) = k = l andalso sames xs ys

   | same (DFree (s, k)) (DFree (t, l)) = s = t andalso k = l

   | same (BVar (k, xs)) (BVar (l, ys)) = k = l andalso sames xs ys

   | same _ _ = false

 and sames xs ys = length xs = length ys andalso forall (uncurry same) (xs ~~ ys);

 (* constructor functions *)

 fun abss n f = Abs ((n, f), []);

 fun apps (Abs ((n, f), xs)) ys = let val k = n - length ys in

       case int_ord (k, 0)

        of EQUAL => f (ys @ xs)

         | LESS => let val (zs, ws) = chop (~ k) ys in apps (f (ws @ xs)) zs end

         | GREATER => Abs ((k, f), ys @ xs) (*note: reverse convention also for apps!*)

       end

   | apps (Const (name, xs)) ys = Const (name, ys @ xs)

   | apps (BVar (n, xs)) ys = BVar (n, ys @ xs);

 (** assembling and compiling ML code from terms **)

 (* abstract ML syntax *)

 infix 9 `$` `$$`;

 fun e1 `$` e2 = "(" ^ e1 ^ " " ^ e2 ^ ")";

 fun e `$$` [] = e

   | e `$$` es = "(" ^ e ^ " " ^ space_implode " " es ^ ")";

 fun ml_abs v e = "(fn " ^ v ^ " => " ^ e ^ ")";

 fun ml_cases t cs =

   "(case " ^ t ^ " of " ^ space_implode " | " (map (fn (p, t) => p ^ " => " ^ t) cs) ^ ")";

 fun ml_Let d e = "let\n" ^ d ^ " in " ^ e ^ " end";

 fun ml_as v t = "(" ^ v ^ " as " ^ t ^ ")";

 fun ml_and [] = "true"

   | ml_and [x] = x

   | ml_and xs = "(" ^ space_implode " andalso " xs ^ ")";

 fun ml_if b x y = "(if " ^ b ^ " then " ^ x ^ " else " ^ y ^ ")";

 fun ml_list es = "[" ^ commas es ^ "]";

 fun ml_fundefs ([(name, [([], e)])]) =

       "val " ^ name ^ " = " ^ e ^ "\n"

   | ml_fundefs (eqs :: eqss) =

       let

         fun fundef (name, eqs) =

           let

             fun eqn (es, e) = name ^ " " ^ space_implode " " es ^ " = " ^ e

           in space_implode "\n  | " (map eqn eqs) end;

       in

         (prefix "fun " o fundef) eqs :: map (prefix "and " o fundef) eqss

         |> cat_lines

         |> suffix "\n"

       end;

 (* nbe specific syntax and sandbox communication *)

 val univs_ref = Unsynchronized.ref (NONE : (unit -> Univ list -> Univ list) option);

 local

   val prefix =      "Nbe.";

   val name_ref =    prefix ^ "univs_ref";

   val name_const =  prefix ^ "Const";

   val name_abss =   prefix ^ "abss";

   val name_apps =   prefix ^ "apps";

   val name_same =   prefix ^ "same";

 in

 val univs_cookie = (name_ref, univs_ref);

 fun nbe_fun 0 "" = "nbe_value"

   | nbe_fun i c = "c_" ^ translate_string (fn "." => "_" | c => c) c ^ "_" ^ string_of_int i;

 fun nbe_dict v n = "d_" ^ v ^ "_" ^ string_of_int n;

 fun nbe_bound v = "v_" ^ v;

 fun nbe_bound_optional NONE = "_"

   | nbe_bound_optional (SOME v) = nbe_bound v;

 fun nbe_default v = "w_" ^ v;

 (*note: these three are the "turning spots" where proper argument order is established!*)

 fun nbe_apps t [] = t

   | nbe_apps t ts = name_apps `$$` [t, ml_list (rev ts)];

 fun nbe_apps_local i c ts = nbe_fun i c `$` ml_list (rev ts);

 fun nbe_apps_constr idx_of c ts =

   let

     val c' = if !trace then string_of_int (idx_of c) ^ " (*" ^ c ^ "*)"

       else string_of_int (idx_of c);

   in name_const `$` ("(" ^ c' ^ ", " ^ ml_list (rev ts) ^ ")") end;

 fun nbe_abss 0 f = f `$` ml_list []

   | nbe_abss n f = name_abss `$$` [string_of_int n, f];

 fun nbe_same v1 v2 = "(" ^ name_same ^ " " ^ nbe_bound v1 ^ " " ^ nbe_bound v2 ^ ")";

 end;

 open Basic_Code_Thingol;

 (* code generation *)

 fun assemble_eqnss idx_of deps eqnss =

   let

     fun prep_eqns (c, (vs, eqns)) =

       let

         val dicts = maps (fn (v, sort) => map_index (nbe_dict v o fst) sort) vs;

         val num_args = length dicts + ((length o fst o hd) eqns);

       in (c, (num_args, (dicts, eqns))) end;

     val eqnss' = map prep_eqns eqnss;

     fun assemble_constapp c dss ts = 

       let

         val ts' = (maps o map) assemble_idict dss @ ts;

       in case AList.lookup (op =) eqnss' c

        of SOME (num_args, _) => if num_args <= length ts'

             then let val (ts1, ts2) = chop num_args ts'

             in nbe_apps (nbe_apps_local 0 c ts1) ts2

             end else nbe_apps (nbe_abss num_args (nbe_fun 0 c)) ts'

         | NONE => if member (op =) deps c

             then nbe_apps (nbe_fun 0 c) ts'

             else nbe_apps_constr idx_of c ts'

       end

     and assemble_idict (DictConst (inst, dss)) =

           assemble_constapp inst dss []

       | assemble_idict (DictVar (supers, (v, (n, _)))) =

           fold_rev (fn super => assemble_constapp super [] o single) supers (nbe_dict v n);

     fun assemble_iterm constapp =

       let

         fun of_iterm match_cont t =

           let

             val (t', ts) = Code_Thingol.unfold_app t

           in of_iapp match_cont t' (fold_rev (cons o of_iterm NONE) ts []) end

         and of_iapp match_cont (IConst (c, ((_, dss), _))) ts = constapp c dss ts

           | of_iapp match_cont (IVar v) ts = nbe_apps (nbe_bound_optional v) ts

           | of_iapp match_cont ((v, _) `|=> t) ts =

               nbe_apps (nbe_abss 1 (ml_abs (ml_list [nbe_bound_optional v]) (of_iterm NONE t))) ts

           | of_iapp match_cont (ICase (((t, _), cs), t0)) ts =

               nbe_apps (ml_cases (of_iterm NONE t)

                 (map (fn (p, t) => (of_iterm NONE p, of_iterm match_cont t)) cs

                   @ [("_", case match_cont of SOME s => s | NONE => of_iterm NONE t0)])) ts

       in of_iterm end;

     fun subst_nonlin_vars args =

       let

         val vs = (fold o Code_Thingol.fold_varnames)

           (fn v => AList.map_default (op =) (v, 0) (Integer.add 1)) args [];

         val names = Name.make_context (map fst vs);

         fun declare v k ctxt = let val vs = Name.invents ctxt v k

           in (vs, fold Name.declare vs ctxt) end;

         val (vs_renames, _) = fold_map (fn (v, k) => if k > 1

           then declare v (k - 1) #>> (fn vs => (v, vs))

           else pair (v, [])) vs names;

         val samepairs = maps (fn (v, vs) => map (pair v) vs) vs_renames;

         fun subst_vars (t as IConst _) samepairs = (t, samepairs)

           | subst_vars (t as IVar NONE) samepairs = (t, samepairs)

           | subst_vars (t as IVar (SOME v)) samepairs = (case AList.lookup (op =) samepairs v

              of SOME v' => (IVar (SOME v'), AList.delete (op =) v samepairs)

               | NONE => (t, samepairs))

           | subst_vars (t1 `$ t2) samepairs = samepairs

               |> subst_vars t1

               ||>> subst_vars t2

               |>> (op `$)

           | subst_vars (ICase (_, t)) samepairs = subst_vars t samepairs;

         val (args', _) = fold_map subst_vars args samepairs;

       in (samepairs, args') end;

     fun assemble_eqn c dicts default_args (i, (args, rhs)) =

       let

         val is_eval = (c = "");

         val default_rhs = nbe_apps_local (i+1) c (dicts @ default_args);

         val match_cont = if is_eval then NONE else SOME default_rhs;

         val assemble_arg = assemble_iterm

           (fn c => fn _ => fn ts => nbe_apps_constr idx_of c ts) NONE;

         val assemble_rhs = assemble_iterm assemble_constapp match_cont;

         val (samepairs, args') = subst_nonlin_vars args;

         val s_args = map assemble_arg args';

         val s_rhs = if null samepairs then assemble_rhs rhs

           else ml_if (ml_and (map (uncurry nbe_same) samepairs))

             (assemble_rhs rhs) default_rhs;

         val eqns = if is_eval then

             [([ml_list (rev (dicts @ s_args))], s_rhs)]

           else

             [([ml_list (rev (dicts @ map2 ml_as default_args s_args))], s_rhs),

               ([ml_list (rev (dicts @ default_args))], default_rhs)]

       in (nbe_fun i c, eqns) end;

     fun assemble_eqns (c, (num_args, (dicts, eqns))) =

       let

         val default_args = map nbe_default

           (Name.invent_list [] "a" (num_args - length dicts));

         val eqns' = map_index (assemble_eqn c dicts default_args) eqns

           @ (if c = "" then [] else [(nbe_fun (length eqns) c,

             [([ml_list (rev (dicts @ default_args))],

               nbe_apps_constr idx_of c (dicts @ default_args))])]);

       in (eqns', nbe_abss num_args (nbe_fun 0 c)) end;

     val (fun_vars, fun_vals) = map_split assemble_eqns eqnss';

     val deps_vars = ml_list (map (nbe_fun 0) deps);

   in ml_abs deps_vars (ml_Let (ml_fundefs (flat fun_vars)) (ml_list fun_vals)) end;

 (* code compilation *)

 fun compile_eqnss ctxt gr raw_deps [] = []

   | compile_eqnss ctxt gr raw_deps eqnss =

       let

         val (deps, deps_vals) = split_list (map_filter

           (fn dep => Option.map (fn univ => (dep, univ)) (fst ((Graph.get_node gr dep)))) raw_deps);

         val idx_of = raw_deps

           |> map (fn dep => (dep, snd (Graph.get_node gr dep)))

           |> AList.lookup (op =)

           |> (fn f => the o f);

         val s = assemble_eqnss idx_of deps eqnss;

         val cs = map fst eqnss;

       in

         s

         |> traced (fn s => "\n--- code to be evaluated:\n" ^ s)

         |> ML_Context.evaluate ctxt (!trace) univs_cookie

         |> (fn f => f deps_vals)

         |> (fn univs => cs ~~ univs)

       end;

 (* preparing function equations *)

 fun eqns_of_stmt (_, Code_Thingol.Fun (_, ((_, []), _))) =

       []

   | eqns_of_stmt (const, Code_Thingol.Fun (_, (((vs, _), eqns), _))) =

       [(const, (vs, map fst eqns))]

   | eqns_of_stmt (_, Code_Thingol.Datatypecons _) =

       []

   | eqns_of_stmt (_, Code_Thingol.Datatype _) =

       []

   | eqns_of_stmt (class, Code_Thingol.Class (_, (v, (super_classes, classparams)))) =

       let

         val names = map snd super_classes @ map fst classparams;

         val params = Name.invent_list [] "d" (length names);

         fun mk (k, name) =

           (name, ([(v, [])],

             [([IConst (class, (([], []), [])) `$$ map (IVar o SOME) params],

               IVar (SOME (nth params k)))]));

       in map_index mk names end

   | eqns_of_stmt (_, Code_Thingol.Classrel _) =

       []

   | eqns_of_stmt (_, Code_Thingol.Classparam _) =

       []

   | eqns_of_stmt (inst, Code_Thingol.Classinst ((class, (_, arity_args)), (super_instances, classparam_instances))) =

       [(inst, (arity_args, [([], IConst (class, (([], []), [])) `$$

         map (fn (_, (_, (inst, dss))) => IConst (inst, (([], dss), []))) super_instances

         @ map (IConst o snd o fst) classparam_instances)]))];

 fun compile_stmts ctxt stmts_deps =

   let

     val names = map (fst o fst) stmts_deps;

     val names_deps = map (fn ((name, _), deps) => (name, deps)) stmts_deps;

     val eqnss = maps (eqns_of_stmt o fst) stmts_deps;

     val refl_deps = names_deps

       |> maps snd

       |> distinct (op =)

       |> fold (insert (op =)) names;

     fun new_node name (gr, (maxidx, idx_tab)) = if can (Graph.get_node gr) name

       then (gr, (maxidx, idx_tab))

       else (Graph.new_node (name, (NONE, maxidx)) gr,

         (maxidx + 1, Inttab.update_new (maxidx, name) idx_tab));

     fun compile gr = eqnss

       |> compile_eqnss ctxt gr refl_deps

       |> rpair gr;

   in

     fold new_node refl_deps

     #> apfst (fold (fn (name, deps) => fold (curry Graph.add_edge name) deps) names_deps

       #> compile

       #-> fold (fn (name, univ) => (Graph.map_node name o apfst) (K (SOME univ))))

   end;

 fun ensure_stmts ctxt program =

   let

     fun add_stmts names (gr, (maxidx, idx_tab)) = if exists ((can o Graph.get_node) gr) names

       then (gr, (maxidx, idx_tab))

       else (gr, (maxidx, idx_tab))

         |> compile_stmts ctxt (map (fn name => ((name, Graph.get_node program name),

           Graph.imm_succs program name)) names);

   in

     fold_rev add_stmts (Graph.strong_conn program)

   end;

 (** evaluation **)

 (* term evaluation *)

 fun eval_term ctxt gr deps (vs : (string * sort) list, t) =

   let 

     val dict_frees = maps (fn (v, sort) => map_index (curry DFree v o fst) sort) vs;

   in

     ("", (vs, [([], t)]))

     |> singleton (compile_eqnss ctxt gr deps)

     |> snd

     |> (fn t => apps t (rev dict_frees))

   end;

 (* reification *)

 fun typ_of_itype program vs (ityco `%% itys) =

       let

         val Code_Thingol.Datatype (tyco, _) = Graph.get_node program ityco;

       in Type (tyco, map (typ_of_itype program vs) itys) end

   | typ_of_itype program vs (ITyVar v) =

       let

         val sort = (the o AList.lookup (op =) vs) v;

       in TFree ("'" ^ v, sort) end;

 fun term_of_univ thy program idx_tab t =

   let

     fun take_until f [] = []

       | take_until f (x::xs) = if f x then [] else x :: take_until f xs;

     fun is_dict (Const (idx, _)) = (case (Graph.get_node program o the o Inttab.lookup idx_tab) idx

          of Code_Thingol.Class _ => true

           | Code_Thingol.Classrel _ => true

           | Code_Thingol.Classinst _ => true

           | _ => false)

       | is_dict (DFree _) = true

       | is_dict _ = false;

     fun const_of_idx idx = (case (Graph.get_node program o the o Inttab.lookup idx_tab) idx

      of Code_Thingol.Fun (c, _) => c

       | Code_Thingol.Datatypecons (c, _) => c

       | Code_Thingol.Classparam (c, _) => c);

     fun of_apps bounds (t, ts) =

       fold_map (of_univ bounds) ts

       #>> (fn ts' => list_comb (t, rev ts'))

     and of_univ bounds (Const (idx, ts)) typidx =

           let

             val ts' = take_until is_dict ts;

             val c = const_of_idx idx;

             val T = map_type_tvar (fn ((v, i), _) =>

               Type_Infer.param typidx (v ^ string_of_int i, []))

                 (Sign.the_const_type thy c);

             val typidx' = typidx + 1;

           in of_apps bounds (Term.Const (c, T), ts') typidx' end

       | of_univ bounds (BVar (n, ts)) typidx =

           of_apps bounds (Bound (bounds - n - 1), ts) typidx

       | of_univ bounds (t as Abs _) typidx =

           typidx

           |> of_univ (bounds + 1) (apps t [BVar (bounds, [])])

           |-> (fn t' => pair (Term.Abs ("u", dummyT, t')))

   in of_univ 0 t 0 |> fst end;

 (* function store *)

 structure Nbe_Functions = Code_Data

 (

   type T = (Univ option * int) Graph.T * (int * string Inttab.table);

   val empty = (Graph.empty, (0, Inttab.empty));

 );

 (* compilation, evaluation and reification *)

 fun compile_eval thy program vs_t deps =

   let

     val ctxt = ProofContext.init_global thy;

     val (gr, (_, idx_tab)) =

       Nbe_Functions.change thy (ensure_stmts ctxt program);

   in

     vs_t

     |> eval_term ctxt gr deps

     |> term_of_univ thy program idx_tab

   end;

 (* evaluation with type reconstruction *)

 fun normalize thy program ((vs0, (vs, ty)), t) deps =

   let

     val ty' = typ_of_itype program vs0 ty;

     fun type_infer t =

       singleton (Type_Infer.infer_types (Syntax.pp_global thy) (Sign.tsig_of thy) I

         (try (Type.strip_sorts o Sign.the_const_type thy)) (K NONE) Name.context 0)

       (Type_Infer.constrain ty' t);

     fun check_tvars t = if null (Term.add_tvars t []) then t else

       error ("Illegal schematic type variables in normalized term: "

         ^ setmp_CRITICAL show_types true (Syntax.string_of_term_global thy) t);

     val string_of_term = setmp_CRITICAL show_types true (Syntax.string_of_term_global thy);

   in

     compile_eval thy program (vs, t) deps

     |> traced (fn t => "Normalized:\n" ^ string_of_term t)

     |> type_infer

     |> traced (fn t => "Types inferred:\n" ^ string_of_term t)

     |> check_tvars

     |> traced (fn _ => "---\n")

   end;

 (* evaluation oracle *)

 fun mk_equals thy lhs raw_rhs =

   let

     val ty = Thm.typ_of (Thm.ctyp_of_term lhs);

     val eq = Thm.cterm_of thy (Term.Const ("==", ty --> ty --> propT));

     val rhs = Thm.cterm_of thy raw_rhs;

   in Thm.mk_binop eq lhs rhs end;

 val (_, raw_norm_oracle) = Context.>>> (Context.map_theory_result

   (Thm.add_oracle (Binding.name "norm", fn (thy, program, vsp_ty_t, deps, ct) =>

     mk_equals thy ct (normalize thy program vsp_ty_t deps))));

 fun norm_oracle thy program vsp_ty_t deps ct =

   raw_norm_oracle (thy, program, vsp_ty_t, deps, ct);

 fun no_frees_rew rew t =

   let

     val frees = map Free (Term.add_frees t []);

   in

     t

     |> fold_rev lambda frees

     |> rew

     |> (fn t' => Term.betapplys (t', frees))

   end;

 val norm_conv = Code_Simp.no_frees_conv (fn ct =>

   let

     val thy = Thm.theory_of_cterm ct;

   in lift_triv_classes_conv thy (Code_Thingol.eval_conv thy (K (norm_oracle thy))) ct end);

 fun norm thy = lift_triv_classes_rew thy (no_frees_rew (Code_Thingol.eval thy I (K (normalize thy))));

 (* evaluation command *)

 fun norm_print_term ctxt modes t =

   let

     val thy = ProofContext.theory_of ctxt;

     val t' = norm thy t;

     val ty' = Term.type_of t';

     val ctxt' = Variable.auto_fixes t ctxt;

     val p = Print_Mode.with_modes modes (fn () =>

       Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk,

         Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) ();

   in Pretty.writeln p end;

 (** Isar setup **)

 fun norm_print_term_cmd (modes, s) state =

   let val ctxt = Toplevel.context_of state

   in norm_print_term ctxt modes (Syntax.read_term ctxt s) end;

 val setup = Value.add_evaluator ("nbe", norm o ProofContext.theory_of);

 val opt_modes =

   Scan.optional (Parse.$$$ "(" |-- Parse.!!! (Scan.repeat1 Parse.xname --| Parse.$$$ ")")) [];

 val _ =

   Outer_Syntax.improper_command "normal_form" "normalize term by evaluation" Keyword.diag

     (opt_modes -- Parse.term >> (Toplevel.keep o norm_print_term_cmd));

 end;