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

    | Free of string * Univ list

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

    | BVar of int * Univ list

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

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

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

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

                                             (*abstractions as closures*)

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

  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*)

  | DFree of string                    (*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 free v = Free (v, []);

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

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);

(* universe graph *)

type univ_gr = Univ option Graph.T;

val compiled : univ_gr -> string -> bool = can o Graph.get_node;

(** 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 ds e = "let\n" ^ space_implode "\n" ds ^ " 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 *)

local

  val prefix =          "Nbe.";

  val name_const =      prefix ^ "Const";

  val name_free =       prefix ^ "free";

  val name_dfree =      prefix ^ "DFree";

  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;

fun nbe_dfree v = name_dfree `$` ML_Syntax.print_string v;

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

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];

val nbe_value = "value";

end;

open BasicCodeThingol;

(* sandbox communication *)

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

val compile = 

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

  #> evaluate ("Nbe.univs_ref", univs_ref) "normalization by evaluation"

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

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

      (!trace);

(* code generation with greetings to Tarski *)

fun assemble_idict (DictConst (inst, dss)) =

      nbe_apps (nbe_fun inst) ((maps o map) assemble_idict dss)

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

      fold_rev (fn super => nbe_apps (nbe_fun super) o single) supers (nbe_dict v n);

fun assemble_iterm 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 @ rev ((maps o map) assemble_idict dss))

      | 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 gr num_args (c, (vs, eqns)) =

  let

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

    val assemble_rhs = assemble_iterm (is_some o Graph.get_node gr) num_args;

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

      |> rev;

    fun assemble_eqn (args, rhs) =

      ([ml_list (map assemble_arg (rev args) @ dict_params)], 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 gr deps [] = ([], ("", []))

  | assemble_eqnss gr deps eqnss =

      let

        val cs = map fst eqnss;

        val num_args = cs ~~ map (fn (_, (vs, (args, rhs) :: _)) =>

          length (maps snd vs) + length args) eqnss;

        val deps' = filter (is_some o Option.join o try (Graph.get_node gr)) deps;

        val bind_deps = ml_list (map nbe_fun deps');

        val bind_locals = ml_fundefs (map nbe_fun cs ~~ map

          (assemble_fun gr (AList.lookup (op =) num_args)) eqnss);

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

        val arg_deps = map (the o Graph.get_node gr) deps';

      in (cs, (ml_abs bind_deps (ml_Let [bind_locals] result), arg_deps)) end;

fun compile_eqnss gr deps eqnss = case assemble_eqnss gr deps eqnss

 of ([], _) => []

  | (cs, (s, deps)) => cs ~~ compile s deps;

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 compiled_deps = names_deps

      |> maps snd

      |> distinct (op =)

      |> subtract (op =) names;

    fun compile gr = eqnss

      |> compile_eqnss gr compiled_deps

      |> rpair gr;

  in

    fold (fn name => Graph.new_node (name, NONE)) names

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

    #> compile

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

  end;

fun ensure_stmts code =

  let

    fun add_stmts names gr = if exists (compiled gr) names then gr else gr

      |> 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;

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

  let

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

    val deps' = filter (is_some o Option.join o try (Graph.get_node gr)) deps;

    val bind_deps = ml_list (map nbe_fun deps');

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

      |> rev;

    val bind_value = ml_fundefs [(nbe_value,

      [([ml_list (map nbe_bound frees @ dict_params)],

        assemble_iterm (is_some o Graph.get_node gr) (K NONE) t)])];

    val result = ml_list [nbe_value `$` ml_list

      (map nbe_free frees @ map nbe_dfree dict_params)];

    val arg_deps = map (the o Graph.get_node gr) deps';

  in (ml_abs bind_deps (ml_Let [bind_value] result), arg_deps) end;

fun eval_term gr deps t' =

  let

    val (s, args) = assemble_eval gr deps t';

  in the_single (compile s args) end;

(** evaluation **)

(* reification *)

fun term_of_univ thy 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 (c, _)) =

          (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

      | 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 (name, ts)) typidx =

          let

            val ts' = take_until is_dict ts;

            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;

(* function store *)

structure Nbe_Functions = CodeDataFun

(

  type T = univ_gr;

  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 =

        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;

);

(* compilation, evaluation and reification *)

fun compile_eval thy code vs_ty_t deps =

  vs_ty_t

  |> eval_term (Nbe_Functions.change thy (ensure_stmts code)) deps

  |> term_of_univ thy;

(* 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);

    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)

    |> anno_vars

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

    |> constrain

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

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

    |> check_tvars

  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;