(*  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 test_fn : (int * int * int -> term list option) Unsynchronized.ref

  val test_term:

    Proof.context -> bool -> term -> int -> term list option * (bool list * bool)

  val setup : theory -> theory

  val quickcheck_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 = Theory_Data

(

  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 extend = I;

  fun merge ({intros=intros1, graph=graph1, eqns=eqns1},

    {intros=intros2, graph=graph2, eqns=eqns2}) : T =

    {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 x g = 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 (@{const_name "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_global 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 = fold_rev (Graph.add_edge o pair s) cs (fold add_node (s :: cs) graph),

           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_global 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_Data.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

    (fn (m, rnd) => string_of_mode m ^

       (if rnd then " (random)" else "")) 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) * bool) * int list * mode option list;

fun needs_random (Mode ((_, b), _, ms)) =

  b orelse exists (fn NONE => false | SOME m => needs_random m) ms;

fun modes_of modes t =

  let

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

    val default = [Mode ((([], ks), false), 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 (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 (@{const_name "op ="}, Type (_, [T, _])), _) =>

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

        (if is_eqT T then [Mode ((([], [1, 2]), false), [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 missing_vars vs ts = subtract (fn (x, ((y, _), _)) => x = y) vs

  (fold Term.add_vars ts []);

fun monomorphic_vars vs = null (fold (Term.add_tvarsT o snd) vs []);

fun mode_ord p = int_ord (pairself (fn (Mode ((_, rnd), _, _), vs) =>

  length vs + (if null vs then 0 else 1) + (if rnd then 1 else 0)) p);

fun select_mode_prem thy modes vs ps =

  sort (mode_ord o pairself (hd o snd))

    (filter_out (null o snd) (ps ~~ map

      (fn Prem (us, t, is_set) => sort mode_ord

          (List.mapPartial (fn m as 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;

              val missing_vs = missing_vars vs (t :: in_ts @ in_ts')

            in

              if forall (is_eqT o fastype_of) in_ts' andalso forall is_eqT dupTs

                andalso monomorphic_vars missing_vs

              then SOME (m, missing_vs)

              else NONE

            end)

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

               else modes_of modes t handle Option =>

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

        | Sidecond t =>

            let val missing_vs = missing_vars vs [t]

            in

              if monomorphic_vars missing_vs

              then [(Mode ((([], []), false), [], []), missing_vs)]

              else []

            end)

              ps));

fun use_random () = "random_ind" mem !Codegen.mode;

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

  let

    val modes' = modes @ map_filter

      (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [(([], js), false)]))

        (arg_vs ~~ iss);

    fun check_mode_prems vs rnd [] = SOME (vs, rnd)

      | check_mode_prems vs rnd ps = (case select_mode_prem thy modes' vs ps of

          (x, (m, []) :: _) :: _ => check_mode_prems

            (case x of Prem (us, _, _) => union (op =) vs (terms_vs us) | _ => vs)

            (rnd orelse needs_random m)

            (filter_out (equal x) ps)

        | (_, (_, vs') :: _) :: _ =>

            if use_random () then

              check_mode_prems (union (op =) vs (map (fst o fst) vs')) true ps

            else NONE

        | _ => NONE);

    val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (get_args is 1 ts));

    val in_vs = terms_vs in_ts;

  in

    if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso

      forall (is_eqT o fastype_of) in_ts'

    then (case check_mode_prems (union (op =) arg_vs in_vs) rnd ps of

       NONE => NONE

     | SOME (vs, rnd') =>

         let val missing_vs = missing_vars vs ts

         in

           if null missing_vs orelse

             use_random () andalso monomorphic_vars missing_vs

           then SOME (rnd' orelse not (null missing_vs))

           else NONE

         end)

    else NONE

  end;

fun check_modes_pred thy arg_vs preds modes (p, ms) =

  let val SOME rs = AList.lookup (op =) preds p

  in (p, List.mapPartial (fn m as (m', _) =>

    let val xs = map (check_mode_clause thy arg_vs modes m) rs

    in case find_index is_none xs of

        ~1 => SOME (m', exists (fn SOME b => b) xs)

      | i => (message ("Clause " ^ string_of_int (i+1) ^ " of " ^

        p ^ " violates mode " ^ string_of_mode m'); NONE)

    end) ms)

  end;

fun fixp f (x : (string * ((int list option list * int list) * bool) 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, map (rpair false) (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 s (names, vs) =

  (case AList.lookup (op =) vs s of

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

  | SOME xs =>

      let val s' = Name.variant names s

      in (s', (s'::names, AList.update (op =) (s, s'::xs) vs)) end);

fun distinct_v (Var ((s, 0), T)) nvs =

      let val (s', nvs') = mk_v s nvs

      in (Var ((s', 0), T), nvs') end

  | distinct_v (t $ u) nvs =

      let

        val (t', nvs') = distinct_v t nvs;

        val (u', nvs'') = distinct_v u nvs';

      in (t' $ u', nvs'') end

  | distinct_v t nvs = (t, nvs);

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), false)]))

        (arg_vs ~~ iss);

    fun check_constrt t (names, eqs) =

      if is_constrt thy t then (t, (names, eqs))

      else

        let val s = Name.variant names "x";

        in (Var ((s, 0), fastype_of t), (s::names, (s, t)::eqs)) 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 (in_ts', (all_vs', eqs)) = fold_map check_constrt in_ts (all_vs, []);

    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 (out_ts'', (names', eqs')) = fold_map check_constrt out_ts' (names, []);

            val (out_ts''', nvs) =

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

            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;

            val vs' = distinct (op =) (flat (vs :: map term_vs out_ts'));

            val missing_vs = missing_vars vs' out_ts;

            val final_p = Pretty.block

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

          in

            if null missing_vs then

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

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

            else

              let

                val (pat_p, gr6) = invoke_codegen thy defs dep module true

                  (HOLogic.mk_tuple (map Var missing_vs)) gr5;

                val gen_p = mk_gen gr6 module true [] ""

                  (HOLogic.mk_tupleT (map snd missing_vs))

              in

                (compile_match (snd nvs) eq_ps' out_ps'

                   (Pretty.block [str "DSeq.generator ", gen_p,

                      str " :->", Pretty.brk 1,

                      compile_match [] eq_ps [pat_p] final_p false])

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

                 gr6)

              end

          end

      | compile_prems out_ts vs names ps gr =

          let

            val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));

            val (out_ts', (names', eqs)) = fold_map check_constrt out_ts (names, []);

            val (out_ts'', nvs) = fold_map distinct_v out_ts' (names', map (fn x => (x, [x])) vs);

            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 hd (select_mode_prem thy modes' vs' ps) of

               (p as Prem (us, t, is_set), (mode as Mode (_, js, _), []) :: _) =>

                 let

                   val ps' = filter_out (equal p) ps;

                   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

                           (SOME 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

             | (p as Sidecond t, [(_, [])]) =>

                 let

                   val ps' = filter_out (equal p) ps;

                   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

             | (_, (_, missing_vs) :: _) =>

                 let

                   val T = HOLogic.mk_tupleT (map snd missing_vs);

                   val (_, gr2) = invoke_tycodegen thy defs dep module false T gr1;

                   val gen_p = mk_gen gr2 module true [] "" T;

                   val (rest, gr3) = compile_prems

                     [HOLogic.mk_tuple (map Var missing_vs)] vs' (fst nvs) ps gr2

                 in

                   (compile_match (snd nvs) eq_ps out_ps

                      (Pretty.block [str "DSeq.generator", Pretty.brk 1,

                        gen_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) * bool) 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.export_without_context) intrs;

fun constrain cs [] = []

  | constrain cs ((s, xs) :: ys) =

      (s,

        case AList.lookup (op =) cs (s : string) of

          NONE => xs

        | SOME xs' => inter (op = o apfst fst) xs' xs) :: constrain cs ys;

fun mk_extra_defs thy defs gr dep names module ts =

  fold (fn name => fn gr =>

    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))

    (fold Term.add_const_names ts []) gr

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 (@{const_name "op :"}, _) $ t $ u)) =

            Prem ([t], Envir.beta_eta_contract u, true)

        | dest_prem (_ $ ((eq as Const (@{const_name "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 _ :: _, @{typ 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 (Const (@{const_name dummy_pattern}, _)) ((ts, mode), i) = ((ts, mode), i + 1)

      | mk_mode t ((ts, mode), i) = ((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 (fold mk_mode ts2 (([], []), 1))

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

    val mode = find_mode gr1 dep s u modes is;

    val _ = if is_query orelse not (needs_random (the mode)) then ()

      else warning ("Illegal use of random data generators in " ^ s);

    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_range (fn i => str ("x" ^ string_of_int i)) (k + 1);

    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 (@{const_name 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 (length Ts - i - 1)) | 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";

(**** Quickcheck involving inductive predicates ****)

val test_fn : (int * int * int -> term list option) Unsynchronized.ref =

  Unsynchronized.ref (fn _ => NONE);

fun strip_imp p =

  let val (q, r) = HOLogic.dest_imp p

  in strip_imp r |>> cons q end

  handle TERM _ => ([], p);

fun deepen bound f i =

  if i > bound then NONE

  else (case f i of

      NONE => deepen bound f (i + 1)

    | SOME x => SOME x);

val (depth_bound, setup_depth_bound) = Attrib.config_int "ind_quickcheck_depth" (K 10);

val (depth_start, setup_depth_start) = Attrib.config_int "ind_quickcheck_depth_start" (K 1);

val (random_values, setup_random_values) = Attrib.config_int "ind_quickcheck_random" (K 5);

val (size_offset, setup_size_offset) = Attrib.config_int "ind_quickcheck_size_offset" (K 0);

fun test_term ctxt report t =

  let

    val thy = ProofContext.theory_of ctxt;

    val (xs, p) = strip_abs t;

    val args' = map_index (fn (i, (_, T)) => ("arg" ^ string_of_int i, T)) xs;

    val args = map Free args';

    val (ps, q) = strip_imp p;

    val Ts = map snd xs;

    val T = Ts ---> HOLogic.boolT;

    val rl = Logic.list_implies

      (map (HOLogic.mk_Trueprop o curry subst_bounds (rev args)) ps @

       [HOLogic.mk_Trueprop (HOLogic.mk_not (subst_bounds (rev args, q)))],

       HOLogic.mk_Trueprop (list_comb (Free ("quickcheckp", T), args)));

    val (_, thy') = Inductive.add_inductive_global

      {quiet_mode=true, verbose=false, alt_name=Binding.empty, coind=false,

       no_elim=true, no_ind=false, skip_mono=false, fork_mono=false}

      [((Binding.name "quickcheckp", T), NoSyn)] []

      [(Attrib.empty_binding, rl)] [] (Theory.copy thy);

    val pred = HOLogic.mk_Trueprop (list_comb

      (Const (Sign.intern_const thy' "quickcheckp", T),

       map Term.dummy_pattern Ts));

    val (code, gr) = setmp_CRITICAL mode ["term_of", "test", "random_ind"]

      (generate_code_i thy' [] "Generated") [("testf", pred)];

    val s = "structure TestTerm =\nstruct\n\n" ^

      cat_lines (map snd code) ^

      "\nopen Generated;\n\n" ^ string_of

        (Pretty.block [str "val () = InductiveCodegen.test_fn :=",

          Pretty.brk 1, str "(fn p =>", Pretty.brk 1,

          str "case Seq.pull (testf p) of", Pretty.brk 1,

          str "SOME ", mk_tuple [mk_tuple (map (str o fst) args'), str "_"],

          str " =>", Pretty.brk 1, str "SOME ",

          Pretty.block (str "[" ::

            Pretty.commas (map (fn (s, T) => Pretty.block

              [mk_term_of gr "Generated" false T, Pretty.brk 1, str s]) args') @

            [str "]"]), Pretty.brk 1,

          str "| NONE => NONE);"]) ^

      "\n\nend;\n";

    val _ = ML_Context.eval_in (SOME ctxt) false Position.none s;

    val values = Config.get ctxt random_values;

    val bound = Config.get ctxt depth_bound;

    val start = Config.get ctxt depth_start;

    val offset = Config.get ctxt size_offset;

    val test_fn' = !test_fn;

    val dummy_report = ([], false)

    fun test k = (deepen bound (fn i =>

      (priority ("Search depth: " ^ string_of_int i);

       test_fn' (i, values, k+offset))) start, dummy_report);

  in test end;

val quickcheck_setup =

  setup_depth_bound #>

  setup_depth_start #>

  setup_random_values #>

  setup_size_offset #>

  Quickcheck.add_generator ("SML_inductive", test_term);

end;