src/HOL/Tools/inductive_codegen.ML
author wenzelm
Mon Aug 08 17:23:15 2011 +0200 (2011-08-08)
changeset 44058 ae85c5d64913
parent 43878 eeb10fdd9535
child 44121 44adaa6db327
permissions -rw-r--r--
misc tuning -- eliminated old-fashioned rep_thm;
     1 (*  Title:      HOL/Tools/inductive_codegen.ML
     2     Author:     Stefan Berghofer, TU Muenchen
     3 
     4 Code generator for inductive predicates.
     5 *)
     6 
     7 signature INDUCTIVE_CODEGEN =
     8 sig
     9   val add: string option -> int option -> attribute
    10   val poke_test_fn: (int * int * int -> term list option) -> unit
    11   val test_term: Proof.context -> (term * term list) list -> int list ->
    12     term list option * Quickcheck.report option
    13   val setup: theory -> theory
    14   val quickcheck_setup: theory -> theory
    15 end;
    16 
    17 structure Inductive_Codegen : INDUCTIVE_CODEGEN =
    18 struct
    19 
    20 (**** theory data ****)
    21 
    22 fun merge_rules tabs =
    23   Symtab.join (fn _ => AList.merge (Thm.eq_thm_prop) (K true)) tabs;
    24 
    25 structure CodegenData = Theory_Data
    26 (
    27   type T =
    28     {intros : (thm * (string * int)) list Symtab.table,
    29      graph : unit Graph.T,
    30      eqns : (thm * string) list Symtab.table};
    31   val empty =
    32     {intros = Symtab.empty, graph = Graph.empty, eqns = Symtab.empty};
    33   val extend = I;
    34   fun merge
    35     ({intros = intros1, graph = graph1, eqns = eqns1},
    36       {intros = intros2, graph = graph2, eqns = eqns2}) : T =
    37     {intros = merge_rules (intros1, intros2),
    38      graph = Graph.merge (K true) (graph1, graph2),
    39      eqns = merge_rules (eqns1, eqns2)};
    40 );
    41 
    42 
    43 fun warn thy thm =
    44   warning ("Inductive_Codegen: Not a proper clause:\n" ^
    45     Display.string_of_thm_global thy thm);
    46 
    47 fun add_node x g = Graph.new_node (x, ()) g handle Graph.DUP _ => g;
    48 
    49 fun add optmod optnparms = Thm.declaration_attribute (fn thm => Context.mapping (fn thy =>
    50   let
    51     val {intros, graph, eqns} = CodegenData.get thy;
    52     fun thyname_of s = (case optmod of
    53       NONE => Codegen.thyname_of_const thy s | SOME s => s);
    54   in
    55     (case Option.map strip_comb (try HOLogic.dest_Trueprop (concl_of thm)) of
    56       SOME (Const (@{const_name HOL.eq}, _), [t, _]) =>
    57         (case head_of t of
    58           Const (s, _) =>
    59             CodegenData.put {intros = intros, graph = graph,
    60                eqns = eqns |> Symtab.map_default (s, [])
    61                  (AList.update Thm.eq_thm_prop (thm, thyname_of s))} thy
    62         | _ => (warn thy thm; thy))
    63     | SOME (Const (s, _), _) =>
    64         let
    65           val cs = fold Term.add_const_names (Thm.prems_of thm) [];
    66           val rules = Symtab.lookup_list intros s;
    67           val nparms =
    68             (case optnparms of
    69               SOME k => k
    70             | NONE =>
    71                 (case rules of
    72                   [] =>
    73                     (case try (Inductive.the_inductive (Proof_Context.init_global thy)) s of
    74                       SOME (_, {raw_induct, ...}) =>
    75                         length (Inductive.params_of raw_induct)
    76                     | NONE => 0)
    77                 | xs => snd (snd (List.last xs))))
    78         in CodegenData.put
    79           {intros = intros |>
    80            Symtab.update (s, (AList.update Thm.eq_thm_prop
    81              (thm, (thyname_of s, nparms)) rules)),
    82            graph = fold_rev (Graph.add_edge o pair s) cs (fold add_node (s :: cs) graph),
    83            eqns = eqns} thy
    84         end
    85     | _ => (warn thy thm; thy))
    86   end) I);
    87 
    88 fun get_clauses thy s =
    89   let val {intros, graph, ...} = CodegenData.get thy in
    90     (case Symtab.lookup intros s of
    91       NONE =>
    92         (case try (Inductive.the_inductive (Proof_Context.init_global thy)) s of
    93           NONE => NONE
    94         | SOME ({names, ...}, {intrs, raw_induct, ...}) =>
    95             SOME (names, Codegen.thyname_of_const thy s,
    96               length (Inductive.params_of raw_induct),
    97               Codegen.preprocess thy intrs))
    98     | SOME _ =>
    99         let
   100           val SOME names = find_first
   101             (fn xs => member (op =) xs s) (Graph.strong_conn graph);
   102           val intrs as (_, (thyname, nparms)) :: _ =
   103             maps (the o Symtab.lookup intros) names;
   104         in SOME (names, thyname, nparms, Codegen.preprocess thy (map fst (rev intrs))) end)
   105   end;
   106 
   107 
   108 (**** check if a term contains only constructor functions ****)
   109 
   110 fun is_constrt thy =
   111   let
   112     val cnstrs = flat (maps
   113       (map (fn (_, (_, _, cs)) => map (apsnd length) cs) o #descr o snd)
   114       (Symtab.dest (Datatype_Data.get_all thy)));
   115     fun check t =
   116       (case strip_comb t of
   117         (Var _, []) => true
   118       | (Const (s, _), ts) =>
   119           (case AList.lookup (op =) cnstrs s of
   120             NONE => false
   121           | SOME i => length ts = i andalso forall check ts)
   122       | _ => false);
   123   in check end;
   124 
   125 
   126 (**** check if a type is an equality type (i.e. doesn't contain fun) ****)
   127 
   128 fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
   129   | is_eqT _ = true;
   130 
   131 
   132 (**** mode inference ****)
   133 
   134 fun string_of_mode (iss, is) = space_implode " -> " (map
   135   (fn NONE => "X"
   136     | SOME js => enclose "[" "]" (commas (map string_of_int js)))
   137        (iss @ [SOME is]));
   138 
   139 fun print_modes modes = Codegen.message ("Inferred modes:\n" ^
   140   cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
   141     (fn (m, rnd) => string_of_mode m ^
   142        (if rnd then " (random)" else "")) ms)) modes));
   143 
   144 val term_vs = map (fst o fst o dest_Var) o OldTerm.term_vars;
   145 val terms_vs = distinct (op =) o maps term_vs;
   146 
   147 (** collect all Vars in a term (with duplicates!) **)
   148 fun term_vTs tm =
   149   fold_aterms (fn Var ((x, _), T) => cons (x, T) | _ => I) tm [];
   150 
   151 fun get_args _ _ [] = ([], [])
   152   | get_args is i (x::xs) = (if member (op =) is i then apfst else apsnd) (cons x)
   153       (get_args is (i+1) xs);
   154 
   155 fun merge xs [] = xs
   156   | merge [] ys = ys
   157   | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)
   158       else y::merge (x::xs) ys;
   159 
   160 fun subsets i j = if i <= j then
   161        let val is = subsets (i+1) j
   162        in merge (map (fn ks => i::ks) is) is end
   163      else [[]];
   164 
   165 fun cprod ([], ys) = []
   166   | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
   167 
   168 fun cprods xss = List.foldr (map op :: o cprod) [[]] xss;
   169 
   170 datatype mode = Mode of ((int list option list * int list) * bool) * int list * mode option list;
   171 
   172 fun needs_random (Mode ((_, b), _, ms)) =
   173   b orelse exists (fn NONE => false | SOME m => needs_random m) ms;
   174 
   175 fun modes_of modes t =
   176   let
   177     val ks = 1 upto length (binder_types (fastype_of t));
   178     val default = [Mode ((([], ks), false), ks, [])];
   179     fun mk_modes name args = Option.map
   180      (maps (fn (m as ((iss, is), _)) =>
   181         let
   182           val (args1, args2) =
   183             if length args < length iss then
   184               error ("Too few arguments for inductive predicate " ^ name)
   185             else chop (length iss) args;
   186           val k = length args2;
   187           val prfx = 1 upto k
   188         in
   189           if not (is_prefix op = prfx is) then [] else
   190           let val is' = map (fn i => i - k) (List.drop (is, k))
   191           in map (fn x => Mode (m, is', x)) (cprods (map
   192             (fn (NONE, _) => [NONE]
   193               | (SOME js, arg) => map SOME (filter
   194                   (fn Mode (_, js', _) => js=js') (modes_of modes arg)))
   195                     (iss ~~ args1)))
   196           end
   197         end)) (AList.lookup op = modes name)
   198 
   199   in
   200     (case strip_comb t of
   201       (Const (@{const_name HOL.eq}, Type (_, [T, _])), _) =>
   202         [Mode ((([], [1]), false), [1], []), Mode ((([], [2]), false), [2], [])] @
   203         (if is_eqT T then [Mode ((([], [1, 2]), false), [1, 2], [])] else [])
   204     | (Const (name, _), args) => the_default default (mk_modes name args)
   205     | (Var ((name, _), _), args) => the (mk_modes name args)
   206     | (Free (name, _), args) => the (mk_modes name args)
   207     | _ => default)
   208   end;
   209 
   210 datatype indprem = Prem of term list * term * bool | Sidecond of term;
   211 
   212 fun missing_vars vs ts = subtract (fn (x, ((y, _), _)) => x = y) vs
   213   (fold Term.add_vars ts []);
   214 
   215 fun monomorphic_vars vs = null (fold (Term.add_tvarsT o snd) vs []);
   216 
   217 fun mode_ord p = int_ord (pairself (fn (Mode ((_, rnd), _, _), vs) =>
   218   length vs + (if null vs then 0 else 1) + (if rnd then 1 else 0)) p);
   219 
   220 fun select_mode_prem thy modes vs ps =
   221   sort (mode_ord o pairself (hd o snd))
   222     (filter_out (null o snd) (ps ~~ map
   223       (fn Prem (us, t, is_set) => sort mode_ord
   224           (map_filter (fn m as Mode (_, is, _) =>
   225             let
   226               val (in_ts, out_ts) = get_args is 1 us;
   227               val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts;
   228               val vTs = maps term_vTs out_ts';
   229               val dupTs = map snd (duplicates (op =) vTs) @
   230                 map_filter (AList.lookup (op =) vTs) vs;
   231               val missing_vs = missing_vars vs (t :: in_ts @ in_ts')
   232             in
   233               if forall (is_eqT o fastype_of) in_ts' andalso forall is_eqT dupTs
   234                 andalso monomorphic_vars missing_vs
   235               then SOME (m, missing_vs)
   236               else NONE
   237             end)
   238               (if is_set then [Mode ((([], []), false), [], [])]
   239                else modes_of modes t handle Option =>
   240                  error ("Bad predicate: " ^ Syntax.string_of_term_global thy t)))
   241         | Sidecond t =>
   242             let val missing_vs = missing_vars vs [t]
   243             in
   244               if monomorphic_vars missing_vs
   245               then [(Mode ((([], []), false), [], []), missing_vs)]
   246               else []
   247             end)
   248               ps));
   249 
   250 fun use_random codegen_mode = member (op =) codegen_mode "random_ind";
   251 
   252 fun check_mode_clause thy codegen_mode arg_vs modes ((iss, is), rnd) (ts, ps) =
   253   let
   254     val modes' = modes @ map_filter
   255       (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [(([], js), false)]))
   256         (arg_vs ~~ iss);
   257     fun check_mode_prems vs rnd [] = SOME (vs, rnd)
   258       | check_mode_prems vs rnd ps =
   259           (case select_mode_prem thy modes' vs ps of
   260             (x, (m, []) :: _) :: _ =>
   261               check_mode_prems
   262                 (case x of Prem (us, _, _) => union (op =) vs (terms_vs us) | _ => vs)
   263                 (rnd orelse needs_random m)
   264                 (filter_out (equal x) ps)
   265           | (_, (_, vs') :: _) :: _ =>
   266               if use_random codegen_mode then
   267                 check_mode_prems (union (op =) vs (map (fst o fst) vs')) true ps
   268               else NONE
   269           | _ => NONE);
   270     val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (get_args is 1 ts));
   271     val in_vs = terms_vs in_ts;
   272   in
   273     if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso
   274       forall (is_eqT o fastype_of) in_ts'
   275     then
   276       (case check_mode_prems (union (op =) arg_vs in_vs) rnd ps of
   277         NONE => NONE
   278       | SOME (vs, rnd') =>
   279           let val missing_vs = missing_vars vs ts
   280           in
   281             if null missing_vs orelse
   282               use_random codegen_mode andalso monomorphic_vars missing_vs
   283             then SOME (rnd' orelse not (null missing_vs))
   284             else NONE
   285           end)
   286     else NONE
   287   end;
   288 
   289 fun check_modes_pred thy codegen_mode arg_vs preds modes (p, ms) =
   290   let val SOME rs = AList.lookup (op =) preds p in
   291     (p, map_filter (fn m as (m', _) =>
   292       let val xs = map (check_mode_clause thy codegen_mode arg_vs modes m) rs in
   293         (case find_index is_none xs of
   294           ~1 => SOME (m', exists (fn SOME b => b) xs)
   295         | i => (Codegen.message ("Clause " ^ string_of_int (i+1) ^ " of " ^
   296           p ^ " violates mode " ^ string_of_mode m'); NONE))
   297       end) ms)
   298   end;
   299 
   300 fun fixp f (x : (string * ((int list option list * int list) * bool) list) list) =
   301   let val y = f x
   302   in if x = y then x else fixp f y end;
   303 
   304 fun infer_modes thy codegen_mode extra_modes arities arg_vs preds = fixp (fn modes =>
   305   map (check_modes_pred thy codegen_mode arg_vs preds (modes @ extra_modes)) modes)
   306     (map (fn (s, (ks, k)) => (s, map (rpair false) (cprod (cprods (map
   307       (fn NONE => [NONE]
   308         | SOME k' => map SOME (subsets 1 k')) ks),
   309       subsets 1 k)))) arities);
   310 
   311 
   312 (**** code generation ****)
   313 
   314 fun mk_eq (x::xs) =
   315   let
   316     fun mk_eqs _ [] = []
   317       | mk_eqs a (b :: cs) = Codegen.str (a ^ " = " ^ b) :: mk_eqs b cs;
   318   in mk_eqs x xs end;
   319 
   320 fun mk_tuple xs =
   321   Pretty.block (Codegen.str "(" ::
   322     flat (separate [Codegen.str ",", Pretty.brk 1] (map single xs)) @
   323     [Codegen.str ")"]);
   324 
   325 fun mk_v s (names, vs) =
   326   (case AList.lookup (op =) vs s of
   327     NONE => (s, (names, (s, [s])::vs))
   328   | SOME xs =>
   329       let val s' = singleton (Name.variant_list names) s
   330       in (s', (s'::names, AList.update (op =) (s, s'::xs) vs)) end);
   331 
   332 fun distinct_v (Var ((s, 0), T)) nvs =
   333       let val (s', nvs') = mk_v s nvs
   334       in (Var ((s', 0), T), nvs') end
   335   | distinct_v (t $ u) nvs =
   336       let
   337         val (t', nvs') = distinct_v t nvs;
   338         val (u', nvs'') = distinct_v u nvs';
   339       in (t' $ u', nvs'') end
   340   | distinct_v t nvs = (t, nvs);
   341 
   342 fun is_exhaustive (Var _) = true
   343   | is_exhaustive (Const (@{const_name Pair}, _) $ t $ u) =
   344       is_exhaustive t andalso is_exhaustive u
   345   | is_exhaustive _ = false;
   346 
   347 fun compile_match nvs eq_ps out_ps success_p can_fail =
   348   let val eqs = flat (separate [Codegen.str " andalso", Pretty.brk 1]
   349     (map single (maps (mk_eq o snd) nvs @ eq_ps)));
   350   in
   351     Pretty.block
   352      ([Codegen.str "(fn ", mk_tuple out_ps, Codegen.str " =>", Pretty.brk 1] @
   353       (Pretty.block ((if null eqs then [] else Codegen.str "if " ::
   354          [Pretty.block eqs, Pretty.brk 1, Codegen.str "then "]) @
   355          (success_p ::
   356           (if null eqs then [] else [Pretty.brk 1, Codegen.str "else DSeq.empty"]))) ::
   357        (if can_fail then
   358           [Pretty.brk 1, Codegen.str "| _ => DSeq.empty)"]
   359         else [Codegen.str ")"])))
   360   end;
   361 
   362 fun modename module s (iss, is) gr =
   363   let val (id, gr') = if s = @{const_name HOL.eq} then (("", "equal"), gr)
   364     else Codegen.mk_const_id module s gr
   365   in (space_implode "__"
   366     (Codegen.mk_qual_id module id ::
   367       map (space_implode "_" o map string_of_int) (map_filter I iss @ [is])), gr')
   368   end;
   369 
   370 fun mk_funcomp brack s k p = (if brack then Codegen.parens else I)
   371   (Pretty.block [Pretty.block ((if k = 0 then [] else [Codegen.str "("]) @
   372     separate (Pretty.brk 1) (Codegen.str s :: replicate k (Codegen.str "|> ???")) @
   373     (if k = 0 then [] else [Codegen.str ")"])), Pretty.brk 1, p]);
   374 
   375 fun compile_expr thy codegen_mode defs dep module brack modes (NONE, t) gr =
   376       apfst single (Codegen.invoke_codegen thy codegen_mode defs dep module brack t gr)
   377   | compile_expr _ _ _ _ _ _ _ (SOME _, Var ((name, _), _)) gr =
   378       ([Codegen.str name], gr)
   379   | compile_expr thy codegen_mode
   380         defs dep module brack modes (SOME (Mode ((mode, _), _, ms)), t) gr =
   381       (case strip_comb t of
   382         (Const (name, _), args) =>
   383           if name = @{const_name HOL.eq} orelse AList.defined op = modes name then
   384             let
   385               val (args1, args2) = chop (length ms) args;
   386               val ((ps, mode_id), gr') =
   387                 gr |> fold_map
   388                   (compile_expr thy codegen_mode defs dep module true modes) (ms ~~ args1)
   389                 ||>> modename module name mode;
   390                val (ps', gr'') =
   391                 (case mode of
   392                    ([], []) => ([Codegen.str "()"], gr')
   393                  | _ => fold_map
   394                      (Codegen.invoke_codegen thy codegen_mode defs dep module true) args2 gr');
   395              in
   396               ((if brack andalso not (null ps andalso null ps') then
   397                 single o Codegen.parens o Pretty.block else I)
   398                   (flat (separate [Pretty.brk 1]
   399                     ([Codegen.str mode_id] :: ps @ map single ps'))), gr')
   400              end
   401           else
   402             apfst (single o mk_funcomp brack "??" (length (binder_types (fastype_of t))))
   403               (Codegen.invoke_codegen thy codegen_mode defs dep module true t gr)
   404       | _ =>
   405         apfst (single o mk_funcomp brack "??" (length (binder_types (fastype_of t))))
   406           (Codegen.invoke_codegen thy codegen_mode defs dep module true t gr));
   407 
   408 fun compile_clause thy codegen_mode defs dep module all_vs arg_vs modes (iss, is) (ts, ps) inp gr =
   409   let
   410     val modes' = modes @ map_filter
   411       (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [(([], js), false)]))
   412         (arg_vs ~~ iss);
   413 
   414     fun check_constrt t (names, eqs) =
   415       if is_constrt thy t then (t, (names, eqs))
   416       else
   417         let val s = singleton (Name.variant_list names) "x";
   418         in (Var ((s, 0), fastype_of t), (s::names, (s, t)::eqs)) end;
   419 
   420     fun compile_eq (s, t) gr =
   421       apfst (Pretty.block o cons (Codegen.str (s ^ " = ")) o single)
   422         (Codegen.invoke_codegen thy codegen_mode defs dep module false t gr);
   423 
   424     val (in_ts, out_ts) = get_args is 1 ts;
   425     val (in_ts', (all_vs', eqs)) = fold_map check_constrt in_ts (all_vs, []);
   426 
   427     fun compile_prems out_ts' vs names [] gr =
   428           let
   429             val (out_ps, gr2) =
   430               fold_map (Codegen.invoke_codegen thy codegen_mode defs dep module false)
   431                 out_ts gr;
   432             val (eq_ps, gr3) = fold_map compile_eq eqs gr2;
   433             val (out_ts'', (names', eqs')) = fold_map check_constrt out_ts' (names, []);
   434             val (out_ts''', nvs) =
   435               fold_map distinct_v out_ts'' (names', map (fn x => (x, [x])) vs);
   436             val (out_ps', gr4) =
   437               fold_map (Codegen.invoke_codegen thy codegen_mode defs dep module false)
   438                 out_ts''' gr3;
   439             val (eq_ps', gr5) = fold_map compile_eq eqs' gr4;
   440             val vs' = distinct (op =) (flat (vs :: map term_vs out_ts'));
   441             val missing_vs = missing_vars vs' out_ts;
   442             val final_p = Pretty.block
   443               [Codegen.str "DSeq.single", Pretty.brk 1, mk_tuple out_ps]
   444           in
   445             if null missing_vs then
   446               (compile_match (snd nvs) (eq_ps @ eq_ps') out_ps'
   447                  final_p (exists (not o is_exhaustive) out_ts'''), gr5)
   448             else
   449               let
   450                 val (pat_p, gr6) =
   451                   Codegen.invoke_codegen thy codegen_mode defs dep module true
   452                     (HOLogic.mk_tuple (map Var missing_vs)) gr5;
   453                 val gen_p =
   454                   Codegen.mk_gen gr6 module true [] ""
   455                     (HOLogic.mk_tupleT (map snd missing_vs));
   456               in
   457                 (compile_match (snd nvs) eq_ps' out_ps'
   458                   (Pretty.block [Codegen.str "DSeq.generator ", gen_p,
   459                     Codegen.str " :->", Pretty.brk 1,
   460                     compile_match [] eq_ps [pat_p] final_p false])
   461                   (exists (not o is_exhaustive) out_ts'''),
   462                  gr6)
   463               end
   464           end
   465       | compile_prems out_ts vs names ps gr =
   466           let
   467             val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
   468             val (out_ts', (names', eqs)) = fold_map check_constrt out_ts (names, []);
   469             val (out_ts'', nvs) =
   470               fold_map distinct_v out_ts' (names', map (fn x => (x, [x])) vs);
   471             val (out_ps, gr0) =
   472               fold_map (Codegen.invoke_codegen thy codegen_mode defs dep module false)
   473                 out_ts'' gr;
   474             val (eq_ps, gr1) = fold_map compile_eq eqs gr0;
   475           in
   476             (case hd (select_mode_prem thy modes' vs' ps) of
   477               (p as Prem (us, t, is_set), (mode as Mode (_, js, _), []) :: _) =>
   478                 let
   479                   val ps' = filter_out (equal p) ps;
   480                   val (in_ts, out_ts''') = get_args js 1 us;
   481                   val (in_ps, gr2) =
   482                     fold_map (Codegen.invoke_codegen thy codegen_mode defs dep module true)
   483                       in_ts gr1;
   484                   val (ps, gr3) =
   485                     if not is_set then
   486                       apfst (fn ps => ps @
   487                           (if null in_ps then [] else [Pretty.brk 1]) @
   488                           separate (Pretty.brk 1) in_ps)
   489                         (compile_expr thy codegen_mode defs dep module false modes
   490                           (SOME mode, t) gr2)
   491                     else
   492                       apfst (fn p =>
   493                         Pretty.breaks [Codegen.str "DSeq.of_list", Codegen.str "(case", p,
   494                         Codegen.str "of", Codegen.str "Set", Codegen.str "xs", Codegen.str "=>",
   495                         Codegen.str "xs)"])
   496                         (*this is a very strong assumption about the generated code!*)
   497                         (Codegen.invoke_codegen thy codegen_mode defs dep module true t gr2);
   498                    val (rest, gr4) = compile_prems out_ts''' vs' (fst nvs) ps' gr3;
   499                  in
   500                    (compile_match (snd nvs) eq_ps out_ps
   501                      (Pretty.block (ps @
   502                        [Codegen.str " :->", Pretty.brk 1, rest]))
   503                        (exists (not o is_exhaustive) out_ts''), gr4)
   504                  end
   505             | (p as Sidecond t, [(_, [])]) =>
   506                 let
   507                   val ps' = filter_out (equal p) ps;
   508                   val (side_p, gr2) =
   509                     Codegen.invoke_codegen thy codegen_mode defs dep module true t gr1;
   510                   val (rest, gr3) = compile_prems [] vs' (fst nvs) ps' gr2;
   511                 in
   512                   (compile_match (snd nvs) eq_ps out_ps
   513                     (Pretty.block [Codegen.str "?? ", side_p,
   514                       Codegen.str " :->", Pretty.brk 1, rest])
   515                     (exists (not o is_exhaustive) out_ts''), gr3)
   516                 end
   517             | (_, (_, missing_vs) :: _) =>
   518                 let
   519                   val T = HOLogic.mk_tupleT (map snd missing_vs);
   520                   val (_, gr2) =
   521                     Codegen.invoke_tycodegen thy codegen_mode defs dep module false T gr1;
   522                   val gen_p = Codegen.mk_gen gr2 module true [] "" T;
   523                   val (rest, gr3) = compile_prems
   524                     [HOLogic.mk_tuple (map Var missing_vs)] vs' (fst nvs) ps gr2;
   525                 in
   526                   (compile_match (snd nvs) eq_ps out_ps
   527                     (Pretty.block [Codegen.str "DSeq.generator", Pretty.brk 1,
   528                       gen_p, Codegen.str " :->", Pretty.brk 1, rest])
   529                     (exists (not o is_exhaustive) out_ts''), gr3)
   530                 end)
   531           end;
   532 
   533     val (prem_p, gr') = compile_prems in_ts' arg_vs all_vs' ps gr ;
   534   in
   535     (Pretty.block [Codegen.str "DSeq.single", Pretty.brk 1, inp,
   536        Codegen.str " :->", Pretty.brk 1, prem_p], gr')
   537   end;
   538 
   539 fun compile_pred thy codegen_mode defs dep module prfx all_vs arg_vs modes s cls mode gr =
   540   let
   541     val xs = map Codegen.str (Name.variant_list arg_vs
   542       (map (fn i => "x" ^ string_of_int i) (snd mode)));
   543     val ((cl_ps, mode_id), gr') = gr |>
   544       fold_map (fn cl => compile_clause thy codegen_mode defs
   545         dep module all_vs arg_vs modes mode cl (mk_tuple xs)) cls ||>>
   546       modename module s mode
   547   in
   548     (Pretty.block
   549       ([Pretty.block (separate (Pretty.brk 1)
   550          (Codegen.str (prfx ^ mode_id) ::
   551            map Codegen.str arg_vs @
   552            (case mode of ([], []) => [Codegen.str "()"] | _ => xs)) @
   553          [Codegen.str " ="]),
   554         Pretty.brk 1] @
   555        flat (separate [Codegen.str " ++", Pretty.brk 1] (map single cl_ps))), (gr', "and "))
   556   end;
   557 
   558 fun compile_preds thy codegen_mode defs dep module all_vs arg_vs modes preds gr =
   559   let val (prs, (gr', _)) = fold_map (fn (s, cls) =>
   560     fold_map (fn (mode, _) => fn (gr', prfx') => compile_pred thy codegen_mode defs
   561       dep module prfx' all_vs arg_vs modes s cls mode gr')
   562         (((the o AList.lookup (op =) modes) s))) preds (gr, "fun ")
   563   in
   564     (space_implode "\n\n" (map Codegen.string_of (flat prs)) ^ ";\n\n", gr')
   565   end;
   566 
   567 (**** processing of introduction rules ****)
   568 
   569 exception Modes of
   570   (string * ((int list option list * int list) * bool) list) list *
   571   (string * (int option list * int)) list;
   572 
   573 fun lookup_modes gr dep = apfst flat (apsnd flat (ListPair.unzip
   574   (map ((fn (SOME (Modes x), _, _) => x | _ => ([], [])) o Codegen.get_node gr)
   575     (Graph.all_preds (fst gr) [dep]))));
   576 
   577 fun print_arities arities = Codegen.message ("Arities:\n" ^
   578   cat_lines (map (fn (s, (ks, k)) => s ^ ": " ^
   579     space_implode " -> " (map
   580       (fn NONE => "X" | SOME k' => string_of_int k')
   581         (ks @ [SOME k]))) arities));
   582 
   583 fun prep_intrs intrs =
   584   map (Codegen.rename_term o Thm.prop_of o Drule.export_without_context) intrs;
   585 
   586 fun constrain cs [] = []
   587   | constrain cs ((s, xs) :: ys) =
   588       (s,
   589         (case AList.lookup (op =) cs (s : string) of
   590           NONE => xs
   591         | SOME xs' => inter (op = o apfst fst) xs' xs)) :: constrain cs ys;
   592 
   593 fun mk_extra_defs thy codegen_mode defs gr dep names module ts =
   594   fold (fn name => fn gr =>
   595     if member (op =) names name then gr
   596     else
   597       (case get_clauses thy name of
   598         NONE => gr
   599       | SOME (names, thyname, nparms, intrs) =>
   600           mk_ind_def thy codegen_mode defs gr dep names
   601             (Codegen.if_library codegen_mode thyname module)
   602             [] (prep_intrs intrs) nparms))
   603     (fold Term.add_const_names ts []) gr
   604 
   605 and mk_ind_def thy codegen_mode defs gr dep names module modecs intrs nparms =
   606   Codegen.add_edge_acyclic (hd names, dep) gr handle
   607     Graph.CYCLES (xs :: _) =>
   608       error ("Inductive_Codegen: illegal cyclic dependencies:\n" ^ commas xs)
   609   | Graph.UNDEF _ =>
   610     let
   611       val _ $ u = Logic.strip_imp_concl (hd intrs);
   612       val args = List.take (snd (strip_comb u), nparms);
   613       val arg_vs = maps term_vs args;
   614 
   615       fun get_nparms s = if member (op =) names s then SOME nparms else
   616         Option.map #3 (get_clauses thy s);
   617 
   618       fun dest_prem (_ $ (Const (@{const_name Set.member}, _) $ t $ u)) =
   619             Prem ([t], Envir.beta_eta_contract u, true)
   620         | dest_prem (_ $ ((eq as Const (@{const_name HOL.eq}, _)) $ t $ u)) =
   621             Prem ([t, u], eq, false)
   622         | dest_prem (_ $ t) =
   623             (case strip_comb t of
   624               (v as Var _, ts) =>
   625                 if member (op =) args v then Prem (ts, v, false) else Sidecond t
   626             | (c as Const (s, _), ts) =>
   627                 (case get_nparms s of
   628                   NONE => Sidecond t
   629                 | SOME k =>
   630                     let val (ts1, ts2) = chop k ts
   631                     in Prem (ts2, list_comb (c, ts1), false) end)
   632             | _ => Sidecond t);
   633 
   634       fun add_clause intr (clauses, arities) =
   635         let
   636           val _ $ t = Logic.strip_imp_concl intr;
   637           val (Const (name, T), ts) = strip_comb t;
   638           val (ts1, ts2) = chop nparms ts;
   639           val prems = map dest_prem (Logic.strip_imp_prems intr);
   640           val (Ts, Us) = chop nparms (binder_types T)
   641         in
   642           (AList.update op = (name, these (AList.lookup op = clauses name) @
   643              [(ts2, prems)]) clauses,
   644            AList.update op = (name, (map (fn U =>
   645               (case strip_type U of
   646                 (Rs as _ :: _, @{typ bool}) => SOME (length Rs)
   647               | _ => NONE)) Ts,
   648              length Us)) arities)
   649         end;
   650 
   651       val gr' = mk_extra_defs thy codegen_mode defs
   652         (Codegen.add_edge (hd names, dep)
   653           (Codegen.new_node (hd names, (NONE, "", "")) gr)) (hd names) names module intrs;
   654       val (extra_modes, extra_arities) = lookup_modes gr' (hd names);
   655       val (clauses, arities) = fold add_clause intrs ([], []);
   656       val modes = constrain modecs
   657         (infer_modes thy codegen_mode extra_modes arities arg_vs clauses);
   658       val _ = print_arities arities;
   659       val _ = print_modes modes;
   660       val (s, gr'') =
   661         compile_preds thy codegen_mode defs (hd names) module (terms_vs intrs)
   662           arg_vs (modes @ extra_modes) clauses gr';
   663     in
   664       (Codegen.map_node (hd names)
   665         (K (SOME (Modes (modes, arities)), module, s)) gr'')
   666     end;
   667 
   668 fun find_mode gr dep s u modes is =
   669   (case find_first (fn Mode (_, js, _) => is = js) (modes_of modes u handle Option => []) of
   670     NONE =>
   671       Codegen.codegen_error gr dep
   672         ("No such mode for " ^ s ^ ": " ^ string_of_mode ([], is))
   673   | mode => mode);
   674 
   675 fun mk_ind_call thy codegen_mode defs dep module is_query s T ts names thyname k intrs gr =
   676   let
   677     val (ts1, ts2) = chop k ts;
   678     val u = list_comb (Const (s, T), ts1);
   679 
   680     fun mk_mode (Const (@{const_name dummy_pattern}, _)) ((ts, mode), i) =
   681           ((ts, mode), i + 1)
   682       | mk_mode t ((ts, mode), i) = ((ts @ [t], mode @ [i]), i + 1);
   683 
   684     val module' = Codegen.if_library codegen_mode thyname module;
   685     val gr1 =
   686       mk_extra_defs thy codegen_mode defs
   687         (mk_ind_def thy codegen_mode defs gr dep names module'
   688         [] (prep_intrs intrs) k) dep names module' [u];
   689     val (modes, _) = lookup_modes gr1 dep;
   690     val (ts', is) =
   691       if is_query then fst (fold mk_mode ts2 (([], []), 1))
   692       else (ts2, 1 upto length (binder_types T) - k);
   693     val mode = find_mode gr1 dep s u modes is;
   694     val _ = if is_query orelse not (needs_random (the mode)) then ()
   695       else warning ("Illegal use of random data generators in " ^ s);
   696     val (in_ps, gr2) =
   697       fold_map (Codegen.invoke_codegen thy codegen_mode defs dep module true)
   698         ts' gr1;
   699     val (ps, gr3) =
   700       compile_expr thy codegen_mode defs dep module false modes (mode, u) gr2;
   701   in
   702     (Pretty.block (ps @ (if null in_ps then [] else [Pretty.brk 1]) @
   703        separate (Pretty.brk 1) in_ps), gr3)
   704   end;
   705 
   706 fun clause_of_eqn eqn =
   707   let
   708     val (t, u) = HOLogic.dest_eq (HOLogic.dest_Trueprop (concl_of eqn));
   709     val (Const (s, T), ts) = strip_comb t;
   710     val (Ts, U) = strip_type T
   711   in
   712     Codegen.rename_term (Logic.list_implies (prems_of eqn, HOLogic.mk_Trueprop
   713       (list_comb (Const (s ^ "_aux", Ts @ [U] ---> HOLogic.boolT), ts @ [u]))))
   714   end;
   715 
   716 fun mk_fun thy codegen_mode defs name eqns dep module module' gr =
   717   (case try (Codegen.get_node gr) name of
   718     NONE =>
   719       let
   720         val clauses = map clause_of_eqn eqns;
   721         val pname = name ^ "_aux";
   722         val arity =
   723           length (snd (strip_comb (fst (HOLogic.dest_eq
   724             (HOLogic.dest_Trueprop (concl_of (hd eqns)))))));
   725         val mode = 1 upto arity;
   726         val ((fun_id, mode_id), gr') = gr |>
   727           Codegen.mk_const_id module' name ||>>
   728           modename module' pname ([], mode);
   729         val vars = map (fn i => Codegen.str ("x" ^ string_of_int i)) mode;
   730         val s = Codegen.string_of (Pretty.block
   731           [Codegen.mk_app false (Codegen.str ("fun " ^ snd fun_id)) vars, Codegen.str " =",
   732            Pretty.brk 1, Codegen.str "DSeq.hd", Pretty.brk 1,
   733            Codegen.parens (Pretty.block (separate (Pretty.brk 1) (Codegen.str mode_id ::
   734              vars)))]) ^ ";\n\n";
   735         val gr'' = mk_ind_def thy codegen_mode defs (Codegen.add_edge (name, dep)
   736           (Codegen.new_node (name, (NONE, module', s)) gr')) name [pname] module'
   737           [(pname, [([], mode)])] clauses 0;
   738         val (modes, _) = lookup_modes gr'' dep;
   739         val _ = find_mode gr'' dep pname (head_of (HOLogic.dest_Trueprop
   740           (Logic.strip_imp_concl (hd clauses)))) modes mode
   741       in (Codegen.mk_qual_id module fun_id, gr'') end
   742   | SOME _ =>
   743       (Codegen.mk_qual_id module (Codegen.get_const_id gr name),
   744         Codegen.add_edge (name, dep) gr));
   745 
   746 (* convert n-tuple to nested pairs *)
   747 
   748 fun conv_ntuple fs ts p =
   749   let
   750     val k = length fs;
   751     val xs = map_range (fn i => Codegen.str ("x" ^ string_of_int i)) (k + 1);
   752     val xs' = map (fn Bound i => nth xs (k - i)) ts;
   753     fun conv xs js =
   754       if member (op =) fs js then
   755         let
   756           val (p, xs') = conv xs (1::js);
   757           val (q, xs'') = conv xs' (2::js)
   758         in (mk_tuple [p, q], xs'') end
   759       else (hd xs, tl xs)
   760   in
   761     if k > 0 then
   762       Pretty.block
   763         [Codegen.str "DSeq.map (fn", Pretty.brk 1,
   764          mk_tuple xs', Codegen.str " =>", Pretty.brk 1, fst (conv xs []),
   765          Codegen.str ")", Pretty.brk 1, Codegen.parens p]
   766     else p
   767   end;
   768 
   769 fun inductive_codegen thy codegen_mode defs dep module brack t gr =
   770   (case strip_comb t of
   771     (Const (@{const_name Collect}, _), [u]) =>
   772       let val (r, Ts, fs) = HOLogic.strip_psplits u in
   773         (case strip_comb r of
   774           (Const (s, T), ts) =>
   775             (case (get_clauses thy s, Codegen.get_assoc_code thy (s, T)) of
   776               (SOME (names, thyname, k, intrs), NONE) =>
   777                 let
   778                   val (ts1, ts2) = chop k ts;
   779                   val ts2' = map
   780                     (fn Bound i => Term.dummy_pattern (nth Ts (length Ts - i - 1)) | t => t) ts2;
   781                   val (ots, its) = List.partition is_Bound ts2;
   782                   val closed = forall (not o Term.is_open);
   783                 in
   784                   if null (duplicates op = ots) andalso
   785                     closed ts1 andalso closed its
   786                   then
   787                     let
   788                       val (call_p, gr') =
   789                         mk_ind_call thy codegen_mode defs dep module true
   790                           s T (ts1 @ ts2') names thyname k intrs gr;
   791                     in
   792                       SOME ((if brack then Codegen.parens else I) (Pretty.block
   793                         [Codegen.str "Set", Pretty.brk 1, Codegen.str "(DSeq.list_of", Pretty.brk 1,
   794                          Codegen.str "(", conv_ntuple fs ots call_p, Codegen.str "))"]),
   795                          (*this is a very strong assumption about the generated code!*)
   796                          gr')
   797                     end
   798                   else NONE
   799                 end
   800             | _ => NONE)
   801         | _ => NONE)
   802       end
   803   | (Const (s, T), ts) =>
   804       (case Symtab.lookup (#eqns (CodegenData.get thy)) s of
   805         NONE =>
   806           (case (get_clauses thy s, Codegen.get_assoc_code thy (s, T)) of
   807             (SOME (names, thyname, k, intrs), NONE) =>
   808               if length ts < k then NONE else
   809                 SOME
   810                   (let
   811                     val (call_p, gr') = mk_ind_call thy codegen_mode defs dep module false
   812                       s T (map Term.no_dummy_patterns ts) names thyname k intrs gr
   813                    in
   814                     (mk_funcomp brack "?!"
   815                       (length (binder_types T) - length ts) (Codegen.parens call_p), gr')
   816                    end
   817                    handle TERM _ =>
   818                     mk_ind_call thy codegen_mode defs dep module true
   819                       s T ts names thyname k intrs gr)
   820           | _ => NONE)
   821       | SOME eqns =>
   822           let
   823             val (_, thyname) :: _ = eqns;
   824             val (id, gr') =
   825               mk_fun thy codegen_mode defs s (Codegen.preprocess thy (map fst (rev eqns)))
   826                 dep module (Codegen.if_library codegen_mode thyname module) gr;
   827             val (ps, gr'') =
   828               fold_map (Codegen.invoke_codegen thy codegen_mode defs dep module true)
   829                 ts gr';
   830           in SOME (Codegen.mk_app brack (Codegen.str id) ps, gr'') end)
   831   | _ => NONE);
   832 
   833 val setup =
   834   Codegen.add_codegen "inductive" inductive_codegen #>
   835   Attrib.setup @{binding code_ind}
   836     (Scan.lift (Scan.option (Args.$$$ "target" |-- Args.colon |-- Args.name) --
   837       Scan.option (Args.$$$ "params" |-- Args.colon |-- Parse.nat) >> uncurry add))
   838     "introduction rules for executable predicates";
   839 
   840 
   841 (**** Quickcheck involving inductive predicates ****)
   842 
   843 structure Result = Proof_Data
   844 (
   845   type T = int * int * int -> term list option;
   846   fun init _ = (fn _ => NONE);
   847 );
   848 
   849 val get_test_fn = Result.get;
   850 fun poke_test_fn f = Context.>> (Context.map_proof (Result.put f));
   851 
   852 
   853 fun strip_imp p =
   854   let val (q, r) = HOLogic.dest_imp p
   855   in strip_imp r |>> cons q end
   856   handle TERM _ => ([], p);
   857 
   858 fun deepen bound f i =
   859   if i > bound then NONE
   860   else
   861     (case f i of
   862       NONE => deepen bound f (i + 1)
   863     | SOME x => SOME x);
   864 
   865 val active = Attrib.setup_config_bool @{binding quickcheck_inductive_SML_active} (K false);
   866     
   867 val depth_bound = Attrib.setup_config_int @{binding ind_quickcheck_depth} (K 10);
   868 val depth_start = Attrib.setup_config_int @{binding ind_quickcheck_depth_start} (K 1);
   869 val random_values = Attrib.setup_config_int @{binding ind_quickcheck_random} (K 5);
   870 val size_offset = Attrib.setup_config_int @{binding ind_quickcheck_size_offset} (K 0);
   871 
   872 fun test_term ctxt [(t, [])] =
   873       let
   874         val t' = list_abs_free (Term.add_frees t [], t)
   875         val thy = Proof_Context.theory_of ctxt;
   876         val (xs, p) = strip_abs t';
   877         val args' = map_index (fn (i, (_, T)) => ("arg" ^ string_of_int i, T)) xs;
   878         val args = map Free args';
   879         val (ps, q) = strip_imp p;
   880         val Ts = map snd xs;
   881         val T = Ts ---> HOLogic.boolT;
   882         val rl = Logic.list_implies
   883           (map (HOLogic.mk_Trueprop o curry subst_bounds (rev args)) ps @
   884            [HOLogic.mk_Trueprop (HOLogic.mk_not (subst_bounds (rev args, q)))],
   885            HOLogic.mk_Trueprop (list_comb (Free ("quickcheckp", T), args)));
   886         val (_, thy') = Inductive.add_inductive_global
   887           {quiet_mode=true, verbose=false, alt_name=Binding.empty, coind=false,
   888            no_elim=true, no_ind=false, skip_mono=false, fork_mono=false}
   889           [((@{binding quickcheckp}, T), NoSyn)] []
   890           [(Attrib.empty_binding, rl)] [] (Theory.copy thy);
   891         val pred = HOLogic.mk_Trueprop (list_comb
   892           (Const (Sign.intern_const thy' "quickcheckp", T),
   893            map Term.dummy_pattern Ts));
   894         val (code, gr) =
   895           Codegen.generate_code_i thy' ["term_of", "test", "random_ind"] [] "Generated"
   896             [("testf", pred)];
   897         val s = "structure Test_Term =\nstruct\n\n" ^
   898           cat_lines (map snd code) ^
   899           "\nopen Generated;\n\n" ^ Codegen.string_of
   900             (Pretty.block [Codegen.str "val () = Inductive_Codegen.poke_test_fn",
   901               Pretty.brk 1, Codegen.str "(fn p =>", Pretty.brk 1,
   902               Codegen.str "case Seq.pull (testf p) of", Pretty.brk 1,
   903               Codegen.str "SOME ",
   904               mk_tuple [mk_tuple (map (Codegen.str o fst) args'), Codegen.str "_"],
   905               Codegen.str " =>", Pretty.brk 1, Codegen.str "SOME ",
   906               Pretty.enum "," "[" "]"
   907                 (map (fn (s, T) => Pretty.block
   908                   [Codegen.mk_term_of gr "Generated" false T, Pretty.brk 1, Codegen.str s]) args'),
   909               Pretty.brk 1,
   910               Codegen.str "| NONE => NONE);"]) ^
   911           "\n\nend;\n";
   912         val test_fn =
   913           ctxt
   914           |> Context.proof_map
   915               (ML_Context.exec (fn () => ML_Context.eval_text false Position.none s))
   916           |> get_test_fn;
   917         val values = Config.get ctxt random_values;
   918         val bound = Config.get ctxt depth_bound;
   919         val start = Config.get ctxt depth_start;
   920         val offset = Config.get ctxt size_offset;
   921         fun test [k] = (deepen bound (fn i =>
   922           (Output.urgent_message ("Search depth: " ^ string_of_int i);
   923            test_fn (i, values, k+offset))) start, NONE);
   924       in test end
   925   | test_term ctxt [_] = error "Option eval is not supported by tester SML_inductive"
   926   | test_term ctxt _ =
   927       error "Compilation of multiple instances is not supported by tester SML_inductive";
   928 
   929 val test_goal = Quickcheck.generator_test_goal_terms test_term;
   930 
   931 val quickcheck_setup =
   932   Context.theory_map (Quickcheck.add_tester ("SML_inductive", (active, test_goal)));
   933 
   934 end;