(*  Title:      Tools/nbe.ML

     ID:         $Id$

     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_term: theory -> term -> term

   datatype Univ =

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

     | Free of string * Univ list             (*free (uninterpreted) variables*)

     | 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 univs_ref: (unit -> Univ list -> Univ list) option ref

   val trace: bool ref

   val setup: class list -> (string * string) list -> theory -> theory

 end;

 structure Nbe: NBE =

 struct

 (* generic non-sense *)

 val trace = ref false;

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

 (** the semantical 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*)

   | Free of string * Univ list         (*free variables*)

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

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

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

                                       (*abstractions as closures*);

 (* constructor functions *)

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

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

       if k = 0 then f (ys @ xs)

       else if k < 0 then

         let val (zs, ws) = chop (~ k) ys

         in apps (f (ws @ xs)) zs end

       else Abs ((k, f), ys @ xs) end (*note: reverse convention also for apps!*)

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

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

   | apps (BVar (name, xs)) ys = BVar (name, 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_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

         |> space_implode "\n"

         |> suffix "\n"

       end;

 (* nbe specific syntax and sandbox communication *)

 val univs_ref = 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";

 in

 val univs_cookie = (name_ref, univs_ref);

 fun nbe_fun "" = "nbe_value"

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

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

 fun nbe_bound v = "v_" ^ 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 c ts = nbe_fun c `$` ml_list (rev ts);

 fun nbe_apps_constr idx ts =

   name_const `$` ("(" ^ string_of_int idx ^ ", " ^ ml_list (rev ts) ^ ")");

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

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

 end;

 open BasicCodeThingol;

 (* 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 (n, _) => if n <= length ts'

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

             in nbe_apps (nbe_apps_local c ts1) ts2

             end else nbe_apps (nbe_abss n (nbe_fun c)) ts'

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

             then nbe_apps (nbe_fun 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 t =

           let

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

           in of_iapp t' (fold_rev (cons o of_iterm) ts []) end

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

           | of_iapp (IVar v) ts = nbe_apps (nbe_bound v) ts

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

               nbe_apps (nbe_abss 1 (ml_abs (ml_list [nbe_bound v]) (of_iterm t))) ts

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

               nbe_apps (ml_cases (of_iterm t) (map (pairself of_iterm) cs

                 @ [("_", of_iterm t0)])) ts

       in of_iterm end;

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

       let

         val assemble_arg = assemble_iterm

           (fn c => fn _ => fn ts => nbe_apps_constr (idx_of c) ts);

         val assemble_rhs = assemble_iterm assemble_constapp;

         fun assemble_eqn (args, rhs) =

           ([ml_list (rev (dicts @ map assemble_arg args))], assemble_rhs rhs);

         val default_args = map nbe_bound (Name.invent_list [] "a" num_args);

         val default_eqn = if c = "" then NONE

           else SOME ([ml_list (rev default_args)],

             nbe_apps_constr (idx_of c) default_args);

       in

         ((nbe_fun c, map assemble_eqn eqns @ the_list default_eqn),

           nbe_abss num_args (nbe_fun c))

       end;

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

     val deps_vars = ml_list (map nbe_fun deps);

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

 (* code compilation *)

 fun compile_eqnss gr raw_deps [] = []

   | compile_eqnss 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

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

         |> ML_Context.evaluate

             (Output.tracing o enclose "\n---compiler echo:\n" "\n---\n",

             Output.tracing o enclose "\n--- compiler echo (with error):\n" "\n---\n")

             (!trace) univs_cookie

         |> (fn f => f deps_vals)

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

       end;

 (* preparing function equations *)

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

       []

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

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

   | eqns_of_stmt (_, CodeThingol.Datatypecons _) =

       []

   | eqns_of_stmt (_, CodeThingol.Datatype _) =

       []

   | eqns_of_stmt (class, CodeThingol.Class (v, (superclasses, classops))) =

       let

         val names = map snd superclasses @ map fst classops;

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

         fun mk (k, name) =

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

             [([IConst (class, ([], [])) `$$ map IVar params], IVar (nth params k))]));

       in map_index mk names end

   | eqns_of_stmt (_, CodeThingol.Classrel _) =

       []

   | eqns_of_stmt (_, CodeThingol.Classparam _) =

       []

   | eqns_of_stmt (inst, CodeThingol.Classinst ((class, (_, arities)), (superinsts, instops))) =

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

         map (fn (_, (_, (inst, dicts))) => IConst (inst, (dicts, []))) superinsts

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

 fun compile_stmts 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 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 code =

   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 (map (fn name => ((name, Graph.get_node code name),

           Graph.imm_succs code name)) names);

   in fold_rev add_stmts (Graph.strong_conn code) end;

 (** evaluation **)

 (* term evaluation *)

 fun eval_term gr deps ((vs, ty), t) =

   let 

     val frees = CodeThingol.fold_unbound_varnames (insert (op =)) t []

     val frees' = map (fn v => Free (v, [])) frees;

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

   in

     ("", (vs, [(map IVar frees, t)]))

     |> singleton (compile_eqnss gr deps)

     |> snd

     |> (fn t => apps t (rev (dict_frees @ frees')))

   end;

 (* reification *)

 fun term_of_univ thy 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, _)) =

           let

             val c = the (Inttab.lookup idx_tab idx);

           in

             (is_some o CodeName.class_rev thy) c

             orelse (is_some o CodeName.classrel_rev thy) c

             orelse (is_some o CodeName.instance_rev thy) c

           end

       | is_dict (DFree _) = true

       | is_dict _ = false;

     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 = (the o CodeName.const_rev thy o the o Inttab.lookup idx_tab) idx;

             val T = Code.default_typ thy c;

             val T' = map_type_tvar (fn ((v, i), S) => TypeInfer.param (typidx + i) (v, [])) T;

             val typidx' = typidx + maxidx_of_typ T' + 1;

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

       | of_univ bounds (Free (name, ts)) typidx =

           of_apps bounds (Term.Free (name, dummyT), ts) typidx

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

           of_apps bounds (Bound (bounds - name - 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 = CodeDataFun

 (

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

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

   fun merge _ ((gr1, (maxidx1, idx_tab1)), (gr2, (maxidx2, idx_tab2))) =

     (Graph.merge (K true) (gr1, gr2), (IntInf.max (maxidx1, maxidx2),

       Inttab.merge (K true) (idx_tab1, idx_tab2)));

   fun purge _ NONE _ = empty

     | purge NONE _ _ = empty

     | purge (SOME thy) (SOME cs) (gr, (maxidx, idx_tab)) =

         let

           val cs_exisiting =

             map_filter (CodeName.const_rev thy) (Graph.keys gr);

           val dels = (Graph.all_preds gr

               o map (CodeName.const thy)

               o filter (member (op =) cs_exisiting)

             ) cs;

         in (Graph.del_nodes dels gr, (maxidx, idx_tab)) end;

 );

 (* compilation, evaluation and reification *)

 fun compile_eval thy code vs_ty_t deps =

   let

     val (gr, (_, idx_tab)) = Nbe_Functions.change thy (ensure_stmts code);

   in

     vs_ty_t

     |> eval_term gr deps

     |> term_of_univ thy idx_tab

   end;

 (* trivial type classes *)

 structure Nbe_Triv_Classes = TheoryDataFun

 (

   type T = class list * (string * string) list;

   val empty = ([], []);

   val copy = I;

   val extend = I;

   fun merge _ ((classes1, consts1), (classes2, consts2)) =

     (Library.merge (op =) (classes1, classes2), Library.merge (op =) (consts1, consts2));

 )

 fun add_triv_classes thy =

   let

     val (trivs, _) = Nbe_Triv_Classes.get thy;

     val inters = curry (Sorts.inter_sort (Sign.classes_of thy)) trivs;

     fun map_sorts f = (map_types o map_atyps)

       (fn TVar (v, sort) => TVar (v, f sort)

         | TFree (v, sort) => TFree (v, f sort));

   in map_sorts inters end;

 fun subst_triv_consts thy =

   let

     fun subst_const f = map_aterms (fn t as Term.Const (c, ty) => (case f c

          of SOME c' => Term.Const (c', ty)

           | NONE => t)

       | t => t);

     val (_, consts) = Nbe_Triv_Classes.get thy;

     val subst_inst = perhaps (Option.map fst o AxClass.inst_of_param thy);

   in map_aterms (subst_const (AList.lookup (op =) consts o subst_inst)) end;

 (* evaluation with type reconstruction *)

 fun eval thy t code vs_ty_t deps =

   let

     val ty = type_of t;

     val type_free = AList.lookup (op =)

       (map (fn (s, T) => (s, Term.Free (s, T))) (Term.add_frees t []));

     val type_frees = Term.map_aterms

       (fn (t as Term.Free (s, _)) => the_default t (type_free s) | t => t);

     fun type_infer t = [(t, ty)]

       |> TypeInfer.infer_types (Sign.pp thy) (Sign.tsig_of thy) I

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

            Name.context 0 NONE

       |> fst |> the_single |> fst;

     fun check_tvars t = if null (Term.term_tvars t) then t else

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

         ^ setmp show_types true (Sign.string_of_term thy) t);

     val string_of_term = setmp show_types true (Sign.string_of_term thy);

   in

     compile_eval thy code vs_ty_t deps

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

     |> subst_triv_consts thy

     |> type_frees

     |> tracing (fn t => "Vars typed:\n" ^ string_of_term t)

     |> type_infer

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

     |> check_tvars

     |> tracing (fn t => "---\n")

   end;

 (* evaluation oracle *)

 exception Norm of term * CodeThingol.code

   * (CodeThingol.typscheme * CodeThingol.iterm) * string list;

 fun norm_oracle (thy, Norm (t, code, vs_ty_t, deps)) =

   Logic.mk_equals (t, eval thy t code vs_ty_t deps);

 fun norm_invoke thy t code vs_ty_t deps =

   Thm.invoke_oracle_i thy "HOL.norm" (thy, Norm (t, code, vs_ty_t, deps));

   (*FIXME get rid of hardwired theory name*)

 fun norm_conv ct =

   let

     val thy = Thm.theory_of_cterm ct;

     fun evaluator' t code vs_ty_t deps = norm_invoke thy t code vs_ty_t deps;

     fun evaluator t = (add_triv_classes thy t, evaluator' t);

   in CodePackage.evaluate_conv thy evaluator ct end;

 fun norm_term thy t =

   let

     fun evaluator' t code vs_ty_t deps = eval thy t code vs_ty_t deps;

     fun evaluator t = (add_triv_classes thy t, evaluator' t);

   in (Code.postprocess_term thy o CodePackage.evaluate_term thy evaluator) t end;

 (* evaluation command *)

 fun norm_print_term ctxt modes t =

   let

     val thy = ProofContext.theory_of ctxt;

     val t' = norm_term thy t;

     val ty' = Term.type_of t';

     val p = PrintMode.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;

 fun setup nbe_classes nbe_consts =

   Theory.add_oracle ("norm", norm_oracle)

   #> Nbe_Triv_Classes.map (K (nbe_classes, nbe_consts));

 local structure P = OuterParse and K = OuterKeyword in

 val opt_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) [];

 val _ =

   OuterSyntax.improper_command "normal_form" "normalize term by evaluation" K.diag

     (opt_modes -- P.typ >> (Toplevel.keep o norm_print_term_cmd));

 end;

 end;