(*  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: 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 variables, named*)

  | 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

      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 (Free (name, xs)) ys = Free (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_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 = 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 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 (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 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 (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 = CodeDataFun

(

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

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

  fun purge thy 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 program vs_ty_t deps =

  let

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

  in

    vs_ty_t

    |> eval_term gr deps

    |> term_of_univ thy idx_tab

  end;

(* evaluation with type reconstruction *)

fun eval thy t program vs_ty_t deps =

  let

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

      | t => t);

    val subst_triv_consts = subst_const (CodeUnit.resubst_alias thy);

    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 =

      singleton (TypeInfer.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)

      (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 (Syntax.string_of_term_global thy) t);

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

  in

    compile_eval thy program vs_ty_t deps

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

    |> subst_triv_consts

    |> 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.program

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

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

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

fun norm_invoke thy t program vs_ty_t deps =

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

  (*FIXME get rid of hardwired theory name*)

fun add_triv_classes thy =

  let

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

      (CodeUnit.triv_classes thy);

    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 norm_conv ct =

  let

    val thy = Thm.theory_of_cterm ct;

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

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

  in CodeThingol.eval_conv thy evaluator ct end;

fun norm_term thy t =

  let

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

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

  in (Code.postprocess_term thy o CodeThingol.eval_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 ctxt' = Variable.auto_fixes t ctxt;

    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;