(*  Title:      HOL/Tools/inductive_codegen.ML

    Author:     Stefan Berghofer, TU Muenchen

Code generator for inductive predicates.

*)

signature INDUCTIVE_CODEGEN =

sig

  val add : string option -> int option -> attribute

  val setup : theory -> theory

end;

structure InductiveCodegen : INDUCTIVE_CODEGEN =

struct

open Codegen;

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

fun merge_rules tabs =

  Symtab.join (fn _ => AList.merge (Thm.eq_thm_prop) (K true)) tabs;

structure CodegenData = TheoryDataFun

(

  type T =

    {intros : (thm * (string * int)) 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 = merge_rules (intros1, intros2),

     graph = Graph.merge (K true) (graph1, graph2),

     eqns = merge_rules (eqns1, eqns2)};

);

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

  Display.string_of_thm_without_context thm);

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

fun add optmod optnparms = Thm.declaration_attribute (fn thm => Context.mapping (fn thy =>

  let

    val {intros, graph, eqns} = CodegenData.get thy;

    fun thyname_of s = (case optmod of

      NONE => Codegen.thyname_of_const thy s | SOME s => s);

  in (case Option.map strip_comb (try HOLogic.dest_Trueprop (concl_of thm)) of

      SOME (Const ("op =", _), [t, _]) => (case head_of t of

        Const (s, _) =>

          CodegenData.put {intros = intros, graph = graph,

             eqns = eqns |> Symtab.map_default (s, [])

               (AList.update Thm.eq_thm_prop (thm, thyname_of s))} thy

      | _ => (warn thm; thy))

    | SOME (Const (s, _), _) =>

        let

          val cs = fold Term.add_const_names (Thm.prems_of thm) [];

          val rules = Symtab.lookup_list intros s;

          val nparms = (case optnparms of

            SOME k => k

          | NONE => (case rules of

             [] => (case try (Inductive.the_inductive (ProofContext.init thy)) s of

                 SOME (_, {raw_induct, ...}) =>

                   length (Inductive.params_of raw_induct)

               | NONE => 0)

            | xs => snd (snd (snd (split_last xs)))))

        in CodegenData.put

          {intros = intros |>

           Symtab.update (s, (AList.update Thm.eq_thm_prop

             (thm, (thyname_of s, nparms)) rules)),

           graph = List.foldr (uncurry (Graph.add_edge o pair s))

             (Library.foldl add_node (graph, s :: cs)) cs,

           eqns = eqns} thy

        end

    | _ => (warn thm; thy))

  end) I);

fun get_clauses thy s =

  let val {intros, graph, ...} = CodegenData.get thy

  in case Symtab.lookup intros s of

      NONE => (case try (Inductive.the_inductive (ProofContext.init thy)) s of

        NONE => NONE

      | SOME ({names, ...}, {intrs, raw_induct, ...}) =>

          SOME (names, Codegen.thyname_of_const thy s,

            length (Inductive.params_of raw_induct),

            preprocess thy intrs))

    | SOME _ =>

        let

          val SOME names = find_first

            (fn xs => member (op =) xs s) (Graph.strong_conn graph);

          val intrs as (_, (thyname, nparms)) :: _ =

            maps (the o Symtab.lookup intros) names;

        in SOME (names, thyname, nparms, preprocess thy (map fst (rev intrs))) end

  end;

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

fun is_constrt thy =

  let

    val cnstrs = flat (maps

      (map (fn (_, (_, _, cs)) => map (apsnd length) cs) o #descr o snd)

      (Symtab.dest (Datatype.get_all 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" ^

  cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map

    string_of_mode ms)) modes));

val term_vs = map (fst o fst o dest_Var) o OldTerm.term_vars;

val terms_vs = distinct (op =) o maps 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 = List.foldr (map op :: o cprod) [[]] xss;

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

fun modes_of modes t =

  let

    val ks = 1 upto length (binder_types (fastype_of t));

    val default = [Mode (([], ks), ks, [])];

    fun mk_modes name args = Option.map

     (maps (fn (m as (iss, is)) =>

        let

          val (args1, args2) =

            if length args < length iss then

              error ("Too few arguments for inductive predicate " ^ name)

            else chop (length iss) args;

          val k = length args2;

          val prfx = 1 upto k

        in

          if not (is_prefix op = prfx is) then [] else

          let val is' = map (fn i => i - k) (List.drop (is, k))

          in map (fn x => Mode (m, is', x)) (cprods (map

            (fn (NONE, _) => [NONE]

              | (SOME js, arg) => map SOME (List.filter

                  (fn Mode (_, js', _) => js=js') (modes_of modes arg)))

                    (iss ~~ args1)))

          end

        end)) (AList.lookup op = modes name)

  in (case strip_comb t of

      (Const ("op =", Type (_, [T, _])), _) =>

        [Mode (([], [1]), [1], []), Mode (([], [2]), [2], [])] @

        (if is_eqT T then [Mode (([], [1, 2]), [1, 2], [])] else [])

    | (Const (name, _), args) => the_default default (mk_modes name args)

    | (Var ((name, _), _), args) => the (mk_modes name args)

    | (Free (name, _), args) => the (mk_modes name args)

    | _ => default)

  end;

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

fun select_mode_prem thy modes vs ps =

  find_first (is_some o snd) (ps ~~ map

    (fn Prem (us, t, is_set) => 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 = maps term_vTs out_ts';

            val dupTs = map snd (duplicates (op =) vTs) @

              map_filter (AList.lookup (op =) vTs) vs;

          in

            gen_subset (op =) (terms_vs (in_ts @ in_ts'), vs) andalso

            forall (is_eqT o fastype_of) in_ts' andalso

            gen_subset (op =) (term_vs t, vs) andalso

            forall is_eqT dupTs

          end)

            (if is_set then [Mode (([], []), [], [])]

             else modes_of modes t handle Option =>

               error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))

      | Sidecond t => if gen_subset (op =) (term_vs t, vs) then SOME (Mode (([], []), [], []))

          else NONE) ps);

fun check_mode_clause thy arg_vs modes (iss, is) (ts, ps) =

  let

    val modes' = modes @ map_filter

      (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, _, _) => gen_union (op =) (vs, 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 (op =) (maps term_vTs in_ts))) andalso

    forall (is_eqT o fastype_of) in_ts' andalso

    (case check_mode_prems (gen_union (op =) (arg_vs, in_vs)) ps of

       NONE => false

     | SOME vs => gen_subset (op =) (concl_vs, 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 : (string * (int list option list * int list) list) list) =

  let val y = f x

  in if x = y then x else fixp f y end;

fun infer_modes thy extra_modes arities arg_vs preds = fixp (fn modes =>

  map (check_modes_pred thy arg_vs preds (modes @ extra_modes)) modes)

    (map (fn (s, (ks, k)) => (s, cprod (cprods (map

      (fn NONE => [NONE]

        | SOME k' => map SOME (subsets 1 k')) ks),

      subsets 1 k))) arities);

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

fun mk_eq (x::xs) =

  let fun mk_eqs _ [] = []

        | mk_eqs a (b::cs) = str (a ^ " = " ^ b) :: mk_eqs b cs

  in mk_eqs x xs end;

fun mk_tuple xs = Pretty.block (str "(" ::

  flat (separate [str ",", Pretty.brk 1] (map single xs)) @

  [str ")"]);

fun mk_v ((names, vs), s) = (case AList.lookup (op =) vs s of

      NONE => ((names, (s, [s])::vs), s)

    | SOME xs => let val s' = Name.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 = flat (separate [str " andalso", Pretty.brk 1]

    (map single (maps (mk_eq o snd) nvs @ eq_ps)));

  in

    Pretty.block

     ([str "(fn ", mk_tuple out_ps, str " =>", Pretty.brk 1] @

      (Pretty.block ((if eqs=[] then [] else str "if " ::

         [Pretty.block eqs, Pretty.brk 1, str "then "]) @

         (success_p ::

          (if eqs=[] then [] else [Pretty.brk 1, str "else DSeq.empty"]))) ::

       (if can_fail then

          [Pretty.brk 1, str "| _ => DSeq.empty)"]

        else [str ")"])))

  end;

fun modename module s (iss, is) gr =

  let val (id, gr') = if s = @{const_name "op ="} then (("", "equal"), gr)

    else mk_const_id module s gr

  in (space_implode "__"

    (mk_qual_id module id ::

      map (space_implode "_" o map string_of_int) (map_filter I iss @ [is])), gr')

  end;

fun mk_funcomp brack s k p = (if brack then parens else I)

  (Pretty.block [Pretty.block ((if k = 0 then [] else [str "("]) @

    separate (Pretty.brk 1) (str s :: replicate k (str "|> ???")) @

    (if k = 0 then [] else [str ")"])), Pretty.brk 1, p]);

fun compile_expr thy defs dep module brack modes (NONE, t) gr =

      apfst single (invoke_codegen thy defs dep module brack t gr)

  | compile_expr _ _ _ _ _ _ (SOME _, Var ((name, _), _)) gr =

      ([str name], gr)

  | compile_expr thy defs dep module brack modes (SOME (Mode (mode, _, ms)), t) gr =

      (case strip_comb t of

         (Const (name, _), args) =>

           if name = @{const_name "op ="} orelse AList.defined op = modes name then

             let

               val (args1, args2) = chop (length ms) args;

               val ((ps, mode_id), gr') = gr |> fold_map

                   (compile_expr thy defs dep module true modes) (ms ~~ args1)

                   ||>> modename module name mode;

               val (ps', gr'') = (case mode of

                   ([], []) => ([str "()"], gr')

                 | _ => fold_map

                     (invoke_codegen thy defs dep module true) args2 gr')

             in ((if brack andalso not (null ps andalso null ps') then

               single o parens o Pretty.block else I)

                 (flat (separate [Pretty.brk 1]

                   ([str mode_id] :: ps @ map single ps'))), gr')

             end

           else apfst (single o mk_funcomp brack "??" (length (binder_types (fastype_of t))))

             (invoke_codegen thy defs dep module true t gr)

       | _ => apfst (single o mk_funcomp brack "??" (length (binder_types (fastype_of t))))

           (invoke_codegen thy defs dep module true t gr));

fun compile_clause thy defs dep module all_vs arg_vs modes (iss, is) (ts, ps) inp gr =

  let

    val modes' = modes @ map_filter

      (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 = Name.variant names "x";

        in ((s::names, (s, t)::eqs), Var ((s, 0), fastype_of t)) end;

    fun compile_eq (s, t) gr =

      apfst (Pretty.block o cons (str (s ^ " = ")) o single)

        (invoke_codegen thy defs dep module false t gr);

    val (in_ts, out_ts) = get_args is 1 ts;

    val ((all_vs', eqs), in_ts') =

      Library.foldl_map check_constrt ((all_vs, []), in_ts);

    fun compile_prems out_ts' vs names [] gr =

          let

            val (out_ps, gr2) = fold_map

              (invoke_codegen thy defs dep module false) out_ts gr;

            val (eq_ps, gr3) = fold_map compile_eq eqs gr2;

            val ((names', eqs'), out_ts'') =

              Library.foldl_map check_constrt ((names, []), out_ts');

            val (nvs, out_ts''') = Library.foldl_map distinct_v

              ((names', map (fn x => (x, [x])) vs), out_ts'');

            val (out_ps', gr4) = fold_map

              (invoke_codegen thy defs dep module false) (out_ts''') gr3;

            val (eq_ps', gr5) = fold_map compile_eq eqs' gr4;

          in

            (compile_match (snd nvs) (eq_ps @ eq_ps') out_ps'

              (Pretty.block [str "DSeq.single", Pretty.brk 1, mk_tuple out_ps])

              (exists (not o is_exhaustive) out_ts'''), gr5)

          end

      | compile_prems out_ts vs names ps gr =

          let

            val vs' = distinct (op =) (flat (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') =

              Library.foldl_map check_constrt ((names, []), out_ts);

            val (nvs, out_ts'') = Library.foldl_map distinct_v

              ((names', map (fn x => (x, [x])) vs), out_ts');

            val (out_ps, gr0) = fold_map

              (invoke_codegen thy defs dep module false) out_ts'' gr;

            val (eq_ps, gr1) = fold_map compile_eq eqs gr0;

          in

            (case p of

               Prem (us, t, is_set) =>

                 let

                   val (in_ts, out_ts''') = get_args js 1 us;

                   val (in_ps, gr2) = fold_map

                     (invoke_codegen thy defs dep module true) in_ts gr1;

                   val (ps, gr3) =

                     if not is_set then

                       apfst (fn ps => ps @

                           (if null in_ps then [] else [Pretty.brk 1]) @

                           separate (Pretty.brk 1) in_ps)

                         (compile_expr thy defs dep module false modes

                           (mode, t) gr2)

                     else

                       apfst (fn p => Pretty.breaks [str "DSeq.of_list", str "(case", p,

                         str "of", str "Set", str "xs", str "=>", str "xs)"])

                         (*this is a very strong assumption about the generated code!*)

                           (invoke_codegen thy defs dep module true t gr2);

                   val (rest, gr4) = compile_prems out_ts''' vs' (fst nvs) ps' gr3;

                 in

                   (compile_match (snd nvs) eq_ps out_ps

                      (Pretty.block (ps @

                         [str " :->", Pretty.brk 1, rest]))

                      (exists (not o is_exhaustive) out_ts''), gr4)

                 end

             | Sidecond t =>

                 let

                   val (side_p, gr2) = invoke_codegen thy defs dep module true t gr1;

                   val (rest, gr3) = compile_prems [] vs' (fst nvs) ps' gr2;

                 in

                   (compile_match (snd nvs) eq_ps out_ps

                      (Pretty.block [str "?? ", side_p,

                        str " :->", Pretty.brk 1, rest])

                      (exists (not o is_exhaustive) out_ts''), gr3)

                 end)

          end;

    val (prem_p, gr') = compile_prems in_ts' arg_vs all_vs' ps gr ;

  in

    (Pretty.block [str "DSeq.single", Pretty.brk 1, inp,

       str " :->", Pretty.brk 1, prem_p], gr')

  end;

fun compile_pred thy defs dep module prfx all_vs arg_vs modes s cls mode gr =

  let

    val xs = map str (Name.variant_list arg_vs

      (map (fn i => "x" ^ string_of_int i) (snd mode)));

    val ((cl_ps, mode_id), gr') = gr |>

      fold_map (fn cl => compile_clause thy defs

        dep module all_vs arg_vs modes mode cl (mk_tuple xs)) cls ||>>

      modename module s mode

  in

    (Pretty.block

      ([Pretty.block (separate (Pretty.brk 1)

         (str (prfx ^ mode_id) ::

           map str arg_vs @

           (case mode of ([], []) => [str "()"] | _ => xs)) @

         [str " ="]),

        Pretty.brk 1] @

       flat (separate [str " ++", Pretty.brk 1] (map single cl_ps))), (gr', "and "))

  end;

fun compile_preds thy defs dep module all_vs arg_vs modes preds gr =

  let val (prs, (gr', _)) = fold_map (fn (s, cls) =>

    fold_map (fn mode => fn (gr', prfx') => compile_pred thy defs

      dep module prfx' all_vs arg_vs modes s cls mode gr')

        (((the o AList.lookup (op =) modes) s))) preds (gr, "fun ")

  in

    (space_implode "\n\n" (map string_of (flat prs)) ^ ";\n\n", gr')

  end;

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

exception Modes of

  (string * (int list option list * int list) list) list *

  (string * (int option list * int)) list;

fun lookup_modes gr dep = apfst flat (apsnd flat (ListPair.unzip

  (map ((fn (SOME (Modes x), _, _) => x | _ => ([], [])) o get_node gr)

    (Graph.all_preds (fst gr) [dep]))));

fun print_arities arities = message ("Arities:\n" ^

  cat_lines (map (fn (s, (ks, k)) => s ^ ": " ^

    space_implode " -> " (map

      (fn NONE => "X" | SOME k' => string_of_int k')

        (ks @ [SOME k]))) arities));

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

fun constrain cs [] = []

  | constrain cs ((s, xs) :: ys) = (s, case AList.lookup (op =) cs (s : string) of

      NONE => xs

    | SOME xs' => gen_inter (op =) (xs, 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, nparms, intrs) =>

          mk_ind_def thy defs gr dep names (if_library thyname module)

            [] (prep_intrs intrs) nparms))

            (gr, fold Term.add_const_names ts [])

and mk_ind_def thy defs gr dep names module modecs intrs nparms =

  add_edge_acyclic (hd names, dep) gr handle

    Graph.CYCLES (xs :: _) =>

      error ("InductiveCodegen: illegal cyclic dependencies:\n" ^ commas xs)

  | Graph.UNDEF _ =>

    let

      val _ $ u = Logic.strip_imp_concl (hd intrs);

      val args = List.take (snd (strip_comb u), nparms);

      val arg_vs = maps term_vs args;

      fun get_nparms s = if s mem names then SOME nparms else

        Option.map #3 (get_clauses thy s);

      fun dest_prem (_ $ (Const ("op :", _) $ t $ u)) = Prem ([t], Envir.beta_eta_contract u, true)

        | dest_prem (_ $ ((eq as Const ("op =", _)) $ t $ u)) = Prem ([t, u], eq, false)

        | dest_prem (_ $ t) =

            (case strip_comb t of

               (v as Var _, ts) => if v mem args then Prem (ts, v, false) else Sidecond t

             | (c as Const (s, _), ts) => (case get_nparms s of

                 NONE => Sidecond t

               | SOME k =>

                   let val (ts1, ts2) = chop k ts

                   in Prem (ts2, list_comb (c, ts1), false) end)

             | _ => Sidecond t);

      fun add_clause intr (clauses, arities) =

        let

          val _ $ t = Logic.strip_imp_concl intr;

          val (Const (name, T), ts) = strip_comb t;

          val (ts1, ts2) = chop nparms ts;

          val prems = map dest_prem (Logic.strip_imp_prems intr);

          val (Ts, Us) = chop nparms (binder_types T)

        in

          (AList.update op = (name, these (AList.lookup op = clauses name) @

             [(ts2, prems)]) clauses,

           AList.update op = (name, (map (fn U => (case strip_type U of

                 (Rs as _ :: _, Type ("bool", [])) => SOME (length Rs)

               | _ => NONE)) Ts,

             length Us)) arities)

        end;

      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_arities) = lookup_modes gr' (hd names);

      val (clauses, arities) = fold add_clause intrs ([], []);

      val modes = constrain modecs

        (infer_modes thy extra_modes arities arg_vs clauses);

      val _ = print_arities arities;

      val _ = print_modes modes;

      val (s, gr'') = compile_preds thy defs (hd names) module (terms_vs intrs)

        arg_vs (modes @ extra_modes) clauses gr';

    in

      (map_node (hd names)

        (K (SOME (Modes (modes, arities)), 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 dep module is_query s T ts names thyname k intrs gr =

  let

    val (ts1, ts2) = chop k ts;

    val u = list_comb (Const (s, T), ts1);

    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) k) dep names module' [u];

    val (modes, _) = lookup_modes gr1 dep;

    val (ts', is) = if is_query then

        fst (Library.foldl mk_mode ((([], []), 1), ts2))

      else (ts2, 1 upto length (binder_types T) - k);

    val mode = find_mode gr1 dep s u modes is;

    val (in_ps, gr2) = fold_map (invoke_codegen thy defs dep module true) ts' gr1;

    val (ps, gr3) = compile_expr thy defs dep module false modes (mode, u) gr2;

  in

    (Pretty.block (ps @ (if null in_ps then [] else [Pretty.brk 1]) @

       separate (Pretty.brk 1) in_ps), gr3)

  end;

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

      (list_comb (Const (s ^ "_aux", Ts @ [U] ---> HOLogic.boolT), 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 ((fun_id, mode_id), gr') = gr |>

        mk_const_id module' name ||>>

        modename module' pname ([], mode);

      val vars = map (fn i => str ("x" ^ string_of_int i)) mode;

      val s = string_of (Pretty.block

        [mk_app false (str ("fun " ^ snd fun_id)) vars, str " =",

         Pretty.brk 1, str "DSeq.hd", Pretty.brk 1,

         parens (Pretty.block (separate (Pretty.brk 1) (str mode_id ::

           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)])] clauses 0;

      val (modes, _) = lookup_modes gr'' dep;

      val _ = find_mode gr'' dep pname (head_of (HOLogic.dest_Trueprop

        (Logic.strip_imp_concl (hd clauses)))) modes mode

    in (mk_qual_id module fun_id, gr'') end

  | SOME _ =>

      (mk_qual_id module (get_const_id gr name), add_edge (name, dep) gr);

(* convert n-tuple to nested pairs *)

fun conv_ntuple fs ts p =

  let

    val k = length fs;

    val xs = map (fn i => str ("x" ^ string_of_int i)) (0 upto k);

    val xs' = map (fn Bound i => nth xs (k - i)) ts;

    fun conv xs js =

      if js mem fs then

        let

          val (p, xs') = conv xs (1::js);

          val (q, xs'') = conv xs' (2::js)

        in (mk_tuple [p, q], xs'') end

      else (hd xs, tl xs)

  in

    if k > 0 then

      Pretty.block

        [str "DSeq.map (fn", Pretty.brk 1,

         mk_tuple xs', str " =>", Pretty.brk 1, fst (conv xs []),

         str ")", Pretty.brk 1, parens p]

    else p

  end;

fun inductive_codegen thy defs dep module brack t gr  = (case strip_comb t of

    (Const ("Collect", _), [u]) =>

      let val (r, Ts, fs) = HOLogic.strip_psplits u

      in case strip_comb r of

          (Const (s, T), ts) =>

            (case (get_clauses thy s, get_assoc_code thy (s, T)) of

              (SOME (names, thyname, k, intrs), NONE) =>

                let

                  val (ts1, ts2) = chop k ts;

                  val ts2' = map

                    (fn Bound i => Term.dummy_pattern (nth Ts i) | t => t) ts2;

                  val (ots, its) = List.partition is_Bound ts2;

                  val no_loose = forall (fn t => not (loose_bvar (t, 0)))

                in

                  if null (duplicates op = ots) andalso

                    no_loose ts1 andalso no_loose its

                  then

                    let val (call_p, gr') = mk_ind_call thy defs dep module true

                      s T (ts1 @ ts2') names thyname k intrs gr 

                    in SOME ((if brack then parens else I) (Pretty.block

                      [str "Set", Pretty.brk 1, str "(DSeq.list_of", Pretty.brk 1, str "(",

                       conv_ntuple fs ots call_p, str "))"]),

                       (*this is a very strong assumption about the generated code!*)

                       gr')

                    end

                  else NONE

                end

            | _ => NONE)

        | _ => NONE

      end

  | (Const (s, T), ts) => (case Symtab.lookup (#eqns (CodegenData.get thy)) s of

      NONE => (case (get_clauses thy s, get_assoc_code thy (s, T)) of

        (SOME (names, thyname, k, intrs), NONE) =>

          if length ts < k then NONE else SOME

            (let val (call_p, gr') = mk_ind_call thy defs dep module false

               s T (map Term.no_dummy_patterns ts) names thyname k intrs gr

             in (mk_funcomp brack "?!"

               (length (binder_types T) - length ts) (parens call_p), gr')

             end handle TERM _ => mk_ind_call thy defs dep module true

               s T ts names thyname k intrs gr )

      | _ => NONE)

    | SOME eqns =>

        let

          val (_, thyname) :: _ = eqns;

          val (id, gr') = mk_fun thy defs s (preprocess thy (map fst (rev eqns)))

            dep module (if_library thyname module) gr;

          val (ps, gr'') = fold_map

            (invoke_codegen thy defs dep module true) ts gr';

        in SOME (mk_app brack (str id) ps, gr'')

        end)

  | _ => NONE);

val setup =

  add_codegen "inductive" inductive_codegen #>

  Attrib.setup @{binding code_ind} (Scan.lift (Scan.option (Args.$$$ "target" |-- Args.colon |-- Args.name) --

    Scan.option (Args.$$$ "params" |-- Args.colon |-- OuterParse.nat) >> uncurry add))

    "introduction rules for executable predicates";

end;