src/Tools/subtyping.ML
author wenzelm
Fri Oct 29 22:07:48 2010 +0200 (2010-10-29)
changeset 40283 805ce1d64af0
parent 40282 329cd9dd5949
child 40284 c9acf88447e6
permissions -rw-r--r--
proper signature constraint for ML structure;
explicit theory setup, which is customary outside Pure;
formal @{binding} instead of Binding.name;
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(*  Title:      Tools/subtyping.ML
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    Author:     Dmitriy Traytel, TU Muenchen
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Coercive subtyping via subtype constraints.
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*)
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signature SUBTYPING =
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sig
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  datatype variance = COVARIANT | CONTRAVARIANT | INVARIANT
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  val infer_types: Proof.context -> (string -> typ option) -> (indexname -> typ option) ->
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    term list -> term list
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  val setup: theory -> theory
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end;
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structure Subtyping: SUBTYPING =
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struct
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(** coercions data **)
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datatype variance = COVARIANT | CONTRAVARIANT | INVARIANT
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datatype data = Data of
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  {coes: term Symreltab.table,  (*coercions table*)
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   coes_graph: unit Graph.T,  (*coercions graph*)
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   tmaps: (term * variance list) Symtab.table};  (*map functions*)
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fun make_data (coes, coes_graph, tmaps) =
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  Data {coes = coes, coes_graph = coes_graph, tmaps = tmaps};
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structure Data = Generic_Data
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(
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  type T = data;
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  val empty = make_data (Symreltab.empty, Graph.empty, Symtab.empty);
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  val extend = I;
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  fun merge
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    (Data {coes = coes1, coes_graph = coes_graph1, tmaps = tmaps1},
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      Data {coes = coes2, coes_graph = coes_graph2, tmaps = tmaps2}) =
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    make_data (Symreltab.merge (op aconv) (coes1, coes2),
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      Graph.merge (op =) (coes_graph1, coes_graph2),
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      Symtab.merge (eq_pair (op aconv) (op =)) (tmaps1, tmaps2));
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);
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fun map_data f =
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  Data.map (fn Data {coes, coes_graph, tmaps} =>
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    make_data (f (coes, coes_graph, tmaps)));
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fun map_coes f =
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  map_data (fn (coes, coes_graph, tmaps) =>
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    (f coes, coes_graph, tmaps));
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fun map_coes_graph f =
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  map_data (fn (coes, coes_graph, tmaps) =>
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    (coes, f coes_graph, tmaps));
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fun map_coes_and_graph f =
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  map_data (fn (coes, coes_graph, tmaps) =>
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    let val (coes', coes_graph') = f (coes, coes_graph);
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    in (coes', coes_graph', tmaps) end);
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fun map_tmaps f =
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  map_data (fn (coes, coes_graph, tmaps) =>
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    (coes, coes_graph, f tmaps));
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fun rep_data context = Data.get context |> (fn Data args => args);
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val coes_of = #coes o rep_data;
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val coes_graph_of = #coes_graph o rep_data;
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val tmaps_of = #tmaps o rep_data;
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(** utils **)
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val is_param = Type_Infer.is_param
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val is_paramT = Type_Infer.is_paramT
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val deref = Type_Infer.deref
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fun mk_param i S = TVar (("?'a", i), S); (* TODO dup? see src/Pure/type_infer.ML *)
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fun nameT (Type (s, [])) = s;
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fun t_of s = Type (s, []);
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fun sort_of (TFree (_, S)) = SOME S
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  | sort_of (TVar (_, S)) = SOME S
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  | sort_of _ = NONE;
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val is_typeT = fn (Type _) => true | _ => false;
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val is_compT = fn (Type (_, _ :: _)) => true | _ => false;
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val is_freeT = fn (TFree _) => true | _ => false;
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val is_fixedvarT = fn (TVar (xi, _)) => not (is_param xi) | _ => false;
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(* unification *)  (* TODO dup? needed for weak unification *)
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exception NO_UNIFIER of string * typ Vartab.table;
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fun unify weak ctxt =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    val pp = Syntax.pp ctxt;
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    val arity_sorts = Type.arity_sorts pp (Sign.tsig_of thy);
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    (* adjust sorts of parameters *)
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    fun not_of_sort x S' S =
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      "Variable " ^ x ^ "::" ^ Syntax.string_of_sort ctxt S' ^ " not of sort " ^
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        Syntax.string_of_sort ctxt S;
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    fun meet (_, []) tye_idx = tye_idx
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      | meet (Type (a, Ts), S) (tye_idx as (tye, _)) =
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          meets (Ts, arity_sorts a S handle ERROR msg => raise NO_UNIFIER (msg, tye)) tye_idx
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      | meet (TFree (x, S'), S) (tye_idx as (tye, _)) =
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          if Sign.subsort thy (S', S) then tye_idx
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          else raise NO_UNIFIER (not_of_sort x S' S, tye)
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      | meet (TVar (xi, S'), S) (tye_idx as (tye, idx)) =
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          if Sign.subsort thy (S', S) then tye_idx
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          else if Type_Infer.is_param xi then
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            (Vartab.update_new (xi, mk_param idx (Sign.inter_sort thy (S', S))) tye, idx + 1)
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          else raise NO_UNIFIER (not_of_sort (Term.string_of_vname xi) S' S, tye)
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    and meets (T :: Ts, S :: Ss) (tye_idx as (tye, _)) =
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          meets (Ts, Ss) (meet (deref tye T, S) tye_idx)
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      | meets _ tye_idx = tye_idx;
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    val weak_meet = if weak then fn _ => I else meet
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    (* occurs check and assignment *)
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    fun occurs_check tye xi (TVar (xi', _)) =
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          if xi = xi' then raise NO_UNIFIER ("Occurs check!", tye)
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          else
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            (case Vartab.lookup tye xi' of
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              NONE => ()
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            | SOME T => occurs_check tye xi T)
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      | occurs_check tye xi (Type (_, Ts)) = List.app (occurs_check tye xi) Ts
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      | occurs_check _ _ _ = ();
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    fun assign xi (T as TVar (xi', _)) S env =
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          if xi = xi' then env
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          else env |> weak_meet (T, S) |>> Vartab.update_new (xi, T)
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      | assign xi T S (env as (tye, _)) =
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          (occurs_check tye xi T; env |> weak_meet (T, S) |>> Vartab.update_new (xi, T));
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    (* unification *)
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    fun show_tycon (a, Ts) =
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      quote (Syntax.string_of_typ ctxt (Type (a, replicate (length Ts) dummyT)));
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    fun unif (T1, T2) (env as (tye, _)) =
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      (case pairself (`is_paramT o deref tye) (T1, T2) of
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        ((true, TVar (xi, S)), (_, T)) => assign xi T S env
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      | ((_, T), (true, TVar (xi, S))) => assign xi T S env
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      | ((_, Type (a, Ts)), (_, Type (b, Us))) =>
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          if weak andalso null Ts andalso null Us then env
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          else if a <> b then
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            raise NO_UNIFIER
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              ("Clash of types " ^ show_tycon (a, Ts) ^ " and " ^ show_tycon (b, Us), tye)
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          else fold unif (Ts ~~ Us) env
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      | ((_, T), (_, U)) => if T = U then env else raise NO_UNIFIER ("", tye));
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  in unif end;
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val weak_unify = unify true;
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val strong_unify = unify false;
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(* Typ_Graph shortcuts *)
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val add_edge = Typ_Graph.add_edge_acyclic;
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fun get_preds G T = Typ_Graph.all_preds G [T];
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fun get_succs G T = Typ_Graph.all_succs G [T];
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fun maybe_new_typnode T G = perhaps (try (Typ_Graph.new_node (T, ()))) G;
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fun maybe_new_typnodes Ts G = fold maybe_new_typnode Ts G;
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fun new_imm_preds G Ts =
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  subtract (op =) Ts (distinct (op =) (maps (Typ_Graph.imm_preds G) Ts));
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fun new_imm_succs G Ts =
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  subtract op= Ts (distinct (op =) (maps (Typ_Graph.imm_succs G) Ts));
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(* Graph shortcuts *)
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fun maybe_new_node s G = perhaps (try (Graph.new_node (s, ()))) G
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fun maybe_new_nodes ss G = fold maybe_new_node ss G
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(** error messages **)
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fun prep_output ctxt tye bs ts Ts =
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  let
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    val (Ts_bTs', ts') = Type_Infer.finish ctxt tye (Ts @ map snd bs, ts);
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    val (Ts', Ts'') = chop (length Ts) Ts_bTs';
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    fun prep t =
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      let val xs = rev (Term.variant_frees t (rev (map fst bs ~~ Ts'')))
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      in Term.subst_bounds (map Syntax.mark_boundT xs, t) end;
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  in (map prep ts', Ts') end;
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fun err_loose i = error ("Loose bound variable: B." ^ string_of_int i);
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fun inf_failed msg =
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  "Subtype inference failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n\n";
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fun err_appl ctxt msg tye bs t T u U =
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  let val ([t', u'], [T', U']) = prep_output ctxt tye bs [t, u] [T, U]
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  in error (inf_failed msg ^ Type.appl_error (Syntax.pp ctxt) t' T' u' U' ^ "\n") end;
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fun err_subtype ctxt msg tye (bs, t $ u, U, V, U') =
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  err_appl ctxt msg tye bs t (U --> V) u U';
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fun err_list ctxt msg tye Ts =
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  let
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    val (_, Ts') = prep_output ctxt tye [] [] Ts;
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    val text = cat_lines ([inf_failed msg,
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      "Cannot unify a list of types that should be the same,",
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      "according to suptype dependencies:",
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      (Pretty.string_of (Pretty.list "[" "]" (map (Pretty.typ (Syntax.pp ctxt)) Ts')))]);
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  in
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    error text
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  end;
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fun err_bound ctxt msg tye packs =
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  let
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    val pp = Syntax.pp ctxt;
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    val (ts, Ts) = fold
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      (fn (bs, t $ u, U, _, U') => fn (ts, Ts) =>
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        let val (t', T') = prep_output ctxt tye bs [t, u] [U, U']
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        in (t' :: ts, T' :: Ts) end)
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      packs ([], []);
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    val text = cat_lines ([inf_failed msg, "Cannot fullfill subtype constraints:"] @
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        (map2 (fn [t, u] => fn [T, U] => Pretty.string_of (
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          Pretty.block [
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            Pretty.typ pp T, Pretty.brk 2, Pretty.str "<:", Pretty.brk 2, Pretty.typ pp U,
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            Pretty.brk 3, Pretty.str "from function application", Pretty.brk 2,
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            Pretty.block [Pretty.term pp t, Pretty.brk 1, Pretty.term pp u]]))
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        ts Ts))
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  in
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    error text
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  end;
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(** constraint generation **)
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fun generate_constraints ctxt =
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  let
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    fun gen cs _ (Const (_, T)) tye_idx = (T, tye_idx, cs)
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      | gen cs _ (Free (_, T)) tye_idx = (T, tye_idx, cs)
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      | gen cs _ (Var (_, T)) tye_idx = (T, tye_idx, cs)
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      | gen cs bs (Bound i) tye_idx =
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          (snd (nth bs i handle Subscript => err_loose i), tye_idx, cs)
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      | gen cs bs (Abs (x, T, t)) tye_idx =
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          let val (U, tye_idx', cs') = gen cs ((x, T) :: bs) t tye_idx
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          in (T --> U, tye_idx', cs') end
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      | gen cs bs (t $ u) tye_idx =
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          let
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            val (T, tye_idx', cs') = gen cs bs t tye_idx;
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            val (U', (tye, idx), cs'') = gen cs' bs u tye_idx';
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            val U = mk_param idx [];
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            val V = mk_param (idx + 1) [];
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            val tye_idx''= strong_unify ctxt (U --> V, T) (tye, idx + 2)
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              handle NO_UNIFIER (msg, tye') => err_appl ctxt msg tye' bs t T u U;
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            val error_pack = (bs, t $ u, U, V, U');
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          in (V, tye_idx'', ((U', U), error_pack) :: cs'') end;
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  in
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    gen [] []
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  end;
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(** constraint resolution **)
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exception BOUND_ERROR of string;
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fun process_constraints ctxt cs tye_idx =
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  let
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    val coes_graph = coes_graph_of (Context.Proof ctxt);
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    val tmaps = tmaps_of (Context.Proof ctxt);
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    val tsig = Sign.tsig_of (ProofContext.theory_of ctxt);
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    val pp = Syntax.pp ctxt;
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    val arity_sorts = Type.arity_sorts pp tsig;
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    val subsort = Type.subsort tsig;
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    fun split_cs _ [] = ([], [])
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      | split_cs f (c :: cs) =
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          (case pairself f (fst c) of
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            (false, false) => apsnd (cons c) (split_cs f cs)
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          | _ => apfst (cons c) (split_cs f cs));
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    (* check whether constraint simplification will terminate using weak unification *)
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    val _ = fold (fn (TU, error_pack) => fn tye_idx =>
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      (weak_unify ctxt TU tye_idx handle NO_UNIFIER (msg, tye) =>
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        err_subtype ctxt ("Weak unification of subtype constraints fails:\n" ^ msg)
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          tye error_pack)) cs tye_idx;
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    (* simplify constraints *)
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    fun simplify_constraints cs tye_idx =
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      let
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        fun contract a Ts Us error_pack done todo tye idx =
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          let
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            val arg_var =
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              (case Symtab.lookup tmaps a of
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                (*everything is invariant for unknown constructors*)
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                NONE => replicate (length Ts) INVARIANT
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              | SOME av => snd av);
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            fun new_constraints (variance, constraint) (cs, tye_idx) =
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              (case variance of
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                COVARIANT => (constraint :: cs, tye_idx)
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              | CONTRAVARIANT => (swap constraint :: cs, tye_idx)
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              | INVARIANT => (cs, strong_unify ctxt constraint tye_idx
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                  handle NO_UNIFIER (msg, tye) => err_subtype ctxt msg tye error_pack));
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            val (new, (tye', idx')) = apfst (fn cs => (cs ~~ replicate (length cs) error_pack))
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              (fold new_constraints (arg_var ~~ (Ts ~~ Us)) ([], (tye, idx)));
wenzelm@40281
   317
            val test_update = is_compT orf is_freeT orf is_fixedvarT;
wenzelm@40281
   318
            val (ch, done') =
wenzelm@40281
   319
              if not (null new) then ([],   done)
wenzelm@40281
   320
              else split_cs (test_update o deref tye') done;
wenzelm@40281
   321
            val todo' = ch @ todo;
wenzelm@40281
   322
          in
wenzelm@40281
   323
            simplify done' (new @ todo') (tye', idx')
wenzelm@40281
   324
          end
wenzelm@40281
   325
        (*xi is definitely a parameter*)
wenzelm@40281
   326
        and expand varleq xi S a Ts error_pack done todo tye idx =
wenzelm@40281
   327
          let
wenzelm@40281
   328
            val n = length Ts;
wenzelm@40281
   329
            val args = map2 mk_param (idx upto idx + n - 1) (arity_sorts a S);
wenzelm@40281
   330
            val tye' = Vartab.update_new (xi, Type(a, args)) tye;
wenzelm@40281
   331
            val (ch, done') = split_cs (is_compT o deref tye') done;
wenzelm@40281
   332
            val todo' = ch @ todo;
wenzelm@40281
   333
            val new =
wenzelm@40281
   334
              if varleq then (Type(a, args), Type (a, Ts))
wenzelm@40281
   335
              else (Type (a, Ts), Type(a, args));
wenzelm@40281
   336
          in
wenzelm@40281
   337
            simplify done' ((new, error_pack) :: todo') (tye', idx + n)
wenzelm@40281
   338
          end
wenzelm@40281
   339
        (*TU is a pair of a parameter and a free/fixed variable*)
wenzelm@40281
   340
        and eliminate TU error_pack done todo tye idx =
wenzelm@40281
   341
          let
wenzelm@40281
   342
            val [TVar (xi, S)] = filter is_paramT TU;
wenzelm@40281
   343
            val [T] = filter_out is_paramT TU;
wenzelm@40281
   344
            val SOME S' = sort_of T;
wenzelm@40281
   345
            val test_update = if is_freeT T then is_freeT else is_fixedvarT;
wenzelm@40281
   346
            val tye' = Vartab.update_new (xi, T) tye;
wenzelm@40281
   347
            val (ch, done') = split_cs (test_update o deref tye') done;
wenzelm@40281
   348
            val todo' = ch @ todo;
wenzelm@40281
   349
          in
wenzelm@40281
   350
            if subsort (S', S) (*TODO check this*)
wenzelm@40281
   351
            then simplify done' todo' (tye', idx)
wenzelm@40281
   352
            else err_subtype ctxt "Sort mismatch" tye error_pack
wenzelm@40281
   353
          end
wenzelm@40281
   354
        and simplify done [] tye_idx = (done, tye_idx)
wenzelm@40281
   355
          | simplify done (((T, U), error_pack) :: todo) (tye_idx as (tye, idx)) =
wenzelm@40281
   356
              (case (deref tye T, deref tye U) of
wenzelm@40281
   357
                (Type (a, []), Type (b, [])) =>
wenzelm@40281
   358
                  if a = b then simplify done todo tye_idx
wenzelm@40281
   359
                  else if Graph.is_edge coes_graph (a, b) then simplify done todo tye_idx
wenzelm@40281
   360
                  else err_subtype ctxt (a ^" is not a subtype of " ^ b) (fst tye_idx) error_pack
wenzelm@40281
   361
              | (Type (a, Ts), Type (b, Us)) =>
wenzelm@40281
   362
                  if a<>b then err_subtype ctxt "Different constructors" (fst tye_idx) error_pack
wenzelm@40281
   363
                  else contract a Ts Us error_pack done todo tye idx
wenzelm@40282
   364
              | (TVar (xi, S), Type (a, Ts as (_ :: _))) =>
wenzelm@40281
   365
                  expand true xi S a Ts error_pack done todo tye idx
wenzelm@40282
   366
              | (Type (a, Ts as (_ :: _)), TVar (xi, S)) =>
wenzelm@40281
   367
                  expand false xi S a Ts error_pack done todo tye idx
wenzelm@40281
   368
              | (T, U) =>
wenzelm@40281
   369
                  if T = U then simplify done todo tye_idx
wenzelm@40282
   370
                  else if exists (is_freeT orf is_fixedvarT) [T, U] andalso
wenzelm@40281
   371
                    exists is_paramT [T, U]
wenzelm@40281
   372
                  then eliminate [T, U] error_pack done todo tye idx
wenzelm@40281
   373
                  else if exists (is_freeT orf is_fixedvarT) [T, U]
wenzelm@40281
   374
                  then err_subtype ctxt "Not eliminated free/fixed variables"
wenzelm@40281
   375
                        (fst tye_idx) error_pack
wenzelm@40282
   376
                  else simplify (((T, U), error_pack) :: done) todo tye_idx);
wenzelm@40281
   377
      in
wenzelm@40281
   378
        simplify [] cs tye_idx
wenzelm@40281
   379
      end;
wenzelm@40281
   380
wenzelm@40281
   381
wenzelm@40281
   382
    (* do simplification *)
wenzelm@40282
   383
wenzelm@40281
   384
    val (cs', tye_idx') = simplify_constraints cs tye_idx;
wenzelm@40281
   385
wenzelm@40281
   386
    fun find_error_pack lower T' =
wenzelm@40281
   387
      map snd (filter (fn ((T, U), _) => if lower then T' = U else T' = T) cs');
wenzelm@40281
   388
wenzelm@40282
   389
    fun unify_list (T :: Ts) tye_idx =
wenzelm@40281
   390
      fold (fn U => fn tye_idx => strong_unify ctxt (T, U) tye_idx
wenzelm@40282
   391
        handle NO_UNIFIER (msg, tye) => err_list ctxt msg tye (T :: Ts))
wenzelm@40281
   392
      Ts tye_idx;
wenzelm@40281
   393
wenzelm@40281
   394
    (*styps stands either for supertypes or for subtypes of a type T
wenzelm@40281
   395
      in terms of the subtype-relation (excluding T itself)*)
wenzelm@40282
   396
    fun styps super T =
wenzelm@40281
   397
      (if super then Graph.imm_succs else Graph.imm_preds) coes_graph T
wenzelm@40281
   398
        handle Graph.UNDEF _ => [];
wenzelm@40281
   399
wenzelm@40282
   400
    fun minmax sup (T :: Ts) =
wenzelm@40281
   401
      let
wenzelm@40281
   402
        fun adjust T U = if sup then (T, U) else (U, T);
wenzelm@40281
   403
        fun extract T [] = T
wenzelm@40282
   404
          | extract T (U :: Us) =
wenzelm@40281
   405
              if Graph.is_edge coes_graph (adjust T U) then extract T Us
wenzelm@40281
   406
              else if Graph.is_edge coes_graph (adjust U T) then extract U Us
wenzelm@40281
   407
              else raise BOUND_ERROR "Uncomparable types in type list";
wenzelm@40281
   408
      in
wenzelm@40281
   409
        t_of (extract T Ts)
wenzelm@40281
   410
      end;
wenzelm@40281
   411
wenzelm@40282
   412
    fun ex_styp_of_sort super T styps_and_sorts =
wenzelm@40281
   413
      let
wenzelm@40281
   414
        fun adjust T U = if super then (T, U) else (U, T);
wenzelm@40282
   415
        fun styp_test U Ts = forall
wenzelm@40281
   416
          (fn T => T = U orelse Graph.is_edge coes_graph (adjust U T)) Ts;
wenzelm@40281
   417
        fun fitting Ts S U = Type.of_sort tsig (t_of U, S) andalso styp_test U Ts
wenzelm@40281
   418
      in
wenzelm@40281
   419
        forall (fn (Ts, S) => exists (fitting Ts S) (T :: styps super T)) styps_and_sorts
wenzelm@40281
   420
      end;
wenzelm@40281
   421
wenzelm@40281
   422
    (* computes the tightest possible, correct assignment for 'a::S
wenzelm@40281
   423
       e.g. in the supremum case (sup = true):
wenzelm@40281
   424
               ------- 'a::S---
wenzelm@40281
   425
              /        /    \  \
wenzelm@40281
   426
             /        /      \  \
wenzelm@40281
   427
        'b::C1   'c::C2 ...  T1 T2 ...
wenzelm@40281
   428
wenzelm@40281
   429
       sorts - list of sorts [C1, C2, ...]
wenzelm@40281
   430
       T::Ts - non-empty list of base types [T1, T2, ...]
wenzelm@40281
   431
    *)
wenzelm@40282
   432
    fun tightest sup S styps_and_sorts (T :: Ts) =
wenzelm@40281
   433
      let
wenzelm@40281
   434
        fun restriction T = Type.of_sort tsig (t_of T, S)
wenzelm@40281
   435
          andalso ex_styp_of_sort (not sup) T styps_and_sorts;
wenzelm@40281
   436
        fun candidates T = inter (op =) (filter restriction (T :: styps sup T));
wenzelm@40281
   437
      in
wenzelm@40281
   438
        (case fold candidates Ts (filter restriction (T :: styps sup T)) of
wenzelm@40281
   439
          [] => raise BOUND_ERROR ("No " ^ (if sup then "supremum" else "infimum"))
wenzelm@40281
   440
        | [T] => t_of T
wenzelm@40281
   441
        | Ts => minmax sup Ts)
wenzelm@40281
   442
      end;
wenzelm@40281
   443
wenzelm@40281
   444
    fun build_graph G [] tye_idx = (G, tye_idx)
wenzelm@40282
   445
      | build_graph G ((T, U) :: cs) tye_idx =
wenzelm@40281
   446
        if T = U then build_graph G cs tye_idx
wenzelm@40281
   447
        else
wenzelm@40281
   448
          let
wenzelm@40281
   449
            val G' = maybe_new_typnodes [T, U] G;
wenzelm@40281
   450
            val (G'', tye_idx') = (add_edge (T, U) G', tye_idx)
wenzelm@40281
   451
              handle Typ_Graph.CYCLES cycles =>
wenzelm@40281
   452
                let
wenzelm@40281
   453
                  val (tye, idx) = fold unify_list cycles tye_idx
wenzelm@40281
   454
                in
wenzelm@40281
   455
                  (*all cycles collapse to one node,
wenzelm@40281
   456
                    because all of them share at least the nodes x and y*)
wenzelm@40281
   457
                  collapse (tye, idx) (distinct (op =) (flat cycles)) G
wenzelm@40281
   458
                end;
wenzelm@40281
   459
          in
wenzelm@40281
   460
            build_graph G'' cs tye_idx'
wenzelm@40281
   461
          end
wenzelm@40281
   462
    and collapse (tye, idx) nodes G = (*nodes non-empty list*)
wenzelm@40281
   463
      let
wenzelm@40281
   464
        val T = hd nodes;
wenzelm@40281
   465
        val P = new_imm_preds G nodes;
wenzelm@40281
   466
        val S = new_imm_succs G nodes;
wenzelm@40281
   467
        val G' = Typ_Graph.del_nodes (tl nodes) G;
wenzelm@40281
   468
      in
wenzelm@40281
   469
        build_graph G' (map (fn x => (x, T)) P @ map (fn x => (T, x)) S) (tye, idx)
wenzelm@40281
   470
      end;
wenzelm@40281
   471
wenzelm@40281
   472
    fun assign_bound lower G key (tye_idx as (tye, _)) =
wenzelm@40281
   473
      if is_paramT (deref tye key) then
wenzelm@40281
   474
        let
wenzelm@40281
   475
          val TVar (xi, S) = deref tye key;
wenzelm@40281
   476
          val get_bound = if lower then get_preds else get_succs;
wenzelm@40281
   477
          val raw_bound = get_bound G key;
wenzelm@40281
   478
          val bound = map (deref tye) raw_bound;
wenzelm@40281
   479
          val not_params = filter_out is_paramT bound;
wenzelm@40282
   480
          fun to_fulfil T =
wenzelm@40281
   481
            (case sort_of T of
wenzelm@40281
   482
              NONE => NONE
wenzelm@40282
   483
            | SOME S =>
wenzelm@40281
   484
                SOME (map nameT (filter_out is_paramT (map (deref tye) (get_bound G T))), S));
wenzelm@40281
   485
          val styps_and_sorts = distinct (op =) (map_filter to_fulfil raw_bound);
wenzelm@40281
   486
          val assignment =
wenzelm@40281
   487
            if null bound orelse null not_params then NONE
wenzelm@40281
   488
            else SOME (tightest lower S styps_and_sorts (map nameT not_params)
wenzelm@40281
   489
                handle BOUND_ERROR msg => err_bound ctxt msg tye (find_error_pack lower key))
wenzelm@40281
   490
        in
wenzelm@40281
   491
          (case assignment of
wenzelm@40281
   492
            NONE => tye_idx
wenzelm@40281
   493
          | SOME T =>
wenzelm@40281
   494
              if is_paramT T then tye_idx
wenzelm@40281
   495
              else if lower then (*upper bound check*)
wenzelm@40281
   496
                let
wenzelm@40281
   497
                  val other_bound = map (deref tye) (get_succs G key);
wenzelm@40281
   498
                  val s = nameT T;
wenzelm@40281
   499
                in
wenzelm@40281
   500
                  if subset (op = o apfst nameT) (filter is_typeT other_bound, s :: styps true s)
wenzelm@40281
   501
                  then apfst (Vartab.update (xi, T)) tye_idx
wenzelm@40281
   502
                  else err_bound ctxt ("Assigned simple type " ^ s ^
wenzelm@40281
   503
                    " clashes with the upper bound of variable " ^
wenzelm@40281
   504
                    Syntax.string_of_typ ctxt (TVar(xi, S))) tye (find_error_pack (not lower) key)
wenzelm@40281
   505
                end
wenzelm@40281
   506
              else apfst (Vartab.update (xi, T)) tye_idx)
wenzelm@40281
   507
        end
wenzelm@40281
   508
      else tye_idx;
wenzelm@40281
   509
wenzelm@40281
   510
    val assign_lb = assign_bound true;
wenzelm@40281
   511
    val assign_ub = assign_bound false;
wenzelm@40281
   512
wenzelm@40281
   513
    fun assign_alternating ts' ts G tye_idx =
wenzelm@40281
   514
      if ts' = ts then tye_idx
wenzelm@40281
   515
      else
wenzelm@40281
   516
        let
wenzelm@40281
   517
          val (tye_idx' as (tye, _)) = fold (assign_lb G) ts tye_idx
wenzelm@40281
   518
            |> fold (assign_ub G) ts;
wenzelm@40281
   519
        in
wenzelm@40281
   520
          assign_alternating ts (filter (is_paramT o deref tye) ts) G tye_idx'
wenzelm@40281
   521
        end;
wenzelm@40281
   522
wenzelm@40281
   523
    (*Unify all weakly connected components of the constraint forest,
wenzelm@40282
   524
      that contain only params. These are the only WCCs that contain
wenzelm@40281
   525
      params anyway.*)
wenzelm@40281
   526
    fun unify_params G (tye_idx as (tye, _)) =
wenzelm@40281
   527
      let
wenzelm@40281
   528
        val max_params = filter (is_paramT o deref tye) (Typ_Graph.maximals G);
wenzelm@40281
   529
        val to_unify = map (fn T => T :: get_preds G T) max_params;
wenzelm@40281
   530
      in
wenzelm@40281
   531
        fold unify_list to_unify tye_idx
wenzelm@40281
   532
      end;
wenzelm@40281
   533
wenzelm@40281
   534
    fun solve_constraints G tye_idx = tye_idx
wenzelm@40281
   535
      |> assign_alternating [] (Typ_Graph.keys G) G
wenzelm@40281
   536
      |> unify_params G;
wenzelm@40281
   537
  in
wenzelm@40281
   538
    build_graph Typ_Graph.empty (map fst cs') tye_idx'
wenzelm@40281
   539
      |-> solve_constraints
wenzelm@40281
   540
  end;
wenzelm@40281
   541
wenzelm@40281
   542
wenzelm@40281
   543
wenzelm@40281
   544
(** coercion insertion **)
wenzelm@40281
   545
wenzelm@40281
   546
fun insert_coercions ctxt tye ts =
wenzelm@40281
   547
  let
wenzelm@40281
   548
    fun deep_deref T =
wenzelm@40281
   549
      (case deref tye T of
wenzelm@40281
   550
        Type (a, Ts) => Type (a, map deep_deref Ts)
wenzelm@40281
   551
      | U => U);
wenzelm@40281
   552
wenzelm@40281
   553
    fun gen_coercion ((Type (a, [])), (Type (b, []))) =
wenzelm@40281
   554
          if a = b
wenzelm@40281
   555
          then Abs (Name.uu, Type (a, []), Bound 0)
wenzelm@40281
   556
          else
wenzelm@40281
   557
            (case Symreltab.lookup (coes_of (Context.Proof ctxt)) (a, b) of
wenzelm@40281
   558
              NONE => raise Fail (a ^ " is not a subtype of " ^ b)
wenzelm@40281
   559
            | SOME co => co)
wenzelm@40281
   560
      | gen_coercion ((Type (a, Ts)), (Type (b, Us))) =
wenzelm@40281
   561
          if a <> b
wenzelm@40281
   562
          then raise raise Fail ("Different constructors: " ^ a ^ " and " ^ b)
wenzelm@40281
   563
          else
wenzelm@40281
   564
            let
wenzelm@40282
   565
              fun inst t Ts =
wenzelm@40282
   566
                Term.subst_vars
wenzelm@40281
   567
                  (((Term.add_tvar_namesT (fastype_of t) []) ~~ rev Ts), []) t;
wenzelm@40281
   568
              fun sub_co (COVARIANT, TU) = gen_coercion TU
wenzelm@40281
   569
                | sub_co (CONTRAVARIANT, TU) = gen_coercion (swap TU);
wenzelm@40281
   570
              fun ts_of [] = []
wenzelm@40282
   571
                | ts_of (Type ("fun", [x1, x2]) :: xs) = x1 :: x2 :: (ts_of xs);
wenzelm@40281
   572
            in
wenzelm@40281
   573
              (case Symtab.lookup (tmaps_of (Context.Proof ctxt)) a of
wenzelm@40281
   574
                NONE => raise Fail ("No map function for " ^ a ^ " known")
wenzelm@40281
   575
              | SOME tmap =>
wenzelm@40281
   576
                  let
wenzelm@40281
   577
                    val used_coes = map sub_co ((snd tmap) ~~ (Ts ~~ Us));
wenzelm@40281
   578
                  in
wenzelm@40281
   579
                    Term.list_comb
wenzelm@40281
   580
                      (inst (fst tmap) (ts_of (map fastype_of used_coes)), used_coes)
wenzelm@40281
   581
                  end)
wenzelm@40281
   582
            end
wenzelm@40281
   583
      | gen_coercion (T, U) =
wenzelm@40281
   584
          if Type.could_unify (T, U)
wenzelm@40281
   585
          then Abs (Name.uu, T, Bound 0)
wenzelm@40281
   586
          else raise Fail ("Cannot generate coercion from "
wenzelm@40281
   587
            ^ Syntax.string_of_typ ctxt T ^ " to " ^ Syntax.string_of_typ ctxt U);
wenzelm@40281
   588
wenzelm@40281
   589
    fun insert _ (Const (c, T)) =
wenzelm@40281
   590
          let val T' = deep_deref T;
wenzelm@40281
   591
          in (Const (c, T'), T') end
wenzelm@40281
   592
      | insert _ (Free (x, T)) =
wenzelm@40281
   593
          let val T' = deep_deref T;
wenzelm@40281
   594
          in (Free (x, T'), T') end
wenzelm@40281
   595
      | insert _ (Var (xi, T)) =
wenzelm@40281
   596
          let val T' = deep_deref T;
wenzelm@40281
   597
          in (Var (xi, T'), T') end
wenzelm@40281
   598
      | insert bs (Bound i) =
wenzelm@40281
   599
          let val T = nth bs i handle Subscript =>
wenzelm@40281
   600
            raise TYPE ("Loose bound variable: B." ^ string_of_int i, [], []);
wenzelm@40281
   601
          in (Bound i, T) end
wenzelm@40281
   602
      | insert bs (Abs (x, T, t)) =
wenzelm@40281
   603
          let
wenzelm@40281
   604
            val T' = deep_deref T;
wenzelm@40282
   605
            val (t', T'') = insert (T' :: bs) t;
wenzelm@40281
   606
          in
wenzelm@40281
   607
            (Abs (x, T', t'), T' --> T'')
wenzelm@40281
   608
          end
wenzelm@40281
   609
      | insert bs (t $ u) =
wenzelm@40281
   610
          let
wenzelm@40281
   611
            val (t', Type ("fun", [U, T])) = insert bs t;
wenzelm@40281
   612
            val (u', U') = insert bs u;
wenzelm@40281
   613
          in
wenzelm@40281
   614
            if U <> U'
wenzelm@40281
   615
            then (t' $ (gen_coercion (U', U) $ u'), T)
wenzelm@40281
   616
            else (t' $ u', T)
wenzelm@40281
   617
          end
wenzelm@40281
   618
  in
wenzelm@40281
   619
    map (fst o insert []) ts
wenzelm@40281
   620
  end;
wenzelm@40281
   621
wenzelm@40281
   622
wenzelm@40281
   623
wenzelm@40281
   624
(** assembling the pipeline **)
wenzelm@40281
   625
wenzelm@40281
   626
fun infer_types ctxt const_type var_type raw_ts =
wenzelm@40281
   627
  let
wenzelm@40281
   628
    val (idx, ts) = Type_Infer.prepare ctxt const_type var_type raw_ts;
wenzelm@40281
   629
wenzelm@40281
   630
    fun gen_all t (tye_idx, constraints) =
wenzelm@40281
   631
      let
wenzelm@40281
   632
        val (_, tye_idx', constraints') = generate_constraints ctxt t tye_idx
wenzelm@40281
   633
      in (tye_idx', constraints' @ constraints) end;
wenzelm@40281
   634
wenzelm@40281
   635
    val (tye_idx, constraints) = fold gen_all ts ((Vartab.empty, idx), []);
wenzelm@40281
   636
    val (tye, _) = process_constraints ctxt constraints tye_idx;
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   637
    val ts' = insert_coercions ctxt tye ts;
wenzelm@40281
   638
wenzelm@40281
   639
    val (_, ts'') = Type_Infer.finish ctxt tye ([], ts');
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   640
  in ts'' end;
wenzelm@40281
   641
wenzelm@40281
   642
wenzelm@40281
   643
wenzelm@40281
   644
(** installation **)
wenzelm@40281
   645
wenzelm@40283
   646
(* term check *)
wenzelm@40283
   647
wenzelm@40281
   648
fun coercion_infer_types ctxt =
wenzelm@40281
   649
  infer_types ctxt
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   650
    (try (Consts.the_constraint (ProofContext.consts_of ctxt)))
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   651
    (ProofContext.def_type ctxt);
wenzelm@40281
   652
wenzelm@40283
   653
val add_term_check =
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   654
  Syntax.add_term_check ~100 "coercions"
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   655
    (fn xs => fn ctxt =>
wenzelm@40283
   656
      let val xs' = coercion_infer_types ctxt xs
wenzelm@40283
   657
      in if eq_list (op aconv) (xs, xs') then NONE else SOME (xs', ctxt) end);
wenzelm@40281
   658
wenzelm@40281
   659
wenzelm@40283
   660
(* declarations *)
wenzelm@40281
   661
wenzelm@40281
   662
fun add_type_map map_fun context =
wenzelm@40281
   663
  let
wenzelm@40281
   664
    val ctxt = Context.proof_of context;
wenzelm@40281
   665
    val t = singleton (Variable.polymorphic ctxt) (Syntax.read_term ctxt map_fun);
wenzelm@40281
   666
wenzelm@40281
   667
    fun err_str () = "\n\nthe general type signature for a map function is" ^
wenzelm@40281
   668
      "\nf1 => f2 => ... => fn => C [x1, ..., xn] => C [x1, ..., xn]" ^
wenzelm@40281
   669
      "\nwhere C is a constructor and fi is of type (xi => yi) or (yi => xi)";
wenzelm@40281
   670
wenzelm@40281
   671
    fun gen_arg_var ([], []) = []
wenzelm@40282
   672
      | gen_arg_var ((T, T') :: Ts, (U, U') :: Us) =
wenzelm@40281
   673
          if T = U andalso T' = U' then COVARIANT :: gen_arg_var (Ts, Us)
wenzelm@40281
   674
          else if T = U' andalso T' = U then CONTRAVARIANT :: gen_arg_var (Ts, Us)
wenzelm@40281
   675
          else error ("Functions do not apply to arguments correctly:" ^ err_str ())
wenzelm@40281
   676
      | gen_arg_var (_, _) =
wenzelm@40281
   677
          error ("Different numbers of functions and arguments\n" ^ err_str ());
wenzelm@40281
   678
wenzelm@40281
   679
    (* TODO: This function is only needed to introde the fun type map
wenzelm@40281
   680
      function: "% f g h . g o h o f". There must be a better solution. *)
wenzelm@40281
   681
    fun balanced (Type (_, [])) (Type (_, [])) = true
wenzelm@40281
   682
      | balanced (Type (a, Ts)) (Type (b, Us)) =
wenzelm@40281
   683
          a = b andalso forall I (map2 balanced Ts Us)
wenzelm@40281
   684
      | balanced (TFree _) (TFree _) = true
wenzelm@40281
   685
      | balanced (TVar _) (TVar _) = true
wenzelm@40281
   686
      | balanced _ _ = false;
wenzelm@40281
   687
wenzelm@40281
   688
    fun check_map_fun (pairs, []) (Type ("fun", [T as Type (C, Ts), U as Type (_, Us)])) =
wenzelm@40281
   689
          if balanced T U
wenzelm@40282
   690
          then ((pairs, Ts ~~ Us), C)
wenzelm@40281
   691
          else if C = "fun"
wenzelm@40281
   692
            then check_map_fun (pairs @ [(hd Ts, hd (tl Ts))], []) U
wenzelm@40281
   693
            else error ("Not a proper map function:" ^ err_str ())
wenzelm@40281
   694
      | check_map_fun _ _ = error ("Not a proper map function:" ^ err_str ());
wenzelm@40281
   695
wenzelm@40281
   696
    val res = check_map_fun ([], []) (fastype_of t);
wenzelm@40281
   697
    val res_av = gen_arg_var (fst res);
wenzelm@40281
   698
  in
wenzelm@40281
   699
    map_tmaps (Symtab.update (snd res, (t, res_av))) context
wenzelm@40281
   700
  end;
wenzelm@40281
   701
wenzelm@40281
   702
fun add_coercion coercion context =
wenzelm@40281
   703
  let
wenzelm@40281
   704
    val ctxt = Context.proof_of context;
wenzelm@40281
   705
    val t = singleton (Variable.polymorphic ctxt) (Syntax.read_term ctxt coercion);
wenzelm@40281
   706
wenzelm@40281
   707
    fun err_coercion () = error ("Bad type for coercion " ^
wenzelm@40281
   708
        Syntax.string_of_term ctxt t ^ ":\n" ^
wenzelm@40281
   709
        Syntax.string_of_typ ctxt (fastype_of t));
wenzelm@40281
   710
wenzelm@40281
   711
    val (Type ("fun", [T1, T2])) = fastype_of t
wenzelm@40281
   712
      handle Bind => err_coercion ();
wenzelm@40281
   713
wenzelm@40281
   714
    val a =
wenzelm@40281
   715
      (case T1 of
wenzelm@40281
   716
        Type (x, []) => x
wenzelm@40281
   717
      | _ => err_coercion ());
wenzelm@40281
   718
wenzelm@40281
   719
    val b =
wenzelm@40281
   720
      (case T2 of
wenzelm@40281
   721
        Type (x, []) => x
wenzelm@40281
   722
      | _ => err_coercion ());
wenzelm@40281
   723
wenzelm@40281
   724
    fun coercion_data_update (tab, G) =
wenzelm@40281
   725
      let
wenzelm@40281
   726
        val G' = maybe_new_nodes [a, b] G
wenzelm@40281
   727
        val G'' = Graph.add_edge_trans_acyclic (a, b) G'
wenzelm@40281
   728
          handle Graph.CYCLES _ => error (a ^ " is already a subtype of " ^ b ^
wenzelm@40281
   729
            "!\n\nCannot add coercion of type: " ^ a ^ " => " ^ b);
wenzelm@40281
   730
        val new_edges =
wenzelm@40281
   731
          flat (Graph.dest G'' |> map (fn (x, ys) => ys |> map_filter (fn y =>
wenzelm@40281
   732
            if Graph.is_edge G' (x, y) then NONE else SOME (x, y))));
wenzelm@40281
   733
        val G_and_new = Graph.add_edge (a, b) G';
wenzelm@40281
   734
wenzelm@40281
   735
        fun complex_coercion tab G (a, b) =
wenzelm@40281
   736
          let
wenzelm@40281
   737
            val path = hd (Graph.irreducible_paths G (a, b))
wenzelm@40281
   738
            val path' = (fst (split_last path)) ~~ tl path
wenzelm@40281
   739
          in Abs (Name.uu, Type (a, []),
wenzelm@40281
   740
              fold (fn t => fn u => t $ u) (map (the o Symreltab.lookup tab) path') (Bound 0))
wenzelm@40281
   741
          end;
wenzelm@40281
   742
wenzelm@40281
   743
        val tab' = fold
wenzelm@40281
   744
          (fn pair => fn tab => Symreltab.update (pair, complex_coercion tab G_and_new pair) tab)
wenzelm@40281
   745
          (filter (fn pair => pair <> (a, b)) new_edges)
wenzelm@40281
   746
          (Symreltab.update ((a, b), t) tab);
wenzelm@40281
   747
      in
wenzelm@40281
   748
        (tab', G'')
wenzelm@40281
   749
      end;
wenzelm@40281
   750
  in
wenzelm@40281
   751
    map_coes_and_graph coercion_data_update context
wenzelm@40281
   752
  end;
wenzelm@40281
   753
wenzelm@40283
   754
wenzelm@40283
   755
(* theory setup *)
wenzelm@40283
   756
wenzelm@40283
   757
val setup =
wenzelm@40283
   758
  Context.theory_map add_term_check #>
wenzelm@40283
   759
  Attrib.setup @{binding coercion} (Scan.lift Parse.term >>
wenzelm@40281
   760
    (fn t => fn (context, thm) => (add_coercion t context, thm)))
wenzelm@40281
   761
    "declaration of new coercions" #>
wenzelm@40283
   762
  Attrib.setup @{binding map_function} (Scan.lift Parse.term >>
wenzelm@40281
   763
    (fn t => fn (context, thm) => (add_type_map t context, thm)))
wenzelm@40283
   764
    "declaration of new map functions";
wenzelm@40281
   765
wenzelm@40281
   766
end;