# File datatype_codegen.ML

    (*  Title:      HOL/datatype_codegen.ML
        ID:         $Id: datatype_codegen.ML,v 1.16 2005/09/20 14:17:34 haftmann Exp $
        Author:     Stefan Berghofer, TU Muenchen

    Code generator for inductive datatypes.
    *)

    signature DATATYPE_CODEGEN =
    sig
      val setup: (theory -> theory) list
    end;

    structure DatatypeCodegen : DATATYPE_CODEGEN =
    struct

    open Codegen;

    fun mk_tuple [p] = p
      | mk_tuple ps = Pretty.block (Pretty.str "(" ::
          List.concat (separate [Pretty.str ",", Pretty.brk 1] (map single ps)) @
            [Pretty.str ")"]);

    (**** datatype definition ****)

    (* find shortest path to constructor with no recursive arguments *)

    fun find_nonempty (descr: DatatypeAux.descr) is i =
      let
        val (_, _, constrs) = valOf (AList.lookup (op =) descr i);
        fun arg_nonempty (_, DatatypeAux.DtRec i) = if i mem is then NONE
              else Option.map (curry op + 1 o snd) (find_nonempty descr (i::is) i)
          | arg_nonempty _ = SOME 0;
        fun max xs = Library.foldl
          (fn (NONE, _) => NONE
            | (SOME i, SOME j) => SOME (Int.max (i, j))
            | (_, NONE) => NONE) (SOME 0, xs);
        val xs = sort (int_ord o pairself snd)
          (List.mapPartial (fn (s, dts) => Option.map (pair s)
            (max (map (arg_nonempty o DatatypeAux.strip_dtyp) dts))) constrs)
      in case xs of [] => NONE | x :: _ => SOME x end;

    fun add_dt_defs thy defs dep module gr (descr: DatatypeAux.descr) =
      let
        val sg = sign_of thy;
        val tab = DatatypePackage.get_datatypes thy;

        val descr' = List.filter (can (map DatatypeAux.dest_DtTFree o #2 o snd)) descr;
        val rtnames = map (#1 o snd) (List.filter (fn (_, (_, _, cs)) =>
          exists (exists DatatypeAux.is_rec_type o snd) cs) descr');

        val (_, (tname, _, _)) :: _ = descr';
        val node_id = tname ^ " (type)";
        val module' = if_library (thyname_of_type tname thy) module;

        fun mk_dtdef gr prfx [] = (gr, [])
          | mk_dtdef gr prfx ((_, (tname, dts, cs))::xs) =
              let
                val tvs = map DatatypeAux.dest_DtTFree dts;
                val sorts = map (rpair []) tvs;
                val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs;
                val (gr', (_, type_id)) = mk_type_id module' tname gr;
                val (gr'', ps) =
                  foldl_map (fn (gr, (cname, cargs)) =>
                    foldl_map (invoke_tycodegen thy defs node_id module' false)
                      (gr, cargs) |>>>
                    mk_const_id module' cname) (gr', cs');
                val (gr''', rest) = mk_dtdef gr'' "and " xs
              in
                (gr''',
                 Pretty.block (Pretty.str prfx ::
                   (if null tvs then [] else
                      [mk_tuple (map Pretty.str tvs), Pretty.str " "]) @
                   [Pretty.str (type_id ^ " ="), Pretty.brk 1] @
                   List.concat (separate [Pretty.brk 1, Pretty.str "| "]
                     (map (fn (ps', (_, cname)) => [Pretty.block
                       (Pretty.str cname ::
                        (if null ps' then [] else
                         List.concat ([Pretty.str " of", Pretty.brk 1] ::
                           separate [Pretty.str " *", Pretty.brk 1]
                             (map single ps'))))]) ps))) :: rest)
              end;

        fun mk_term_of_def gr prfx [] = []
          | mk_term_of_def gr prfx ((_, (tname, dts, cs)) :: xs) =
              let
                val tvs = map DatatypeAux.dest_DtTFree dts;
                val sorts = map (rpair []) tvs;
                val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs;
                val dts' = map (DatatypeAux.typ_of_dtyp descr sorts) dts;
                val T = Type (tname, dts');
                val rest = mk_term_of_def gr "and " xs;
                val (_, eqs) = foldl_map (fn (prfx, (cname, Ts)) =>
                  let val args = map (fn i =>
                    Pretty.str ("x" ^ string_of_int i)) (1 upto length Ts)
                  in ("  | ", Pretty.blk (4,
                    [Pretty.str prfx, mk_term_of gr module' false T, Pretty.brk 1,
                     if null Ts then Pretty.str (snd (get_const_id cname gr))
                     else parens (Pretty.block
                       [Pretty.str (snd (get_const_id cname gr)),
                        Pretty.brk 1, mk_tuple args]),
                     Pretty.str " =", Pretty.brk 1] @
                     List.concat (separate [Pretty.str " $", Pretty.brk 1]
                       ([Pretty.str ("Const (\"" ^ cname ^ "\","), Pretty.brk 1,
                         mk_type false (Ts ---> T), Pretty.str ")"] ::
                        map (fn (x, U) => [Pretty.block [mk_term_of gr module' false U,
                          Pretty.brk 1, x]]) (args ~~ Ts)))))
                  end) (prfx, cs')
              in eqs @ rest end;

        fun mk_gen_of_def gr prfx [] = []
          | mk_gen_of_def gr prfx ((i, (tname, dts, cs)) :: xs) =
              let
                val tvs = map DatatypeAux.dest_DtTFree dts;
                val sorts = map (rpair []) tvs;
                val (cs1, cs2) =
                  List.partition (exists DatatypeAux.is_rec_type o snd) cs;
                val SOME (cname, _) = find_nonempty descr [i] i;

                fun mk_delay p = Pretty.block
                  [Pretty.str "fn () =>", Pretty.brk 1, p];

                fun mk_constr s b (cname, dts) =
                  let
                    val gs = map (fn dt => mk_app false (mk_gen gr module' false rtnames s
                        (DatatypeAux.typ_of_dtyp descr sorts dt))
                      [Pretty.str (if b andalso DatatypeAux.is_rec_type dt then "0"
                         else "j")]) dts;
                    val (_, id) = get_const_id cname gr
                  in case gs of
                      _ :: _ :: _ => Pretty.block
                        [Pretty.str id, Pretty.brk 1, mk_tuple gs]
                    | _ => mk_app false (Pretty.str id) (map parens gs)
                  end;

                fun mk_choice [c] = mk_constr "(i-1)" false c
                  | mk_choice cs = Pretty.block [Pretty.str "one_of",
                      Pretty.brk 1, Pretty.blk (1, Pretty.str "[" ::
                      List.concat (separate [Pretty.str ",", Pretty.fbrk]
                        (map (single o mk_delay o mk_constr "(i-1)" false) cs)) @
                      [Pretty.str "]"]), Pretty.brk 1, Pretty.str "()"];

                val gs = map (Pretty.str o suffix "G" o strip_tname) tvs;
                val gen_name = "gen_" ^ snd (get_type_id tname gr)

              in
                Pretty.blk (4, separate (Pretty.brk 1)
                    (Pretty.str (prfx ^ gen_name ^
                       (if null cs1 then "" else "'")) :: gs @
                     (if null cs1 then [] else [Pretty.str "i"]) @
                     [Pretty.str "j"]) @
                  [Pretty.str " =", Pretty.brk 1] @
                  (if not (null cs1) andalso not (null cs2)
                   then [Pretty.str "frequency", Pretty.brk 1,
                     Pretty.blk (1, [Pretty.str "[",
                       mk_tuple [Pretty.str "i", mk_delay (mk_choice cs1)],
                       Pretty.str ",", Pretty.fbrk,
                       mk_tuple [Pretty.str "1", mk_delay (mk_choice cs2)],
                       Pretty.str "]"]), Pretty.brk 1, Pretty.str "()"]
                   else if null cs2 then
                     [Pretty.block [Pretty.str "(case", Pretty.brk 1,
                       Pretty.str "i", Pretty.brk 1, Pretty.str "of",
                       Pretty.brk 1, Pretty.str "0 =>", Pretty.brk 1,
                       mk_constr "0" true (cname, valOf (AList.lookup (op =) cs cname)),
                       Pretty.brk 1, Pretty.str "| _ =>", Pretty.brk 1,
                       mk_choice cs1, Pretty.str ")"]]
                   else [mk_choice cs2])) ::
                (if null cs1 then []
                 else [Pretty.blk (4, separate (Pretty.brk 1)
                     (Pretty.str ("and " ^ gen_name) :: gs @ [Pretty.str "i"]) @
                   [Pretty.str " =", Pretty.brk 1] @
                   separate (Pretty.brk 1) (Pretty.str (gen_name ^ "'") :: gs @
                     [Pretty.str "i", Pretty.str "i"]))]) @
                mk_gen_of_def gr "and " xs
              end

      in
        (add_edge_acyclic (node_id, dep) gr
            handle Graph.CYCLES _ => gr) handle Graph.UNDEF _ =>
             let
               val gr1 = add_edge (node_id, dep)
                 (new_node (node_id, (NONE, "", "")) gr);
               val (gr2, dtdef) = mk_dtdef gr1 "datatype " descr';
             in
               map_node node_id (K (NONE, module',
                 Pretty.string_of (Pretty.blk (0, separate Pretty.fbrk dtdef @
                   [Pretty.str ";"])) ^ "\n\n" ^
                 (if "term_of" mem !mode then
                    Pretty.string_of (Pretty.blk (0, separate Pretty.fbrk
                      (mk_term_of_def gr2 "fun " descr') @ [Pretty.str ";"])) ^ "\n\n"
                  else "") ^
                 (if "test" mem !mode then
                    Pretty.string_of (Pretty.blk (0, separate Pretty.fbrk
                      (mk_gen_of_def gr2 "fun " descr') @ [Pretty.str ";"])) ^ "\n\n"
                  else ""))) gr2
             end
      end;

    (**** case expressions ****)

    fun pretty_case thy defs gr dep module brack constrs (c as Const (_, T)) ts =
      let val i = length constrs
      in if length ts <= i then
           invoke_codegen thy defs dep module brack (gr, eta_expand c ts (i+1))
        else
          let
            val ts1 = Library.take (i, ts);
            val t :: ts2 = Library.drop (i, ts);
            val names = foldr add_term_names
              (map (fst o fst o dest_Var) (foldr add_term_vars [] ts1)) ts1;
            val (Ts, dT) = split_last (Library.take (i+1, fst (strip_type T)));

            fun pcase gr [] [] [] = ([], gr)
              | pcase gr ((cname, cargs)::cs) (t::ts) (U::Us) =
                  let
                    val j = length cargs;
                    val xs = variantlist (replicate j "x", names);
                    val Us' = Library.take (j, fst (strip_type U));
                    val frees = map Free (xs ~~ Us');
                    val (gr0, cp) = invoke_codegen thy defs dep module false
                      (gr, list_comb (Const (cname, Us' ---> dT), frees));
                    val t' = Envir.beta_norm (list_comb (t, frees));
                    val (gr1, p) = invoke_codegen thy defs dep module false (gr0, t');
                    val (ps, gr2) = pcase gr1 cs ts Us;
                  in
                    ([Pretty.block [cp, Pretty.str " =>", Pretty.brk 1, p]] :: ps, gr2)
                  end;

            val (ps1, gr1) = pcase gr constrs ts1 Ts;
            val ps = List.concat (separate [Pretty.brk 1, Pretty.str "| "] ps1);
            val (gr2, p) = invoke_codegen thy defs dep module false (gr1, t);
            val (gr3, ps2) = foldl_map (invoke_codegen thy defs dep module true) (gr2, ts2)
          in (gr3, (if not (null ts2) andalso brack then parens else I)
            (Pretty.block (separate (Pretty.brk 1)
              (Pretty.block ([Pretty.str "(case ", p, Pretty.str " of",
                 Pretty.brk 1] @ ps @ [Pretty.str ")"]) :: ps2))))
          end
      end;

    (**** constructors ****)

    fun pretty_constr thy defs gr dep module brack args (c as Const (s, T)) ts =
      let val i = length args
      in if i > 1 andalso length ts < i then
          invoke_codegen thy defs dep module brack (gr, eta_expand c ts i)
         else
           let
             val id = mk_qual_id module (get_const_id s gr);
             val (gr', ps) = foldl_map
               (invoke_codegen thy defs dep module (i = 1)) (gr, ts);
           in (case args of
              _ :: _ :: _ => (gr', (if brack then parens else I)
                (Pretty.block [Pretty.str id, Pretty.brk 1, mk_tuple ps]))
            | _ => (gr', mk_app brack (Pretty.str id) ps))
           end
      end;

    (**** code generators for terms and types ****)

    fun datatype_codegen thy defs gr dep module brack t = (case strip_comb t of
       (c as Const (s, T), ts) =>
           (case find_first (fn (_, {index, descr, case_name, ...}) =>
             s = case_name orelse
               AList.defined (op =) ((#3 o the o AList.lookup (op =) descr) index) s)
                 (Symtab.dest (DatatypePackage.get_datatypes thy)) of
              NONE => NONE
            | SOME (tname, {index, descr, ...}) =>
               if isSome (get_assoc_code thy s T) then NONE else
               let val SOME (_, _, constrs) = AList.lookup (op =) descr index
               in (case (AList.lookup (op =) constrs s, strip_type T) of
                   (NONE, _) => SOME (pretty_case thy defs gr dep module brack
                     (#3 (valOf (AList.lookup (op =) descr index))) c ts)
                 | (SOME args, (_, Type _)) => SOME (pretty_constr thy defs
                     (fst (invoke_tycodegen thy defs dep module false
                        (gr, snd (strip_type T))))
                     dep module brack args c ts)
                 | _ => NONE)
               end)
     |  _ => NONE);

    fun datatype_tycodegen thy defs gr dep module brack (Type (s, Ts)) =
          (case Symtab.lookup (DatatypePackage.get_datatypes thy) s of
             NONE => NONE
           | SOME {descr, ...} =>
               if isSome (get_assoc_type thy s) then NONE else
               let
                 val (gr', ps) = foldl_map
                   (invoke_tycodegen thy defs dep module false) (gr, Ts);
                 val gr'' = add_dt_defs thy defs dep module gr' descr
               in SOME (gr'',
                 Pretty.block ((if null Ts then [] else
                   [mk_tuple ps, Pretty.str " "]) @
                   [Pretty.str (mk_qual_id module (get_type_id s gr''))]))
               end)
      | datatype_tycodegen _ _ _ _ _ _ _ = NONE;

    val setup =
      [add_codegen "datatype" datatype_codegen,
       add_tycodegen "datatype" datatype_tycodegen];

    end;