src/HOL/Tools/inductive_codegen.ML
author berghofe
Thu Aug 25 16:10:16 2005 +0200 (2005-08-25)
changeset 17144 6642e0f96f44
parent 16861 7446b4be013b
child 17261 193b84a70ca4
permissions -rw-r--r--
Implemented incremental code generation.
     1 (*  Title:      HOL/inductive_codegen.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4 
     5 Code generator for inductive predicates.
     6 *)
     7 
     8 signature INDUCTIVE_CODEGEN =
     9 sig
    10   val add : string option -> theory attribute
    11   val setup : (theory -> theory) list
    12 end;
    13 
    14 structure InductiveCodegen : INDUCTIVE_CODEGEN =
    15 struct
    16 
    17 open Codegen;
    18 
    19 (**** theory data ****)
    20 
    21 structure CodegenData = TheoryDataFun
    22 (struct
    23   val name = "HOL/inductive_codegen";
    24   type T =
    25     {intros : (thm * string) list Symtab.table,
    26      graph : unit Graph.T,
    27      eqns : (thm * string) list Symtab.table};
    28   val empty =
    29     {intros = Symtab.empty, graph = Graph.empty, eqns = Symtab.empty};
    30   val copy = I;
    31   val extend = I;
    32   fun merge _ ({intros=intros1, graph=graph1, eqns=eqns1},
    33     {intros=intros2, graph=graph2, eqns=eqns2}) =
    34     {intros = Symtab.merge_multi (Drule.eq_thm_prop o pairself fst)
    35        (intros1, intros2),
    36      graph = Graph.merge (K true) (graph1, graph2),
    37      eqns = Symtab.merge_multi (Drule.eq_thm_prop o pairself fst)
    38        (eqns1, eqns2)};
    39   fun print _ _ = ();
    40 end);
    41 
    42 
    43 fun warn thm = warning ("InductiveCodegen: Not a proper clause:\n" ^
    44   string_of_thm thm);
    45 
    46 fun add_node (g, x) = Graph.new_node (x, ()) g handle Graph.DUP _ => g;
    47 
    48 fun add optmod (p as (thy, thm)) =
    49   let
    50     val {intros, graph, eqns} = CodegenData.get thy;
    51     fun thyname_of s = (case optmod of
    52       NONE => thyname_of_const s thy | SOME s => s);
    53   in (case concl_of thm of
    54       _ $ (Const ("op :", _) $ _ $ t) => (case head_of t of
    55         Const (s, _) =>
    56           let val cs = foldr add_term_consts [] (prems_of thm)
    57           in (CodegenData.put
    58             {intros = Symtab.update ((s,
    59                getOpt (Symtab.lookup (intros, s), []) @
    60                  [(thm, thyname_of s)]), intros),
    61              graph = foldr (uncurry (Graph.add_edge o pair s))
    62                (Library.foldl add_node (graph, s :: cs)) cs,
    63              eqns = eqns} thy, thm)
    64           end
    65       | _ => (warn thm; p))
    66     | _ $ (Const ("op =", _) $ t $ _) => (case head_of t of
    67         Const (s, _) =>
    68           (CodegenData.put {intros = intros, graph = graph,
    69              eqns = Symtab.update ((s,
    70                getOpt (Symtab.lookup (eqns, s), []) @
    71                  [(thm, thyname_of s)]), eqns)} thy, thm)
    72       | _ => (warn thm; p))
    73     | _ => (warn thm; p))
    74   end;
    75 
    76 fun get_clauses thy s =
    77   let val {intros, graph, ...} = CodegenData.get thy
    78   in case Symtab.lookup (intros, s) of
    79       NONE => (case InductivePackage.get_inductive thy s of
    80         NONE => NONE
    81       | SOME ({names, ...}, {intrs, ...}) =>
    82           SOME (names, thyname_of_const s thy,
    83             preprocess thy intrs))
    84     | SOME _ =>
    85         let
    86           val SOME names = find_first
    87             (fn xs => s mem xs) (Graph.strong_conn graph);
    88           val intrs = List.concat (map
    89             (fn s => valOf (Symtab.lookup (intros, s))) names);
    90           val (_, (_, thyname)) = split_last intrs
    91         in SOME (names, thyname, preprocess thy (map fst intrs)) end
    92   end;
    93 
    94 
    95 (**** improper tuples ****)
    96 
    97 fun prod_factors p (Const ("Pair", _) $ t $ u) =
    98       p :: prod_factors (1::p) t @ prod_factors (2::p) u
    99   | prod_factors p _ = [];
   100 
   101 fun split_prod p ps t = if p mem ps then (case t of
   102        Const ("Pair", _) $ t $ u =>
   103          split_prod (1::p) ps t @ split_prod (2::p) ps u
   104      | _ => error "Inconsistent use of products") else [t];
   105 
   106 fun full_split_prod (Const ("Pair", _) $ t $ u) =
   107       full_split_prod t @ full_split_prod u
   108   | full_split_prod t = [t];
   109 
   110 datatype factors = FVar of int list list | FFix of int list list;
   111 
   112 exception Factors;
   113 
   114 fun mg_factor (FVar f) (FVar f') = FVar (f inter f')
   115   | mg_factor (FVar f) (FFix f') =
   116       if f' subset f then FFix f' else raise Factors
   117   | mg_factor (FFix f) (FVar f') =
   118       if f subset f' then FFix f else raise Factors
   119   | mg_factor (FFix f) (FFix f') =
   120       if f subset f' andalso f' subset f then FFix f else raise Factors;
   121 
   122 fun dest_factors (FVar f) = f
   123   | dest_factors (FFix f) = f;
   124 
   125 fun infer_factors sg extra_fs (fs, (optf, t)) =
   126   let fun err s = error (s ^ "\n" ^ Sign.string_of_term sg t)
   127   in (case (optf, strip_comb t) of
   128       (SOME f, (Const (name, _), args)) =>
   129         (case assoc (extra_fs, name) of
   130            NONE => overwrite (fs, (name, getOpt
   131              (Option.map (mg_factor f) (assoc (fs, name)), f)))
   132          | SOME (fs', f') => (mg_factor f (FFix f');
   133              Library.foldl (infer_factors sg extra_fs)
   134                (fs, map (Option.map FFix) fs' ~~ args)))
   135     | (SOME f, (Var ((name, _), _), [])) =>
   136         overwrite (fs, (name, getOpt
   137           (Option.map (mg_factor f) (assoc (fs, name)), f)))
   138     | (NONE, _) => fs
   139     | _ => err "Illegal term")
   140       handle Factors => err "Product factor mismatch in"
   141   end;
   142 
   143 fun string_of_factors p ps = if p mem ps then
   144     "(" ^ string_of_factors (1::p) ps ^ ", " ^ string_of_factors (2::p) ps ^ ")"
   145   else "_";
   146 
   147 
   148 (**** check if a term contains only constructor functions ****)
   149 
   150 fun is_constrt thy =
   151   let
   152     val cnstrs = List.concat (List.concat (map
   153       (map (fn (_, (_, _, cs)) => map (apsnd length) cs) o #descr o snd)
   154       (Symtab.dest (DatatypePackage.get_datatypes thy))));
   155     fun check t = (case strip_comb t of
   156         (Var _, []) => true
   157       | (Const (s, _), ts) => (case assoc (cnstrs, s) of
   158             NONE => false
   159           | SOME i => length ts = i andalso forall check ts)
   160       | _ => false)
   161   in check end;
   162 
   163 (**** check if a type is an equality type (i.e. doesn't contain fun) ****)
   164 
   165 fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
   166   | is_eqT _ = true;
   167 
   168 (**** mode inference ****)
   169 
   170 fun string_of_mode (iss, is) = space_implode " -> " (map
   171   (fn NONE => "X"
   172     | SOME js => enclose "[" "]" (commas (map string_of_int js)))
   173        (iss @ [SOME is]));
   174 
   175 fun print_modes modes = message ("Inferred modes:\n" ^
   176   space_implode "\n" (map (fn (s, ms) => s ^ ": " ^ commas (map
   177     string_of_mode ms)) modes));
   178 
   179 val term_vs = map (fst o fst o dest_Var) o term_vars;
   180 val terms_vs = distinct o List.concat o (map term_vs);
   181 
   182 (** collect all Vars in a term (with duplicates!) **)
   183 fun term_vTs tm =
   184   fold_aterms (fn Var ((x, _), T) => cons (x, T) | _ => I) tm [];
   185 
   186 fun get_args _ _ [] = ([], [])
   187   | get_args is i (x::xs) = (if i mem is then apfst else apsnd) (cons x)
   188       (get_args is (i+1) xs);
   189 
   190 fun merge xs [] = xs
   191   | merge [] ys = ys
   192   | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)
   193       else y::merge (x::xs) ys;
   194 
   195 fun subsets i j = if i <= j then
   196        let val is = subsets (i+1) j
   197        in merge (map (fn ks => i::ks) is) is end
   198      else [[]];
   199 
   200 fun cprod ([], ys) = []
   201   | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
   202 
   203 fun cprods xss = foldr (map op :: o cprod) [[]] xss;
   204 
   205 datatype mode = Mode of (int list option list * int list) * mode option list;
   206 
   207 fun modes_of modes t =
   208   let
   209     fun mk_modes name args = List.concat
   210       (map (fn (m as (iss, is)) => map (Mode o pair m) (cprods (map
   211         (fn (NONE, _) => [NONE]
   212           | (SOME js, arg) => map SOME
   213               (List.filter (fn Mode ((_, js'), _) => js=js') (modes_of modes arg)))
   214                 (iss ~~ args)))) (valOf (assoc (modes, name))))
   215 
   216   in (case strip_comb t of
   217       (Const ("op =", Type (_, [T, _])), _) =>
   218         [Mode (([], [1]), []), Mode (([], [2]), [])] @
   219         (if is_eqT T then [Mode (([], [1, 2]), [])] else [])
   220     | (Const (name, _), args) => mk_modes name args
   221     | (Var ((name, _), _), args) => mk_modes name args
   222     | (Free (name, _), args) => mk_modes name args)
   223   end;
   224 
   225 datatype indprem = Prem of term list * term | Sidecond of term;
   226 
   227 fun select_mode_prem thy modes vs ps =
   228   find_first (isSome o snd) (ps ~~ map
   229     (fn Prem (us, t) => find_first (fn Mode ((_, is), _) =>
   230           let
   231             val (in_ts, out_ts) = get_args is 1 us;
   232             val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts;
   233             val vTs = List.concat (map term_vTs out_ts');
   234             val dupTs = map snd (duplicates vTs) @
   235               List.mapPartial (curry assoc vTs) vs;
   236           in
   237             terms_vs (in_ts @ in_ts') subset vs andalso
   238             forall (is_eqT o fastype_of) in_ts' andalso
   239             term_vs t subset vs andalso
   240             forall is_eqT dupTs
   241           end)
   242             (modes_of modes t handle Option => [Mode (([], []), [])])
   243       | Sidecond t => if term_vs t subset vs then SOME (Mode (([], []), []))
   244           else NONE) ps);
   245 
   246 fun check_mode_clause thy arg_vs modes (iss, is) (ts, ps) =
   247   let
   248     val modes' = modes @ List.mapPartial
   249       (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
   250         (arg_vs ~~ iss);
   251     fun check_mode_prems vs [] = SOME vs
   252       | check_mode_prems vs ps = (case select_mode_prem thy modes' vs ps of
   253           NONE => NONE
   254         | SOME (x, _) => check_mode_prems
   255             (case x of Prem (us, _) => vs union terms_vs us | _ => vs)
   256             (filter_out (equal x) ps));
   257     val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (get_args is 1 ts));
   258     val in_vs = terms_vs in_ts;
   259     val concl_vs = terms_vs ts
   260   in
   261     forall is_eqT (map snd (duplicates (List.concat (map term_vTs in_ts)))) andalso
   262     forall (is_eqT o fastype_of) in_ts' andalso
   263     (case check_mode_prems (arg_vs union in_vs) ps of
   264        NONE => false
   265      | SOME vs => concl_vs subset vs)
   266   end;
   267 
   268 fun check_modes_pred thy arg_vs preds modes (p, ms) =
   269   let val SOME rs = assoc (preds, p)
   270   in (p, List.filter (fn m => case find_index
   271     (not o check_mode_clause thy arg_vs modes m) rs of
   272       ~1 => true
   273     | i => (message ("Clause " ^ string_of_int (i+1) ^ " of " ^
   274       p ^ " violates mode " ^ string_of_mode m); false)) ms)
   275   end;
   276 
   277 fun fixp f x =
   278   let val y = f x
   279   in if x = y then x else fixp f y end;
   280 
   281 fun infer_modes thy extra_modes factors arg_vs preds = fixp (fn modes =>
   282   map (check_modes_pred thy arg_vs preds (modes @ extra_modes)) modes)
   283     (map (fn (s, (fs, f)) => (s, cprod (cprods (map
   284       (fn NONE => [NONE]
   285         | SOME f' => map SOME (subsets 1 (length f' + 1))) fs),
   286       subsets 1 (length f + 1)))) factors);
   287 
   288 (**** code generation ****)
   289 
   290 fun mk_eq (x::xs) =
   291   let fun mk_eqs _ [] = []
   292         | mk_eqs a (b::cs) = Pretty.str (a ^ " = " ^ b) :: mk_eqs b cs
   293   in mk_eqs x xs end;
   294 
   295 fun mk_tuple xs = Pretty.block (Pretty.str "(" ::
   296   List.concat (separate [Pretty.str ",", Pretty.brk 1] (map single xs)) @
   297   [Pretty.str ")"]);
   298 
   299 (* convert nested pairs to n-tuple *)
   300 
   301 fun conv_ntuple [_] t ps = ps
   302   | conv_ntuple [_, _] t ps = ps
   303   | conv_ntuple us t ps =
   304       let
   305         val xs = map (fn i => Pretty.str ("x" ^ string_of_int i))
   306           (1 upto length us);
   307         fun ntuple (ys as (x, T) :: xs) U =
   308           if T = U then (x, xs)
   309           else
   310             let
   311               val Type ("*", [U1, U2]) = U;
   312               val (p1, ys1) = ntuple ys U1;
   313               val (p2, ys2) = ntuple ys1 U2
   314             in (mk_tuple [p1, p2], ys2) end
   315       in
   316         [Pretty.str "Seq.map (fn", Pretty.brk 1,
   317          fst (ntuple (xs ~~ map fastype_of us) (HOLogic.dest_setT (fastype_of t))),
   318          Pretty.str " =>", Pretty.brk 1, mk_tuple xs, Pretty.str ")",
   319          Pretty.brk 1, parens (Pretty.block ps)]
   320       end;
   321 
   322 (* convert n-tuple to nested pairs *)
   323 
   324 fun conv_ntuple' fs T ps =
   325   let
   326     fun mk_x i = Pretty.str ("x" ^ string_of_int i);
   327     fun conv i js (Type ("*", [T, U])) =
   328           if js mem fs then
   329             let
   330               val (p, i') = conv i (1::js) T;
   331               val (q, i'') = conv i' (2::js) U
   332             in (mk_tuple [p, q], i'') end
   333           else (mk_x i, i+1)
   334       | conv i js _ = (mk_x i, i+1)
   335     val (p, i) = conv 1 [] T
   336   in
   337     if i > 3 then
   338       [Pretty.str "Seq.map (fn", Pretty.brk 1,
   339        mk_tuple (map mk_x (1 upto i-1)), Pretty.str " =>", Pretty.brk 1,
   340        p, Pretty.str ")", Pretty.brk 1, parens (Pretty.block ps)]
   341     else ps
   342   end;
   343 
   344 fun mk_v ((names, vs), s) = (case assoc (vs, s) of
   345       NONE => ((names, (s, [s])::vs), s)
   346     | SOME xs => let val s' = variant names s in
   347         ((s'::names, overwrite (vs, (s, s'::xs))), s') end);
   348 
   349 fun distinct_v (nvs, Var ((s, 0), T)) =
   350       apsnd (Var o rpair T o rpair 0) (mk_v (nvs, s))
   351   | distinct_v (nvs, t $ u) =
   352       let
   353         val (nvs', t') = distinct_v (nvs, t);
   354         val (nvs'', u') = distinct_v (nvs', u);
   355       in (nvs'', t' $ u') end
   356   | distinct_v x = x;
   357 
   358 fun is_exhaustive (Var _) = true
   359   | is_exhaustive (Const ("Pair", _) $ t $ u) =
   360       is_exhaustive t andalso is_exhaustive u
   361   | is_exhaustive _ = false;
   362 
   363 fun compile_match nvs eq_ps out_ps success_p can_fail =
   364   let val eqs = List.concat (separate [Pretty.str " andalso", Pretty.brk 1]
   365     (map single (List.concat (map (mk_eq o snd) nvs) @ eq_ps)));
   366   in
   367     Pretty.block
   368      ([Pretty.str "(fn ", mk_tuple out_ps, Pretty.str " =>", Pretty.brk 1] @
   369       (Pretty.block ((if eqs=[] then [] else Pretty.str "if " ::
   370          [Pretty.block eqs, Pretty.brk 1, Pretty.str "then "]) @
   371          (success_p ::
   372           (if eqs=[] then [] else [Pretty.brk 1, Pretty.str "else Seq.empty"]))) ::
   373        (if can_fail then
   374           [Pretty.brk 1, Pretty.str "| _ => Seq.empty)"]
   375         else [Pretty.str ")"])))
   376   end;
   377 
   378 fun modename module s (iss, is) gr =
   379   let val (gr', id) = if s = "op =" then (gr, ("", "equal"))
   380     else mk_const_id module s gr
   381   in (gr', space_implode "__"
   382     (mk_qual_id module id ::
   383       map (space_implode "_" o map string_of_int) (List.mapPartial I iss @ [is])))
   384   end;
   385 
   386 fun compile_expr thy defs dep module brack (gr, (NONE, t)) =
   387       apsnd single (invoke_codegen thy defs dep module brack (gr, t))
   388   | compile_expr _ _ _ _ _ (gr, (SOME _, Var ((name, _), _))) =
   389       (gr, [Pretty.str name])
   390   | compile_expr thy defs dep module brack (gr, (SOME (Mode (mode, ms)), t)) =
   391       let
   392         val (Const (name, _), args) = strip_comb t;
   393         val (gr', (ps, mode_id)) = foldl_map
   394             (compile_expr thy defs dep module true) (gr, ms ~~ args) |>>>
   395           modename module name mode;
   396       in (gr', (if brack andalso not (null ps) then
   397         single o parens o Pretty.block else I)
   398           (List.concat (separate [Pretty.brk 1]
   399             ([Pretty.str mode_id] :: ps))))
   400       end;
   401 
   402 fun compile_clause thy defs gr dep module all_vs arg_vs modes (iss, is) (ts, ps) =
   403   let
   404     val modes' = modes @ List.mapPartial
   405       (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
   406         (arg_vs ~~ iss);
   407 
   408     fun check_constrt ((names, eqs), t) =
   409       if is_constrt thy t then ((names, eqs), t) else
   410         let val s = variant names "x";
   411         in ((s::names, (s, t)::eqs), Var ((s, 0), fastype_of t)) end;
   412 
   413     fun compile_eq (gr, (s, t)) =
   414       apsnd (Pretty.block o cons (Pretty.str (s ^ " = ")) o single)
   415         (invoke_codegen thy defs dep module false (gr, t));
   416 
   417     val (in_ts, out_ts) = get_args is 1 ts;
   418     val ((all_vs', eqs), in_ts') =
   419       foldl_map check_constrt ((all_vs, []), in_ts);
   420 
   421     fun is_ind t = (case head_of t of
   422           Const (s, _) => s = "op =" orelse isSome (assoc (modes, s))
   423         | Var ((s, _), _) => s mem arg_vs);
   424 
   425     fun compile_prems out_ts' vs names gr [] =
   426           let
   427             val (gr2, out_ps) = foldl_map
   428               (invoke_codegen thy defs dep module false) (gr, out_ts);
   429             val (gr3, eq_ps) = foldl_map compile_eq (gr2, eqs);
   430             val ((names', eqs'), out_ts'') =
   431               foldl_map check_constrt ((names, []), out_ts');
   432             val (nvs, out_ts''') = foldl_map distinct_v
   433               ((names', map (fn x => (x, [x])) vs), out_ts'');
   434             val (gr4, out_ps') = foldl_map
   435               (invoke_codegen thy defs dep module false) (gr3, out_ts''');
   436             val (gr5, eq_ps') = foldl_map compile_eq (gr4, eqs')
   437           in
   438             (gr5, compile_match (snd nvs) (eq_ps @ eq_ps') out_ps'
   439               (Pretty.block [Pretty.str "Seq.single", Pretty.brk 1, mk_tuple out_ps])
   440               (exists (not o is_exhaustive) out_ts'''))
   441           end
   442       | compile_prems out_ts vs names gr ps =
   443           let
   444             val vs' = distinct (List.concat (vs :: map term_vs out_ts));
   445             val SOME (p, mode as SOME (Mode ((_, js), _))) =
   446               select_mode_prem thy modes' vs' ps;
   447             val ps' = filter_out (equal p) ps;
   448             val ((names', eqs), out_ts') =
   449               foldl_map check_constrt ((names, []), out_ts);
   450             val (nvs, out_ts'') = foldl_map distinct_v
   451               ((names', map (fn x => (x, [x])) vs), out_ts');
   452             val (gr0, out_ps) = foldl_map
   453               (invoke_codegen thy defs dep module false) (gr, out_ts'');
   454             val (gr1, eq_ps) = foldl_map compile_eq (gr0, eqs)
   455           in
   456             (case p of
   457                Prem (us, t) =>
   458                  let
   459                    val (in_ts, out_ts''') = get_args js 1 us;
   460                    val (gr2, in_ps) = foldl_map
   461                      (invoke_codegen thy defs dep module false) (gr1, in_ts);
   462                    val (gr3, ps) = if is_ind t then
   463                        apsnd (fn ps => ps @ [Pretty.brk 1, mk_tuple in_ps])
   464                          (compile_expr thy defs dep module false
   465                            (gr2, (mode, t)))
   466                      else
   467                        apsnd (fn p => conv_ntuple us t
   468                          [Pretty.str "Seq.of_list", Pretty.brk 1, p])
   469                            (invoke_codegen thy defs dep module true (gr2, t));
   470                    val (gr4, rest) = compile_prems out_ts''' vs' (fst nvs) gr3 ps';
   471                  in
   472                    (gr4, compile_match (snd nvs) eq_ps out_ps
   473                       (Pretty.block (ps @
   474                          [Pretty.str " :->", Pretty.brk 1, rest]))
   475                       (exists (not o is_exhaustive) out_ts''))
   476                  end
   477              | Sidecond t =>
   478                  let
   479                    val (gr2, side_p) = invoke_codegen thy defs dep module true (gr1, t);
   480                    val (gr3, rest) = compile_prems [] vs' (fst nvs) gr2 ps';
   481                  in
   482                    (gr3, compile_match (snd nvs) eq_ps out_ps
   483                       (Pretty.block [Pretty.str "?? ", side_p,
   484                         Pretty.str " :->", Pretty.brk 1, rest])
   485                       (exists (not o is_exhaustive) out_ts''))
   486                  end)
   487           end;
   488 
   489     val (gr', prem_p) = compile_prems in_ts' arg_vs all_vs' gr ps;
   490   in
   491     (gr', Pretty.block [Pretty.str "Seq.single inp :->", Pretty.brk 1, prem_p])
   492   end;
   493 
   494 fun compile_pred thy defs gr dep module prfx all_vs arg_vs modes s cls mode =
   495   let val (gr', (cl_ps, mode_id)) =
   496     foldl_map (fn (gr, cl) => compile_clause thy defs
   497       gr dep module all_vs arg_vs modes mode cl) (gr, cls) |>>>
   498     modename module s mode
   499   in
   500     ((gr', "and "), Pretty.block
   501       ([Pretty.block (separate (Pretty.brk 1)
   502          (Pretty.str (prfx ^ mode_id) ::
   503            map Pretty.str arg_vs) @
   504          [Pretty.str " inp ="]),
   505         Pretty.brk 1] @
   506        List.concat (separate [Pretty.str " ++", Pretty.brk 1] (map single cl_ps))))
   507   end;
   508 
   509 fun compile_preds thy defs gr dep module all_vs arg_vs modes preds =
   510   let val ((gr', _), prs) = foldl_map (fn ((gr, prfx), (s, cls)) =>
   511     foldl_map (fn ((gr', prfx'), mode) => compile_pred thy defs gr'
   512       dep module prfx' all_vs arg_vs modes s cls mode)
   513         ((gr, prfx), valOf (assoc (modes, s)))) ((gr, "fun "), preds)
   514   in
   515     (gr', space_implode "\n\n" (map Pretty.string_of (List.concat prs)) ^ ";\n\n")
   516   end;
   517 
   518 (**** processing of introduction rules ****)
   519 
   520 exception Modes of
   521   (string * (int list option list * int list) list) list *
   522   (string * (int list list option list * int list list)) list;
   523 
   524 fun lookup_modes gr dep = apfst List.concat (apsnd List.concat (ListPair.unzip
   525   (map ((fn (SOME (Modes x), _, _) => x | _ => ([], [])) o get_node gr)
   526     (Graph.all_preds (fst gr) [dep]))));
   527 
   528 fun print_factors factors = message ("Factors:\n" ^
   529   space_implode "\n" (map (fn (s, (fs, f)) => s ^ ": " ^
   530     space_implode " -> " (map
   531       (fn NONE => "X" | SOME f' => string_of_factors [] f')
   532         (fs @ [SOME f]))) factors));
   533 
   534 fun prep_intrs intrs = map (rename_term o #prop o rep_thm o standard) intrs;
   535 
   536 fun constrain cs [] = []
   537   | constrain cs ((s, xs) :: ys) = (s, case assoc (cs, s) of
   538       NONE => xs
   539     | SOME xs' => xs inter xs') :: constrain cs ys;
   540 
   541 fun mk_extra_defs thy defs gr dep names module ts =
   542   Library.foldl (fn (gr, name) =>
   543     if name mem names then gr
   544     else (case get_clauses thy name of
   545         NONE => gr
   546       | SOME (names, thyname, intrs) =>
   547           mk_ind_def thy defs gr dep names (if_library thyname module)
   548             [] [] (prep_intrs intrs)))
   549             (gr, foldr add_term_consts [] ts)
   550 
   551 and mk_ind_def thy defs gr dep names module modecs factorcs intrs =
   552   add_edge (hd names, dep) gr handle Graph.UNDEF _ =>
   553     let
   554       val _ $ (_ $ _ $ u) = Logic.strip_imp_concl (hd intrs);
   555       val (_, args) = strip_comb u;
   556       val arg_vs = List.concat (map term_vs args);
   557 
   558       fun dest_prem factors (_ $ (p as (Const ("op :", _) $ t $ u))) =
   559             (case assoc (factors, case head_of u of
   560                  Const (name, _) => name | Var ((name, _), _) => name) of
   561                NONE => Prem (full_split_prod t, u)
   562              | SOME f => Prem (split_prod [] f t, u))
   563         | dest_prem factors (_ $ ((eq as Const ("op =", _)) $ t $ u)) =
   564             Prem ([t, u], eq)
   565         | dest_prem factors (_ $ t) = Sidecond t;
   566 
   567       fun add_clause factors (clauses, intr) =
   568         let
   569           val _ $ (_ $ t $ u) = Logic.strip_imp_concl intr;
   570           val Const (name, _) = head_of u;
   571           val prems = map (dest_prem factors) (Logic.strip_imp_prems intr);
   572         in
   573           (overwrite (clauses, (name, getOpt (assoc (clauses, name), []) @
   574              [(split_prod [] (valOf (assoc (factors, name))) t, prems)])))
   575         end;
   576 
   577       fun check_set (Const (s, _)) = s mem names orelse isSome (get_clauses thy s)
   578         | check_set (Var ((s, _), _)) = s mem arg_vs
   579         | check_set _ = false;
   580 
   581       fun add_prod_factors extra_fs (fs, _ $ (Const ("op :", _) $ t $ u)) =
   582             if check_set (head_of u)
   583             then infer_factors (sign_of thy) extra_fs
   584               (fs, (SOME (FVar (prod_factors [] t)), u))
   585             else fs
   586         | add_prod_factors _ (fs, _) = fs;
   587 
   588       val gr' = mk_extra_defs thy defs
   589         (add_edge (hd names, dep)
   590           (new_node (hd names, (NONE, "", "")) gr)) (hd names) names module intrs;
   591       val (extra_modes, extra_factors) = lookup_modes gr' (hd names);
   592       val fs = constrain factorcs (map (apsnd dest_factors)
   593         (Library.foldl (add_prod_factors extra_factors) ([], List.concat (map (fn t =>
   594           Logic.strip_imp_concl t :: Logic.strip_imp_prems t) intrs))));
   595       val factors = List.mapPartial (fn (name, f) =>
   596         if name mem arg_vs then NONE
   597         else SOME (name, (map (curry assoc fs) arg_vs, f))) fs;
   598       val clauses =
   599         Library.foldl (add_clause (fs @ map (apsnd snd) extra_factors)) ([], intrs);
   600       val modes = constrain modecs
   601         (infer_modes thy extra_modes factors arg_vs clauses);
   602       val _ = print_factors factors;
   603       val _ = print_modes modes;
   604       val (gr'', s) = compile_preds thy defs gr' (hd names) module (terms_vs intrs)
   605         arg_vs (modes @ extra_modes) clauses;
   606     in
   607       (map_node (hd names)
   608         (K (SOME (Modes (modes, factors)), module, s)) gr'')
   609     end;
   610 
   611 fun find_mode gr dep s u modes is = (case find_first (fn Mode ((_, js), _) => is=js)
   612   (modes_of modes u handle Option => []) of
   613      NONE => codegen_error gr dep
   614        ("No such mode for " ^ s ^ ": " ^ string_of_mode ([], is))
   615    | mode => mode);
   616 
   617 fun mk_ind_call thy defs gr dep module t u is_query = (case head_of u of
   618   Const (s, T) => (case (get_clauses thy s, get_assoc_code thy s T) of
   619        (NONE, _) => NONE
   620      | (SOME (names, thyname, intrs), NONE) =>
   621          let
   622           fun mk_mode (((ts, mode), i), Const ("dummy_pattern", _)) =
   623                 ((ts, mode), i+1)
   624             | mk_mode (((ts, mode), i), t) = ((ts @ [t], mode @ [i]), i+1);
   625 
   626            val module' = if_library thyname module;
   627            val gr1 = mk_extra_defs thy defs
   628              (mk_ind_def thy defs gr dep names module'
   629              [] [] (prep_intrs intrs)) dep names module' [u];
   630            val (modes, factors) = lookup_modes gr1 dep;
   631            val ts = split_prod [] (snd (valOf (assoc (factors, s)))) t;
   632            val (ts', is) = if is_query then
   633                fst (Library.foldl mk_mode ((([], []), 1), ts))
   634              else (ts, 1 upto length ts);
   635            val mode = find_mode gr1 dep s u modes is;
   636            val (gr2, in_ps) = foldl_map
   637              (invoke_codegen thy defs dep module false) (gr1, ts');
   638            val (gr3, ps) =
   639              compile_expr thy defs dep module false (gr2, (mode, u))
   640          in
   641            SOME (gr3, Pretty.block
   642              (ps @ [Pretty.brk 1, mk_tuple in_ps]))
   643          end
   644      | _ => NONE)
   645   | _ => NONE);
   646 
   647 fun list_of_indset thy defs gr dep module brack u = (case head_of u of
   648   Const (s, T) => (case (get_clauses thy s, get_assoc_code thy s T) of
   649        (NONE, _) => NONE
   650      | (SOME (names, thyname, intrs), NONE) =>
   651          let
   652            val module' = if_library thyname module;
   653            val gr1 = mk_extra_defs thy defs
   654              (mk_ind_def thy defs gr dep names module'
   655              [] [] (prep_intrs intrs)) dep names module' [u];
   656            val (modes, factors) = lookup_modes gr1 dep;
   657            val mode = find_mode gr1 dep s u modes [];
   658            val (gr2, ps) =
   659              compile_expr thy defs dep module false (gr1, (mode, u))
   660          in
   661            SOME (gr2, (if brack then parens else I)
   662              (Pretty.block ([Pretty.str "Seq.list_of", Pretty.brk 1,
   663                Pretty.str "("] @
   664                conv_ntuple' (snd (valOf (assoc (factors, s))))
   665                  (HOLogic.dest_setT (fastype_of u))
   666                  (ps @ [Pretty.brk 1, Pretty.str "()"]) @
   667                [Pretty.str ")"])))
   668          end
   669      | _ => NONE)
   670   | _ => NONE);
   671 
   672 fun clause_of_eqn eqn =
   673   let
   674     val (t, u) = HOLogic.dest_eq (HOLogic.dest_Trueprop (concl_of eqn));
   675     val (Const (s, T), ts) = strip_comb t;
   676     val (Ts, U) = strip_type T
   677   in
   678     rename_term
   679       (Logic.list_implies (prems_of eqn, HOLogic.mk_Trueprop (HOLogic.mk_mem
   680         (foldr1 HOLogic.mk_prod (ts @ [u]), Const (s ^ "_aux",
   681           HOLogic.mk_setT (foldr1 HOLogic.mk_prodT (Ts @ [U])))))))
   682   end;
   683 
   684 fun mk_fun thy defs name eqns dep module module' gr =
   685   case try (get_node gr) name of
   686     NONE =>
   687     let
   688       val clauses = map clause_of_eqn eqns;
   689       val pname = name ^ "_aux";
   690       val arity = length (snd (strip_comb (fst (HOLogic.dest_eq
   691         (HOLogic.dest_Trueprop (concl_of (hd eqns)))))));
   692       val mode = 1 upto arity;
   693       val (gr', (fun_id, mode_id)) = gr |>
   694         mk_const_id module' name |>>>
   695         modename module' pname ([], mode);
   696       val vars = map (fn i => Pretty.str ("x" ^ string_of_int i)) mode;
   697       val s = Pretty.string_of (Pretty.block
   698         [mk_app false (Pretty.str ("fun " ^ snd fun_id)) vars, Pretty.str " =",
   699          Pretty.brk 1, Pretty.str "Seq.hd", Pretty.brk 1,
   700          parens (Pretty.block [Pretty.str mode_id,
   701            Pretty.brk 1, mk_tuple vars])]) ^ ";\n\n";
   702       val gr'' = mk_ind_def thy defs (add_edge (name, dep)
   703         (new_node (name, (NONE, module', s)) gr')) name [pname] module'
   704         [(pname, [([], mode)])]
   705         [(pname, map (fn i => replicate i 2) (0 upto arity-1))]
   706         clauses;
   707       val (modes, _) = lookup_modes gr'' dep;
   708       val _ = find_mode gr'' dep pname (snd (HOLogic.dest_mem (HOLogic.dest_Trueprop
   709         (Logic.strip_imp_concl (hd clauses))))) modes mode
   710     in (gr'', mk_qual_id module fun_id) end
   711   | SOME _ =>
   712       (add_edge (name, dep) gr, mk_qual_id module (get_const_id name gr));
   713 
   714 fun inductive_codegen thy defs gr dep module brack (Const ("op :", _) $ t $ u) =
   715       ((case mk_ind_call thy defs gr dep module (Term.no_dummy_patterns t) u false of
   716          NONE => NONE
   717        | SOME (gr', call_p) => SOME (gr', (if brack then parens else I)
   718            (Pretty.block [Pretty.str "?! (", call_p, Pretty.str ")"])))
   719         handle TERM _ => mk_ind_call thy defs gr dep module t u true)
   720   | inductive_codegen thy defs gr dep module brack t = (case strip_comb t of
   721       (Const (s, _), ts) => (case Symtab.lookup (#eqns (CodegenData.get thy), s) of
   722         NONE => list_of_indset thy defs gr dep module brack t
   723       | SOME eqns =>
   724           let
   725             val (_, (_, thyname)) = split_last eqns;
   726             val (gr', id) = mk_fun thy defs s (preprocess thy (map fst eqns))
   727               dep module (if_library thyname module) gr;
   728             val (gr'', ps) = foldl_map
   729               (invoke_codegen thy defs dep module true) (gr', ts);
   730           in SOME (gr'', mk_app brack (Pretty.str id) ps)
   731           end)
   732     | _ => NONE);
   733 
   734 val setup =
   735   [add_codegen "inductive" inductive_codegen,
   736    CodegenData.init,
   737    add_attribute "ind"
   738      (Scan.option (Args.$$$ "target" |-- Args.colon |-- Args.name) >> add)];
   739 
   740 end;
   741 
   742 
   743 (**** combinators for code generated from inductive predicates ****)
   744 
   745 infix 5 :->;
   746 infix 3 ++;
   747 
   748 fun s :-> f = Seq.flat (Seq.map f s);
   749 
   750 fun s1 ++ s2 = Seq.append (s1, s2);
   751 
   752 fun ?? b = if b then Seq.single () else Seq.empty;
   753 
   754 fun ?! s = isSome (Seq.pull s);    
   755 
   756 fun equal__1 x = Seq.single x;
   757 
   758 val equal__2 = equal__1;
   759 
   760 fun equal__1_2 (x, y) = ?? (x = y);