src/HOL/Tools/datatype_codegen.ML
author wenzelm
Thu Aug 03 17:30:36 2006 +0200 (2006-08-03)
changeset 20328 5b240a4216b0
parent 20192 956cd30ef3be
child 20382 39964c8dcd54
permissions -rw-r--r--
RuleInsts.bires_inst_tac;
     1 (*  Title:      HOL/datatype_codegen.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer & Florian Haftmann, TU Muenchen
     4 
     5 Code generator for inductive datatypes.
     6 *)
     7 
     8 signature DATATYPE_CODEGEN =
     9 sig
    10   val get_datatype_spec_thms: theory -> string
    11     -> (((string * sort) list * (string * typ list) list) * tactic) option
    12   val get_all_datatype_cons: theory -> (string * string) list
    13   val dest_case_expr: theory -> term
    14     -> ((string * typ) list * ((term * typ) * (term * term) list)) option
    15   val add_datatype_case_const: string -> theory -> theory
    16   val add_datatype_case_defs: string -> theory -> theory
    17   val datatypes_dependency: theory -> string list list
    18   val get_datatype_mut_specs: theory -> string list
    19     -> ((string * sort) list * (string * (string * typ list) list) list)
    20   val get_datatype_arities: theory -> string list -> sort
    21     -> (string * (((string * sort list) * sort) * term list)) list option
    22   val prove_arities: (thm list -> tactic) -> string list -> sort
    23     -> (((string * sort list) * sort) list -> (string * term list) list
    24     -> ((bstring * attribute list) * term) list) -> theory -> theory
    25   val setup: theory -> theory
    26 end;
    27 
    28 structure DatatypeCodegen : DATATYPE_CODEGEN =
    29 struct
    30 
    31 open Codegen;
    32 
    33 fun mk_tuple [p] = p
    34   | mk_tuple ps = Pretty.block (Pretty.str "(" ::
    35       List.concat (separate [Pretty.str ",", Pretty.brk 1] (map single ps)) @
    36         [Pretty.str ")"]);
    37 
    38 (**** datatype definition ****)
    39 
    40 (* find shortest path to constructor with no recursive arguments *)
    41 
    42 fun find_nonempty (descr: DatatypeAux.descr) is i =
    43   let
    44     val (_, _, constrs) = valOf (AList.lookup (op =) descr i);
    45     fun arg_nonempty (_, DatatypeAux.DtRec i) = if i mem is then NONE
    46           else Option.map (curry op + 1 o snd) (find_nonempty descr (i::is) i)
    47       | arg_nonempty _ = SOME 0;
    48     fun max xs = Library.foldl
    49       (fn (NONE, _) => NONE
    50         | (SOME i, SOME j) => SOME (Int.max (i, j))
    51         | (_, NONE) => NONE) (SOME 0, xs);
    52     val xs = sort (int_ord o pairself snd)
    53       (List.mapPartial (fn (s, dts) => Option.map (pair s)
    54         (max (map (arg_nonempty o DatatypeAux.strip_dtyp) dts))) constrs)
    55   in case xs of [] => NONE | x :: _ => SOME x end;
    56 
    57 fun add_dt_defs thy defs dep module gr (descr: DatatypeAux.descr) =
    58   let
    59     val sg = sign_of thy;
    60     val tab = DatatypePackage.get_datatypes thy;
    61 
    62     val descr' = List.filter (can (map DatatypeAux.dest_DtTFree o #2 o snd)) descr;
    63     val rtnames = map (#1 o snd) (List.filter (fn (_, (_, _, cs)) =>
    64       exists (exists DatatypeAux.is_rec_type o snd) cs) descr');
    65 
    66     val (_, (tname, _, _)) :: _ = descr';
    67     val node_id = tname ^ " (type)";
    68     val module' = if_library (thyname_of_type tname thy) module;
    69 
    70     fun mk_dtdef gr prfx [] = (gr, [])
    71       | mk_dtdef gr prfx ((_, (tname, dts, cs))::xs) =
    72           let
    73             val tvs = map DatatypeAux.dest_DtTFree dts;
    74             val sorts = map (rpair []) tvs;
    75             val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs;
    76             val (gr', (_, type_id)) = mk_type_id module' tname gr;
    77             val (gr'', ps) =
    78               foldl_map (fn (gr, (cname, cargs)) =>
    79                 foldl_map (invoke_tycodegen thy defs node_id module' false)
    80                   (gr, cargs) |>>>
    81                 mk_const_id module' cname) (gr', cs');
    82             val (gr''', rest) = mk_dtdef gr'' "and " xs
    83           in
    84             (gr''',
    85              Pretty.block (Pretty.str prfx ::
    86                (if null tvs then [] else
    87                   [mk_tuple (map Pretty.str tvs), Pretty.str " "]) @
    88                [Pretty.str (type_id ^ " ="), Pretty.brk 1] @
    89                List.concat (separate [Pretty.brk 1, Pretty.str "| "]
    90                  (map (fn (ps', (_, cname)) => [Pretty.block
    91                    (Pretty.str cname ::
    92                     (if null ps' then [] else
    93                      List.concat ([Pretty.str " of", Pretty.brk 1] ::
    94                        separate [Pretty.str " *", Pretty.brk 1]
    95                          (map single ps'))))]) ps))) :: rest)
    96           end;
    97 
    98     fun mk_term_of_def gr prfx [] = []
    99       | mk_term_of_def gr prfx ((_, (tname, dts, cs)) :: xs) =
   100           let
   101             val tvs = map DatatypeAux.dest_DtTFree dts;
   102             val sorts = map (rpair []) tvs;
   103             val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs;
   104             val dts' = map (DatatypeAux.typ_of_dtyp descr sorts) dts;
   105             val T = Type (tname, dts');
   106             val rest = mk_term_of_def gr "and " xs;
   107             val (_, eqs) = foldl_map (fn (prfx, (cname, Ts)) =>
   108               let val args = map (fn i =>
   109                 Pretty.str ("x" ^ string_of_int i)) (1 upto length Ts)
   110               in ("  | ", Pretty.blk (4,
   111                 [Pretty.str prfx, mk_term_of gr module' false T, Pretty.brk 1,
   112                  if null Ts then Pretty.str (snd (get_const_id cname gr))
   113                  else parens (Pretty.block
   114                    [Pretty.str (snd (get_const_id cname gr)),
   115                     Pretty.brk 1, mk_tuple args]),
   116                  Pretty.str " =", Pretty.brk 1] @
   117                  List.concat (separate [Pretty.str " $", Pretty.brk 1]
   118                    ([Pretty.str ("Const (\"" ^ cname ^ "\","), Pretty.brk 1,
   119                      mk_type false (Ts ---> T), Pretty.str ")"] ::
   120                     map (fn (x, U) => [Pretty.block [mk_term_of gr module' false U,
   121                       Pretty.brk 1, x]]) (args ~~ Ts)))))
   122               end) (prfx, cs')
   123           in eqs @ rest end;
   124 
   125     fun mk_gen_of_def gr prfx [] = []
   126       | mk_gen_of_def gr prfx ((i, (tname, dts, cs)) :: xs) =
   127           let
   128             val tvs = map DatatypeAux.dest_DtTFree dts;
   129             val sorts = map (rpair []) tvs;
   130             val (cs1, cs2) =
   131               List.partition (exists DatatypeAux.is_rec_type o snd) cs;
   132             val SOME (cname, _) = find_nonempty descr [i] i;
   133 
   134             fun mk_delay p = Pretty.block
   135               [Pretty.str "fn () =>", Pretty.brk 1, p];
   136 
   137             fun mk_constr s b (cname, dts) =
   138               let
   139                 val gs = map (fn dt => mk_app false (mk_gen gr module' false rtnames s
   140                     (DatatypeAux.typ_of_dtyp descr sorts dt))
   141                   [Pretty.str (if b andalso DatatypeAux.is_rec_type dt then "0"
   142                      else "j")]) dts;
   143                 val (_, id) = get_const_id cname gr
   144               in case gs of
   145                   _ :: _ :: _ => Pretty.block
   146                     [Pretty.str id, Pretty.brk 1, mk_tuple gs]
   147                 | _ => mk_app false (Pretty.str id) (map parens gs)
   148               end;
   149 
   150             fun mk_choice [c] = mk_constr "(i-1)" false c
   151               | mk_choice cs = Pretty.block [Pretty.str "one_of",
   152                   Pretty.brk 1, Pretty.blk (1, Pretty.str "[" ::
   153                   List.concat (separate [Pretty.str ",", Pretty.fbrk]
   154                     (map (single o mk_delay o mk_constr "(i-1)" false) cs)) @
   155                   [Pretty.str "]"]), Pretty.brk 1, Pretty.str "()"];
   156 
   157             val gs = map (Pretty.str o suffix "G" o strip_tname) tvs;
   158             val gen_name = "gen_" ^ snd (get_type_id tname gr)
   159 
   160           in
   161             Pretty.blk (4, separate (Pretty.brk 1) 
   162                 (Pretty.str (prfx ^ gen_name ^
   163                    (if null cs1 then "" else "'")) :: gs @
   164                  (if null cs1 then [] else [Pretty.str "i"]) @
   165                  [Pretty.str "j"]) @
   166               [Pretty.str " =", Pretty.brk 1] @
   167               (if not (null cs1) andalso not (null cs2)
   168                then [Pretty.str "frequency", Pretty.brk 1,
   169                  Pretty.blk (1, [Pretty.str "[",
   170                    mk_tuple [Pretty.str "i", mk_delay (mk_choice cs1)],
   171                    Pretty.str ",", Pretty.fbrk,
   172                    mk_tuple [Pretty.str "1", mk_delay (mk_choice cs2)],
   173                    Pretty.str "]"]), Pretty.brk 1, Pretty.str "()"]
   174                else if null cs2 then
   175                  [Pretty.block [Pretty.str "(case", Pretty.brk 1,
   176                    Pretty.str "i", Pretty.brk 1, Pretty.str "of",
   177                    Pretty.brk 1, Pretty.str "0 =>", Pretty.brk 1,
   178                    mk_constr "0" true (cname, valOf (AList.lookup (op =) cs cname)),
   179                    Pretty.brk 1, Pretty.str "| _ =>", Pretty.brk 1,
   180                    mk_choice cs1, Pretty.str ")"]]
   181                else [mk_choice cs2])) ::
   182             (if null cs1 then []
   183              else [Pretty.blk (4, separate (Pretty.brk 1) 
   184                  (Pretty.str ("and " ^ gen_name) :: gs @ [Pretty.str "i"]) @
   185                [Pretty.str " =", Pretty.brk 1] @
   186                separate (Pretty.brk 1) (Pretty.str (gen_name ^ "'") :: gs @
   187                  [Pretty.str "i", Pretty.str "i"]))]) @
   188             mk_gen_of_def gr "and " xs
   189           end
   190 
   191   in
   192     (add_edge_acyclic (node_id, dep) gr
   193         handle Graph.CYCLES _ => gr) handle Graph.UNDEF _ =>
   194          let
   195            val gr1 = add_edge (node_id, dep)
   196              (new_node (node_id, (NONE, "", "")) gr);
   197            val (gr2, dtdef) = mk_dtdef gr1 "datatype " descr';
   198          in
   199            map_node node_id (K (NONE, module',
   200              Pretty.string_of (Pretty.blk (0, separate Pretty.fbrk dtdef @
   201                [Pretty.str ";"])) ^ "\n\n" ^
   202              (if "term_of" mem !mode then
   203                 Pretty.string_of (Pretty.blk (0, separate Pretty.fbrk
   204                   (mk_term_of_def gr2 "fun " descr') @ [Pretty.str ";"])) ^ "\n\n"
   205               else "") ^
   206              (if "test" mem !mode then
   207                 Pretty.string_of (Pretty.blk (0, separate Pretty.fbrk
   208                   (mk_gen_of_def gr2 "fun " descr') @ [Pretty.str ";"])) ^ "\n\n"
   209               else ""))) gr2
   210          end
   211   end;
   212 
   213 
   214 (**** case expressions ****)
   215 
   216 fun pretty_case thy defs gr dep module brack constrs (c as Const (_, T)) ts =
   217   let val i = length constrs
   218   in if length ts <= i then
   219        invoke_codegen thy defs dep module brack (gr, eta_expand c ts (i+1))
   220     else
   221       let
   222         val ts1 = Library.take (i, ts);
   223         val t :: ts2 = Library.drop (i, ts);
   224         val names = foldr add_term_names
   225           (map (fst o fst o dest_Var) (foldr add_term_vars [] ts1)) ts1;
   226         val (Ts, dT) = split_last (Library.take (i+1, fst (strip_type T)));
   227 
   228         fun pcase gr [] [] [] = ([], gr)
   229           | pcase gr ((cname, cargs)::cs) (t::ts) (U::Us) =
   230               let
   231                 val j = length cargs;
   232                 val xs = Name.variant_list names (replicate j "x");
   233                 val Us' = Library.take (j, fst (strip_type U));
   234                 val frees = map Free (xs ~~ Us');
   235                 val (gr0, cp) = invoke_codegen thy defs dep module false
   236                   (gr, list_comb (Const (cname, Us' ---> dT), frees));
   237                 val t' = Envir.beta_norm (list_comb (t, frees));
   238                 val (gr1, p) = invoke_codegen thy defs dep module false (gr0, t');
   239                 val (ps, gr2) = pcase gr1 cs ts Us;
   240               in
   241                 ([Pretty.block [cp, Pretty.str " =>", Pretty.brk 1, p]] :: ps, gr2)
   242               end;
   243 
   244         val (ps1, gr1) = pcase gr constrs ts1 Ts;
   245         val ps = List.concat (separate [Pretty.brk 1, Pretty.str "| "] ps1);
   246         val (gr2, p) = invoke_codegen thy defs dep module false (gr1, t);
   247         val (gr3, ps2) = foldl_map (invoke_codegen thy defs dep module true) (gr2, ts2)
   248       in (gr3, (if not (null ts2) andalso brack then parens else I)
   249         (Pretty.block (separate (Pretty.brk 1)
   250           (Pretty.block ([Pretty.str "(case ", p, Pretty.str " of",
   251              Pretty.brk 1] @ ps @ [Pretty.str ")"]) :: ps2))))
   252       end
   253   end;
   254 
   255 
   256 (**** constructors ****)
   257 
   258 fun pretty_constr thy defs gr dep module brack args (c as Const (s, T)) ts =
   259   let val i = length args
   260   in if i > 1 andalso length ts < i then
   261       invoke_codegen thy defs dep module brack (gr, eta_expand c ts i)
   262      else
   263        let
   264          val id = mk_qual_id module (get_const_id s gr);
   265          val (gr', ps) = foldl_map
   266            (invoke_codegen thy defs dep module (i = 1)) (gr, ts);
   267        in (case args of
   268           _ :: _ :: _ => (gr', (if brack then parens else I)
   269             (Pretty.block [Pretty.str id, Pretty.brk 1, mk_tuple ps]))
   270         | _ => (gr', mk_app brack (Pretty.str id) ps))
   271        end
   272   end;
   273 
   274 
   275 (**** code generators for terms and types ****)
   276 
   277 fun datatype_codegen thy defs gr dep module brack t = (case strip_comb t of
   278    (c as Const (s, T), ts) =>
   279        (case Library.find_first (fn (_, {index, descr, case_name, ...}) =>
   280          s = case_name orelse
   281            AList.defined (op =) ((#3 o the o AList.lookup (op =) descr) index) s)
   282              (Symtab.dest (DatatypePackage.get_datatypes thy)) of
   283           NONE => NONE
   284         | SOME (tname, {index, descr, ...}) =>
   285            if is_some (get_assoc_code thy s T) then NONE else
   286            let val SOME (_, _, constrs) = AList.lookup (op =) descr index
   287            in (case (AList.lookup (op =) constrs s, strip_type T) of
   288                (NONE, _) => SOME (pretty_case thy defs gr dep module brack
   289                  ((#3 o the o AList.lookup (op =) descr) index) c ts)
   290              | (SOME args, (_, Type _)) => SOME (pretty_constr thy defs
   291                  (fst (invoke_tycodegen thy defs dep module false
   292                     (gr, snd (strip_type T))))
   293                  dep module brack args c ts)
   294              | _ => NONE)
   295            end)
   296  |  _ => NONE);
   297 
   298 fun datatype_tycodegen thy defs gr dep module brack (Type (s, Ts)) =
   299       (case Symtab.lookup (DatatypePackage.get_datatypes thy) s of
   300          NONE => NONE
   301        | SOME {descr, ...} =>
   302            if isSome (get_assoc_type thy s) then NONE else
   303            let
   304              val (gr', ps) = foldl_map
   305                (invoke_tycodegen thy defs dep module false) (gr, Ts);
   306              val gr'' = add_dt_defs thy defs dep module gr' descr
   307            in SOME (gr'',
   308              Pretty.block ((if null Ts then [] else
   309                [mk_tuple ps, Pretty.str " "]) @
   310                [Pretty.str (mk_qual_id module (get_type_id s gr''))]))
   311            end)
   312   | datatype_tycodegen _ _ _ _ _ _ _ = NONE;
   313 
   314 
   315 (** code 2nd generation **)
   316 
   317 fun datatypes_dependency thy =
   318   let
   319     val dtnames = DatatypePackage.get_datatypes thy;
   320     fun add_node (dtname, _) =
   321       let
   322         fun add_tycos (Type (tyco, tys)) = insert (op =) tyco #> fold add_tycos tys
   323           | add_tycos _ = I;
   324         val deps = (filter (Symtab.defined dtnames) o maps (fn ty =>
   325           add_tycos ty [])
   326             o maps snd o snd o the o DatatypePackage.get_datatype_spec thy) dtname
   327       in
   328         Graph.default_node (dtname, ())
   329         #> fold (fn dtname' =>
   330              Graph.default_node (dtname', ())
   331              #> Graph.add_edge (dtname', dtname)
   332            ) deps
   333       end
   334   in
   335     Graph.empty
   336     |> Symtab.fold add_node dtnames
   337     |> Graph.strong_conn
   338   end;
   339 
   340 fun get_datatype_mut_specs thy (tycos as tyco :: _) =
   341   let
   342     val tycos' = (map (#1 o snd) o #descr o DatatypePackage.the_datatype thy) tyco;
   343     val _ = if gen_subset (op =) (tycos, tycos') then () else
   344       error ("datatype constructors are not mutually recursive: " ^ (commas o map quote) tycos);
   345     val (vs::_, css) = split_list (map (the o DatatypePackage.get_datatype_spec thy) tycos);
   346   in (vs, tycos ~~ css) end;
   347 
   348 fun get_datatype_arities thy tycos sort =
   349   let
   350     val algebra = Sign.classes_of thy;
   351     val (vs_proto, css_proto) = get_datatype_mut_specs thy tycos;
   352     val vs = map (fn (v, vsort) => (v, Sorts.inter_sort algebra (vsort, sort))) vs_proto;
   353     fun inst_type tyco (c, tys) =
   354       let
   355         val tys' = (map o map_atyps)
   356           (fn TFree (v, _) => TFree (v, the (AList.lookup (op =) vs v))) tys
   357       in (c, tys') end;
   358     val css = map (fn (tyco, cs) => (tyco, (map (inst_type tyco) cs))) css_proto;
   359     fun mk_arity tyco =
   360       ((tyco, map snd vs), sort);
   361     fun typ_of_sort ty =
   362       let
   363         val arities = map (fn (tyco, _) => ((tyco, map snd vs), sort)) css;
   364       in ClassPackage.assume_arities_of_sort thy arities (ty, sort) end;
   365     fun mk_cons tyco (c, tys) =
   366       let
   367         val ts = Name.names Name.context "a" tys;
   368         val ty = tys ---> Type (tyco, map TFree vs);
   369       in list_comb (Const (c, ty), map Free ts) end;
   370   in if forall (fn (_, cs) => forall (fn (_, tys) => forall typ_of_sort tys) cs) css
   371     then SOME (
   372       map (fn (tyco, cs) => (tyco, (mk_arity tyco, map (mk_cons tyco) cs))) css
   373     ) else NONE
   374   end;
   375 
   376 fun prove_arities tac tycos sort f thy =
   377   case get_datatype_arities thy tycos sort
   378    of NONE => thy
   379     | SOME insts => let
   380         fun proven ((tyco, asorts), sort) =
   381           Sorts.of_sort (Sign.classes_of thy)
   382             (Type (tyco, map TFree (Name.names Name.context "'a" asorts)), sort);
   383         val (arities, css) = (split_list o map_filter
   384           (fn (tyco, (arity, cs)) => if proven arity
   385             then NONE else SOME (arity, (tyco, cs)))) insts;
   386       in
   387         thy
   388         |> K ((not o null) arities) ? ClassPackage.prove_instance_arity tac
   389              arities ("", []) (f arities css)
   390       end;
   391 
   392 fun dtyp_of_case_const thy c =
   393   get_first (fn (dtco, { case_name, ... }) => if case_name = c then SOME dtco else NONE)
   394     ((Symtab.dest o DatatypePackage.get_datatypes) thy);
   395 
   396 fun dest_case_app cs ts tys =
   397   let
   398     val abs = Name.names Name.context "a" (Library.drop (length ts, tys));
   399     val (ts', t) = split_last (ts @ map Free abs);
   400     val (tys', sty) = split_last tys;
   401     fun freenames_of t = fold_aterms
   402       (fn Free (v, _) => insert (op =) v | _ => I) t [];
   403     fun dest_case ((c, tys_decl), ty) t =
   404       let
   405         val (vs, t') = Term.strip_abs_eta (length tys_decl) t;
   406         val c' = list_comb (Const (c, map snd vs ---> sty), map Free vs);
   407       in (c', t') end;
   408   in (abs, ((t, sty), map2 dest_case (cs ~~ tys') ts')) end;
   409 
   410 fun dest_case_expr thy t =
   411   case strip_comb t
   412    of (Const (c, ty), ts) =>
   413         (case dtyp_of_case_const thy c
   414          of SOME dtco =>
   415               let val (vs, cs) = (the o DatatypePackage.get_datatype_spec thy) dtco;
   416               in SOME (dest_case_app cs ts (Library.take (length cs + 1, (fst o strip_type) ty))) end
   417           | _ => NONE)
   418     | _ => NONE;
   419 
   420 fun datatype_tac thy dtco =
   421   let
   422     val ctxt = Context.init_proof thy;
   423     val inject = (#inject o DatatypePackage.the_datatype thy) dtco;
   424     val simpset = Simplifier.context ctxt
   425       (MetaSimplifier.empty_ss addsimprocs [distinct_simproc]);
   426   in
   427     (TRY o ALLGOALS o match_tac) [HOL.eq_reflection]
   428     THEN (
   429       (ALLGOALS o match_tac) (eqTrueI :: inject)
   430       ORELSE (ALLGOALS o simp_tac) simpset
   431     )
   432     THEN (ALLGOALS o match_tac) [HOL.refl, Drule.reflexive_thm]
   433   end;
   434 
   435 fun get_datatype_spec_thms thy dtco =
   436   case DatatypePackage.get_datatype_spec thy dtco
   437    of SOME vs_cos =>
   438         SOME (vs_cos, datatype_tac thy dtco)
   439     | NONE => NONE;
   440 
   441 fun get_all_datatype_cons thy =
   442   Symtab.fold (fn (dtco, _) => fold
   443     (fn (co, _) => cons (co, dtco))
   444       ((snd o the oo DatatypePackage.get_datatype_spec) thy dtco))
   445         (DatatypePackage.get_datatypes thy) [];
   446 
   447 fun add_datatype_case_const dtco thy =
   448   let
   449     val {case_name, index, descr, ...} = DatatypePackage.the_datatype thy dtco;
   450   in
   451     CodegenPackage.add_appconst_i (case_name, CodegenPackage.appgen_case dest_case_expr) thy
   452   end;
   453 
   454 fun add_datatype_case_defs dtco thy =
   455   let
   456     val {case_rewrites, ...} = DatatypePackage.the_datatype thy dtco
   457   in
   458     fold CodegenTheorems.add_fun case_rewrites thy
   459   end;
   460 
   461 val setup = 
   462   add_codegen "datatype" datatype_codegen #>
   463   add_tycodegen "datatype" datatype_tycodegen #>
   464   CodegenTheorems.add_datatype_extr
   465     get_datatype_spec_thms #>
   466   CodegenPackage.set_get_all_datatype_cons
   467     get_all_datatype_cons #>
   468   DatatypeHooks.add (fold add_datatype_case_const) #>
   469   DatatypeHooks.add (fold add_datatype_case_defs)
   470 
   471 end;