# File inductive_codegen.ML

    (*  Title:      HOL/inductive_codegen.ML
        ID:         $Id: inductive_codegen.ML,v 1.31 2005/09/20 14:18:15 haftmann Exp $
        Author:     Stefan Berghofer, TU Muenchen

    Code generator for inductive predicates.
    *)

    signature INDUCTIVE_CODEGEN =
    sig
      val add : string option -> theory attribute
      val setup : (theory -> theory) list
    end;

    structure InductiveCodegen : INDUCTIVE_CODEGEN =
    struct

    open Codegen;

    (**** theory data ****)

    structure CodegenData = TheoryDataFun
    (struct
      val name = "HOL/inductive_codegen";
      type T =
        {intros : (thm * string) list Symtab.table,
         graph : unit Graph.T,
         eqns : (thm * string) list Symtab.table};
      val empty =
        {intros = Symtab.empty, graph = Graph.empty, eqns = Symtab.empty};
      val copy = I;
      val extend = I;
      fun merge _ ({intros=intros1, graph=graph1, eqns=eqns1},
        {intros=intros2, graph=graph2, eqns=eqns2}) =
        {intros = Symtab.merge_multi (Drule.eq_thm_prop o pairself fst)
           (intros1, intros2),
         graph = Graph.merge (K true) (graph1, graph2),
         eqns = Symtab.merge_multi (Drule.eq_thm_prop o pairself fst)
           (eqns1, eqns2)};
      fun print _ _ = ();
    end);

    fun warn thm = warning ("InductiveCodegen: Not a proper clause:\n" ^
      string_of_thm thm);

    fun add_node (g, x) = Graph.new_node (x, ()) g handle Graph.DUP _ => g;

    fun add optmod (p as (thy, thm)) =
      let
        val {intros, graph, eqns} = CodegenData.get thy;
        fun thyname_of s = (case optmod of
          NONE => thyname_of_const s thy | SOME s => s);
      in (case concl_of thm of
          _ $ (Const ("op :", _) $ _ $ t) => (case head_of t of
            Const (s, _) =>
              let val cs = foldr add_term_consts [] (prems_of thm)
              in (CodegenData.put
                {intros = intros |>
                 Symtab.update (s, Symtab.lookup_multi intros s @ [(thm, thyname_of s)]),
                 graph = foldr (uncurry (Graph.add_edge o pair s))
                   (Library.foldl add_node (graph, s :: cs)) cs,
                 eqns = eqns} thy, thm)
              end
          | _ => (warn thm; p))
        | _ $ (Const ("op =", _) $ t $ _) => (case head_of t of
            Const (s, _) =>
              (CodegenData.put {intros = intros, graph = graph,
                 eqns = eqns |> Symtab.update
                   (s, Symtab.lookup_multi eqns s @ [(thm, thyname_of s)])} thy, thm)
          | _ => (warn thm; p))
        | _ => (warn thm; p))
      end;

    fun get_clauses thy s =
      let val {intros, graph, ...} = CodegenData.get thy
      in case Symtab.lookup intros s of
          NONE => (case InductivePackage.get_inductive thy s of
            NONE => NONE
          | SOME ({names, ...}, {intrs, ...}) =>
              SOME (names, thyname_of_const s thy,
                preprocess thy intrs))
        | SOME _ =>
            let
              val SOME names = find_first
                (fn xs => s mem xs) (Graph.strong_conn graph);
              val intrs = List.concat (map
                (fn s => the (Symtab.lookup intros s)) names);
              val (_, (_, thyname)) = split_last intrs
            in SOME (names, thyname, preprocess thy (map fst intrs)) end
      end;

    (**** improper tuples ****)

    fun prod_factors p (Const ("Pair", _) $ t $ u) =
          p :: prod_factors (1::p) t @ prod_factors (2::p) u
      | prod_factors p _ = [];

    fun split_prod p ps t = if p mem ps then (case t of
           Const ("Pair", _) $ t $ u =>
             split_prod (1::p) ps t @ split_prod (2::p) ps u
         | _ => error "Inconsistent use of products") else [t];

    fun full_split_prod (Const ("Pair", _) $ t $ u) =
          full_split_prod t @ full_split_prod u
      | full_split_prod t = [t];

    datatype factors = FVar of int list list | FFix of int list list;

    exception Factors;

    fun mg_factor (FVar f) (FVar f') = FVar (f inter f')
      | mg_factor (FVar f) (FFix f') =
          if f' subset f then FFix f' else raise Factors
      | mg_factor (FFix f) (FVar f') =
          if f subset f' then FFix f else raise Factors
      | mg_factor (FFix f) (FFix f') =
          if f subset f' andalso f' subset f then FFix f else raise Factors;

    fun dest_factors (FVar f) = f
      | dest_factors (FFix f) = f;

    fun infer_factors sg extra_fs (fs, (optf, t)) =
      let fun err s = error (s ^ "\n" ^ Sign.string_of_term sg t)
      in (case (optf, strip_comb t) of
          (SOME f, (Const (name, _), args)) =>
            (case AList.lookup (op =) extra_fs name of
               NONE => AList.update (op =) (name, getOpt
                 (Option.map (mg_factor f) (AList.lookup (op =) fs name), f)) fs
             | SOME (fs', f') => (mg_factor f (FFix f');
                 Library.foldl (infer_factors sg extra_fs)
                   (fs, map (Option.map FFix) fs' ~~ args)))
        | (SOME f, (Var ((name, _), _), [])) =>
            AList.update (op =) (name, getOpt
              (Option.map (mg_factor f) (AList.lookup (op =) fs name), f)) fs
        | (NONE, _) => fs
        | _ => err "Illegal term")
          handle Factors => err "Product factor mismatch in"
      end;

    fun string_of_factors p ps = if p mem ps then
        "(" ^ string_of_factors (1::p) ps ^ ", " ^ string_of_factors (2::p) ps ^ ")"
      else "_";

    (**** check if a term contains only constructor functions ****)

    fun is_constrt thy =
      let
        val cnstrs = List.concat (List.concat (map
          (map (fn (_, (_, _, cs)) => map (apsnd length) cs) o #descr o snd)
          (Symtab.dest (DatatypePackage.get_datatypes thy))));
        fun check t = (case strip_comb t of
            (Var _, []) => true
          | (Const (s, _), ts) => (case AList.lookup (op =) cnstrs s of
                NONE => false
              | SOME i => length ts = i andalso forall check ts)
          | _ => false)
      in check end;

    (**** check if a type is an equality type (i.e. doesn't contain fun) ****)

    fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
      | is_eqT _ = true;

    (**** mode inference ****)

    fun string_of_mode (iss, is) = space_implode " -> " (map
      (fn NONE => "X"
        | SOME js => enclose "[" "]" (commas (map string_of_int js)))
           (iss @ [SOME is]));

    fun print_modes modes = message ("Inferred modes:\n" ^
      space_implode "\n" (map (fn (s, ms) => s ^ ": " ^ commas (map
        string_of_mode ms)) modes));

    val term_vs = map (fst o fst o dest_Var) o term_vars;
    val terms_vs = distinct o List.concat o (map term_vs);

    (** collect all Vars in a term (with duplicates!) **)
    fun term_vTs tm =
      fold_aterms (fn Var ((x, _), T) => cons (x, T) | _ => I) tm [];

    fun get_args _ _ [] = ([], [])
      | get_args is i (x::xs) = (if i mem is then apfst else apsnd) (cons x)
          (get_args is (i+1) xs);

    fun merge xs [] = xs
      | merge [] ys = ys
      | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)
          else y::merge (x::xs) ys;

    fun subsets i j = if i <= j then
           let val is = subsets (i+1) j
           in merge (map (fn ks => i::ks) is) is end
         else [[]];

    fun cprod ([], ys) = []
      | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);

    fun cprods xss = foldr (map op :: o cprod) [[]] xss;

    datatype mode = Mode of (int list option list * int list) * mode option list;

    fun modes_of modes t =
      let
        fun mk_modes name args = List.concat
          (map (fn (m as (iss, is)) => map (Mode o pair m) (cprods (map
            (fn (NONE, _) => [NONE]
              | (SOME js, arg) => map SOME
                  (List.filter (fn Mode ((_, js'), _) => js=js') (modes_of modes arg)))
                    (iss ~~ args)))) ((the o AList.lookup (op =) modes) name))

      in (case strip_comb t of
          (Const ("op =", Type (_, [T, _])), _) =>
            [Mode (([], [1]), []), Mode (([], [2]), [])] @
            (if is_eqT T then [Mode (([], [1, 2]), [])] else [])
        | (Const (name, _), args) => mk_modes name args
        | (Var ((name, _), _), args) => mk_modes name args
        | (Free (name, _), args) => mk_modes name args)
      end;

    datatype indprem = Prem of term list * term | Sidecond of term;

    fun select_mode_prem thy modes vs ps =
      find_first (isSome o snd) (ps ~~ map
        (fn Prem (us, t) => find_first (fn Mode ((_, is), _) =>
              let
                val (in_ts, out_ts) = get_args is 1 us;
                val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts;
                val vTs = List.concat (map term_vTs out_ts');
                val dupTs = map snd (duplicates vTs) @
                  List.mapPartial (AList.lookup (op =) vTs) vs;
              in
                terms_vs (in_ts @ in_ts') subset vs andalso
                forall (is_eqT o fastype_of) in_ts' andalso
                term_vs t subset vs andalso
                forall is_eqT dupTs
              end)
                (modes_of modes t handle Option => [Mode (([], []), [])])
          | Sidecond t => if term_vs t subset vs then SOME (Mode (([], []), []))
              else NONE) ps);

    fun check_mode_clause thy arg_vs modes (iss, is) (ts, ps) =
      let
        val modes' = modes @ List.mapPartial
          (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
            (arg_vs ~~ iss);
        fun check_mode_prems vs [] = SOME vs
          | check_mode_prems vs ps = (case select_mode_prem thy modes' vs ps of
              NONE => NONE
            | SOME (x, _) => check_mode_prems
                (case x of Prem (us, _) => vs union terms_vs us | _ => vs)
                (filter_out (equal x) ps));
        val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (get_args is 1 ts));
        val in_vs = terms_vs in_ts;
        val concl_vs = terms_vs ts
      in
        forall is_eqT (map snd (duplicates (List.concat (map term_vTs in_ts)))) andalso
        forall (is_eqT o fastype_of) in_ts' andalso
        (case check_mode_prems (arg_vs union in_vs) ps of
           NONE => false
         | SOME vs => concl_vs subset vs)
      end;

    fun check_modes_pred thy arg_vs preds modes (p, ms) =
      let val SOME rs = AList.lookup (op =) preds p
      in (p, List.filter (fn m => case find_index
        (not o check_mode_clause thy arg_vs modes m) rs of
          ~1 => true
        | i => (message ("Clause " ^ string_of_int (i+1) ^ " of " ^
          p ^ " violates mode " ^ string_of_mode m); false)) ms)
      end;

    fun fixp f x =
      let val y = f x
      in if x = y then x else fixp f y end;

    fun infer_modes thy extra_modes factors arg_vs preds = fixp (fn modes =>
      map (check_modes_pred thy arg_vs preds (modes @ extra_modes)) modes)
        (map (fn (s, (fs, f)) => (s, cprod (cprods (map
          (fn NONE => [NONE]
            | SOME f' => map SOME (subsets 1 (length f' + 1))) fs),
          subsets 1 (length f + 1)))) factors);

    (**** code generation ****)

    fun mk_eq (x::xs) =
      let fun mk_eqs _ [] = []
            | mk_eqs a (b::cs) = Pretty.str (a ^ " = " ^ b) :: mk_eqs b cs
      in mk_eqs x xs end;

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

    (* convert nested pairs to n-tuple *)

    fun conv_ntuple [_] t ps = ps
      | conv_ntuple [_, _] t ps = ps
      | conv_ntuple us t ps =
          let
            val xs = map (fn i => Pretty.str ("x" ^ string_of_int i))
              (1 upto length us);
            fun ntuple (ys as (x, T) :: xs) U =
              if T = U then (x, xs)
              else
                let
                  val Type ("*", [U1, U2]) = U;
                  val (p1, ys1) = ntuple ys U1;
                  val (p2, ys2) = ntuple ys1 U2
                in (mk_tuple [p1, p2], ys2) end
          in
            [Pretty.str "Seq.map (fn", Pretty.brk 1,
             fst (ntuple (xs ~~ map fastype_of us) (HOLogic.dest_setT (fastype_of t))),
             Pretty.str " =>", Pretty.brk 1, mk_tuple xs, Pretty.str ")",
             Pretty.brk 1, parens (Pretty.block ps)]
          end;

    (* convert n-tuple to nested pairs *)

    fun conv_ntuple' fs T ps =
      let
        fun mk_x i = Pretty.str ("x" ^ string_of_int i);
        fun conv i js (Type ("*", [T, U])) =
              if js mem fs then
                let
                  val (p, i') = conv i (1::js) T;
                  val (q, i'') = conv i' (2::js) U
                in (mk_tuple [p, q], i'') end
              else (mk_x i, i+1)
          | conv i js _ = (mk_x i, i+1)
        val (p, i) = conv 1 [] T
      in
        if i > 3 then
          [Pretty.str "Seq.map (fn", Pretty.brk 1,
           mk_tuple (map mk_x (1 upto i-1)), Pretty.str " =>", Pretty.brk 1,
           p, Pretty.str ")", Pretty.brk 1, parens (Pretty.block ps)]
        else ps
      end;

    fun mk_v ((names, vs), s) = (case AList.lookup (op =) vs s of
          NONE => ((names, (s, [s])::vs), s)
        | SOME xs => let val s' = variant names s in
            ((s'::names, AList.update (op =) (s, s'::xs) vs), s') end);

    fun distinct_v (nvs, Var ((s, 0), T)) =
          apsnd (Var o rpair T o rpair 0) (mk_v (nvs, s))
      | distinct_v (nvs, t $ u) =
          let
            val (nvs', t') = distinct_v (nvs, t);
            val (nvs'', u') = distinct_v (nvs', u);
          in (nvs'', t' $ u') end
      | distinct_v x = x;

    fun is_exhaustive (Var _) = true
      | is_exhaustive (Const ("Pair", _) $ t $ u) =
          is_exhaustive t andalso is_exhaustive u
      | is_exhaustive _ = false;

    fun compile_match nvs eq_ps out_ps success_p can_fail =
      let val eqs = List.concat (separate [Pretty.str " andalso", Pretty.brk 1]
        (map single (List.concat (map (mk_eq o snd) nvs) @ eq_ps)));
      in
        Pretty.block
         ([Pretty.str "(fn ", mk_tuple out_ps, Pretty.str " =>", Pretty.brk 1] @
          (Pretty.block ((if eqs=[] then [] else Pretty.str "if " ::
             [Pretty.block eqs, Pretty.brk 1, Pretty.str "then "]) @
             (success_p ::
              (if eqs=[] then [] else [Pretty.brk 1, Pretty.str "else Seq.empty"]))) ::
           (if can_fail then
              [Pretty.brk 1, Pretty.str "| _ => Seq.empty)"]
            else [Pretty.str ")"])))
      end;

    fun modename module s (iss, is) gr =
      let val (gr', id) = if s = "op =" then (gr, ("", "equal"))
        else mk_const_id module s gr
      in (gr', space_implode "__"
        (mk_qual_id module id ::
          map (space_implode "_" o map string_of_int) (List.mapPartial I iss @ [is])))
      end;

    fun compile_expr thy defs dep module brack (gr, (NONE, t)) =
          apsnd single (invoke_codegen thy defs dep module brack (gr, t))
      | compile_expr _ _ _ _ _ (gr, (SOME _, Var ((name, _), _))) =
          (gr, [Pretty.str name])
      | compile_expr thy defs dep module brack (gr, (SOME (Mode (mode, ms)), t)) =
          let
            val (Const (name, _), args) = strip_comb t;
            val (gr', (ps, mode_id)) = foldl_map
                (compile_expr thy defs dep module true) (gr, ms ~~ args) |>>>
              modename module name mode;
          in (gr', (if brack andalso not (null ps) then
            single o parens o Pretty.block else I)
              (List.concat (separate [Pretty.brk 1]
                ([Pretty.str mode_id] :: ps))))
          end;

    fun compile_clause thy defs gr dep module all_vs arg_vs modes (iss, is) (ts, ps) =
      let
        val modes' = modes @ List.mapPartial
          (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
            (arg_vs ~~ iss);

        fun check_constrt ((names, eqs), t) =
          if is_constrt thy t then ((names, eqs), t) else
            let val s = variant names "x";
            in ((s::names, (s, t)::eqs), Var ((s, 0), fastype_of t)) end;

        fun compile_eq (gr, (s, t)) =
          apsnd (Pretty.block o cons (Pretty.str (s ^ " = ")) o single)
            (invoke_codegen thy defs dep module false (gr, t));

        val (in_ts, out_ts) = get_args is 1 ts;
        val ((all_vs', eqs), in_ts') =
          foldl_map check_constrt ((all_vs, []), in_ts);

        fun is_ind t = (case head_of t of
              Const (s, _) => s = "op =" orelse AList.defined (op =) modes s
            | Var ((s, _), _) => s mem arg_vs);

        fun compile_prems out_ts' vs names gr [] =
              let
                val (gr2, out_ps) = foldl_map
                  (invoke_codegen thy defs dep module false) (gr, out_ts);
                val (gr3, eq_ps) = foldl_map compile_eq (gr2, eqs);
                val ((names', eqs'), out_ts'') =
                  foldl_map check_constrt ((names, []), out_ts');
                val (nvs, out_ts''') = foldl_map distinct_v
                  ((names', map (fn x => (x, [x])) vs), out_ts'');
                val (gr4, out_ps') = foldl_map
                  (invoke_codegen thy defs dep module false) (gr3, out_ts''');
                val (gr5, eq_ps') = foldl_map compile_eq (gr4, eqs')
              in
                (gr5, compile_match (snd nvs) (eq_ps @ eq_ps') out_ps'
                  (Pretty.block [Pretty.str "Seq.single", Pretty.brk 1, mk_tuple out_ps])
                  (exists (not o is_exhaustive) out_ts'''))
              end
          | compile_prems out_ts vs names gr ps =
              let
                val vs' = distinct (List.concat (vs :: map term_vs out_ts));
                val SOME (p, mode as SOME (Mode ((_, js), _))) =
                  select_mode_prem thy modes' vs' ps;
                val ps' = filter_out (equal p) ps;
                val ((names', eqs), out_ts') =
                  foldl_map check_constrt ((names, []), out_ts);
                val (nvs, out_ts'') = foldl_map distinct_v
                  ((names', map (fn x => (x, [x])) vs), out_ts');
                val (gr0, out_ps) = foldl_map
                  (invoke_codegen thy defs dep module false) (gr, out_ts'');
                val (gr1, eq_ps) = foldl_map compile_eq (gr0, eqs)
              in
                (case p of
                   Prem (us, t) =>
                     let
                       val (in_ts, out_ts''') = get_args js 1 us;
                       val (gr2, in_ps) = foldl_map
                         (invoke_codegen thy defs dep module false) (gr1, in_ts);
                       val (gr3, ps) = if is_ind t then
                           apsnd (fn ps => ps @ [Pretty.brk 1, mk_tuple in_ps])
                             (compile_expr thy defs dep module false
                               (gr2, (mode, t)))
                         else
                           apsnd (fn p => conv_ntuple us t
                             [Pretty.str "Seq.of_list", Pretty.brk 1, p])
                               (invoke_codegen thy defs dep module true (gr2, t));
                       val (gr4, rest) = compile_prems out_ts''' vs' (fst nvs) gr3 ps';
                     in
                       (gr4, compile_match (snd nvs) eq_ps out_ps
                          (Pretty.block (ps @
                             [Pretty.str " :->", Pretty.brk 1, rest]))
                          (exists (not o is_exhaustive) out_ts''))
                     end
                 | Sidecond t =>
                     let
                       val (gr2, side_p) = invoke_codegen thy defs dep module true (gr1, t);
                       val (gr3, rest) = compile_prems [] vs' (fst nvs) gr2 ps';
                     in
                       (gr3, compile_match (snd nvs) eq_ps out_ps
                          (Pretty.block [Pretty.str "?? ", side_p,
                            Pretty.str " :->", Pretty.brk 1, rest])
                          (exists (not o is_exhaustive) out_ts''))
                     end)
              end;

        val (gr', prem_p) = compile_prems in_ts' arg_vs all_vs' gr ps;
      in
        (gr', Pretty.block [Pretty.str "Seq.single inp :->", Pretty.brk 1, prem_p])
      end;

    fun compile_pred thy defs gr dep module prfx all_vs arg_vs modes s cls mode =
      let val (gr', (cl_ps, mode_id)) =
        foldl_map (fn (gr, cl) => compile_clause thy defs
          gr dep module all_vs arg_vs modes mode cl) (gr, cls) |>>>
        modename module s mode
      in
        ((gr', "and "), Pretty.block
          ([Pretty.block (separate (Pretty.brk 1)
             (Pretty.str (prfx ^ mode_id) ::
               map Pretty.str arg_vs) @
             [Pretty.str " inp ="]),
            Pretty.brk 1] @
           List.concat (separate [Pretty.str " ++", Pretty.brk 1] (map single cl_ps))))
      end;

    fun compile_preds thy defs gr dep module all_vs arg_vs modes preds =
      let val ((gr', _), prs) = foldl_map (fn ((gr, prfx), (s, cls)) =>
        foldl_map (fn ((gr', prfx'), mode) => compile_pred thy defs gr'
          dep module prfx' all_vs arg_vs modes s cls mode)
            ((gr, prfx), ((the o AList.lookup (op =) modes) s))) ((gr, "fun "), preds)
      in
        (gr', space_implode "\n\n" (map Pretty.string_of (List.concat prs)) ^ ";\n\n")
      end;

    (**** processing of introduction rules ****)

    exception Modes of
      (string * (int list option list * int list) list) list *
      (string * (int list list option list * int list list)) list;

    fun lookup_modes gr dep = apfst List.concat (apsnd List.concat (ListPair.unzip
      (map ((fn (SOME (Modes x), _, _) => x | _ => ([], [])) o get_node gr)
        (Graph.all_preds (fst gr) [dep]))));

    fun print_factors factors = message ("Factors:\n" ^
      space_implode "\n" (map (fn (s, (fs, f)) => s ^ ": " ^
        space_implode " -> " (map
          (fn NONE => "X" | SOME f' => string_of_factors [] f')
            (fs @ [SOME f]))) factors));

    fun prep_intrs intrs = map (rename_term o #prop o rep_thm o standard) intrs;

    fun constrain cs [] = []
      | constrain cs ((s, xs) :: ys) = (s, case AList.lookup (op =) cs s of
          NONE => xs
        | SOME xs' => xs inter xs') :: constrain cs ys;

    fun mk_extra_defs thy defs gr dep names module ts =
      Library.foldl (fn (gr, name) =>
        if name mem names then gr
        else (case get_clauses thy name of
            NONE => gr
          | SOME (names, thyname, intrs) =>
              mk_ind_def thy defs gr dep names (if_library thyname module)
                [] [] (prep_intrs intrs)))
                (gr, foldr add_term_consts [] ts)

    and mk_ind_def thy defs gr dep names module modecs factorcs intrs =
      add_edge (hd names, dep) gr handle Graph.UNDEF _ =>
        let
          val _ $ (_ $ _ $ u) = Logic.strip_imp_concl (hd intrs);
          val (_, args) = strip_comb u;
          val arg_vs = List.concat (map term_vs args);

          fun dest_prem factors (_ $ (p as (Const ("op :", _) $ t $ u))) =
                (case AList.lookup (op =) factors (case head_of u of
                     Const (name, _) => name | Var ((name, _), _) => name) of
                   NONE => Prem (full_split_prod t, u)
                 | SOME f => Prem (split_prod [] f t, u))
            | dest_prem factors (_ $ ((eq as Const ("op =", _)) $ t $ u)) =
                Prem ([t, u], eq)
            | dest_prem factors (_ $ t) = Sidecond t;

          fun add_clause factors (clauses, intr) =
            let
              val _ $ (_ $ t $ u) = Logic.strip_imp_concl intr;
              val Const (name, _) = head_of u;
              val prems = map (dest_prem factors) (Logic.strip_imp_prems intr);
            in
              AList.update (op =) (name, ((these o AList.lookup (op =) clauses) name) @
                 [(split_prod [] ((the o AList.lookup (op =) factors) name) t, prems)]) clauses
            end;

          fun check_set (Const (s, _)) = s mem names orelse isSome (get_clauses thy s)
            | check_set (Var ((s, _), _)) = s mem arg_vs
            | check_set _ = false;

          fun add_prod_factors extra_fs (fs, _ $ (Const ("op :", _) $ t $ u)) =
                if check_set (head_of u)
                then infer_factors (sign_of thy) extra_fs
                  (fs, (SOME (FVar (prod_factors [] t)), u))
                else fs
            | add_prod_factors _ (fs, _) = fs;

          val gr' = mk_extra_defs thy defs
            (add_edge (hd names, dep)
              (new_node (hd names, (NONE, "", "")) gr)) (hd names) names module intrs;
          val (extra_modes, extra_factors) = lookup_modes gr' (hd names);
          val fs = constrain factorcs (map (apsnd dest_factors)
            (Library.foldl (add_prod_factors extra_factors) ([], List.concat (map (fn t =>
              Logic.strip_imp_concl t :: Logic.strip_imp_prems t) intrs))));
          val factors = List.mapPartial (fn (name, f) =>
            if name mem arg_vs then NONE
            else SOME (name, (map (AList.lookup (op =) fs) arg_vs, f))) fs;
          val clauses =
            Library.foldl (add_clause (fs @ map (apsnd snd) extra_factors)) ([], intrs);
          val modes = constrain modecs
            (infer_modes thy extra_modes factors arg_vs clauses);
          val _ = print_factors factors;
          val _ = print_modes modes;
          val (gr'', s) = compile_preds thy defs gr' (hd names) module (terms_vs intrs)
            arg_vs (modes @ extra_modes) clauses;
        in
          (map_node (hd names)
            (K (SOME (Modes (modes, factors)), module, s)) gr'')
        end;

    fun find_mode gr dep s u modes is = (case find_first (fn Mode ((_, js), _) => is=js)
      (modes_of modes u handle Option => []) of
         NONE => codegen_error gr dep
           ("No such mode for " ^ s ^ ": " ^ string_of_mode ([], is))
       | mode => mode);

    fun mk_ind_call thy defs gr dep module t u is_query = (case head_of u of
      Const (s, T) => (case (get_clauses thy s, get_assoc_code thy s T) of
           (NONE, _) => NONE
         | (SOME (names, thyname, intrs), NONE) =>
             let
              fun mk_mode (((ts, mode), i), Const ("dummy_pattern", _)) =
                    ((ts, mode), i+1)
                | mk_mode (((ts, mode), i), t) = ((ts @ [t], mode @ [i]), i+1);

               val module' = if_library thyname module;
               val gr1 = mk_extra_defs thy defs
                 (mk_ind_def thy defs gr dep names module'
                 [] [] (prep_intrs intrs)) dep names module' [u];
               val (modes, factors) = lookup_modes gr1 dep;
               val ts = split_prod [] ((snd o the o AList.lookup (op =) factors) s) t;
               val (ts', is) = if is_query then
                   fst (Library.foldl mk_mode ((([], []), 1), ts))
                 else (ts, 1 upto length ts);
               val mode = find_mode gr1 dep s u modes is;
               val (gr2, in_ps) = foldl_map
                 (invoke_codegen thy defs dep module false) (gr1, ts');
               val (gr3, ps) =
                 compile_expr thy defs dep module false (gr2, (mode, u))
             in
               SOME (gr3, Pretty.block
                 (ps @ [Pretty.brk 1, mk_tuple in_ps]))
             end
         | _ => NONE)
      | _ => NONE);

    fun list_of_indset thy defs gr dep module brack u = (case head_of u of
      Const (s, T) => (case (get_clauses thy s, get_assoc_code thy s T) of
           (NONE, _) => NONE
         | (SOME (names, thyname, intrs), NONE) =>
             let
               val module' = if_library thyname module;
               val gr1 = mk_extra_defs thy defs
                 (mk_ind_def thy defs gr dep names module'
                 [] [] (prep_intrs intrs)) dep names module' [u];
               val (modes, factors) = lookup_modes gr1 dep;
               val mode = find_mode gr1 dep s u modes [];
               val (gr2, ps) =
                 compile_expr thy defs dep module false (gr1, (mode, u))
             in
               SOME (gr2, (if brack then parens else I)
                 (Pretty.block ([Pretty.str "Seq.list_of", Pretty.brk 1,
                   Pretty.str "("] @
                    conv_ntuple' (snd (valOf (AList.lookup (op =) factors s)))
                     (HOLogic.dest_setT (fastype_of u))
                     (ps @ [Pretty.brk 1, Pretty.str "()"]) @
                   [Pretty.str ")"])))
             end
         | _ => NONE)
      | _ => NONE);

    fun clause_of_eqn eqn =
      let
        val (t, u) = HOLogic.dest_eq (HOLogic.dest_Trueprop (concl_of eqn));
        val (Const (s, T), ts) = strip_comb t;
        val (Ts, U) = strip_type T
      in
        rename_term
          (Logic.list_implies (prems_of eqn, HOLogic.mk_Trueprop (HOLogic.mk_mem
            (foldr1 HOLogic.mk_prod (ts @ [u]), Const (s ^ "_aux",
              HOLogic.mk_setT (foldr1 HOLogic.mk_prodT (Ts @ [U])))))))
      end;

    fun mk_fun thy defs name eqns dep module module' gr =
      case try (get_node gr) name of
        NONE =>
        let
          val clauses = map clause_of_eqn eqns;
          val pname = name ^ "_aux";
          val arity = length (snd (strip_comb (fst (HOLogic.dest_eq
            (HOLogic.dest_Trueprop (concl_of (hd eqns)))))));
          val mode = 1 upto arity;
          val (gr', (fun_id, mode_id)) = gr |>
            mk_const_id module' name |>>>
            modename module' pname ([], mode);
          val vars = map (fn i => Pretty.str ("x" ^ string_of_int i)) mode;
          val s = Pretty.string_of (Pretty.block
            [mk_app false (Pretty.str ("fun " ^ snd fun_id)) vars, Pretty.str " =",
             Pretty.brk 1, Pretty.str "Seq.hd", Pretty.brk 1,
             parens (Pretty.block [Pretty.str mode_id,
               Pretty.brk 1, mk_tuple vars])]) ^ ";\n\n";
          val gr'' = mk_ind_def thy defs (add_edge (name, dep)
            (new_node (name, (NONE, module', s)) gr')) name [pname] module'
            [(pname, [([], mode)])]
            [(pname, map (fn i => replicate i 2) (0 upto arity-1))]
            clauses;
          val (modes, _) = lookup_modes gr'' dep;
          val _ = find_mode gr'' dep pname (snd (HOLogic.dest_mem (HOLogic.dest_Trueprop
            (Logic.strip_imp_concl (hd clauses))))) modes mode
        in (gr'', mk_qual_id module fun_id) end
      | SOME _ =>
          (add_edge (name, dep) gr, mk_qual_id module (get_const_id name gr));

    fun inductive_codegen thy defs gr dep module brack (Const ("op :", _) $ t $ u) =
          ((case mk_ind_call thy defs gr dep module (Term.no_dummy_patterns t) u false of
             NONE => NONE
           | SOME (gr', call_p) => SOME (gr', (if brack then parens else I)
               (Pretty.block [Pretty.str "?! (", call_p, Pretty.str ")"])))
            handle TERM _ => mk_ind_call thy defs gr dep module t u true)
      | inductive_codegen thy defs gr dep module brack t = (case strip_comb t of
          (Const (s, _), ts) => (case Symtab.lookup (#eqns (CodegenData.get thy)) s of
            NONE => list_of_indset thy defs gr dep module brack t
          | SOME eqns =>
              let
                val (_, (_, thyname)) = split_last eqns;
                val (gr', id) = mk_fun thy defs s (preprocess thy (map fst eqns))
                  dep module (if_library thyname module) gr;
                val (gr'', ps) = foldl_map
                  (invoke_codegen thy defs dep module true) (gr', ts);
              in SOME (gr'', mk_app brack (Pretty.str id) ps)
              end)
        | _ => NONE);

    val setup =
      [add_codegen "inductive" inductive_codegen,
       CodegenData.init,
       add_attribute "ind"
         (Scan.option (Args.$$$ "target" |-- Args.colon |-- Args.name) >> add)];

    end;

    (**** combinators for code generated from inductive predicates ****)

    infix 5 :->;
    infix 3 ++;

    fun s :-> f = Seq.flat (Seq.map f s);

    fun s1 ++ s2 = Seq.append (s1, s2);

    fun ?? b = if b then Seq.single () else Seq.empty;

    fun ?! s = isSome (Seq.pull s);

    fun equal__1 x = Seq.single x;

    val equal__2 = equal__1;

    fun equal__1_2 (x, y) = ?? (x = y);