(*  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

   datatype Univ = 

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

     | Free of string * Univ list

     | BVar of int * Univ list

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

   val free: string -> Univ list -> Univ       (*free (uninterpreted) variables*)

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

                                             (*abstractions as functions*)

   val app: Univ -> Univ -> Univ              (*explicit application*)

   val univs_ref: (unit -> Univ list) ref 

   val lookup_fun: string -> Univ

   val norm_conv: cterm -> thm

   val norm_term: theory -> term -> term

   val trace: bool ref

   val setup: 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 string * Univ list        (*named (uninterpreted) constants*)

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

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

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

                                       (*abstractions as closures*);

 (* constructor functions *)

 val free = curry Free;

 fun abs n f ts = Abs ((n, f), ts);

 fun app (Abs ((1, f), xs)) x = f (x :: xs)

   | app (Abs ((n, f), xs)) x = Abs ((n - 1, f), x :: xs)

   | app (Const (name, args)) x = Const (name, x :: args)

   | app (Free (name, args)) x = Free (name, x :: args)

   | app (BVar (name, args)) x = BVar (name, x :: args);

 (* global functions store *)

 structure Nbe_Functions = CodeDataFun

 (

   type T = Univ Graph.T;

   val empty = Graph.empty;

   fun merge _ = Graph.merge (K true);

   fun purge _ NONE _ = Graph.empty

     | purge NONE _ _ = Graph.empty

     | purge (SOME thy) (SOME cs) gr = Graph.empty

         (*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 end*);

 );

 fun defined gr = can (Graph.get_node gr);

 (* sandbox communication *)

 val univs_ref = ref (fn () => [] : Univ list);

 local

 val gr_ref = ref NONE : Nbe_Functions.T option ref;

 in

 fun lookup_fun s = case ! gr_ref

  of NONE => error "compile_univs"

   | SOME gr => Graph.get_node gr s;

 fun compile_univs tab ([], _) = []

   | compile_univs tab (cs, raw_s) =

       let

         val _ = univs_ref := (fn () => []);

         val s = "Nbe.univs_ref := " ^ raw_s;

         val _ = tracing (fn () => "\n--- generated code:\n" ^ s) ();

         val _ = gr_ref := SOME tab;

         val _ = use_text "" (Output.tracing o enclose "\n---compiler echo:\n" "\n---\n",

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

           (!trace) s;

         val _ = gr_ref := NONE;

         val univs = case !univs_ref () of [] => error "compile_univs" | univs => univs;

       in cs ~~ univs end;

 end; (*local*)

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

 (* abstract ML syntax *)

 infix 9 `$` `$$`;

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

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

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

 fun ml_Val v s = "val " ^ v ^ " = " ^ s;

 fun ml_cases t cs =

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

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

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

 val ml_delay = ml_abs "()"

 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 *)

 local

   val prefix =          "Nbe.";

   val name_const =      prefix ^ "Const";

   val name_free =       prefix ^ "free";

   val name_abs =        prefix ^ "abs";

   val name_app =        prefix ^ "app";

   val name_lookup_fun = prefix ^ "lookup_fun";

 in

 fun nbe_const c ts = name_const `$` ("(" ^ ML_Syntax.print_string c ^ ", " ^ ml_list ts ^ ")");

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

 fun nbe_free v = name_free `$$` [ML_Syntax.print_string v, ml_list []];

 fun nbe_bound v = "v_" ^ v;

 fun nbe_apps e es =

   Library.foldr (fn (s, e) => name_app `$$` [e, s]) (es, e);

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

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

 fun nbe_lookup c = ml_Val (nbe_fun c) (name_lookup_fun `$` ML_Syntax.print_string c);

 val nbe_value = "value";

 end;

 open BasicCodeThingol;

 (* greetings to Tarski *)

 fun assemble_iterm thy is_fun num_args =

   let

     fun of_iterm t =

       let

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

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

     and of_iconst c ts = case num_args c

      of SOME n => if n <= length ts

           then let val (args2, args1) = chop (length ts - n) ts

           in nbe_apps (nbe_fun c `$` ml_list args1) args2

           end else nbe_const c ts

       | NONE => if is_fun c then nbe_apps (nbe_fun c) ts

           else nbe_const c ts

     and of_iapp (IConst (c, (dss, _))) ts = of_iconst c 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_fun thy is_fun num_args (c, eqns) =

   let

     val assemble_arg = assemble_iterm thy (K false) (K NONE);

     val assemble_rhs = assemble_iterm thy is_fun num_args;

     fun assemble_eqn (args, rhs) =

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

     val default_params = map nbe_bound

       (Name.invent_list [] "a" ((the o num_args) c));

     val default_eqn = ([ml_list default_params], nbe_const c default_params);

   in map assemble_eqn eqns @ [default_eqn] end;

 fun assemble_eqnss thy is_fun ([], deps) = ([], "")

   | assemble_eqnss thy is_fun (eqnss, deps) =

       let

         val cs = map fst eqnss;

         val num_args = cs ~~ map (fn (_, (args, rhs) :: _) => length args) eqnss;

         val funs = fold (fold (CodeThingol.fold_constnames

           (insert (op =))) o map snd o snd) eqnss [];

         val bind_funs = map nbe_lookup (filter is_fun funs);

         val bind_locals = ml_fundefs (map nbe_fun cs ~~ map

           (assemble_fun thy is_fun (AList.lookup (op =) num_args)) eqnss);

         val result = ml_list (map (fn (c, n) => nbe_abss n (nbe_fun c)) num_args)

           |> ml_delay;

       in (cs, ml_Let (bind_funs @ [bind_locals]) result) end;

 fun assemble_eval thy is_fun (((vs, ty), t), deps) =

   let

     val funs = CodeThingol.fold_constnames (insert (op =)) t [];

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

     val bind_funs = map nbe_lookup (filter is_fun funs);

     val bind_value = ml_fundefs [(nbe_value, [([ml_list (map nbe_bound frees)],

       assemble_iterm thy is_fun (K NONE) t)])];

     val result = ml_list [nbe_value `$` ml_list (map nbe_free frees)]

       |> ml_delay;

   in ([nbe_value], ml_Let (bind_funs @ [bind_value]) result) end;

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

       NONE

   | eqns_of_stmt ((name, CodeThingol.Fun (_, eqns)), deps) =

       SOME ((name, map fst eqns), deps)

   | eqns_of_stmt ((_, CodeThingol.Datatypecons _), _) =

       NONE

   | eqns_of_stmt ((_, CodeThingol.Datatype _), _) =

       NONE

   | eqns_of_stmt ((_, CodeThingol.Class _), _) =

       NONE

   | eqns_of_stmt ((_, CodeThingol.Classrel _), _) =

       NONE

   | eqns_of_stmt ((_, CodeThingol.Classparam _), _) =

       NONE

   | eqns_of_stmt ((_, CodeThingol.Classinst _), _) =

       NONE;

 fun compile_stmts thy is_fun =

   map_filter eqns_of_stmt

   #> split_list

   #> assemble_eqnss thy is_fun

   #> compile_univs (Nbe_Functions.get thy);

 fun eval_term thy is_fun =

   assemble_eval thy is_fun

   #> compile_univs (Nbe_Functions.get thy)

   #> the_single

   #> snd;

 (** compilation and evaluation **)

 (* ensure global functions *)

 fun ensure_funs thy code =

   let

     fun add_dep (name, dep) gr =

       if can (Graph.get_node gr) name andalso can (Graph.get_node gr) dep

       then Graph.add_edge (name, dep) gr else gr;

     fun compile' stmts gr =

       let

         val compiled = compile_stmts thy (defined gr) stmts;

         val names = map (fst o fst) stmts;

         val deps = maps snd stmts;

       in

         Nbe_Functions.change thy (fold Graph.new_node compiled

           #> fold (fn name => fold (curry add_dep name) deps) names)

       end;

     val nbe_gr = Nbe_Functions.get thy;

     val stmtss = rev (Graph.strong_conn code)

       |> (map o map_filter) (fn name => if defined nbe_gr name

            then NONE

            else SOME ((name, Graph.get_node code name), Graph.imm_succs code name))

       |> filter_out null

   in fold compile' stmtss nbe_gr end;

 (* reification *)

 fun term_of_univ thy t =

   let

     fun of_apps bounds (t, ts) =

       fold_map (of_univ bounds) ts

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

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

           let

             val SOME c = CodeName.const_rev thy name;

             val T = Code.default_typ thy c;

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

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

   in of_univ 0 t 0 |> fst end;

 (* evaluation with type reconstruction *)

 fun eval thy code t vs_ty_t deps =

   let

     val ty = type_of t;

     fun subst_Frees [] = I

       | subst_Frees inst =

           Term.map_aterms (fn (t as Term.Free (s, _)) => the_default t (AList.lookup (op =) inst s)

                             | t => t);

     val anno_vars =

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

       #> subst_Vars (map (fn (ixn, T) => (ixn, Var (ixn, T))) (Term.add_vars t []))

     fun constrain t =

       singleton (Syntax.check_terms (ProofContext.init thy)) (TypeInfer.constrain ty t);

     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);

   in

     (vs_ty_t, deps)

     |> eval_term thy (defined (ensure_funs thy code))

     |> term_of_univ thy

     |> tracing (fn t => "Normalized:\n" ^ setmp show_types true Display.raw_string_of_term t)

     |> anno_vars

     |> tracing (fn t => "Vars typed:\n" ^ setmp show_types true Display.raw_string_of_term t)

     |> constrain

     |> tracing (fn t => "Types inferred:\n" ^ setmp show_types true Display.raw_string_of_term t)

     |> check_tvars

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

   end;

 (* evaluation oracle *)

 exception Norm of CodeThingol.code * term

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

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

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

 fun norm_invoke thy code t vs_ty_t deps =

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

   (*FIXME get rid of hardwired theory name*)

 fun norm_conv ct =

   let

     val thy = Thm.theory_of_cterm ct;

     fun conv code vs_ty_t deps ct =

       let

         val t = Thm.term_of ct;

       in norm_invoke thy code t vs_ty_t deps end;

   in CodePackage.eval_conv thy conv ct end;

 fun norm_term thy =

   let

     fun invoke code vs_ty_t deps t =

       eval thy code t vs_ty_t deps;

   in CodePackage.eval_term thy invoke #> Code.postprocess_term thy 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;

 val setup = Theory.add_oracle ("norm", norm_oracle)

 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;