src/Tools/subtyping.ML
author wenzelm
Mon Feb 03 19:50:16 2014 +0100 (2014-02-03)
changeset 55305 70e7ac6af16f
parent 55304 55ac31bc08a4
child 55763 4b3907cb5654
permissions -rw-r--r--
unused;
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
traytel@45059
    12
  val print_coercions: Proof.context -> unit
wenzelm@40283
    13
  val setup: theory -> theory
wenzelm@40281
    14
end;
wenzelm@40281
    15
wenzelm@40283
    16
structure Subtyping: SUBTYPING =
wenzelm@40281
    17
struct
wenzelm@40281
    18
wenzelm@40281
    19
(** coercions data **)
wenzelm@40281
    20
traytel@41353
    21
datatype variance = COVARIANT | CONTRAVARIANT | INVARIANT | INVARIANT_TO of typ;
traytel@51327
    22
datatype coerce_arg = PERMIT | FORBID | LEAVE
wenzelm@40281
    23
wenzelm@40281
    24
datatype data = Data of
traytel@45060
    25
  {coes: (term * ((typ list * typ list) * term list)) Symreltab.table,  (*coercions table*)
traytel@45060
    26
   (*full coercions graph - only used at coercion declaration/deletion*)
traytel@45060
    27
   full_graph: int Graph.T,
wenzelm@52432
    28
   (*coercions graph restricted to base types - for efficiency reasons stored in the context*)
traytel@45060
    29
   coes_graph: int Graph.T,
traytel@51319
    30
   tmaps: (term * variance list) Symtab.table,  (*map functions*)
traytel@51327
    31
   coerce_args: coerce_arg list Symtab.table  (*special constants with non-coercible arguments*)};
wenzelm@40281
    32
traytel@51319
    33
fun make_data (coes, full_graph, coes_graph, tmaps, coerce_args) =
traytel@51319
    34
  Data {coes = coes, full_graph = full_graph, coes_graph = coes_graph,
traytel@51319
    35
    tmaps = tmaps, coerce_args = coerce_args};
wenzelm@40281
    36
traytel@45935
    37
fun merge_error_coes (a, b) =
traytel@45935
    38
  error ("Cannot merge coercion tables.\nConflicting declarations for coercions from " ^
traytel@45935
    39
    quote a ^ " to " ^ quote b ^ ".");
traytel@45935
    40
traytel@45935
    41
fun merge_error_tmaps C =
traytel@45935
    42
  error ("Cannot merge coercion map tables.\nConflicting declarations for the constructor " ^
traytel@45935
    43
    quote C ^ ".");
traytel@45935
    44
traytel@51319
    45
fun merge_error_coerce_args C =
wenzelm@55303
    46
  error ("Cannot merge tables for constants with coercion-invariant arguments.\n" ^
wenzelm@55303
    47
    "Conflicting declarations for the constant " ^ quote C ^ ".");
traytel@51319
    48
wenzelm@40281
    49
structure Data = Generic_Data
wenzelm@40281
    50
(
wenzelm@40281
    51
  type T = data;
traytel@51319
    52
  val empty = make_data (Symreltab.empty, Graph.empty, Graph.empty, Symtab.empty, Symtab.empty);
wenzelm@40281
    53
  val extend = I;
wenzelm@40281
    54
  fun merge
traytel@51319
    55
    (Data {coes = coes1, full_graph = full_graph1, coes_graph = coes_graph1,
traytel@51319
    56
      tmaps = tmaps1, coerce_args = coerce_args1},
traytel@51319
    57
      Data {coes = coes2, full_graph = full_graph2, coes_graph = coes_graph2,
traytel@51319
    58
        tmaps = tmaps2, coerce_args = coerce_args2}) =
traytel@45060
    59
    make_data (Symreltab.merge (eq_pair (op aconv)
traytel@45060
    60
        (eq_pair (eq_pair (eq_list (op =)) (eq_list (op =))) (eq_list (op aconv))))
traytel@45935
    61
        (coes1, coes2) handle Symreltab.DUP key => merge_error_coes key,
traytel@45060
    62
      Graph.merge (op =) (full_graph1, full_graph2),
wenzelm@40281
    63
      Graph.merge (op =) (coes_graph1, coes_graph2),
traytel@45935
    64
      Symtab.merge (eq_pair (op aconv) (op =)) (tmaps1, tmaps2)
traytel@51319
    65
        handle Symtab.DUP key => merge_error_tmaps key,
traytel@51319
    66
      Symtab.merge (eq_list (op =)) (coerce_args1, coerce_args2)
traytel@51319
    67
        handle Symtab.DUP key => merge_error_coerce_args key);
wenzelm@40281
    68
);
wenzelm@40281
    69
wenzelm@40281
    70
fun map_data f =
traytel@51319
    71
  Data.map (fn Data {coes, full_graph, coes_graph, tmaps, coerce_args} =>
traytel@51319
    72
    make_data (f (coes, full_graph, coes_graph, tmaps, coerce_args)));
wenzelm@40281
    73
traytel@45060
    74
fun map_coes_and_graphs f =
traytel@51319
    75
  map_data (fn (coes, full_graph, coes_graph, tmaps, coerce_args) =>
traytel@45060
    76
    let val (coes', full_graph', coes_graph') = f (coes, full_graph, coes_graph);
traytel@51319
    77
    in (coes', full_graph', coes_graph', tmaps, coerce_args) end);
wenzelm@40281
    78
wenzelm@40281
    79
fun map_tmaps f =
traytel@51319
    80
  map_data (fn (coes, full_graph, coes_graph, tmaps, coerce_args) =>
traytel@51319
    81
    (coes, full_graph, coes_graph, f tmaps, coerce_args));
traytel@51319
    82
traytel@51319
    83
fun map_coerce_args f =
traytel@51319
    84
  map_data (fn (coes, full_graph, coes_graph, tmaps, coerce_args) =>
traytel@51319
    85
    (coes, full_graph, coes_graph, tmaps, f coerce_args));
wenzelm@40281
    86
wenzelm@40285
    87
val rep_data = (fn Data args => args) o Data.get o Context.Proof;
wenzelm@40281
    88
wenzelm@40281
    89
val coes_of = #coes o rep_data;
wenzelm@40281
    90
val coes_graph_of = #coes_graph o rep_data;
wenzelm@40281
    91
val tmaps_of = #tmaps o rep_data;
traytel@51319
    92
val coerce_args_of = #coerce_args o rep_data;
wenzelm@40281
    93
wenzelm@40281
    94
wenzelm@40281
    95
wenzelm@40281
    96
(** utils **)
wenzelm@40281
    97
wenzelm@46614
    98
fun restrict_graph G = Graph.restrict (fn x => Graph.get_node G x = 0) G;
traytel@45060
    99
wenzelm@40281
   100
fun nameT (Type (s, [])) = s;
wenzelm@40281
   101
fun t_of s = Type (s, []);
wenzelm@40286
   102
wenzelm@40281
   103
fun sort_of (TFree (_, S)) = SOME S
wenzelm@40281
   104
  | sort_of (TVar (_, S)) = SOME S
wenzelm@40281
   105
  | sort_of _ = NONE;
wenzelm@40281
   106
wenzelm@40281
   107
val is_typeT = fn (Type _) => true | _ => false;
wenzelm@40282
   108
val is_compT = fn (Type (_, _ :: _)) => true | _ => false;
wenzelm@40281
   109
val is_freeT = fn (TFree _) => true | _ => false;
wenzelm@40286
   110
val is_fixedvarT = fn (TVar (xi, _)) => not (Type_Infer.is_param xi) | _ => false;
traytel@41353
   111
val is_funtype = fn (Type ("fun", [_, _])) => true | _ => false;
traytel@51335
   112
traytel@51335
   113
fun mk_identity T = Abs (Name.uu, T, Bound 0);
traytel@43591
   114
val is_identity = fn (Abs (_, _, Bound 0)) => true | _ => false;
wenzelm@40281
   115
traytel@45060
   116
fun instantiate t Ts = Term.subst_TVars
traytel@45060
   117
  ((Term.add_tvar_namesT (fastype_of t) []) ~~ rev Ts) t;
traytel@45060
   118
wenzelm@55303
   119
exception COERCION_GEN_ERROR of unit -> string * Buffer.T;
traytel@54584
   120
wenzelm@55303
   121
infixr ++>  (*composition with deferred error message*)
wenzelm@55303
   122
fun (err : unit -> string * Buffer.T) ++> s =
wenzelm@55303
   123
  err #> apsnd (Buffer.add s);
traytel@54584
   124
wenzelm@55303
   125
fun eval_err err =
wenzelm@55303
   126
  let val (s, buf) = err ()
wenzelm@55303
   127
  in s ^ Markup.markup Markup.text_fold (Buffer.content buf) end;
traytel@54584
   128
wenzelm@55303
   129
fun eval_error err = error (eval_err err);
traytel@45060
   130
traytel@45060
   131
fun inst_collect tye err T U =
traytel@45060
   132
  (case (T, Type_Infer.deref tye U) of
traytel@54584
   133
    (TVar (xi, _), U) => [(xi, U)]
traytel@45060
   134
  | (Type (a, Ts), Type (b, Us)) =>
wenzelm@55303
   135
      if a <> b then eval_error err else inst_collects tye err Ts Us
wenzelm@55303
   136
  | (_, U') => if T <> U' then eval_error err else [])
traytel@45060
   137
and inst_collects tye err Ts Us =
traytel@45060
   138
  fold2 (fn T => fn U => fn is => inst_collect tye err T U @ is) Ts Us [];
traytel@45060
   139
wenzelm@40281
   140
traytel@40836
   141
(* unification *)
wenzelm@40281
   142
wenzelm@40281
   143
exception NO_UNIFIER of string * typ Vartab.table;
wenzelm@40281
   144
wenzelm@40281
   145
fun unify weak ctxt =
wenzelm@40281
   146
  let
wenzelm@42361
   147
    val thy = Proof_Context.theory_of ctxt;
wenzelm@42386
   148
    val arity_sorts = Type.arity_sorts (Context.pretty ctxt) (Sign.tsig_of thy);
wenzelm@40281
   149
wenzelm@40282
   150
wenzelm@40281
   151
    (* adjust sorts of parameters *)
wenzelm@40281
   152
wenzelm@40281
   153
    fun not_of_sort x S' S =
wenzelm@40281
   154
      "Variable " ^ x ^ "::" ^ Syntax.string_of_sort ctxt S' ^ " not of sort " ^
wenzelm@40281
   155
        Syntax.string_of_sort ctxt S;
wenzelm@40281
   156
wenzelm@40281
   157
    fun meet (_, []) tye_idx = tye_idx
wenzelm@40281
   158
      | meet (Type (a, Ts), S) (tye_idx as (tye, _)) =
wenzelm@40281
   159
          meets (Ts, arity_sorts a S handle ERROR msg => raise NO_UNIFIER (msg, tye)) tye_idx
wenzelm@40281
   160
      | meet (TFree (x, S'), S) (tye_idx as (tye, _)) =
wenzelm@40281
   161
          if Sign.subsort thy (S', S) then tye_idx
wenzelm@40281
   162
          else raise NO_UNIFIER (not_of_sort x S' S, tye)
wenzelm@40281
   163
      | meet (TVar (xi, S'), S) (tye_idx as (tye, idx)) =
wenzelm@40281
   164
          if Sign.subsort thy (S', S) then tye_idx
wenzelm@40281
   165
          else if Type_Infer.is_param xi then
wenzelm@40286
   166
            (Vartab.update_new
wenzelm@40286
   167
              (xi, Type_Infer.mk_param idx (Sign.inter_sort thy (S', S))) tye, idx + 1)
wenzelm@40281
   168
          else raise NO_UNIFIER (not_of_sort (Term.string_of_vname xi) S' S, tye)
wenzelm@40281
   169
    and meets (T :: Ts, S :: Ss) (tye_idx as (tye, _)) =
wenzelm@40286
   170
          meets (Ts, Ss) (meet (Type_Infer.deref tye T, S) tye_idx)
wenzelm@40281
   171
      | meets _ tye_idx = tye_idx;
wenzelm@40281
   172
wenzelm@55301
   173
    val weak_meet = if weak then fn _ => I else meet;
wenzelm@40281
   174
wenzelm@40281
   175
wenzelm@40281
   176
    (* occurs check and assignment *)
wenzelm@40281
   177
wenzelm@40281
   178
    fun occurs_check tye xi (TVar (xi', _)) =
wenzelm@40281
   179
          if xi = xi' then raise NO_UNIFIER ("Occurs check!", tye)
wenzelm@40281
   180
          else
wenzelm@40281
   181
            (case Vartab.lookup tye xi' of
wenzelm@40281
   182
              NONE => ()
wenzelm@40281
   183
            | SOME T => occurs_check tye xi T)
wenzelm@40281
   184
      | occurs_check tye xi (Type (_, Ts)) = List.app (occurs_check tye xi) Ts
wenzelm@40281
   185
      | occurs_check _ _ _ = ();
wenzelm@40281
   186
wenzelm@40281
   187
    fun assign xi (T as TVar (xi', _)) S env =
wenzelm@40281
   188
          if xi = xi' then env
wenzelm@40281
   189
          else env |> weak_meet (T, S) |>> Vartab.update_new (xi, T)
wenzelm@40281
   190
      | assign xi T S (env as (tye, _)) =
wenzelm@40281
   191
          (occurs_check tye xi T; env |> weak_meet (T, S) |>> Vartab.update_new (xi, T));
wenzelm@40281
   192
wenzelm@40281
   193
wenzelm@40281
   194
    (* unification *)
wenzelm@40281
   195
wenzelm@40281
   196
    fun show_tycon (a, Ts) =
wenzelm@40281
   197
      quote (Syntax.string_of_typ ctxt (Type (a, replicate (length Ts) dummyT)));
wenzelm@40281
   198
wenzelm@40281
   199
    fun unif (T1, T2) (env as (tye, _)) =
wenzelm@40286
   200
      (case pairself (`Type_Infer.is_paramT o Type_Infer.deref tye) (T1, T2) of
wenzelm@40281
   201
        ((true, TVar (xi, S)), (_, T)) => assign xi T S env
wenzelm@40281
   202
      | ((_, T), (true, TVar (xi, S))) => assign xi T S env
wenzelm@40281
   203
      | ((_, Type (a, Ts)), (_, Type (b, Us))) =>
wenzelm@40281
   204
          if weak andalso null Ts andalso null Us then env
wenzelm@40281
   205
          else if a <> b then
wenzelm@40281
   206
            raise NO_UNIFIER
wenzelm@40281
   207
              ("Clash of types " ^ show_tycon (a, Ts) ^ " and " ^ show_tycon (b, Us), tye)
wenzelm@40281
   208
          else fold unif (Ts ~~ Us) env
wenzelm@40281
   209
      | ((_, T), (_, U)) => if T = U then env else raise NO_UNIFIER ("", tye));
wenzelm@40281
   210
wenzelm@40281
   211
  in unif end;
wenzelm@40281
   212
wenzelm@40281
   213
val weak_unify = unify true;
wenzelm@40281
   214
val strong_unify = unify false;
wenzelm@40281
   215
wenzelm@40281
   216
wenzelm@40281
   217
(* Typ_Graph shortcuts *)
wenzelm@40281
   218
wenzelm@40281
   219
fun get_preds G T = Typ_Graph.all_preds G [T];
wenzelm@40281
   220
fun get_succs G T = Typ_Graph.all_succs G [T];
wenzelm@40281
   221
fun maybe_new_typnode T G = perhaps (try (Typ_Graph.new_node (T, ()))) G;
wenzelm@40281
   222
fun maybe_new_typnodes Ts G = fold maybe_new_typnode Ts G;
wenzelm@44338
   223
fun new_imm_preds G Ts =  (* FIXME inefficient *)
wenzelm@44338
   224
  subtract (op =) Ts (distinct (op =) (maps (Typ_Graph.immediate_preds G) Ts));
wenzelm@44338
   225
fun new_imm_succs G Ts =  (* FIXME inefficient *)
wenzelm@44338
   226
  subtract (op =) Ts (distinct (op =) (maps (Typ_Graph.immediate_succs G) Ts));
wenzelm@40281
   227
wenzelm@40281
   228
wenzelm@40281
   229
(* Graph shortcuts *)
wenzelm@40281
   230
wenzelm@55301
   231
fun maybe_new_node s G = perhaps (try (Graph.new_node s)) G;
wenzelm@55301
   232
fun maybe_new_nodes ss G = fold maybe_new_node ss G;
wenzelm@40281
   233
wenzelm@40281
   234
wenzelm@40281
   235
wenzelm@40281
   236
(** error messages **)
wenzelm@40281
   237
traytel@54584
   238
fun gen_err err msg =
wenzelm@55303
   239
  err ++> ("\nNow trying to infer coercions globally.\n\nCoercion inference failed" ^
wenzelm@55303
   240
    (if msg = "" then "" else ":\n" ^ msg) ^ "\n");
traytel@45060
   241
traytel@54584
   242
val gen_msg = eval_err oo gen_err
traytel@40836
   243
wenzelm@40281
   244
fun prep_output ctxt tye bs ts Ts =
wenzelm@40281
   245
  let
wenzelm@40281
   246
    val (Ts_bTs', ts') = Type_Infer.finish ctxt tye (Ts @ map snd bs, ts);
wenzelm@40281
   247
    val (Ts', Ts'') = chop (length Ts) Ts_bTs';
wenzelm@40281
   248
    fun prep t =
wenzelm@40281
   249
      let val xs = rev (Term.variant_frees t (rev (map fst bs ~~ Ts'')))
wenzelm@49660
   250
      in Term.subst_bounds (map Syntax_Trans.mark_bound_abs xs, t) end;
wenzelm@40281
   251
  in (map prep ts', Ts') end;
wenzelm@40281
   252
wenzelm@40281
   253
fun err_loose i = error ("Loose bound variable: B." ^ string_of_int i);
wenzelm@42383
   254
traytel@40836
   255
fun unif_failed msg =
traytel@40836
   256
  "Type unification failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n\n";
wenzelm@42383
   257
traytel@40836
   258
fun err_appl_msg ctxt msg tye bs t T u U () =
wenzelm@55301
   259
  let val ([t', u'], [T', U']) = prep_output ctxt tye bs [t, u] [T, U] in
wenzelm@55301
   260
    (unif_failed msg ^ Type.appl_error ctxt t' T' u' U' ^ "\n\n",
wenzelm@55303
   261
      Buffer.empty |> Buffer.add "Coercion Inference:\n\n")
wenzelm@55301
   262
  end;
wenzelm@40281
   263
traytel@54584
   264
fun err_list ctxt err tye Ts =
wenzelm@55303
   265
  let val (_, Ts') = prep_output ctxt tye [] [] Ts in
wenzelm@55303
   266
    eval_error (err ++>
wenzelm@55303
   267
      ("\nCannot unify a list of types that should be the same:\n" ^
wenzelm@55303
   268
        Pretty.string_of (Pretty.list "[" "]" (map (Syntax.pretty_typ ctxt) Ts'))))
wenzelm@40281
   269
  end;
wenzelm@40281
   270
traytel@54584
   271
fun err_bound ctxt err tye packs =
wenzelm@40281
   272
  let
wenzelm@40281
   273
    val (ts, Ts) = fold
wenzelm@40281
   274
      (fn (bs, t $ u, U, _, U') => fn (ts, Ts) =>
traytel@40836
   275
        let val (t', T') = prep_output ctxt tye bs [t, u] [U', U]
wenzelm@40282
   276
        in (t' :: ts, T' :: Ts) end)
wenzelm@40281
   277
      packs ([], []);
wenzelm@55303
   278
    val msg =
wenzelm@55303
   279
      Pretty.string_of (Pretty.big_list "Cannot fulfil subtype constraints:"
traytel@45060
   280
        (map2 (fn [t, u] => fn [T, U] =>
wenzelm@40281
   281
          Pretty.block [
wenzelm@42383
   282
            Syntax.pretty_typ ctxt T, Pretty.brk 2, Pretty.str "<:", Pretty.brk 2,
wenzelm@42383
   283
            Syntax.pretty_typ ctxt U, Pretty.brk 3,
wenzelm@42383
   284
            Pretty.str "from function application", Pretty.brk 2,
traytel@45060
   285
            Pretty.block [Syntax.pretty_term ctxt (t $ u)]])
wenzelm@55303
   286
          ts Ts));
wenzelm@55303
   287
  in eval_error (err ++> ("\n" ^ msg)) end;
wenzelm@40281
   288
wenzelm@40281
   289
wenzelm@40281
   290
wenzelm@40281
   291
(** constraint generation **)
wenzelm@40281
   292
traytel@51319
   293
fun update_coerce_arg ctxt old t =
traytel@51319
   294
  let
traytel@51319
   295
    val mk_coerce_args = the_default [] o Symtab.lookup (coerce_args_of ctxt);
traytel@51319
   296
    fun update _ [] = old
traytel@51327
   297
      | update 0 (coerce :: _) = (case coerce of LEAVE => old | PERMIT => true | FORBID => false)
traytel@51319
   298
      | update n (_ :: cs) = update (n - 1) cs;
traytel@51319
   299
    val (f, n) = Term.strip_comb (Type.strip_constraints t) ||> length;
traytel@51319
   300
  in
traytel@51319
   301
    update n (case f of Const (name, _) => mk_coerce_args name | _ => [])
traytel@51319
   302
  end;
traytel@51319
   303
traytel@40836
   304
fun generate_constraints ctxt err =
wenzelm@40281
   305
  let
traytel@51319
   306
    fun gen _ cs _ (Const (_, T)) tye_idx = (T, tye_idx, cs)
traytel@51319
   307
      | gen _ cs _ (Free (_, T)) tye_idx = (T, tye_idx, cs)
traytel@51319
   308
      | gen _ cs _ (Var (_, T)) tye_idx = (T, tye_idx, cs)
traytel@51319
   309
      | gen _ cs bs (Bound i) tye_idx =
wenzelm@43278
   310
          (snd (nth bs i handle General.Subscript => err_loose i), tye_idx, cs)
traytel@51319
   311
      | gen coerce cs bs (Abs (x, T, t)) tye_idx =
traytel@51319
   312
          let val (U, tye_idx', cs') = gen coerce cs ((x, T) :: bs) t tye_idx
wenzelm@40281
   313
          in (T --> U, tye_idx', cs') end
traytel@51319
   314
      | gen coerce cs bs (t $ u) tye_idx =
wenzelm@40281
   315
          let
traytel@51319
   316
            val (T, tye_idx', cs') = gen coerce cs bs t tye_idx;
traytel@51319
   317
            val coerce' = update_coerce_arg ctxt coerce t;
traytel@51319
   318
            val (U', (tye, idx), cs'') = gen coerce' cs' bs u tye_idx';
wenzelm@40286
   319
            val U = Type_Infer.mk_param idx [];
wenzelm@40286
   320
            val V = Type_Infer.mk_param (idx + 1) [];
traytel@45060
   321
            val tye_idx'' = strong_unify ctxt (U --> V, T) (tye, idx + 2)
traytel@41353
   322
              handle NO_UNIFIER (msg, _) => error (gen_msg err msg);
wenzelm@40281
   323
            val error_pack = (bs, t $ u, U, V, U');
wenzelm@52432
   324
          in
traytel@51319
   325
            if coerce'
traytel@51319
   326
            then (V, tye_idx'', ((U', U), error_pack) :: cs'')
traytel@51319
   327
            else (V,
traytel@51319
   328
              strong_unify ctxt (U, U') tye_idx''
traytel@51319
   329
                handle NO_UNIFIER (msg, _) => error (gen_msg err msg),
traytel@51319
   330
              cs'')
traytel@51319
   331
          end;
wenzelm@40281
   332
  in
traytel@51319
   333
    gen true [] []
wenzelm@40281
   334
  end;
wenzelm@40281
   335
wenzelm@40281
   336
wenzelm@40281
   337
wenzelm@40281
   338
(** constraint resolution **)
wenzelm@40281
   339
wenzelm@40281
   340
exception BOUND_ERROR of string;
wenzelm@40281
   341
traytel@40836
   342
fun process_constraints ctxt err cs tye_idx =
wenzelm@40281
   343
  let
wenzelm@42388
   344
    val thy = Proof_Context.theory_of ctxt;
wenzelm@42388
   345
wenzelm@40285
   346
    val coes_graph = coes_graph_of ctxt;
wenzelm@40285
   347
    val tmaps = tmaps_of ctxt;
wenzelm@42388
   348
    val arity_sorts = Type.arity_sorts (Context.pretty ctxt) (Sign.tsig_of thy);
wenzelm@40281
   349
wenzelm@40281
   350
    fun split_cs _ [] = ([], [])
wenzelm@40282
   351
      | split_cs f (c :: cs) =
wenzelm@40281
   352
          (case pairself f (fst c) of
wenzelm@40281
   353
            (false, false) => apsnd (cons c) (split_cs f cs)
wenzelm@40281
   354
          | _ => apfst (cons c) (split_cs f cs));
wenzelm@42383
   355
traytel@41353
   356
    fun unify_list (T :: Ts) tye_idx =
wenzelm@42383
   357
      fold (fn U => fn tye_idx' => strong_unify ctxt (T, U) tye_idx') Ts tye_idx;
wenzelm@40281
   358
wenzelm@40282
   359
wenzelm@40281
   360
    (* check whether constraint simplification will terminate using weak unification *)
wenzelm@40282
   361
traytel@41353
   362
    val _ = fold (fn (TU, _) => fn tye_idx =>
traytel@41353
   363
      weak_unify ctxt TU tye_idx handle NO_UNIFIER (msg, _) =>
traytel@40836
   364
        error (gen_msg err ("weak unification of subtype constraints fails\n" ^ msg))) cs tye_idx;
wenzelm@40281
   365
wenzelm@40281
   366
wenzelm@40281
   367
    (* simplify constraints *)
wenzelm@40282
   368
wenzelm@40281
   369
    fun simplify_constraints cs tye_idx =
wenzelm@40281
   370
      let
wenzelm@40281
   371
        fun contract a Ts Us error_pack done todo tye idx =
wenzelm@40281
   372
          let
wenzelm@40281
   373
            val arg_var =
wenzelm@40281
   374
              (case Symtab.lookup tmaps a of
wenzelm@40281
   375
                (*everything is invariant for unknown constructors*)
wenzelm@40281
   376
                NONE => replicate (length Ts) INVARIANT
wenzelm@40281
   377
              | SOME av => snd av);
wenzelm@40281
   378
            fun new_constraints (variance, constraint) (cs, tye_idx) =
wenzelm@40281
   379
              (case variance of
wenzelm@40281
   380
                COVARIANT => (constraint :: cs, tye_idx)
wenzelm@40281
   381
              | CONTRAVARIANT => (swap constraint :: cs, tye_idx)
traytel@41353
   382
              | INVARIANT_TO T => (cs, unify_list [T, fst constraint, snd constraint] tye_idx
wenzelm@42383
   383
                  handle NO_UNIFIER (msg, _) =>
traytel@54584
   384
                    err_list ctxt (gen_err err
traytel@54584
   385
                      ("failed to unify invariant arguments w.r.t. to the known map function\n" ^
traytel@54584
   386
                        msg))
traytel@45060
   387
                      (fst tye_idx) (T :: Ts))
wenzelm@40281
   388
              | INVARIANT => (cs, strong_unify ctxt constraint tye_idx
wenzelm@42383
   389
                  handle NO_UNIFIER (msg, _) =>
traytel@51248
   390
                    error (gen_msg err ("failed to unify invariant arguments\n" ^ msg))));
wenzelm@40281
   391
            val (new, (tye', idx')) = apfst (fn cs => (cs ~~ replicate (length cs) error_pack))
wenzelm@40281
   392
              (fold new_constraints (arg_var ~~ (Ts ~~ Us)) ([], (tye, idx)));
traytel@49142
   393
            val test_update = is_typeT orf is_freeT orf is_fixedvarT;
wenzelm@40281
   394
            val (ch, done') =
traytel@51246
   395
              done
traytel@51246
   396
              |> map (apfst (pairself (Type_Infer.deref tye')))
traytel@51246
   397
              |> (if not (null new) then rpair []  else split_cs test_update);
wenzelm@40281
   398
            val todo' = ch @ todo;
wenzelm@40281
   399
          in
wenzelm@40281
   400
            simplify done' (new @ todo') (tye', idx')
wenzelm@40281
   401
          end
wenzelm@40281
   402
        (*xi is definitely a parameter*)
wenzelm@40281
   403
        and expand varleq xi S a Ts error_pack done todo tye idx =
wenzelm@40281
   404
          let
wenzelm@40281
   405
            val n = length Ts;
wenzelm@40286
   406
            val args = map2 Type_Infer.mk_param (idx upto idx + n - 1) (arity_sorts a S);
wenzelm@40281
   407
            val tye' = Vartab.update_new (xi, Type(a, args)) tye;
wenzelm@40286
   408
            val (ch, done') = split_cs (is_compT o Type_Infer.deref tye') done;
wenzelm@40281
   409
            val todo' = ch @ todo;
wenzelm@40281
   410
            val new =
wenzelm@40281
   411
              if varleq then (Type(a, args), Type (a, Ts))
wenzelm@40286
   412
              else (Type (a, Ts), Type (a, args));
wenzelm@40281
   413
          in
wenzelm@40281
   414
            simplify done' ((new, error_pack) :: todo') (tye', idx + n)
wenzelm@40281
   415
          end
wenzelm@40281
   416
        (*TU is a pair of a parameter and a free/fixed variable*)
traytel@41353
   417
        and eliminate TU done todo tye idx =
wenzelm@40281
   418
          let
wenzelm@40286
   419
            val [TVar (xi, S)] = filter Type_Infer.is_paramT TU;
wenzelm@40286
   420
            val [T] = filter_out Type_Infer.is_paramT TU;
wenzelm@40281
   421
            val SOME S' = sort_of T;
wenzelm@40281
   422
            val test_update = if is_freeT T then is_freeT else is_fixedvarT;
wenzelm@40281
   423
            val tye' = Vartab.update_new (xi, T) tye;
wenzelm@40286
   424
            val (ch, done') = split_cs (test_update o Type_Infer.deref tye') done;
wenzelm@40281
   425
            val todo' = ch @ todo;
wenzelm@40281
   426
          in
wenzelm@42388
   427
            if Sign.subsort thy (S', S) (*TODO check this*)
wenzelm@40281
   428
            then simplify done' todo' (tye', idx)
traytel@40836
   429
            else error (gen_msg err "sort mismatch")
wenzelm@40281
   430
          end
wenzelm@40281
   431
        and simplify done [] tye_idx = (done, tye_idx)
wenzelm@40281
   432
          | simplify done (((T, U), error_pack) :: todo) (tye_idx as (tye, idx)) =
wenzelm@40286
   433
              (case (Type_Infer.deref tye T, Type_Infer.deref tye U) of
traytel@45060
   434
                (T1 as Type (a, []), T2 as Type (b, [])) =>
wenzelm@40281
   435
                  if a = b then simplify done todo tye_idx
wenzelm@40281
   436
                  else if Graph.is_edge coes_graph (a, b) then simplify done todo tye_idx
wenzelm@55303
   437
                  else
wenzelm@55303
   438
                    error (gen_msg err (quote (Syntax.string_of_typ ctxt T1) ^
wenzelm@55303
   439
                      " is not a subtype of " ^ quote (Syntax.string_of_typ ctxt T2)))
wenzelm@40281
   440
              | (Type (a, Ts), Type (b, Us)) =>
wenzelm@55303
   441
                  if a <> b then
wenzelm@55303
   442
                    error (gen_msg err "different constructors") (fst tye_idx) error_pack
wenzelm@40281
   443
                  else contract a Ts Us error_pack done todo tye idx
wenzelm@40282
   444
              | (TVar (xi, S), Type (a, Ts as (_ :: _))) =>
wenzelm@40281
   445
                  expand true xi S a Ts error_pack done todo tye idx
wenzelm@40282
   446
              | (Type (a, Ts as (_ :: _)), TVar (xi, S)) =>
wenzelm@40281
   447
                  expand false xi S a Ts error_pack done todo tye idx
wenzelm@40281
   448
              | (T, U) =>
wenzelm@40281
   449
                  if T = U then simplify done todo tye_idx
wenzelm@40282
   450
                  else if exists (is_freeT orf is_fixedvarT) [T, U] andalso
wenzelm@40286
   451
                    exists Type_Infer.is_paramT [T, U]
traytel@41353
   452
                  then eliminate [T, U] done todo tye idx
wenzelm@40281
   453
                  else if exists (is_freeT orf is_fixedvarT) [T, U]
traytel@40836
   454
                  then error (gen_msg err "not eliminated free/fixed variables")
wenzelm@40282
   455
                  else simplify (((T, U), error_pack) :: done) todo tye_idx);
wenzelm@40281
   456
      in
wenzelm@40281
   457
        simplify [] cs tye_idx
wenzelm@40281
   458
      end;
wenzelm@40281
   459
wenzelm@40281
   460
wenzelm@40281
   461
    (* do simplification *)
wenzelm@40282
   462
wenzelm@40281
   463
    val (cs', tye_idx') = simplify_constraints cs tye_idx;
wenzelm@42383
   464
wenzelm@42383
   465
    fun find_error_pack lower T' = map_filter
traytel@40836
   466
      (fn ((T, U), pack) => if if lower then T' = U else T' = T then SOME pack else NONE) cs';
wenzelm@42383
   467
wenzelm@42383
   468
    fun find_cycle_packs nodes =
traytel@40836
   469
      let
traytel@40836
   470
        val (but_last, last) = split_last nodes
traytel@40836
   471
        val pairs = (last, hd nodes) :: (but_last ~~ tl nodes);
traytel@40836
   472
      in
traytel@40836
   473
        map_filter
wenzelm@40838
   474
          (fn (TU, pack) => if member (op =) pairs TU then SOME pack else NONE)
traytel@40836
   475
          cs'
traytel@40836
   476
      end;
wenzelm@40281
   477
wenzelm@40281
   478
    (*styps stands either for supertypes or for subtypes of a type T
wenzelm@40281
   479
      in terms of the subtype-relation (excluding T itself)*)
wenzelm@40282
   480
    fun styps super T =
wenzelm@44338
   481
      (if super then Graph.immediate_succs else Graph.immediate_preds) coes_graph T
wenzelm@40281
   482
        handle Graph.UNDEF _ => [];
wenzelm@40281
   483
wenzelm@40282
   484
    fun minmax sup (T :: Ts) =
wenzelm@40281
   485
      let
wenzelm@40281
   486
        fun adjust T U = if sup then (T, U) else (U, T);
wenzelm@40281
   487
        fun extract T [] = T
wenzelm@40282
   488
          | extract T (U :: Us) =
wenzelm@40281
   489
              if Graph.is_edge coes_graph (adjust T U) then extract T Us
wenzelm@40281
   490
              else if Graph.is_edge coes_graph (adjust U T) then extract U Us
traytel@40836
   491
              else raise BOUND_ERROR "uncomparable types in type list";
wenzelm@40281
   492
      in
wenzelm@40281
   493
        t_of (extract T Ts)
wenzelm@40281
   494
      end;
wenzelm@40281
   495
wenzelm@40282
   496
    fun ex_styp_of_sort super T styps_and_sorts =
wenzelm@40281
   497
      let
wenzelm@40281
   498
        fun adjust T U = if super then (T, U) else (U, T);
wenzelm@40282
   499
        fun styp_test U Ts = forall
wenzelm@40281
   500
          (fn T => T = U orelse Graph.is_edge coes_graph (adjust U T)) Ts;
wenzelm@55301
   501
        fun fitting Ts S U = Sign.of_sort thy (t_of U, S) andalso styp_test U Ts;
wenzelm@40281
   502
      in
wenzelm@40281
   503
        forall (fn (Ts, S) => exists (fitting Ts S) (T :: styps super T)) styps_and_sorts
wenzelm@40281
   504
      end;
wenzelm@40281
   505
wenzelm@40281
   506
    (* computes the tightest possible, correct assignment for 'a::S
wenzelm@40281
   507
       e.g. in the supremum case (sup = true):
wenzelm@40281
   508
               ------- 'a::S---
wenzelm@40281
   509
              /        /    \  \
wenzelm@40281
   510
             /        /      \  \
wenzelm@40281
   511
        'b::C1   'c::C2 ...  T1 T2 ...
wenzelm@40281
   512
wenzelm@40281
   513
       sorts - list of sorts [C1, C2, ...]
wenzelm@40281
   514
       T::Ts - non-empty list of base types [T1, T2, ...]
wenzelm@40281
   515
    *)
wenzelm@40282
   516
    fun tightest sup S styps_and_sorts (T :: Ts) =
wenzelm@40281
   517
      let
wenzelm@42388
   518
        fun restriction T = Sign.of_sort thy (t_of T, S)
wenzelm@40281
   519
          andalso ex_styp_of_sort (not sup) T styps_and_sorts;
wenzelm@40281
   520
        fun candidates T = inter (op =) (filter restriction (T :: styps sup T));
wenzelm@40281
   521
      in
wenzelm@40281
   522
        (case fold candidates Ts (filter restriction (T :: styps sup T)) of
traytel@40836
   523
          [] => raise BOUND_ERROR ("no " ^ (if sup then "supremum" else "infimum"))
wenzelm@40281
   524
        | [T] => t_of T
wenzelm@40281
   525
        | Ts => minmax sup Ts)
wenzelm@40281
   526
      end;
wenzelm@40281
   527
wenzelm@40281
   528
    fun build_graph G [] tye_idx = (G, tye_idx)
wenzelm@40282
   529
      | build_graph G ((T, U) :: cs) tye_idx =
wenzelm@40281
   530
        if T = U then build_graph G cs tye_idx
wenzelm@40281
   531
        else
wenzelm@40281
   532
          let
wenzelm@40281
   533
            val G' = maybe_new_typnodes [T, U] G;
traytel@45059
   534
            val (G'', tye_idx') = (Typ_Graph.add_edge_acyclic (T, U) G', tye_idx)
wenzelm@40281
   535
              handle Typ_Graph.CYCLES cycles =>
wenzelm@40281
   536
                let
wenzelm@42383
   537
                  val (tye, idx) =
wenzelm@42383
   538
                    fold
traytel@40836
   539
                      (fn cycle => fn tye_idx' => (unify_list cycle tye_idx'
wenzelm@42383
   540
                        handle NO_UNIFIER (msg, _) =>
wenzelm@42383
   541
                          err_bound ctxt
traytel@54584
   542
                            (gen_err err ("constraint cycle not unifiable\n" ^ msg)) (fst tye_idx)
traytel@40836
   543
                            (find_cycle_packs cycle)))
traytel@40836
   544
                      cycles tye_idx
wenzelm@40281
   545
                in
traytel@40836
   546
                  collapse (tye, idx) cycles G
traytel@40836
   547
                end
wenzelm@40281
   548
          in
wenzelm@40281
   549
            build_graph G'' cs tye_idx'
wenzelm@40281
   550
          end
traytel@40836
   551
    and collapse (tye, idx) cycles G = (*nodes non-empty list*)
wenzelm@40281
   552
      let
traytel@40836
   553
        (*all cycles collapse to one node,
traytel@40836
   554
          because all of them share at least the nodes x and y*)
traytel@40836
   555
        val nodes = (distinct (op =) (flat cycles));
traytel@40836
   556
        val T = Type_Infer.deref tye (hd nodes);
wenzelm@40281
   557
        val P = new_imm_preds G nodes;
wenzelm@40281
   558
        val S = new_imm_succs G nodes;
wenzelm@46665
   559
        val G' = fold Typ_Graph.del_node (tl nodes) G;
traytel@40836
   560
        fun check_and_gen super T' =
traytel@40836
   561
          let val U = Type_Infer.deref tye T';
traytel@40836
   562
          in
traytel@40836
   563
            if not (is_typeT T) orelse not (is_typeT U) orelse T = U
traytel@40836
   564
            then if super then (hd nodes, T') else (T', hd nodes)
wenzelm@42383
   565
            else
wenzelm@42383
   566
              if super andalso
traytel@40836
   567
                Graph.is_edge coes_graph (nameT T, nameT U) then (hd nodes, T')
wenzelm@42383
   568
              else if not super andalso
traytel@40836
   569
                Graph.is_edge coes_graph (nameT U, nameT T) then (T', hd nodes)
wenzelm@55303
   570
              else
wenzelm@55303
   571
                err_bound ctxt (gen_err err "cycle elimination produces inconsistent graph")
wenzelm@55303
   572
                  (fst tye_idx)
wenzelm@55303
   573
                  (maps find_cycle_packs cycles @ find_error_pack super T')
traytel@40836
   574
          end;
wenzelm@40281
   575
      in
traytel@40836
   576
        build_graph G' (map (check_and_gen false) P @ map (check_and_gen true) S) (tye, idx)
wenzelm@40281
   577
      end;
wenzelm@40281
   578
wenzelm@40281
   579
    fun assign_bound lower G key (tye_idx as (tye, _)) =
wenzelm@40286
   580
      if Type_Infer.is_paramT (Type_Infer.deref tye key) then
wenzelm@40281
   581
        let
wenzelm@40286
   582
          val TVar (xi, S) = Type_Infer.deref tye key;
wenzelm@40281
   583
          val get_bound = if lower then get_preds else get_succs;
wenzelm@40281
   584
          val raw_bound = get_bound G key;
wenzelm@40286
   585
          val bound = map (Type_Infer.deref tye) raw_bound;
wenzelm@40286
   586
          val not_params = filter_out Type_Infer.is_paramT bound;
wenzelm@40282
   587
          fun to_fulfil T =
wenzelm@40281
   588
            (case sort_of T of
wenzelm@40281
   589
              NONE => NONE
wenzelm@40282
   590
            | SOME S =>
wenzelm@40286
   591
                SOME
wenzelm@40286
   592
                  (map nameT
wenzelm@42405
   593
                    (filter_out Type_Infer.is_paramT
wenzelm@42405
   594
                      (map (Type_Infer.deref tye) (get_bound G T))), S));
wenzelm@40281
   595
          val styps_and_sorts = distinct (op =) (map_filter to_fulfil raw_bound);
wenzelm@40281
   596
          val assignment =
wenzelm@40281
   597
            if null bound orelse null not_params then NONE
wenzelm@40281
   598
            else SOME (tightest lower S styps_and_sorts (map nameT not_params)
traytel@54584
   599
                handle BOUND_ERROR msg => err_bound ctxt (gen_err err msg) tye
wenzelm@55301
   600
                  (maps (find_error_pack (not lower)) raw_bound));
wenzelm@40281
   601
        in
wenzelm@40281
   602
          (case assignment of
wenzelm@40281
   603
            NONE => tye_idx
wenzelm@40281
   604
          | SOME T =>
wenzelm@40286
   605
              if Type_Infer.is_paramT T then tye_idx
wenzelm@40281
   606
              else if lower then (*upper bound check*)
wenzelm@40281
   607
                let
wenzelm@40286
   608
                  val other_bound = map (Type_Infer.deref tye) (get_succs G key);
wenzelm@40281
   609
                  val s = nameT T;
wenzelm@40281
   610
                in
wenzelm@40281
   611
                  if subset (op = o apfst nameT) (filter is_typeT other_bound, s :: styps true s)
wenzelm@40281
   612
                  then apfst (Vartab.update (xi, T)) tye_idx
wenzelm@55303
   613
                  else
wenzelm@55303
   614
                    err_bound ctxt
wenzelm@55303
   615
                      (gen_err err
wenzelm@55303
   616
                        (Pretty.string_of (Pretty.block
wenzelm@55303
   617
                          [Pretty.str "assigned base type", Pretty.brk 1,
wenzelm@55303
   618
                            Pretty.quote (Syntax.pretty_typ ctxt T), Pretty.brk 1,
wenzelm@55303
   619
                            Pretty.str "clashes with the upper bound of variable", Pretty.brk 1,
wenzelm@55303
   620
                            Syntax.pretty_typ ctxt (TVar (xi, S))])))
wenzelm@55303
   621
                      tye
wenzelm@55303
   622
                      (maps (find_error_pack lower) other_bound)
wenzelm@40281
   623
                end
wenzelm@40281
   624
              else apfst (Vartab.update (xi, T)) tye_idx)
wenzelm@40281
   625
        end
wenzelm@40281
   626
      else tye_idx;
wenzelm@40281
   627
wenzelm@40281
   628
    val assign_lb = assign_bound true;
wenzelm@40281
   629
    val assign_ub = assign_bound false;
wenzelm@40281
   630
wenzelm@40281
   631
    fun assign_alternating ts' ts G tye_idx =
wenzelm@40281
   632
      if ts' = ts then tye_idx
wenzelm@40281
   633
      else
wenzelm@40281
   634
        let
wenzelm@40281
   635
          val (tye_idx' as (tye, _)) = fold (assign_lb G) ts tye_idx
wenzelm@40281
   636
            |> fold (assign_ub G) ts;
wenzelm@40281
   637
        in
wenzelm@42383
   638
          assign_alternating ts
traytel@40836
   639
            (filter (Type_Infer.is_paramT o Type_Infer.deref tye) ts) G tye_idx'
wenzelm@40281
   640
        end;
wenzelm@40281
   641
wenzelm@40281
   642
    (*Unify all weakly connected components of the constraint forest,
wenzelm@40282
   643
      that contain only params. These are the only WCCs that contain
wenzelm@40281
   644
      params anyway.*)
wenzelm@40281
   645
    fun unify_params G (tye_idx as (tye, _)) =
wenzelm@40281
   646
      let
wenzelm@40286
   647
        val max_params =
wenzelm@40286
   648
          filter (Type_Infer.is_paramT o Type_Infer.deref tye) (Typ_Graph.maximals G);
wenzelm@40281
   649
        val to_unify = map (fn T => T :: get_preds G T) max_params;
wenzelm@40281
   650
      in
wenzelm@42383
   651
        fold
traytel@40836
   652
          (fn Ts => fn tye_idx' => unify_list Ts tye_idx'
traytel@54584
   653
            handle NO_UNIFIER (msg, _) => err_list ctxt (gen_err err msg) (fst tye_idx) Ts)
traytel@40836
   654
          to_unify tye_idx
wenzelm@40281
   655
      end;
wenzelm@40281
   656
wenzelm@40281
   657
    fun solve_constraints G tye_idx = tye_idx
wenzelm@40281
   658
      |> assign_alternating [] (Typ_Graph.keys G) G
wenzelm@40281
   659
      |> unify_params G;
wenzelm@40281
   660
  in
wenzelm@40281
   661
    build_graph Typ_Graph.empty (map fst cs') tye_idx'
wenzelm@40281
   662
      |-> solve_constraints
wenzelm@40281
   663
  end;
wenzelm@40281
   664
wenzelm@40281
   665
wenzelm@40281
   666
wenzelm@40281
   667
(** coercion insertion **)
wenzelm@40281
   668
traytel@45060
   669
fun gen_coercion ctxt err tye TU =
traytel@45060
   670
  let
traytel@45060
   671
    fun gen (T1, T2) = (case pairself (Type_Infer.deref tye) (T1, T2) of
traytel@45060
   672
        (T1 as (Type (a, [])), T2 as (Type (b, []))) =>
traytel@45060
   673
            if a = b
traytel@51335
   674
            then mk_identity T1
traytel@45060
   675
            else
traytel@45060
   676
              (case Symreltab.lookup (coes_of ctxt) (a, b) of
wenzelm@55303
   677
                NONE =>
wenzelm@55303
   678
                  raise COERCION_GEN_ERROR (err ++>
wenzelm@55303
   679
                    (Pretty.string_of o Pretty.block)
wenzelm@55303
   680
                      [Pretty.quote (Syntax.pretty_typ ctxt T1), Pretty.brk 1,
wenzelm@55303
   681
                        Pretty.str "is not a subtype of", Pretty.brk 1,
wenzelm@55303
   682
                        Pretty.quote (Syntax.pretty_typ ctxt T2)])
traytel@45060
   683
              | SOME (co, _) => co)
traytel@45102
   684
      | (T1 as Type (a, Ts), T2 as Type (b, Us)) =>
traytel@45060
   685
            if a <> b
traytel@45060
   686
            then
traytel@45060
   687
              (case Symreltab.lookup (coes_of ctxt) (a, b) of
traytel@45060
   688
                (*immediate error - cannot fix complex coercion with the global algorithm*)
wenzelm@55303
   689
                NONE =>
wenzelm@55303
   690
                  eval_error (err ++>
wenzelm@55304
   691
                    ("No coercion known for type constructors: " ^
wenzelm@55304
   692
                      quote (Proof_Context.markup_type ctxt a) ^ " and " ^
wenzelm@55304
   693
                      quote (Proof_Context.markup_type ctxt b)))
traytel@45060
   694
              | SOME (co, ((Ts', Us'), _)) =>
traytel@45060
   695
                  let
traytel@45060
   696
                    val co_before = gen (T1, Type (a, Ts'));
traytel@45060
   697
                    val coT = range_type (fastype_of co_before);
wenzelm@55303
   698
                    val insts =
wenzelm@55303
   699
                      inst_collect tye (err ++> "Could not insert complex coercion")
wenzelm@55303
   700
                        (domain_type (fastype_of co)) coT;
traytel@45060
   701
                    val co' = Term.subst_TVars insts co;
traytel@45060
   702
                    val co_after = gen (Type (b, (map (typ_subst_TVars insts) Us')), T2);
traytel@45060
   703
                  in
traytel@45060
   704
                    Abs (Name.uu, T1, Library.foldr (op $)
traytel@45060
   705
                      (filter (not o is_identity) [co_after, co', co_before], Bound 0))
traytel@45060
   706
                  end)
traytel@45060
   707
            else
traytel@45060
   708
              let
traytel@51335
   709
                fun sub_co (COVARIANT, TU) = (SOME (gen TU), NONE)
traytel@51335
   710
                  | sub_co (CONTRAVARIANT, TU) = (SOME (gen (swap TU)), NONE)
traytel@51335
   711
                  | sub_co (INVARIANT, (T, _)) = (NONE, SOME T)
traytel@51335
   712
                  | sub_co (INVARIANT_TO T, _) = (NONE, NONE);
traytel@45060
   713
                fun ts_of [] = []
traytel@45060
   714
                  | ts_of (Type ("fun", [x1, x2]) :: xs) = x1 :: x2 :: (ts_of xs);
traytel@45060
   715
              in
traytel@45060
   716
                (case Symtab.lookup (tmaps_of ctxt) a of
traytel@45102
   717
                  NONE =>
traytel@45102
   718
                    if Type.could_unify (T1, T2)
traytel@51335
   719
                    then mk_identity T1
wenzelm@55303
   720
                    else
wenzelm@55303
   721
                      raise COERCION_GEN_ERROR
wenzelm@55304
   722
                        (err ++>
wenzelm@55304
   723
                          ("No map function for " ^ quote (Proof_Context.markup_type ctxt a)
wenzelm@55304
   724
                            ^ " known"))
traytel@51335
   725
                | SOME (tmap, variances) =>
traytel@45060
   726
                    let
traytel@51335
   727
                      val (used_coes, invarTs) =
traytel@51335
   728
                        map_split sub_co (variances ~~ (Ts ~~ Us))
traytel@51335
   729
                        |>> map_filter I
traytel@51335
   730
                        ||> map_filter I;
traytel@51335
   731
                      val Tinsts = ts_of (map fastype_of used_coes) @ invarTs;
traytel@45060
   732
                    in
traytel@45060
   733
                      if null (filter (not o is_identity) used_coes)
traytel@51335
   734
                      then mk_identity (Type (a, Ts))
traytel@51335
   735
                      else Term.list_comb (instantiate tmap Tinsts, used_coes)
traytel@45060
   736
                    end)
traytel@45060
   737
              end
traytel@45060
   738
      | (T, U) =>
traytel@45060
   739
            if Type.could_unify (T, U)
traytel@51335
   740
            then mk_identity T
wenzelm@55303
   741
            else raise COERCION_GEN_ERROR (err ++>
wenzelm@55303
   742
              (Pretty.string_of o Pretty.block)
wenzelm@55303
   743
               [Pretty.str "Cannot generate coercion from", Pretty.brk 1,
wenzelm@55303
   744
                Pretty.quote (Syntax.pretty_typ ctxt T), Pretty.brk 1,
wenzelm@55303
   745
                Pretty.str "to", Pretty.brk 1,
wenzelm@55303
   746
                Pretty.quote (Syntax.pretty_typ ctxt U)]));
traytel@45060
   747
  in
traytel@45060
   748
    gen TU
traytel@45060
   749
  end;
traytel@40836
   750
traytel@45060
   751
fun function_of ctxt err tye T =
traytel@45060
   752
  (case Type_Infer.deref tye T of
traytel@45060
   753
    Type (C, Ts) =>
traytel@45060
   754
      (case Symreltab.lookup (coes_of ctxt) (C, "fun") of
wenzelm@55304
   755
        NONE =>
wenzelm@55304
   756
          eval_error (err ++> ("No complex coercion from " ^
wenzelm@55304
   757
            quote (Proof_Context.markup_type ctxt C) ^ " to " ^
wenzelm@55304
   758
            quote (Proof_Context.markup_type ctxt "fun")))
traytel@45060
   759
      | SOME (co, ((Ts', _), _)) =>
traytel@45060
   760
        let
traytel@45060
   761
          val co_before = gen_coercion ctxt err tye (Type (C, Ts), Type (C, Ts'));
traytel@45060
   762
          val coT = range_type (fastype_of co_before);
wenzelm@55303
   763
          val insts =
wenzelm@55303
   764
            inst_collect tye (err ++> "Could not insert complex coercion")
wenzelm@55303
   765
              (domain_type (fastype_of co)) coT;
traytel@45060
   766
          val co' = Term.subst_TVars insts co;
traytel@45060
   767
        in
traytel@45060
   768
          Abs (Name.uu, Type (C, Ts), Library.foldr (op $)
traytel@45060
   769
            (filter (not o is_identity) [co', co_before], Bound 0))
traytel@45060
   770
        end)
wenzelm@55303
   771
  | T' =>
wenzelm@55303
   772
      eval_error (err ++>
wenzelm@55303
   773
        (Pretty.string_of o Pretty.block)
wenzelm@55303
   774
         [Pretty.str "No complex coercion from", Pretty.brk 1,
wenzelm@55304
   775
          Pretty.quote (Syntax.pretty_typ ctxt T'), Pretty.brk 1,
wenzelm@55304
   776
          Pretty.str "to", Pretty.brk 1, Proof_Context.pretty_type ctxt "fun"]));
traytel@45060
   777
traytel@45060
   778
fun insert_coercions ctxt (tye, idx) ts =
wenzelm@40281
   779
  let
traytel@45060
   780
    fun insert _ (Const (c, T)) = (Const (c, T), T)
traytel@45060
   781
      | insert _ (Free (x, T)) = (Free (x, T), T)
traytel@45060
   782
      | insert _ (Var (xi, T)) = (Var (xi, T), T)
wenzelm@40281
   783
      | insert bs (Bound i) =
wenzelm@43278
   784
          let val T = nth bs i handle General.Subscript => err_loose i;
wenzelm@40281
   785
          in (Bound i, T) end
wenzelm@40281
   786
      | insert bs (Abs (x, T, t)) =
traytel@45060
   787
          let val (t', T') = insert (T :: bs) t;
traytel@45060
   788
          in (Abs (x, T, t'), T --> T') end
wenzelm@40281
   789
      | insert bs (t $ u) =
wenzelm@40281
   790
          let
traytel@45060
   791
            val (t', Type ("fun", [U, T])) = apsnd (Type_Infer.deref tye) (insert bs t);
wenzelm@40281
   792
            val (u', U') = insert bs u;
wenzelm@40281
   793
          in
traytel@40836
   794
            if can (fn TU => strong_unify ctxt TU (tye, 0)) (U, U')
traytel@40836
   795
            then (t' $ u', T)
wenzelm@55303
   796
            else (t' $ (gen_coercion ctxt (K ("", Buffer.empty)) tye (U', U) $ u'), T)
wenzelm@40281
   797
          end
wenzelm@40281
   798
  in
wenzelm@40281
   799
    map (fst o insert []) ts
wenzelm@40281
   800
  end;
wenzelm@40281
   801
wenzelm@40281
   802
wenzelm@40281
   803
wenzelm@40281
   804
(** assembling the pipeline **)
wenzelm@40281
   805
wenzelm@42398
   806
fun coercion_infer_types ctxt raw_ts =
wenzelm@40281
   807
  let
wenzelm@42405
   808
    val (idx, ts) = Type_Infer_Context.prepare ctxt raw_ts;
wenzelm@40281
   809
traytel@51319
   810
    fun inf _ _ (t as (Const (_, T))) tye_idx = (t, T, tye_idx)
traytel@51319
   811
      | inf _ _ (t as (Free (_, T))) tye_idx = (t, T, tye_idx)
traytel@51319
   812
      | inf _ _ (t as (Var (_, T))) tye_idx = (t, T, tye_idx)
traytel@51319
   813
      | inf _ bs (t as (Bound i)) tye_idx =
wenzelm@43278
   814
          (t, snd (nth bs i handle General.Subscript => err_loose i), tye_idx)
traytel@51319
   815
      | inf coerce bs (Abs (x, T, t)) tye_idx =
traytel@51319
   816
          let val (t', U, tye_idx') = inf coerce ((x, T) :: bs) t tye_idx
traytel@40836
   817
          in (Abs (x, T, t'), T --> U, tye_idx') end
traytel@51319
   818
      | inf coerce bs (t $ u) tye_idx =
traytel@40836
   819
          let
traytel@51319
   820
            val (t', T, tye_idx') = inf coerce bs t tye_idx;
traytel@51319
   821
            val coerce' = update_coerce_arg ctxt coerce t;
traytel@51319
   822
            val (u', U, (tye, idx)) = inf coerce' bs u tye_idx';
traytel@40836
   823
            val V = Type_Infer.mk_param idx [];
traytel@40836
   824
            val (tu, tye_idx'') = (t' $ u', strong_unify ctxt (U --> V, T) (tye, idx + 1))
wenzelm@42383
   825
              handle NO_UNIFIER (msg, tye') =>
traytel@45060
   826
                let
traytel@45060
   827
                  val err = err_appl_msg ctxt msg tye' bs t T u U;
traytel@45060
   828
                  val W = Type_Infer.mk_param (idx + 1) [];
traytel@45060
   829
                  val (t'', (tye', idx')) =
traytel@45060
   830
                    (t', strong_unify ctxt (W --> V, T) (tye, idx + 2))
traytel@45060
   831
                      handle NO_UNIFIER _ =>
traytel@45060
   832
                        let
wenzelm@55303
   833
                          val err' = err ++> "Local coercion insertion on the operator failed:\n";
traytel@45060
   834
                          val co = function_of ctxt err' tye T;
traytel@51319
   835
                          val (t'', T'', tye_idx'') = inf coerce bs (co $ t') (tye, idx + 2);
traytel@45060
   836
                        in
traytel@45060
   837
                          (t'', strong_unify ctxt (W --> V, T'') tye_idx''
wenzelm@55303
   838
                            handle NO_UNIFIER (msg, _) => eval_error (err' ++> msg))
traytel@45060
   839
                        end;
wenzelm@55303
   840
                  val err' = err ++>
traytel@54584
   841
                    ((if t' aconv t'' then ""
wenzelm@55303
   842
                      else "Successfully coerced the operator to a function of type:\n" ^
wenzelm@55303
   843
                        Syntax.string_of_typ ctxt
wenzelm@55303
   844
                          (the_single (snd (prep_output ctxt tye' bs [] [W --> V]))) ^ "\n") ^
wenzelm@55303
   845
                     (if coerce' then "Local coercion insertion on the operand failed:\n"
wenzelm@55303
   846
                      else "Local coercion insertion on the operand disallowed:\n"));
traytel@45060
   847
                  val (u'', U', tye_idx') =
wenzelm@52432
   848
                    if coerce' then
traytel@51319
   849
                      let val co = gen_coercion ctxt err' tye' (U, W);
traytel@51319
   850
                      in inf coerce' bs (if is_identity co then u else co $ u) (tye', idx') end
traytel@51319
   851
                    else (u, U, (tye', idx'));
traytel@45060
   852
                in
traytel@45060
   853
                  (t'' $ u'', strong_unify ctxt (U', W) tye_idx'
wenzelm@55303
   854
                    handle NO_UNIFIER (msg, _) => raise COERCION_GEN_ERROR (err' ++> msg))
traytel@45060
   855
                end;
traytel@40836
   856
          in (tu, V, tye_idx'') end;
wenzelm@40281
   857
wenzelm@42383
   858
    fun infer_single t tye_idx =
traytel@51319
   859
      let val (t, _, tye_idx') = inf true [] t tye_idx
traytel@40938
   860
      in (t, tye_idx') end;
wenzelm@42383
   861
traytel@40938
   862
    val (ts', (tye, _)) = (fold_map infer_single ts (Vartab.empty, idx)
traytel@45060
   863
      handle COERCION_GEN_ERROR err =>
traytel@40836
   864
        let
traytel@40836
   865
          fun gen_single t (tye_idx, constraints) =
traytel@45060
   866
            let val (_, tye_idx', constraints') =
wenzelm@55303
   867
              generate_constraints ctxt (err ++> "\n") t tye_idx
traytel@40836
   868
            in (tye_idx', constraints' @ constraints) end;
wenzelm@42383
   869
traytel@40836
   870
          val (tye_idx, constraints) = fold gen_single ts ((Vartab.empty, idx), []);
wenzelm@55303
   871
          val (tye, idx) = process_constraints ctxt (err ++> "\n") constraints tye_idx;
wenzelm@42383
   872
        in
traytel@45060
   873
          (insert_coercions ctxt (tye, idx) ts, (tye, idx))
traytel@40836
   874
        end);
wenzelm@40281
   875
wenzelm@40281
   876
    val (_, ts'') = Type_Infer.finish ctxt tye ([], ts');
wenzelm@40281
   877
  in ts'' end;
wenzelm@40281
   878
wenzelm@40281
   879
wenzelm@40281
   880
wenzelm@40281
   881
(** installation **)
wenzelm@40281
   882
wenzelm@40283
   883
(* term check *)
wenzelm@40283
   884
wenzelm@42616
   885
val coercion_enabled = Attrib.setup_config_bool @{binding coercion_enabled} (K false);
wenzelm@40939
   886
wenzelm@40283
   887
val add_term_check =
wenzelm@45429
   888
  Syntax_Phases.term_check ~100 "coercions"
wenzelm@42402
   889
    (fn ctxt => Config.get ctxt coercion_enabled ? coercion_infer_types ctxt);
wenzelm@40281
   890
wenzelm@40281
   891
wenzelm@40283
   892
(* declarations *)
wenzelm@40281
   893
wenzelm@40284
   894
fun add_type_map raw_t context =
wenzelm@40281
   895
  let
wenzelm@40281
   896
    val ctxt = Context.proof_of context;
wenzelm@40284
   897
    val t = singleton (Variable.polymorphic ctxt) raw_t;
wenzelm@40281
   898
traytel@45059
   899
    fun err_str t = "\n\nThe provided function has the type:\n" ^
wenzelm@42383
   900
      Syntax.string_of_typ ctxt (fastype_of t) ^
traytel@45059
   901
      "\n\nThe general type signature of a map function is:" ^
traytel@41353
   902
      "\nf1 => f2 => ... => fn => C [x1, ..., xn] => C [y1, ..., yn]" ^
traytel@45059
   903
      "\nwhere C is a constructor and fi is of type (xi => yi) or (yi => xi).";
wenzelm@42383
   904
traytel@41353
   905
    val ((fis, T1), T2) = apfst split_last (strip_type (fastype_of t))
wenzelm@47060
   906
      handle List.Empty => error ("Not a proper map function:" ^ err_str t);
wenzelm@42383
   907
wenzelm@40281
   908
    fun gen_arg_var ([], []) = []
traytel@51335
   909
      | gen_arg_var (Ts, (U, U') :: Us) =
traytel@41353
   910
          if U = U' then
traytel@51335
   911
            if null (Term.add_tvarsT U []) then INVARIANT_TO U :: gen_arg_var (Ts, Us)
traytel@51335
   912
            else if Term.is_TVar U then INVARIANT :: gen_arg_var (Ts, Us)
traytel@51335
   913
            else error ("Invariant xi and yi should be variables or variable-free:" ^ err_str t)
traytel@51335
   914
          else
traytel@51335
   915
            (case Ts of
traytel@51335
   916
              [] => error ("Different numbers of functions and variant arguments\n" ^ err_str t)
traytel@51335
   917
            | (T, T') :: Ts =>
traytel@51335
   918
              if T = U andalso T' = U' then COVARIANT :: gen_arg_var (Ts, Us)
traytel@51335
   919
              else if T = U' andalso T' = U then CONTRAVARIANT :: gen_arg_var (Ts, Us)
traytel@51335
   920
              else error ("Functions do not apply to arguments correctly:" ^ err_str t));
wenzelm@40281
   921
traytel@41353
   922
    (*retry flag needed to adjust the type lists, when given a map over type constructor fun*)
wenzelm@55305
   923
    fun check_map_fun fis (Type (C1, Ts)) (Type (C2, Us)) _ =
traytel@41353
   924
          if C1 = C2 andalso not (null fis) andalso forall is_funtype fis
traytel@41353
   925
          then ((map dest_funT fis, Ts ~~ Us), C1)
traytel@41353
   926
          else error ("Not a proper map function:" ^ err_str t)
traytel@41353
   927
      | check_map_fun fis T1 T2 true =
traytel@41353
   928
          let val (fis', T') = split_last fis
traytel@41353
   929
          in check_map_fun fis' T' (T1 --> T2) false end
traytel@41353
   930
      | check_map_fun _ _ _ _ = error ("Not a proper map function:" ^ err_str t);
wenzelm@40281
   931
traytel@41353
   932
    val res = check_map_fun fis T1 T2 true;
wenzelm@40281
   933
    val res_av = gen_arg_var (fst res);
wenzelm@40281
   934
  in
wenzelm@40281
   935
    map_tmaps (Symtab.update (snd res, (t, res_av))) context
wenzelm@40281
   936
  end;
wenzelm@40281
   937
traytel@45060
   938
fun transitive_coercion ctxt tab G (a, b) =
traytel@45059
   939
  let
traytel@45060
   940
    fun safe_app t (Abs (x, T', u)) =
traytel@45060
   941
      let
traytel@45060
   942
        val t' = map_types Type_Infer.paramify_vars t;
traytel@45060
   943
      in
traytel@45060
   944
        singleton (coercion_infer_types ctxt) (Abs(x, T', (t' $ u)))
traytel@45060
   945
      end;
traytel@45059
   946
    val path = hd (Graph.irreducible_paths G (a, b));
traytel@45059
   947
    val path' = fst (split_last path) ~~ tl path;
traytel@45059
   948
    val coercions = map (fst o the o Symreltab.lookup tab) path';
traytel@45060
   949
    val trans_co = singleton (Variable.polymorphic ctxt)
traytel@51335
   950
      (fold safe_app coercions (mk_identity dummyT));
traytel@45060
   951
    val (Ts, Us) = pairself (snd o Term.dest_Type) (Term.dest_funT (type_of trans_co))
traytel@45060
   952
  in
traytel@45060
   953
    (trans_co, ((Ts, Us), coercions))
traytel@45059
   954
  end;
traytel@45059
   955
wenzelm@40284
   956
fun add_coercion raw_t context =
wenzelm@40281
   957
  let
wenzelm@40281
   958
    val ctxt = Context.proof_of context;
wenzelm@40284
   959
    val t = singleton (Variable.polymorphic ctxt) raw_t;
wenzelm@40281
   960
wenzelm@55303
   961
    fun err_coercion () =
wenzelm@55303
   962
      error ("Bad type for a coercion:\n" ^
traytel@45059
   963
        Syntax.string_of_term ctxt t ^ " :: " ^
wenzelm@40281
   964
        Syntax.string_of_typ ctxt (fastype_of t));
wenzelm@40281
   965
wenzelm@40840
   966
    val (T1, T2) = Term.dest_funT (fastype_of t)
wenzelm@40840
   967
      handle TYPE _ => err_coercion ();
wenzelm@40281
   968
traytel@45060
   969
    val (a, Ts) = Term.dest_Type T1
traytel@45060
   970
      handle TYPE _ => err_coercion ();
wenzelm@40281
   971
traytel@45060
   972
    val (b, Us) = Term.dest_Type T2
traytel@45060
   973
      handle TYPE _ => err_coercion ();
wenzelm@40281
   974
traytel@45060
   975
    fun coercion_data_update (tab, G, _) =
wenzelm@40281
   976
      let
traytel@45060
   977
        val G' = maybe_new_nodes [(a, length Ts), (b, length Us)] G
wenzelm@40281
   978
        val G'' = Graph.add_edge_trans_acyclic (a, b) G'
traytel@45059
   979
          handle Graph.CYCLES _ => error (
traytel@45060
   980
            Syntax.string_of_typ ctxt T2 ^ " is already a subtype of " ^
traytel@45060
   981
            Syntax.string_of_typ ctxt T1 ^ "!\n\nCannot add coercion of type: " ^
traytel@45059
   982
            Syntax.string_of_typ ctxt (T1 --> T2));
wenzelm@40281
   983
        val new_edges =
wenzelm@49560
   984
          flat (Graph.dest G'' |> map (fn ((x, _), ys) => ys |> map_filter (fn y =>
wenzelm@40281
   985
            if Graph.is_edge G' (x, y) then NONE else SOME (x, y))));
wenzelm@40281
   986
        val G_and_new = Graph.add_edge (a, b) G';
wenzelm@40281
   987
wenzelm@40281
   988
        val tab' = fold
traytel@45059
   989
          (fn pair => fn tab =>
traytel@45060
   990
            Symreltab.update (pair, transitive_coercion ctxt tab G_and_new pair) tab)
wenzelm@40281
   991
          (filter (fn pair => pair <> (a, b)) new_edges)
traytel@45060
   992
          (Symreltab.update ((a, b), (t, ((Ts, Us), []))) tab);
wenzelm@40281
   993
      in
traytel@45060
   994
        (tab', G'', restrict_graph G'')
wenzelm@40281
   995
      end;
wenzelm@40281
   996
  in
traytel@45060
   997
    map_coes_and_graphs coercion_data_update context
wenzelm@40281
   998
  end;
wenzelm@40281
   999
traytel@45059
  1000
fun delete_coercion raw_t context =
traytel@45059
  1001
  let
traytel@45059
  1002
    val ctxt = Context.proof_of context;
traytel@45059
  1003
    val t = singleton (Variable.polymorphic ctxt) raw_t;
traytel@45059
  1004
wenzelm@55303
  1005
    fun err_coercion the =
wenzelm@55303
  1006
      error ("Not" ^
traytel@45059
  1007
        (if the then " the defined " else  " a ") ^ "coercion:\n" ^
traytel@45059
  1008
        Syntax.string_of_term ctxt t ^ " :: " ^
traytel@45059
  1009
        Syntax.string_of_typ ctxt (fastype_of t));
traytel@45059
  1010
traytel@45059
  1011
    val (T1, T2) = Term.dest_funT (fastype_of t)
traytel@45059
  1012
      handle TYPE _ => err_coercion false;
traytel@45059
  1013
traytel@54584
  1014
    val (a, _) = dest_Type T1
traytel@45060
  1015
      handle TYPE _ => err_coercion false;
traytel@45059
  1016
traytel@54584
  1017
    val (b, _) = dest_Type T2
traytel@45060
  1018
      handle TYPE _ => err_coercion false;
traytel@45059
  1019
traytel@45059
  1020
    fun delete_and_insert tab G =
traytel@45059
  1021
      let
traytel@45059
  1022
        val pairs =
traytel@45060
  1023
          Symreltab.fold (fn ((a, b), (_, (_, ts))) => fn pairs =>
traytel@45059
  1024
            if member (op aconv) ts t then (a, b) :: pairs else pairs) tab [(a, b)];
traytel@45059
  1025
        fun delete pair (G, tab) = (Graph.del_edge pair G, Symreltab.delete_safe pair tab);
traytel@45059
  1026
        val (G', tab') = fold delete pairs (G, tab);
wenzelm@49564
  1027
        fun reinsert pair (G, xs) =
wenzelm@49564
  1028
          (case Graph.irreducible_paths G pair of
wenzelm@49564
  1029
            [] => (G, xs)
wenzelm@49564
  1030
          | _ => (Graph.add_edge pair G, (pair, transitive_coercion ctxt tab' G' pair) :: xs));
traytel@45059
  1031
        val (G'', ins) = fold reinsert pairs (G', []);
traytel@45059
  1032
      in
traytel@45060
  1033
        (fold Symreltab.update ins tab', G'', restrict_graph G'')
traytel@45059
  1034
      end
traytel@45059
  1035
wenzelm@55303
  1036
    fun show_term t =
wenzelm@55303
  1037
      Pretty.block [Syntax.pretty_term ctxt t,
wenzelm@55303
  1038
        Pretty.str " :: ", Syntax.pretty_typ ctxt (fastype_of t)];
traytel@45059
  1039
traytel@45060
  1040
    fun coercion_data_update (tab, G, _) =
wenzelm@55303
  1041
      (case Symreltab.lookup tab (a, b) of
wenzelm@55303
  1042
        NONE => err_coercion false
wenzelm@55303
  1043
      | SOME (t', (_, [])) =>
wenzelm@55303
  1044
          if t aconv t'
wenzelm@55303
  1045
          then delete_and_insert tab G
wenzelm@55303
  1046
          else err_coercion true
wenzelm@55303
  1047
      | SOME (t', (_, ts)) =>
wenzelm@55303
  1048
          if t aconv t' then
wenzelm@55303
  1049
            error ("Cannot delete the automatically derived coercion:\n" ^
traytel@45059
  1050
              Syntax.string_of_term ctxt t ^ " :: " ^
wenzelm@55303
  1051
              Syntax.string_of_typ ctxt (fastype_of t) ^ "\n\n" ^
wenzelm@55303
  1052
              Pretty.string_of
wenzelm@55303
  1053
                (Pretty.big_list "Deleting one of the coercions:" (map show_term ts)) ^
traytel@45059
  1054
              "\nwill also remove the transitive coercion.")
wenzelm@55303
  1055
          else err_coercion true);
traytel@45059
  1056
  in
traytel@45060
  1057
    map_coes_and_graphs coercion_data_update context
traytel@45059
  1058
  end;
traytel@45059
  1059
traytel@45059
  1060
fun print_coercions ctxt =
traytel@45059
  1061
  let
traytel@45060
  1062
    fun separate _ [] = ([], [])
wenzelm@52432
  1063
      | separate P (x :: xs) = (if P x then apfst else apsnd) (cons x) (separate P xs);
traytel@45060
  1064
    val (simple, complex) =
traytel@45060
  1065
      separate (fn (_, (_, ((Ts, Us), _))) => null Ts andalso null Us)
traytel@45060
  1066
        (Symreltab.dest (coes_of ctxt));
wenzelm@52432
  1067
    fun show_coercion ((a, b), (t, ((Ts, Us), _))) =
wenzelm@52432
  1068
      Pretty.item [Pretty.block
wenzelm@52432
  1069
       [Syntax.pretty_typ ctxt (Type (a, Ts)), Pretty.brk 1,
wenzelm@52432
  1070
        Pretty.str "<:", Pretty.brk 1,
wenzelm@52432
  1071
        Syntax.pretty_typ ctxt (Type (b, Us)), Pretty.brk 3,
wenzelm@52432
  1072
        Pretty.block
wenzelm@52432
  1073
         [Pretty.keyword "using", Pretty.brk 1,
wenzelm@52432
  1074
          Pretty.quote (Syntax.pretty_term ctxt t)]]];
wenzelm@52432
  1075
wenzelm@52432
  1076
    val type_space = Proof_Context.type_space ctxt;
wenzelm@52432
  1077
    val tmaps =
wenzelm@52432
  1078
      sort (Name_Space.extern_ord ctxt type_space o pairself #1)
wenzelm@52432
  1079
        (Symtab.dest (tmaps_of ctxt));
wenzelm@53539
  1080
    fun show_map (c, (t, _)) =
wenzelm@52432
  1081
      Pretty.block
wenzelm@53539
  1082
       [Name_Space.pretty ctxt type_space c, Pretty.str ":",
wenzelm@52432
  1083
        Pretty.brk 1, Pretty.quote (Syntax.pretty_term ctxt t)];
traytel@45059
  1084
  in
wenzelm@52432
  1085
   [Pretty.big_list "coercions between base types:" (map show_coercion simple),
wenzelm@52432
  1086
    Pretty.big_list "other coercions:" (map show_coercion complex),
wenzelm@52432
  1087
    Pretty.big_list "coercion maps:" (map show_map tmaps)]
wenzelm@52432
  1088
  end |> Pretty.chunks |> Pretty.writeln;
traytel@45059
  1089
traytel@45059
  1090
traytel@51319
  1091
(* theory setup *)
wenzelm@40283
  1092
traytel@51319
  1093
val parse_coerce_args =
traytel@51327
  1094
  Args.$$$ "+" >> K PERMIT || Args.$$$ "-" >> K FORBID || Args.$$$ "0" >> K LEAVE
wenzelm@40283
  1095
wenzelm@40283
  1096
val setup =
wenzelm@40283
  1097
  Context.theory_map add_term_check #>
wenzelm@40284
  1098
  Attrib.setup @{binding coercion}
wenzelm@40284
  1099
    (Args.term >> (fn t => Thm.declaration_attribute (K (add_coercion t))))
wenzelm@40281
  1100
    "declaration of new coercions" #>
traytel@45059
  1101
  Attrib.setup @{binding coercion_delete}
traytel@45059
  1102
    (Args.term >> (fn t => Thm.declaration_attribute (K (delete_coercion t))))
traytel@45059
  1103
    "deletion of coercions" #>
traytel@40297
  1104
  Attrib.setup @{binding coercion_map}
wenzelm@40284
  1105
    (Args.term >> (fn t => Thm.declaration_attribute (K (add_type_map t))))
traytel@51319
  1106
    "declaration of new map functions" #>
traytel@51319
  1107
  Attrib.setup @{binding coercion_args}
traytel@51319
  1108
    (Args.const false -- Scan.lift (Scan.repeat1 parse_coerce_args) >>
traytel@51319
  1109
      (fn spec => Thm.declaration_attribute (K (map_coerce_args (Symtab.update spec)))))
traytel@51319
  1110
    "declaration of new constants with coercion-invariant arguments";
wenzelm@40281
  1111
traytel@45059
  1112
traytel@45059
  1113
(* outer syntax commands *)
traytel@45059
  1114
traytel@45059
  1115
val _ =
wenzelm@52432
  1116
  Outer_Syntax.improper_command @{command_spec "print_coercions"}
wenzelm@52432
  1117
    "print information about coercions"
wenzelm@52432
  1118
    (Scan.succeed (Toplevel.keep (print_coercions o Toplevel.context_of)));
traytel@45059
  1119
wenzelm@40281
  1120
end;