src/Tools/subtyping.ML
author wenzelm
Sat Aug 20 23:35:30 2011 +0200 (2011-08-20)
changeset 44338 700008399ee5
parent 43591 d4cbd6feffdf
child 45059 28d3e387f22e
permissions -rw-r--r--
refined Graph implementation: more abstract/scalable Graph.Keys instead of plain lists -- order of adjacency is now standardized wrt. Key.ord;
wenzelm@40281
     1
(*  Title:      Tools/subtyping.ML
wenzelm@40281
     2
    Author:     Dmitriy Traytel, TU Muenchen
wenzelm@40281
     3
wenzelm@40281
     4
Coercive subtyping via subtype constraints.
wenzelm@40281
     5
*)
wenzelm@40281
     6
wenzelm@40281
     7
signature SUBTYPING =
wenzelm@40281
     8
sig
wenzelm@40939
     9
  val coercion_enabled: bool Config.T
wenzelm@40284
    10
  val add_type_map: term -> Context.generic -> Context.generic
wenzelm@40284
    11
  val add_coercion: term -> Context.generic -> Context.generic
wenzelm@40283
    12
  val setup: theory -> theory
wenzelm@40281
    13
end;
wenzelm@40281
    14
wenzelm@40283
    15
structure Subtyping: SUBTYPING =
wenzelm@40281
    16
struct
wenzelm@40281
    17
wenzelm@40281
    18
(** coercions data **)
wenzelm@40281
    19
traytel@41353
    20
datatype variance = COVARIANT | CONTRAVARIANT | INVARIANT | INVARIANT_TO of typ;
wenzelm@40281
    21
wenzelm@40281
    22
datatype data = Data of
wenzelm@40282
    23
  {coes: term Symreltab.table,  (*coercions table*)
wenzelm@40282
    24
   coes_graph: unit Graph.T,  (*coercions graph*)
wenzelm@40282
    25
   tmaps: (term * variance list) Symtab.table};  (*map functions*)
wenzelm@40281
    26
wenzelm@40281
    27
fun make_data (coes, coes_graph, tmaps) =
wenzelm@40281
    28
  Data {coes = coes, coes_graph = coes_graph, tmaps = tmaps};
wenzelm@40281
    29
wenzelm@40281
    30
structure Data = Generic_Data
wenzelm@40281
    31
(
wenzelm@40281
    32
  type T = data;
wenzelm@40281
    33
  val empty = make_data (Symreltab.empty, Graph.empty, Symtab.empty);
wenzelm@40281
    34
  val extend = I;
wenzelm@40281
    35
  fun merge
wenzelm@40281
    36
    (Data {coes = coes1, coes_graph = coes_graph1, tmaps = tmaps1},
wenzelm@40281
    37
      Data {coes = coes2, coes_graph = coes_graph2, tmaps = tmaps2}) =
wenzelm@40281
    38
    make_data (Symreltab.merge (op aconv) (coes1, coes2),
wenzelm@40281
    39
      Graph.merge (op =) (coes_graph1, coes_graph2),
wenzelm@40281
    40
      Symtab.merge (eq_pair (op aconv) (op =)) (tmaps1, tmaps2));
wenzelm@40281
    41
);
wenzelm@40281
    42
wenzelm@40281
    43
fun map_data f =
wenzelm@40281
    44
  Data.map (fn Data {coes, coes_graph, tmaps} =>
wenzelm@40281
    45
    make_data (f (coes, coes_graph, tmaps)));
wenzelm@40281
    46
wenzelm@40281
    47
fun map_coes f =
wenzelm@40281
    48
  map_data (fn (coes, coes_graph, tmaps) =>
wenzelm@40281
    49
    (f coes, coes_graph, tmaps));
wenzelm@40281
    50
wenzelm@40281
    51
fun map_coes_graph f =
wenzelm@40281
    52
  map_data (fn (coes, coes_graph, tmaps) =>
wenzelm@40281
    53
    (coes, f coes_graph, tmaps));
wenzelm@40281
    54
wenzelm@40281
    55
fun map_coes_and_graph f =
wenzelm@40281
    56
  map_data (fn (coes, coes_graph, tmaps) =>
wenzelm@40281
    57
    let val (coes', coes_graph') = f (coes, coes_graph);
wenzelm@40281
    58
    in (coes', coes_graph', tmaps) end);
wenzelm@40281
    59
wenzelm@40281
    60
fun map_tmaps f =
wenzelm@40281
    61
  map_data (fn (coes, coes_graph, tmaps) =>
wenzelm@40281
    62
    (coes, coes_graph, f tmaps));
wenzelm@40281
    63
wenzelm@40285
    64
val rep_data = (fn Data args => args) o Data.get o Context.Proof;
wenzelm@40281
    65
wenzelm@40281
    66
val coes_of = #coes o rep_data;
wenzelm@40281
    67
val coes_graph_of = #coes_graph o rep_data;
wenzelm@40281
    68
val tmaps_of = #tmaps o rep_data;
wenzelm@40281
    69
wenzelm@40281
    70
wenzelm@40281
    71
wenzelm@40281
    72
(** utils **)
wenzelm@40281
    73
wenzelm@40281
    74
fun nameT (Type (s, [])) = s;
wenzelm@40281
    75
fun t_of s = Type (s, []);
wenzelm@40286
    76
wenzelm@40281
    77
fun sort_of (TFree (_, S)) = SOME S
wenzelm@40281
    78
  | sort_of (TVar (_, S)) = SOME S
wenzelm@40281
    79
  | sort_of _ = NONE;
wenzelm@40281
    80
wenzelm@40281
    81
val is_typeT = fn (Type _) => true | _ => false;
traytel@41353
    82
val is_stypeT = fn (Type (_, [])) => true | _ => false;
wenzelm@40282
    83
val is_compT = fn (Type (_, _ :: _)) => true | _ => false;
wenzelm@40281
    84
val is_freeT = fn (TFree _) => true | _ => false;
wenzelm@40286
    85
val is_fixedvarT = fn (TVar (xi, _)) => not (Type_Infer.is_param xi) | _ => false;
traytel@41353
    86
val is_funtype = fn (Type ("fun", [_, _])) => true | _ => false;
traytel@43591
    87
val is_identity = fn (Abs (_, _, Bound 0)) => true | _ => false;
wenzelm@40281
    88
wenzelm@40281
    89
traytel@40836
    90
(* unification *)
wenzelm@40281
    91
traytel@40836
    92
exception TYPE_INFERENCE_ERROR of unit -> string;
wenzelm@40281
    93
exception NO_UNIFIER of string * typ Vartab.table;
wenzelm@40281
    94
wenzelm@40281
    95
fun unify weak ctxt =
wenzelm@40281
    96
  let
wenzelm@42361
    97
    val thy = Proof_Context.theory_of ctxt;
wenzelm@42386
    98
    val arity_sorts = Type.arity_sorts (Context.pretty ctxt) (Sign.tsig_of thy);
wenzelm@40281
    99
wenzelm@40282
   100
wenzelm@40281
   101
    (* adjust sorts of parameters *)
wenzelm@40281
   102
wenzelm@40281
   103
    fun not_of_sort x S' S =
wenzelm@40281
   104
      "Variable " ^ x ^ "::" ^ Syntax.string_of_sort ctxt S' ^ " not of sort " ^
wenzelm@40281
   105
        Syntax.string_of_sort ctxt S;
wenzelm@40281
   106
wenzelm@40281
   107
    fun meet (_, []) tye_idx = tye_idx
wenzelm@40281
   108
      | meet (Type (a, Ts), S) (tye_idx as (tye, _)) =
wenzelm@40281
   109
          meets (Ts, arity_sorts a S handle ERROR msg => raise NO_UNIFIER (msg, tye)) tye_idx
wenzelm@40281
   110
      | meet (TFree (x, S'), S) (tye_idx as (tye, _)) =
wenzelm@40281
   111
          if Sign.subsort thy (S', S) then tye_idx
wenzelm@40281
   112
          else raise NO_UNIFIER (not_of_sort x S' S, tye)
wenzelm@40281
   113
      | meet (TVar (xi, S'), S) (tye_idx as (tye, idx)) =
wenzelm@40281
   114
          if Sign.subsort thy (S', S) then tye_idx
wenzelm@40281
   115
          else if Type_Infer.is_param xi then
wenzelm@40286
   116
            (Vartab.update_new
wenzelm@40286
   117
              (xi, Type_Infer.mk_param idx (Sign.inter_sort thy (S', S))) tye, idx + 1)
wenzelm@40281
   118
          else raise NO_UNIFIER (not_of_sort (Term.string_of_vname xi) S' S, tye)
wenzelm@40281
   119
    and meets (T :: Ts, S :: Ss) (tye_idx as (tye, _)) =
wenzelm@40286
   120
          meets (Ts, Ss) (meet (Type_Infer.deref tye T, S) tye_idx)
wenzelm@40281
   121
      | meets _ tye_idx = tye_idx;
wenzelm@40281
   122
wenzelm@40281
   123
    val weak_meet = if weak then fn _ => I else meet
wenzelm@40281
   124
wenzelm@40281
   125
wenzelm@40281
   126
    (* occurs check and assignment *)
wenzelm@40281
   127
wenzelm@40281
   128
    fun occurs_check tye xi (TVar (xi', _)) =
wenzelm@40281
   129
          if xi = xi' then raise NO_UNIFIER ("Occurs check!", tye)
wenzelm@40281
   130
          else
wenzelm@40281
   131
            (case Vartab.lookup tye xi' of
wenzelm@40281
   132
              NONE => ()
wenzelm@40281
   133
            | SOME T => occurs_check tye xi T)
wenzelm@40281
   134
      | occurs_check tye xi (Type (_, Ts)) = List.app (occurs_check tye xi) Ts
wenzelm@40281
   135
      | occurs_check _ _ _ = ();
wenzelm@40281
   136
wenzelm@40281
   137
    fun assign xi (T as TVar (xi', _)) S env =
wenzelm@40281
   138
          if xi = xi' then env
wenzelm@40281
   139
          else env |> weak_meet (T, S) |>> Vartab.update_new (xi, T)
wenzelm@40281
   140
      | assign xi T S (env as (tye, _)) =
wenzelm@40281
   141
          (occurs_check tye xi T; env |> weak_meet (T, S) |>> Vartab.update_new (xi, T));
wenzelm@40281
   142
wenzelm@40281
   143
wenzelm@40281
   144
    (* unification *)
wenzelm@40281
   145
wenzelm@40281
   146
    fun show_tycon (a, Ts) =
wenzelm@40281
   147
      quote (Syntax.string_of_typ ctxt (Type (a, replicate (length Ts) dummyT)));
wenzelm@40281
   148
wenzelm@40281
   149
    fun unif (T1, T2) (env as (tye, _)) =
wenzelm@40286
   150
      (case pairself (`Type_Infer.is_paramT o Type_Infer.deref tye) (T1, T2) of
wenzelm@40281
   151
        ((true, TVar (xi, S)), (_, T)) => assign xi T S env
wenzelm@40281
   152
      | ((_, T), (true, TVar (xi, S))) => assign xi T S env
wenzelm@40281
   153
      | ((_, Type (a, Ts)), (_, Type (b, Us))) =>
wenzelm@40281
   154
          if weak andalso null Ts andalso null Us then env
wenzelm@40281
   155
          else if a <> b then
wenzelm@40281
   156
            raise NO_UNIFIER
wenzelm@40281
   157
              ("Clash of types " ^ show_tycon (a, Ts) ^ " and " ^ show_tycon (b, Us), tye)
wenzelm@40281
   158
          else fold unif (Ts ~~ Us) env
wenzelm@40281
   159
      | ((_, T), (_, U)) => if T = U then env else raise NO_UNIFIER ("", tye));
wenzelm@40281
   160
wenzelm@40281
   161
  in unif end;
wenzelm@40281
   162
wenzelm@40281
   163
val weak_unify = unify true;
wenzelm@40281
   164
val strong_unify = unify false;
wenzelm@40281
   165
wenzelm@40281
   166
wenzelm@40281
   167
(* Typ_Graph shortcuts *)
wenzelm@40281
   168
wenzelm@40281
   169
val add_edge = Typ_Graph.add_edge_acyclic;
wenzelm@40281
   170
fun get_preds G T = Typ_Graph.all_preds G [T];
wenzelm@40281
   171
fun get_succs G T = Typ_Graph.all_succs G [T];
wenzelm@40281
   172
fun maybe_new_typnode T G = perhaps (try (Typ_Graph.new_node (T, ()))) G;
wenzelm@40281
   173
fun maybe_new_typnodes Ts G = fold maybe_new_typnode Ts G;
wenzelm@44338
   174
fun new_imm_preds G Ts =  (* FIXME inefficient *)
wenzelm@44338
   175
  subtract (op =) Ts (distinct (op =) (maps (Typ_Graph.immediate_preds G) Ts));
wenzelm@44338
   176
fun new_imm_succs G Ts =  (* FIXME inefficient *)
wenzelm@44338
   177
  subtract (op =) Ts (distinct (op =) (maps (Typ_Graph.immediate_succs G) Ts));
wenzelm@40281
   178
wenzelm@40281
   179
wenzelm@40281
   180
(* Graph shortcuts *)
wenzelm@40281
   181
wenzelm@40281
   182
fun maybe_new_node s G = perhaps (try (Graph.new_node (s, ()))) G
wenzelm@40281
   183
fun maybe_new_nodes ss G = fold maybe_new_node ss G
wenzelm@40281
   184
wenzelm@40281
   185
wenzelm@40281
   186
wenzelm@40281
   187
(** error messages **)
wenzelm@40281
   188
wenzelm@42383
   189
fun gen_msg err msg =
wenzelm@42383
   190
  err () ^ "\nNow trying to infer coercions:\n\nCoercion inference failed" ^
traytel@40836
   191
  (if msg = "" then "" else ": " ^ msg) ^ "\n";
traytel@40836
   192
wenzelm@40281
   193
fun prep_output ctxt tye bs ts Ts =
wenzelm@40281
   194
  let
wenzelm@40281
   195
    val (Ts_bTs', ts') = Type_Infer.finish ctxt tye (Ts @ map snd bs, ts);
wenzelm@40281
   196
    val (Ts', Ts'') = chop (length Ts) Ts_bTs';
wenzelm@40281
   197
    fun prep t =
wenzelm@40281
   198
      let val xs = rev (Term.variant_frees t (rev (map fst bs ~~ Ts'')))
wenzelm@42284
   199
      in Term.subst_bounds (map Syntax_Trans.mark_boundT xs, t) end;
wenzelm@40281
   200
  in (map prep ts', Ts') end;
wenzelm@40281
   201
wenzelm@40281
   202
fun err_loose i = error ("Loose bound variable: B." ^ string_of_int i);
wenzelm@42383
   203
traytel@40836
   204
fun unif_failed msg =
traytel@40836
   205
  "Type unification failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n\n";
wenzelm@42383
   206
traytel@40836
   207
fun err_appl_msg ctxt msg tye bs t T u U () =
traytel@40836
   208
  let val ([t', u'], [T', U']) = prep_output ctxt tye bs [t, u] [T, U]
wenzelm@42383
   209
  in unif_failed msg ^ Type.appl_error ctxt t' T' u' U' ^ "\n" end;
wenzelm@40281
   210
wenzelm@40281
   211
fun err_list ctxt msg tye Ts =
wenzelm@40281
   212
  let
wenzelm@40281
   213
    val (_, Ts') = prep_output ctxt tye [] [] Ts;
wenzelm@42383
   214
    val text =
wenzelm@42383
   215
      msg ^ "\n" ^ "Cannot unify a list of types that should be the same:" ^ "\n" ^
wenzelm@42383
   216
        Pretty.string_of (Pretty.list "[" "]" (map (Syntax.pretty_typ ctxt) Ts'));
wenzelm@40281
   217
  in
wenzelm@40281
   218
    error text
wenzelm@40281
   219
  end;
wenzelm@40281
   220
wenzelm@40281
   221
fun err_bound ctxt msg tye packs =
wenzelm@40281
   222
  let
wenzelm@40281
   223
    val (ts, Ts) = fold
wenzelm@40281
   224
      (fn (bs, t $ u, U, _, U') => fn (ts, Ts) =>
traytel@40836
   225
        let val (t', T') = prep_output ctxt tye bs [t, u] [U', U]
wenzelm@40282
   226
        in (t' :: ts, T' :: Ts) end)
wenzelm@40281
   227
      packs ([], []);
traytel@40836
   228
    val text = cat_lines ([msg, "Cannot fulfil subtype constraints:"] @
wenzelm@40281
   229
        (map2 (fn [t, u] => fn [T, U] => Pretty.string_of (
wenzelm@40281
   230
          Pretty.block [
wenzelm@42383
   231
            Syntax.pretty_typ ctxt T, Pretty.brk 2, Pretty.str "<:", Pretty.brk 2,
wenzelm@42383
   232
            Syntax.pretty_typ ctxt U, Pretty.brk 3,
wenzelm@42383
   233
            Pretty.str "from function application", Pretty.brk 2,
wenzelm@42383
   234
            Pretty.block [Syntax.pretty_term ctxt (t $ u)]]))
wenzelm@40281
   235
        ts Ts))
wenzelm@40281
   236
  in
wenzelm@40281
   237
    error text
wenzelm@40281
   238
  end;
wenzelm@40281
   239
wenzelm@40281
   240
wenzelm@40281
   241
wenzelm@40281
   242
(** constraint generation **)
wenzelm@40281
   243
traytel@40836
   244
fun generate_constraints ctxt err =
wenzelm@40281
   245
  let
wenzelm@40281
   246
    fun gen cs _ (Const (_, T)) tye_idx = (T, tye_idx, cs)
wenzelm@40281
   247
      | gen cs _ (Free (_, T)) tye_idx = (T, tye_idx, cs)
wenzelm@40281
   248
      | gen cs _ (Var (_, T)) tye_idx = (T, tye_idx, cs)
wenzelm@40281
   249
      | gen cs bs (Bound i) tye_idx =
wenzelm@43278
   250
          (snd (nth bs i handle General.Subscript => err_loose i), tye_idx, cs)
wenzelm@40281
   251
      | gen cs bs (Abs (x, T, t)) tye_idx =
wenzelm@40281
   252
          let val (U, tye_idx', cs') = gen cs ((x, T) :: bs) t tye_idx
wenzelm@40281
   253
          in (T --> U, tye_idx', cs') end
wenzelm@40281
   254
      | gen cs bs (t $ u) tye_idx =
wenzelm@40281
   255
          let
wenzelm@40281
   256
            val (T, tye_idx', cs') = gen cs bs t tye_idx;
wenzelm@40281
   257
            val (U', (tye, idx), cs'') = gen cs' bs u tye_idx';
wenzelm@40286
   258
            val U = Type_Infer.mk_param idx [];
wenzelm@40286
   259
            val V = Type_Infer.mk_param (idx + 1) [];
wenzelm@40281
   260
            val tye_idx''= strong_unify ctxt (U --> V, T) (tye, idx + 2)
traytel@41353
   261
              handle NO_UNIFIER (msg, _) => error (gen_msg err msg);
wenzelm@40281
   262
            val error_pack = (bs, t $ u, U, V, U');
wenzelm@40281
   263
          in (V, tye_idx'', ((U', U), error_pack) :: cs'') end;
wenzelm@40281
   264
  in
wenzelm@40281
   265
    gen [] []
wenzelm@40281
   266
  end;
wenzelm@40281
   267
wenzelm@40281
   268
wenzelm@40281
   269
wenzelm@40281
   270
(** constraint resolution **)
wenzelm@40281
   271
wenzelm@40281
   272
exception BOUND_ERROR of string;
wenzelm@40281
   273
traytel@40836
   274
fun process_constraints ctxt err cs tye_idx =
wenzelm@40281
   275
  let
wenzelm@42388
   276
    val thy = Proof_Context.theory_of ctxt;
wenzelm@42388
   277
wenzelm@40285
   278
    val coes_graph = coes_graph_of ctxt;
wenzelm@40285
   279
    val tmaps = tmaps_of ctxt;
wenzelm@42388
   280
    val arity_sorts = Type.arity_sorts (Context.pretty ctxt) (Sign.tsig_of thy);
wenzelm@40281
   281
wenzelm@40281
   282
    fun split_cs _ [] = ([], [])
wenzelm@40282
   283
      | split_cs f (c :: cs) =
wenzelm@40281
   284
          (case pairself f (fst c) of
wenzelm@40281
   285
            (false, false) => apsnd (cons c) (split_cs f cs)
wenzelm@40281
   286
          | _ => apfst (cons c) (split_cs f cs));
wenzelm@42383
   287
traytel@41353
   288
    fun unify_list (T :: Ts) tye_idx =
wenzelm@42383
   289
      fold (fn U => fn tye_idx' => strong_unify ctxt (T, U) tye_idx') Ts tye_idx;
wenzelm@40281
   290
wenzelm@40282
   291
wenzelm@40281
   292
    (* check whether constraint simplification will terminate using weak unification *)
wenzelm@40282
   293
traytel@41353
   294
    val _ = fold (fn (TU, _) => fn tye_idx =>
traytel@41353
   295
      weak_unify ctxt TU tye_idx handle NO_UNIFIER (msg, _) =>
traytel@40836
   296
        error (gen_msg err ("weak unification of subtype constraints fails\n" ^ msg))) cs tye_idx;
wenzelm@40281
   297
wenzelm@40281
   298
wenzelm@40281
   299
    (* simplify constraints *)
wenzelm@40282
   300
wenzelm@40281
   301
    fun simplify_constraints cs tye_idx =
wenzelm@40281
   302
      let
wenzelm@40281
   303
        fun contract a Ts Us error_pack done todo tye idx =
wenzelm@40281
   304
          let
wenzelm@40281
   305
            val arg_var =
wenzelm@40281
   306
              (case Symtab.lookup tmaps a of
wenzelm@40281
   307
                (*everything is invariant for unknown constructors*)
wenzelm@40281
   308
                NONE => replicate (length Ts) INVARIANT
wenzelm@40281
   309
              | SOME av => snd av);
wenzelm@40281
   310
            fun new_constraints (variance, constraint) (cs, tye_idx) =
wenzelm@40281
   311
              (case variance of
wenzelm@40281
   312
                COVARIANT => (constraint :: cs, tye_idx)
wenzelm@40281
   313
              | CONTRAVARIANT => (swap constraint :: cs, tye_idx)
traytel@41353
   314
              | INVARIANT_TO T => (cs, unify_list [T, fst constraint, snd constraint] tye_idx
wenzelm@42383
   315
                  handle NO_UNIFIER (msg, _) =>
wenzelm@42383
   316
                    err_list ctxt (gen_msg err
wenzelm@42383
   317
                      "failed to unify invariant arguments w.r.t. to the known map function")
traytel@41353
   318
                      (fst tye_idx) Ts)
wenzelm@40281
   319
              | INVARIANT => (cs, strong_unify ctxt constraint tye_idx
wenzelm@42383
   320
                  handle NO_UNIFIER (msg, _) =>
traytel@41353
   321
                    error (gen_msg err ("failed to unify invariant arguments" ^ msg))));
wenzelm@40281
   322
            val (new, (tye', idx')) = apfst (fn cs => (cs ~~ replicate (length cs) error_pack))
wenzelm@40281
   323
              (fold new_constraints (arg_var ~~ (Ts ~~ Us)) ([], (tye, idx)));
wenzelm@40281
   324
            val test_update = is_compT orf is_freeT orf is_fixedvarT;
wenzelm@40281
   325
            val (ch, done') =
wenzelm@40286
   326
              if not (null new) then ([], done)
wenzelm@40286
   327
              else split_cs (test_update o Type_Infer.deref tye') done;
wenzelm@40281
   328
            val todo' = ch @ todo;
wenzelm@40281
   329
          in
wenzelm@40281
   330
            simplify done' (new @ todo') (tye', idx')
wenzelm@40281
   331
          end
wenzelm@40281
   332
        (*xi is definitely a parameter*)
wenzelm@40281
   333
        and expand varleq xi S a Ts error_pack done todo tye idx =
wenzelm@40281
   334
          let
wenzelm@40281
   335
            val n = length Ts;
wenzelm@40286
   336
            val args = map2 Type_Infer.mk_param (idx upto idx + n - 1) (arity_sorts a S);
wenzelm@40281
   337
            val tye' = Vartab.update_new (xi, Type(a, args)) tye;
wenzelm@40286
   338
            val (ch, done') = split_cs (is_compT o Type_Infer.deref tye') done;
wenzelm@40281
   339
            val todo' = ch @ todo;
wenzelm@40281
   340
            val new =
wenzelm@40281
   341
              if varleq then (Type(a, args), Type (a, Ts))
wenzelm@40286
   342
              else (Type (a, Ts), Type (a, args));
wenzelm@40281
   343
          in
wenzelm@40281
   344
            simplify done' ((new, error_pack) :: todo') (tye', idx + n)
wenzelm@40281
   345
          end
wenzelm@40281
   346
        (*TU is a pair of a parameter and a free/fixed variable*)
traytel@41353
   347
        and eliminate TU done todo tye idx =
wenzelm@40281
   348
          let
wenzelm@40286
   349
            val [TVar (xi, S)] = filter Type_Infer.is_paramT TU;
wenzelm@40286
   350
            val [T] = filter_out Type_Infer.is_paramT TU;
wenzelm@40281
   351
            val SOME S' = sort_of T;
wenzelm@40281
   352
            val test_update = if is_freeT T then is_freeT else is_fixedvarT;
wenzelm@40281
   353
            val tye' = Vartab.update_new (xi, T) tye;
wenzelm@40286
   354
            val (ch, done') = split_cs (test_update o Type_Infer.deref tye') done;
wenzelm@40281
   355
            val todo' = ch @ todo;
wenzelm@40281
   356
          in
wenzelm@42388
   357
            if Sign.subsort thy (S', S) (*TODO check this*)
wenzelm@40281
   358
            then simplify done' todo' (tye', idx)
traytel@40836
   359
            else error (gen_msg err "sort mismatch")
wenzelm@40281
   360
          end
wenzelm@40281
   361
        and simplify done [] tye_idx = (done, tye_idx)
wenzelm@40281
   362
          | simplify done (((T, U), error_pack) :: todo) (tye_idx as (tye, idx)) =
wenzelm@40286
   363
              (case (Type_Infer.deref tye T, Type_Infer.deref tye U) of
wenzelm@40281
   364
                (Type (a, []), Type (b, [])) =>
wenzelm@40281
   365
                  if a = b then simplify done todo tye_idx
wenzelm@40281
   366
                  else if Graph.is_edge coes_graph (a, b) then simplify done todo tye_idx
traytel@40836
   367
                  else error (gen_msg err (a ^ " is not a subtype of " ^ b))
wenzelm@40281
   368
              | (Type (a, Ts), Type (b, Us)) =>
traytel@40836
   369
                  if a <> b then error (gen_msg err "different constructors")
traytel@40836
   370
                    (fst tye_idx) error_pack
wenzelm@40281
   371
                  else contract a Ts Us error_pack done todo tye idx
wenzelm@40282
   372
              | (TVar (xi, S), Type (a, Ts as (_ :: _))) =>
wenzelm@40281
   373
                  expand true xi S a Ts error_pack done todo tye idx
wenzelm@40282
   374
              | (Type (a, Ts as (_ :: _)), TVar (xi, S)) =>
wenzelm@40281
   375
                  expand false xi S a Ts error_pack done todo tye idx
wenzelm@40281
   376
              | (T, U) =>
wenzelm@40281
   377
                  if T = U then simplify done todo tye_idx
wenzelm@40282
   378
                  else if exists (is_freeT orf is_fixedvarT) [T, U] andalso
wenzelm@40286
   379
                    exists Type_Infer.is_paramT [T, U]
traytel@41353
   380
                  then eliminate [T, U] done todo tye idx
wenzelm@40281
   381
                  else if exists (is_freeT orf is_fixedvarT) [T, U]
traytel@40836
   382
                  then error (gen_msg err "not eliminated free/fixed variables")
wenzelm@40282
   383
                  else simplify (((T, U), error_pack) :: done) todo tye_idx);
wenzelm@40281
   384
      in
wenzelm@40281
   385
        simplify [] cs tye_idx
wenzelm@40281
   386
      end;
wenzelm@40281
   387
wenzelm@40281
   388
wenzelm@40281
   389
    (* do simplification *)
wenzelm@40282
   390
wenzelm@40281
   391
    val (cs', tye_idx') = simplify_constraints cs tye_idx;
wenzelm@42383
   392
wenzelm@42383
   393
    fun find_error_pack lower T' = map_filter
traytel@40836
   394
      (fn ((T, U), pack) => if if lower then T' = U else T' = T then SOME pack else NONE) cs';
wenzelm@42383
   395
wenzelm@42383
   396
    fun find_cycle_packs nodes =
traytel@40836
   397
      let
traytel@40836
   398
        val (but_last, last) = split_last nodes
traytel@40836
   399
        val pairs = (last, hd nodes) :: (but_last ~~ tl nodes);
traytel@40836
   400
      in
traytel@40836
   401
        map_filter
wenzelm@40838
   402
          (fn (TU, pack) => if member (op =) pairs TU then SOME pack else NONE)
traytel@40836
   403
          cs'
traytel@40836
   404
      end;
wenzelm@40281
   405
wenzelm@40281
   406
    (*styps stands either for supertypes or for subtypes of a type T
wenzelm@40281
   407
      in terms of the subtype-relation (excluding T itself)*)
wenzelm@40282
   408
    fun styps super T =
wenzelm@44338
   409
      (if super then Graph.immediate_succs else Graph.immediate_preds) coes_graph T
wenzelm@40281
   410
        handle Graph.UNDEF _ => [];
wenzelm@40281
   411
wenzelm@40282
   412
    fun minmax sup (T :: Ts) =
wenzelm@40281
   413
      let
wenzelm@40281
   414
        fun adjust T U = if sup then (T, U) else (U, T);
wenzelm@40281
   415
        fun extract T [] = T
wenzelm@40282
   416
          | extract T (U :: Us) =
wenzelm@40281
   417
              if Graph.is_edge coes_graph (adjust T U) then extract T Us
wenzelm@40281
   418
              else if Graph.is_edge coes_graph (adjust U T) then extract U Us
traytel@40836
   419
              else raise BOUND_ERROR "uncomparable types in type list";
wenzelm@40281
   420
      in
wenzelm@40281
   421
        t_of (extract T Ts)
wenzelm@40281
   422
      end;
wenzelm@40281
   423
wenzelm@40282
   424
    fun ex_styp_of_sort super T styps_and_sorts =
wenzelm@40281
   425
      let
wenzelm@40281
   426
        fun adjust T U = if super then (T, U) else (U, T);
wenzelm@40282
   427
        fun styp_test U Ts = forall
wenzelm@40281
   428
          (fn T => T = U orelse Graph.is_edge coes_graph (adjust U T)) Ts;
wenzelm@42388
   429
        fun fitting Ts S U = Sign.of_sort thy (t_of U, S) andalso styp_test U Ts
wenzelm@40281
   430
      in
wenzelm@40281
   431
        forall (fn (Ts, S) => exists (fitting Ts S) (T :: styps super T)) styps_and_sorts
wenzelm@40281
   432
      end;
wenzelm@40281
   433
wenzelm@40281
   434
    (* computes the tightest possible, correct assignment for 'a::S
wenzelm@40281
   435
       e.g. in the supremum case (sup = true):
wenzelm@40281
   436
               ------- 'a::S---
wenzelm@40281
   437
              /        /    \  \
wenzelm@40281
   438
             /        /      \  \
wenzelm@40281
   439
        'b::C1   'c::C2 ...  T1 T2 ...
wenzelm@40281
   440
wenzelm@40281
   441
       sorts - list of sorts [C1, C2, ...]
wenzelm@40281
   442
       T::Ts - non-empty list of base types [T1, T2, ...]
wenzelm@40281
   443
    *)
wenzelm@40282
   444
    fun tightest sup S styps_and_sorts (T :: Ts) =
wenzelm@40281
   445
      let
wenzelm@42388
   446
        fun restriction T = Sign.of_sort thy (t_of T, S)
wenzelm@40281
   447
          andalso ex_styp_of_sort (not sup) T styps_and_sorts;
wenzelm@40281
   448
        fun candidates T = inter (op =) (filter restriction (T :: styps sup T));
wenzelm@40281
   449
      in
wenzelm@40281
   450
        (case fold candidates Ts (filter restriction (T :: styps sup T)) of
traytel@40836
   451
          [] => raise BOUND_ERROR ("no " ^ (if sup then "supremum" else "infimum"))
wenzelm@40281
   452
        | [T] => t_of T
wenzelm@40281
   453
        | Ts => minmax sup Ts)
wenzelm@40281
   454
      end;
wenzelm@40281
   455
wenzelm@40281
   456
    fun build_graph G [] tye_idx = (G, tye_idx)
wenzelm@40282
   457
      | build_graph G ((T, U) :: cs) tye_idx =
wenzelm@40281
   458
        if T = U then build_graph G cs tye_idx
wenzelm@40281
   459
        else
wenzelm@40281
   460
          let
wenzelm@40281
   461
            val G' = maybe_new_typnodes [T, U] G;
wenzelm@40281
   462
            val (G'', tye_idx') = (add_edge (T, U) G', tye_idx)
wenzelm@40281
   463
              handle Typ_Graph.CYCLES cycles =>
wenzelm@40281
   464
                let
wenzelm@42383
   465
                  val (tye, idx) =
wenzelm@42383
   466
                    fold
traytel@40836
   467
                      (fn cycle => fn tye_idx' => (unify_list cycle tye_idx'
wenzelm@42383
   468
                        handle NO_UNIFIER (msg, _) =>
wenzelm@42383
   469
                          err_bound ctxt
traytel@40836
   470
                            (gen_msg err ("constraint cycle not unifiable" ^ msg)) (fst tye_idx)
traytel@40836
   471
                            (find_cycle_packs cycle)))
traytel@40836
   472
                      cycles tye_idx
wenzelm@40281
   473
                in
traytel@40836
   474
                  collapse (tye, idx) cycles G
traytel@40836
   475
                end
wenzelm@40281
   476
          in
wenzelm@40281
   477
            build_graph G'' cs tye_idx'
wenzelm@40281
   478
          end
traytel@40836
   479
    and collapse (tye, idx) cycles G = (*nodes non-empty list*)
wenzelm@40281
   480
      let
traytel@40836
   481
        (*all cycles collapse to one node,
traytel@40836
   482
          because all of them share at least the nodes x and y*)
traytel@40836
   483
        val nodes = (distinct (op =) (flat cycles));
traytel@40836
   484
        val T = Type_Infer.deref tye (hd nodes);
wenzelm@40281
   485
        val P = new_imm_preds G nodes;
wenzelm@40281
   486
        val S = new_imm_succs G nodes;
wenzelm@40281
   487
        val G' = Typ_Graph.del_nodes (tl nodes) G;
traytel@40836
   488
        fun check_and_gen super T' =
traytel@40836
   489
          let val U = Type_Infer.deref tye T';
traytel@40836
   490
          in
traytel@40836
   491
            if not (is_typeT T) orelse not (is_typeT U) orelse T = U
traytel@40836
   492
            then if super then (hd nodes, T') else (T', hd nodes)
wenzelm@42383
   493
            else
wenzelm@42383
   494
              if super andalso
traytel@40836
   495
                Graph.is_edge coes_graph (nameT T, nameT U) then (hd nodes, T')
wenzelm@42383
   496
              else if not super andalso
traytel@40836
   497
                Graph.is_edge coes_graph (nameT U, nameT T) then (T', hd nodes)
traytel@40836
   498
              else err_bound ctxt (gen_msg err "cycle elimination produces inconsistent graph")
wenzelm@42383
   499
                    (fst tye_idx)
traytel@40836
   500
                    (maps find_cycle_packs cycles @ find_error_pack super T')
traytel@40836
   501
          end;
wenzelm@40281
   502
      in
traytel@40836
   503
        build_graph G' (map (check_and_gen false) P @ map (check_and_gen true) S) (tye, idx)
wenzelm@40281
   504
      end;
wenzelm@40281
   505
wenzelm@40281
   506
    fun assign_bound lower G key (tye_idx as (tye, _)) =
wenzelm@40286
   507
      if Type_Infer.is_paramT (Type_Infer.deref tye key) then
wenzelm@40281
   508
        let
wenzelm@40286
   509
          val TVar (xi, S) = Type_Infer.deref tye key;
wenzelm@40281
   510
          val get_bound = if lower then get_preds else get_succs;
wenzelm@40281
   511
          val raw_bound = get_bound G key;
wenzelm@40286
   512
          val bound = map (Type_Infer.deref tye) raw_bound;
wenzelm@40286
   513
          val not_params = filter_out Type_Infer.is_paramT bound;
wenzelm@40282
   514
          fun to_fulfil T =
wenzelm@40281
   515
            (case sort_of T of
wenzelm@40281
   516
              NONE => NONE
wenzelm@40282
   517
            | SOME S =>
wenzelm@40286
   518
                SOME
wenzelm@40286
   519
                  (map nameT
wenzelm@42405
   520
                    (filter_out Type_Infer.is_paramT
wenzelm@42405
   521
                      (map (Type_Infer.deref tye) (get_bound G T))), S));
wenzelm@40281
   522
          val styps_and_sorts = distinct (op =) (map_filter to_fulfil raw_bound);
wenzelm@40281
   523
          val assignment =
wenzelm@40281
   524
            if null bound orelse null not_params then NONE
wenzelm@40281
   525
            else SOME (tightest lower S styps_and_sorts (map nameT not_params)
wenzelm@42383
   526
                handle BOUND_ERROR msg =>
traytel@40836
   527
                  err_bound ctxt (gen_msg err msg) tye (find_error_pack lower key))
wenzelm@40281
   528
        in
wenzelm@40281
   529
          (case assignment of
wenzelm@40281
   530
            NONE => tye_idx
wenzelm@40281
   531
          | SOME T =>
wenzelm@40286
   532
              if Type_Infer.is_paramT T then tye_idx
wenzelm@40281
   533
              else if lower then (*upper bound check*)
wenzelm@40281
   534
                let
wenzelm@40286
   535
                  val other_bound = map (Type_Infer.deref tye) (get_succs G key);
wenzelm@40281
   536
                  val s = nameT T;
wenzelm@40281
   537
                in
wenzelm@40281
   538
                  if subset (op = o apfst nameT) (filter is_typeT other_bound, s :: styps true s)
wenzelm@40281
   539
                  then apfst (Vartab.update (xi, T)) tye_idx
traytel@40836
   540
                  else err_bound ctxt (gen_msg err ("assigned simple type " ^ s ^
wenzelm@40281
   541
                    " clashes with the upper bound of variable " ^
traytel@40836
   542
                    Syntax.string_of_typ ctxt (TVar(xi, S)))) tye (find_error_pack (not lower) key)
wenzelm@40281
   543
                end
wenzelm@40281
   544
              else apfst (Vartab.update (xi, T)) tye_idx)
wenzelm@40281
   545
        end
wenzelm@40281
   546
      else tye_idx;
wenzelm@40281
   547
wenzelm@40281
   548
    val assign_lb = assign_bound true;
wenzelm@40281
   549
    val assign_ub = assign_bound false;
wenzelm@40281
   550
wenzelm@40281
   551
    fun assign_alternating ts' ts G tye_idx =
wenzelm@40281
   552
      if ts' = ts then tye_idx
wenzelm@40281
   553
      else
wenzelm@40281
   554
        let
wenzelm@40281
   555
          val (tye_idx' as (tye, _)) = fold (assign_lb G) ts tye_idx
wenzelm@40281
   556
            |> fold (assign_ub G) ts;
wenzelm@40281
   557
        in
wenzelm@42383
   558
          assign_alternating ts
traytel@40836
   559
            (filter (Type_Infer.is_paramT o Type_Infer.deref tye) ts) G tye_idx'
wenzelm@40281
   560
        end;
wenzelm@40281
   561
wenzelm@40281
   562
    (*Unify all weakly connected components of the constraint forest,
wenzelm@40282
   563
      that contain only params. These are the only WCCs that contain
wenzelm@40281
   564
      params anyway.*)
wenzelm@40281
   565
    fun unify_params G (tye_idx as (tye, _)) =
wenzelm@40281
   566
      let
wenzelm@40286
   567
        val max_params =
wenzelm@40286
   568
          filter (Type_Infer.is_paramT o Type_Infer.deref tye) (Typ_Graph.maximals G);
wenzelm@40281
   569
        val to_unify = map (fn T => T :: get_preds G T) max_params;
wenzelm@40281
   570
      in
wenzelm@42383
   571
        fold
traytel@40836
   572
          (fn Ts => fn tye_idx' => unify_list Ts tye_idx'
traytel@41353
   573
            handle NO_UNIFIER (msg, _) => err_list ctxt (gen_msg err msg) (fst tye_idx) Ts)
traytel@40836
   574
          to_unify tye_idx
wenzelm@40281
   575
      end;
wenzelm@40281
   576
wenzelm@40281
   577
    fun solve_constraints G tye_idx = tye_idx
wenzelm@40281
   578
      |> assign_alternating [] (Typ_Graph.keys G) G
wenzelm@40281
   579
      |> unify_params G;
wenzelm@40281
   580
  in
wenzelm@40281
   581
    build_graph Typ_Graph.empty (map fst cs') tye_idx'
wenzelm@40281
   582
      |-> solve_constraints
wenzelm@40281
   583
  end;
wenzelm@40281
   584
wenzelm@40281
   585
wenzelm@40281
   586
wenzelm@40281
   587
(** coercion insertion **)
wenzelm@40281
   588
traytel@40836
   589
fun gen_coercion ctxt tye (T1, T2) =
traytel@40836
   590
  (case pairself (Type_Infer.deref tye) (T1, T2) of
traytel@40836
   591
    ((Type (a, [])), (Type (b, []))) =>
traytel@40836
   592
        if a = b
traytel@40836
   593
        then Abs (Name.uu, Type (a, []), Bound 0)
traytel@40836
   594
        else
traytel@40836
   595
          (case Symreltab.lookup (coes_of ctxt) (a, b) of
traytel@40836
   596
            NONE => raise Fail (a ^ " is not a subtype of " ^ b)
traytel@40836
   597
          | SOME co => co)
traytel@40836
   598
  | ((Type (a, Ts)), (Type (b, Us))) =>
traytel@40836
   599
        if a <> b
traytel@40836
   600
        then raise Fail ("Different constructors: " ^ a ^ " and " ^ b)
traytel@40836
   601
        else
traytel@40836
   602
          let
traytel@40836
   603
            fun inst t Ts =
traytel@40836
   604
              Term.subst_vars
traytel@40836
   605
                (((Term.add_tvar_namesT (fastype_of t) []) ~~ rev Ts), []) t;
traytel@41353
   606
            fun sub_co (COVARIANT, TU) = SOME (gen_coercion ctxt tye TU)
traytel@41353
   607
              | sub_co (CONTRAVARIANT, TU) = SOME (gen_coercion ctxt tye (swap TU))
traytel@41353
   608
              | sub_co (INVARIANT_TO T, _) = NONE;
traytel@40836
   609
            fun ts_of [] = []
traytel@40836
   610
              | ts_of (Type ("fun", [x1, x2]) :: xs) = x1 :: x2 :: (ts_of xs);
traytel@40836
   611
          in
traytel@40836
   612
            (case Symtab.lookup (tmaps_of ctxt) a of
traytel@40836
   613
              NONE => raise Fail ("No map function for " ^ a ^ " known")
traytel@40836
   614
            | SOME tmap =>
traytel@40836
   615
                let
traytel@41353
   616
                  val used_coes = map_filter sub_co ((snd tmap) ~~ (Ts ~~ Us));
traytel@40836
   617
                in
traytel@43591
   618
                  if null (filter (not o is_identity) used_coes)
traytel@43591
   619
                  then Abs (Name.uu, Type (a, Ts), Bound 0)
traytel@43591
   620
                  else Term.list_comb
traytel@40836
   621
                    (inst (fst tmap) (ts_of (map fastype_of used_coes)), used_coes)
traytel@40836
   622
                end)
traytel@40836
   623
          end
traytel@40836
   624
  | (T, U) =>
traytel@40836
   625
        if Type.could_unify (T, U)
traytel@40836
   626
        then Abs (Name.uu, T, Bound 0)
traytel@40836
   627
        else raise Fail ("Cannot generate coercion from "
traytel@40836
   628
          ^ Syntax.string_of_typ ctxt T ^ " to " ^ Syntax.string_of_typ ctxt U));
traytel@40836
   629
wenzelm@40281
   630
fun insert_coercions ctxt tye ts =
wenzelm@40281
   631
  let
wenzelm@40281
   632
    fun insert _ (Const (c, T)) =
traytel@40836
   633
          let val T' = T;
wenzelm@40281
   634
          in (Const (c, T'), T') end
wenzelm@40281
   635
      | insert _ (Free (x, T)) =
traytel@40836
   636
          let val T' = T;
wenzelm@40281
   637
          in (Free (x, T'), T') end
wenzelm@40281
   638
      | insert _ (Var (xi, T)) =
traytel@40836
   639
          let val T' = T;
wenzelm@40281
   640
          in (Var (xi, T'), T') end
wenzelm@40281
   641
      | insert bs (Bound i) =
wenzelm@43278
   642
          let val T = nth bs i handle General.Subscript => err_loose i;
wenzelm@40281
   643
          in (Bound i, T) end
wenzelm@40281
   644
      | insert bs (Abs (x, T, t)) =
wenzelm@40281
   645
          let
traytel@40836
   646
            val T' = T;
wenzelm@40282
   647
            val (t', T'') = insert (T' :: bs) t;
wenzelm@40281
   648
          in
wenzelm@40281
   649
            (Abs (x, T', t'), T' --> T'')
wenzelm@40281
   650
          end
wenzelm@40281
   651
      | insert bs (t $ u) =
wenzelm@40281
   652
          let
wenzelm@42405
   653
            val (t', Type ("fun", [U, T])) =
wenzelm@42405
   654
              apsnd (Type_Infer.deref tye) (insert bs t);
wenzelm@40281
   655
            val (u', U') = insert bs u;
wenzelm@40281
   656
          in
traytel@40836
   657
            if can (fn TU => strong_unify ctxt TU (tye, 0)) (U, U')
traytel@40836
   658
            then (t' $ u', T)
traytel@40836
   659
            else (t' $ (gen_coercion ctxt tye (U', U) $ u'), T)
wenzelm@40281
   660
          end
wenzelm@40281
   661
  in
wenzelm@40281
   662
    map (fst o insert []) ts
wenzelm@40281
   663
  end;
wenzelm@40281
   664
wenzelm@40281
   665
wenzelm@40281
   666
wenzelm@40281
   667
(** assembling the pipeline **)
wenzelm@40281
   668
wenzelm@42398
   669
fun coercion_infer_types ctxt raw_ts =
wenzelm@40281
   670
  let
wenzelm@42405
   671
    val (idx, ts) = Type_Infer_Context.prepare ctxt raw_ts;
wenzelm@40281
   672
traytel@40836
   673
    fun inf _ (t as (Const (_, T))) tye_idx = (t, T, tye_idx)
traytel@40836
   674
      | inf _ (t as (Free (_, T))) tye_idx = (t, T, tye_idx)
traytel@40836
   675
      | inf _ (t as (Var (_, T))) tye_idx = (t, T, tye_idx)
traytel@40836
   676
      | inf bs (t as (Bound i)) tye_idx =
wenzelm@43278
   677
          (t, snd (nth bs i handle General.Subscript => err_loose i), tye_idx)
traytel@40836
   678
      | inf bs (Abs (x, T, t)) tye_idx =
traytel@40836
   679
          let val (t', U, tye_idx') = inf ((x, T) :: bs) t tye_idx
traytel@40836
   680
          in (Abs (x, T, t'), T --> U, tye_idx') end
traytel@40836
   681
      | inf bs (t $ u) tye_idx =
traytel@40836
   682
          let
traytel@40836
   683
            val (t', T, tye_idx') = inf bs t tye_idx;
traytel@40836
   684
            val (u', U, (tye, idx)) = inf bs u tye_idx';
traytel@40836
   685
            val V = Type_Infer.mk_param idx [];
traytel@40836
   686
            val (tu, tye_idx'') = (t' $ u', strong_unify ctxt (U --> V, T) (tye, idx + 1))
wenzelm@42383
   687
              handle NO_UNIFIER (msg, tye') =>
traytel@40836
   688
                raise TYPE_INFERENCE_ERROR (err_appl_msg ctxt msg tye' bs t T u U);
traytel@40836
   689
          in (tu, V, tye_idx'') end;
wenzelm@40281
   690
wenzelm@42383
   691
    fun infer_single t tye_idx =
traytel@40836
   692
      let val (t, _, tye_idx') = inf [] t tye_idx;
traytel@40938
   693
      in (t, tye_idx') end;
wenzelm@42383
   694
traytel@40938
   695
    val (ts', (tye, _)) = (fold_map infer_single ts (Vartab.empty, idx)
wenzelm@42383
   696
      handle TYPE_INFERENCE_ERROR err =>
traytel@40836
   697
        let
traytel@40836
   698
          fun gen_single t (tye_idx, constraints) =
traytel@40836
   699
            let val (_, tye_idx', constraints') = generate_constraints ctxt err t tye_idx
traytel@40836
   700
            in (tye_idx', constraints' @ constraints) end;
wenzelm@42383
   701
traytel@40836
   702
          val (tye_idx, constraints) = fold gen_single ts ((Vartab.empty, idx), []);
traytel@40836
   703
          val (tye, idx) = process_constraints ctxt err constraints tye_idx;
wenzelm@42383
   704
        in
traytel@40836
   705
          (insert_coercions ctxt tye ts, (tye, idx))
traytel@40836
   706
        end);
wenzelm@40281
   707
wenzelm@40281
   708
    val (_, ts'') = Type_Infer.finish ctxt tye ([], ts');
wenzelm@40281
   709
  in ts'' end;
wenzelm@40281
   710
wenzelm@40281
   711
wenzelm@40281
   712
wenzelm@40281
   713
(** installation **)
wenzelm@40281
   714
wenzelm@40283
   715
(* term check *)
wenzelm@40283
   716
wenzelm@42616
   717
val coercion_enabled = Attrib.setup_config_bool @{binding coercion_enabled} (K false);
wenzelm@40939
   718
wenzelm@40283
   719
val add_term_check =
wenzelm@40283
   720
  Syntax.add_term_check ~100 "coercions"
wenzelm@42402
   721
    (fn ctxt => Config.get ctxt coercion_enabled ? coercion_infer_types ctxt);
wenzelm@40281
   722
wenzelm@40281
   723
wenzelm@40283
   724
(* declarations *)
wenzelm@40281
   725
wenzelm@40284
   726
fun add_type_map raw_t context =
wenzelm@40281
   727
  let
wenzelm@40281
   728
    val ctxt = Context.proof_of context;
wenzelm@40284
   729
    val t = singleton (Variable.polymorphic ctxt) raw_t;
wenzelm@40281
   730
wenzelm@42383
   731
    fun err_str t = "\n\nThe provided function has the type\n" ^
wenzelm@42383
   732
      Syntax.string_of_typ ctxt (fastype_of t) ^
traytel@41353
   733
      "\n\nThe general type signature of a map function is" ^
traytel@41353
   734
      "\nf1 => f2 => ... => fn => C [x1, ..., xn] => C [y1, ..., yn]" ^
wenzelm@40281
   735
      "\nwhere C is a constructor and fi is of type (xi => yi) or (yi => xi)";
wenzelm@42383
   736
traytel@41353
   737
    val ((fis, T1), T2) = apfst split_last (strip_type (fastype_of t))
traytel@41353
   738
      handle Empty => error ("Not a proper map function:" ^ err_str t);
wenzelm@42383
   739
wenzelm@40281
   740
    fun gen_arg_var ([], []) = []
wenzelm@40282
   741
      | gen_arg_var ((T, T') :: Ts, (U, U') :: Us) =
traytel@41353
   742
          if U = U' then
traytel@41353
   743
            if is_stypeT U then INVARIANT_TO U :: gen_arg_var ((T, T') :: Ts, Us)
traytel@41353
   744
            else error ("Invariant xi and yi should be base types:" ^ err_str t)
traytel@41353
   745
          else if T = U andalso T' = U' then COVARIANT :: gen_arg_var (Ts, Us)
wenzelm@40281
   746
          else if T = U' andalso T' = U then CONTRAVARIANT :: gen_arg_var (Ts, Us)
traytel@41353
   747
          else error ("Functions do not apply to arguments correctly:" ^ err_str t)
wenzelm@42383
   748
      | gen_arg_var (_, Ts) =
wenzelm@42383
   749
          if forall (op = andf is_stypeT o fst) Ts
traytel@41353
   750
          then map (INVARIANT_TO o fst) Ts
traytel@41353
   751
          else error ("Different numbers of functions and variant arguments\n" ^ err_str t);
wenzelm@40281
   752
traytel@41353
   753
    (*retry flag needed to adjust the type lists, when given a map over type constructor fun*)
traytel@41353
   754
    fun check_map_fun fis (Type (C1, Ts)) (Type (C2, Us)) retry =
traytel@41353
   755
          if C1 = C2 andalso not (null fis) andalso forall is_funtype fis
traytel@41353
   756
          then ((map dest_funT fis, Ts ~~ Us), C1)
traytel@41353
   757
          else error ("Not a proper map function:" ^ err_str t)
traytel@41353
   758
      | check_map_fun fis T1 T2 true =
traytel@41353
   759
          let val (fis', T') = split_last fis
traytel@41353
   760
          in check_map_fun fis' T' (T1 --> T2) false end
traytel@41353
   761
      | check_map_fun _ _ _ _ = error ("Not a proper map function:" ^ err_str t);
wenzelm@40281
   762
traytel@41353
   763
    val res = check_map_fun fis T1 T2 true;
wenzelm@40281
   764
    val res_av = gen_arg_var (fst res);
wenzelm@40281
   765
  in
wenzelm@40281
   766
    map_tmaps (Symtab.update (snd res, (t, res_av))) context
wenzelm@40281
   767
  end;
wenzelm@40281
   768
wenzelm@40284
   769
fun add_coercion raw_t context =
wenzelm@40281
   770
  let
wenzelm@40281
   771
    val ctxt = Context.proof_of context;
wenzelm@40284
   772
    val t = singleton (Variable.polymorphic ctxt) raw_t;
wenzelm@40281
   773
wenzelm@40281
   774
    fun err_coercion () = error ("Bad type for coercion " ^
wenzelm@40281
   775
        Syntax.string_of_term ctxt t ^ ":\n" ^
wenzelm@40281
   776
        Syntax.string_of_typ ctxt (fastype_of t));
wenzelm@40281
   777
wenzelm@40840
   778
    val (T1, T2) = Term.dest_funT (fastype_of t)
wenzelm@40840
   779
      handle TYPE _ => err_coercion ();
wenzelm@40281
   780
wenzelm@40281
   781
    val a =
wenzelm@40281
   782
      (case T1 of
wenzelm@40281
   783
        Type (x, []) => x
wenzelm@40281
   784
      | _ => err_coercion ());
wenzelm@40281
   785
wenzelm@40281
   786
    val b =
wenzelm@40281
   787
      (case T2 of
wenzelm@40281
   788
        Type (x, []) => x
wenzelm@40281
   789
      | _ => err_coercion ());
wenzelm@40281
   790
wenzelm@40281
   791
    fun coercion_data_update (tab, G) =
wenzelm@40281
   792
      let
wenzelm@40281
   793
        val G' = maybe_new_nodes [a, b] G
wenzelm@40281
   794
        val G'' = Graph.add_edge_trans_acyclic (a, b) G'
wenzelm@40281
   795
          handle Graph.CYCLES _ => error (a ^ " is already a subtype of " ^ b ^
wenzelm@40281
   796
            "!\n\nCannot add coercion of type: " ^ a ^ " => " ^ b);
wenzelm@40281
   797
        val new_edges =
wenzelm@40281
   798
          flat (Graph.dest G'' |> map (fn (x, ys) => ys |> map_filter (fn y =>
wenzelm@40281
   799
            if Graph.is_edge G' (x, y) then NONE else SOME (x, y))));
wenzelm@40281
   800
        val G_and_new = Graph.add_edge (a, b) G';
wenzelm@40281
   801
wenzelm@40281
   802
        fun complex_coercion tab G (a, b) =
wenzelm@40281
   803
          let
wenzelm@40281
   804
            val path = hd (Graph.irreducible_paths G (a, b))
traytel@40836
   805
            val path' = fst (split_last path) ~~ tl path
wenzelm@40281
   806
          in Abs (Name.uu, Type (a, []),
wenzelm@40281
   807
              fold (fn t => fn u => t $ u) (map (the o Symreltab.lookup tab) path') (Bound 0))
wenzelm@40281
   808
          end;
wenzelm@40281
   809
wenzelm@40281
   810
        val tab' = fold
wenzelm@40281
   811
          (fn pair => fn tab => Symreltab.update (pair, complex_coercion tab G_and_new pair) tab)
wenzelm@40281
   812
          (filter (fn pair => pair <> (a, b)) new_edges)
wenzelm@40281
   813
          (Symreltab.update ((a, b), t) tab);
wenzelm@40281
   814
      in
wenzelm@40281
   815
        (tab', G'')
wenzelm@40281
   816
      end;
wenzelm@40281
   817
  in
wenzelm@40281
   818
    map_coes_and_graph coercion_data_update context
wenzelm@40281
   819
  end;
wenzelm@40281
   820
wenzelm@40283
   821
wenzelm@40283
   822
(* theory setup *)
wenzelm@40283
   823
wenzelm@40283
   824
val setup =
wenzelm@40283
   825
  Context.theory_map add_term_check #>
wenzelm@40284
   826
  Attrib.setup @{binding coercion}
wenzelm@40284
   827
    (Args.term >> (fn t => Thm.declaration_attribute (K (add_coercion t))))
wenzelm@40281
   828
    "declaration of new coercions" #>
traytel@40297
   829
  Attrib.setup @{binding coercion_map}
wenzelm@40284
   830
    (Args.term >> (fn t => Thm.declaration_attribute (K (add_type_map t))))
wenzelm@40283
   831
    "declaration of new map functions";
wenzelm@40281
   832
wenzelm@40281
   833
end;