src/Tools/subtyping.ML
author wenzelm
Wed Dec 01 13:09:08 2010 +0100 (2010-12-01)
changeset 40840 2f97215e79bf
parent 40838 d9bd6df700a8
child 40938 e258f6817add
permissions -rw-r--r--
just one Term.dest_funT;
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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 add_type_map: term -> Context.generic -> Context.generic
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  val add_coercion: term -> Context.generic -> Context.generic
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  val gen_coercion: Proof.context -> typ Vartab.table -> (typ * typ) -> term
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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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val rep_data = (fn Data args => args) o Data.get o Context.Proof;
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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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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 (Type_Infer.is_param xi) | _ => false;
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(* unification *)
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exception TYPE_INFERENCE_ERROR of unit -> string;
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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
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              (xi, Type_Infer.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 (Type_Infer.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 (`Type_Infer.is_paramT o Type_Infer.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 gen_msg err msg = 
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  err () ^ "\nNow trying to infer coercions:\n\nCoercion inference failed" ^ 
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  (if msg = "" then "" else ": " ^ msg) ^ "\n";
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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 unif_failed msg =
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  "Type unification failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n\n";
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fun subtyping_err_appl_msg 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 msg ^ Type.appl_error (Syntax.pp ctxt) t' T' u' U' ^ "\n" end;
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fun err_appl_msg 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 unif_failed msg ^ Type.appl_error (Syntax.pp ctxt) t' T' u' U' ^ "\n" end;
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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 ([msg,
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      "Cannot unify a list of types that should be the same:",
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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 ([msg, "Cannot fulfil 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 $ 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 err =
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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 = Type_Infer.mk_param idx [];
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            val V = Type_Infer.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') => error (gen_msg err msg);
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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 err cs tye_idx =
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  let
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    val coes_graph = coes_graph_of ctxt;
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    val tmaps = tmaps_of 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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        error (gen_msg err ("weak unification of subtype constraints fails\n" ^ msg))) 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
traytel@40836
   318
                  handle NO_UNIFIER (msg, tye) => 
traytel@40836
   319
                    error (gen_msg err ("failed to unify invariant arguments\n" ^ msg))));
wenzelm@40281
   320
            val (new, (tye', idx')) = apfst (fn cs => (cs ~~ replicate (length cs) error_pack))
wenzelm@40281
   321
              (fold new_constraints (arg_var ~~ (Ts ~~ Us)) ([], (tye, idx)));
wenzelm@40281
   322
            val test_update = is_compT orf is_freeT orf is_fixedvarT;
wenzelm@40281
   323
            val (ch, done') =
wenzelm@40286
   324
              if not (null new) then ([], done)
wenzelm@40286
   325
              else split_cs (test_update o Type_Infer.deref tye') done;
wenzelm@40281
   326
            val todo' = ch @ todo;
wenzelm@40281
   327
          in
wenzelm@40281
   328
            simplify done' (new @ todo') (tye', idx')
wenzelm@40281
   329
          end
wenzelm@40281
   330
        (*xi is definitely a parameter*)
wenzelm@40281
   331
        and expand varleq xi S a Ts error_pack done todo tye idx =
wenzelm@40281
   332
          let
wenzelm@40281
   333
            val n = length Ts;
wenzelm@40286
   334
            val args = map2 Type_Infer.mk_param (idx upto idx + n - 1) (arity_sorts a S);
wenzelm@40281
   335
            val tye' = Vartab.update_new (xi, Type(a, args)) tye;
wenzelm@40286
   336
            val (ch, done') = split_cs (is_compT o Type_Infer.deref tye') done;
wenzelm@40281
   337
            val todo' = ch @ todo;
wenzelm@40281
   338
            val new =
wenzelm@40281
   339
              if varleq then (Type(a, args), Type (a, Ts))
wenzelm@40286
   340
              else (Type (a, Ts), Type (a, args));
wenzelm@40281
   341
          in
wenzelm@40281
   342
            simplify done' ((new, error_pack) :: todo') (tye', idx + n)
wenzelm@40281
   343
          end
wenzelm@40281
   344
        (*TU is a pair of a parameter and a free/fixed variable*)
wenzelm@40281
   345
        and eliminate TU error_pack done todo tye idx =
wenzelm@40281
   346
          let
wenzelm@40286
   347
            val [TVar (xi, S)] = filter Type_Infer.is_paramT TU;
wenzelm@40286
   348
            val [T] = filter_out Type_Infer.is_paramT TU;
wenzelm@40281
   349
            val SOME S' = sort_of T;
wenzelm@40281
   350
            val test_update = if is_freeT T then is_freeT else is_fixedvarT;
wenzelm@40281
   351
            val tye' = Vartab.update_new (xi, T) tye;
wenzelm@40286
   352
            val (ch, done') = split_cs (test_update o Type_Infer.deref tye') done;
wenzelm@40281
   353
            val todo' = ch @ todo;
wenzelm@40281
   354
          in
wenzelm@40281
   355
            if subsort (S', S) (*TODO check this*)
wenzelm@40281
   356
            then simplify done' todo' (tye', idx)
traytel@40836
   357
            else error (gen_msg err "sort mismatch")
wenzelm@40281
   358
          end
wenzelm@40281
   359
        and simplify done [] tye_idx = (done, tye_idx)
wenzelm@40281
   360
          | simplify done (((T, U), error_pack) :: todo) (tye_idx as (tye, idx)) =
wenzelm@40286
   361
              (case (Type_Infer.deref tye T, Type_Infer.deref tye U) of
wenzelm@40281
   362
                (Type (a, []), Type (b, [])) =>
wenzelm@40281
   363
                  if a = b then simplify done todo tye_idx
wenzelm@40281
   364
                  else if Graph.is_edge coes_graph (a, b) then simplify done todo tye_idx
traytel@40836
   365
                  else error (gen_msg err (a ^ " is not a subtype of " ^ b))
wenzelm@40281
   366
              | (Type (a, Ts), Type (b, Us)) =>
traytel@40836
   367
                  if a <> b then error (gen_msg err "different constructors")
traytel@40836
   368
                    (fst tye_idx) error_pack
wenzelm@40281
   369
                  else contract a Ts Us error_pack done todo tye idx
wenzelm@40282
   370
              | (TVar (xi, S), Type (a, Ts as (_ :: _))) =>
wenzelm@40281
   371
                  expand true xi S a Ts error_pack done todo tye idx
wenzelm@40282
   372
              | (Type (a, Ts as (_ :: _)), TVar (xi, S)) =>
wenzelm@40281
   373
                  expand false xi S a Ts error_pack done todo tye idx
wenzelm@40281
   374
              | (T, U) =>
wenzelm@40281
   375
                  if T = U then simplify done todo tye_idx
wenzelm@40282
   376
                  else if exists (is_freeT orf is_fixedvarT) [T, U] andalso
wenzelm@40286
   377
                    exists Type_Infer.is_paramT [T, U]
wenzelm@40281
   378
                  then eliminate [T, U] error_pack done todo tye idx
wenzelm@40281
   379
                  else if exists (is_freeT orf is_fixedvarT) [T, U]
traytel@40836
   380
                  then error (gen_msg err "not eliminated free/fixed variables")
wenzelm@40282
   381
                  else simplify (((T, U), error_pack) :: done) todo tye_idx);
wenzelm@40281
   382
      in
wenzelm@40281
   383
        simplify [] cs tye_idx
wenzelm@40281
   384
      end;
wenzelm@40281
   385
wenzelm@40281
   386
wenzelm@40281
   387
    (* do simplification *)
wenzelm@40282
   388
wenzelm@40281
   389
    val (cs', tye_idx') = simplify_constraints cs tye_idx;
traytel@40836
   390
    
traytel@40836
   391
    fun find_error_pack lower T' = map_filter 
traytel@40836
   392
      (fn ((T, U), pack) => if if lower then T' = U else T' = T then SOME pack else NONE) cs';
traytel@40836
   393
      
traytel@40836
   394
    fun find_cycle_packs nodes = 
traytel@40836
   395
      let
traytel@40836
   396
        val (but_last, last) = split_last nodes
traytel@40836
   397
        val pairs = (last, hd nodes) :: (but_last ~~ tl nodes);
traytel@40836
   398
      in
traytel@40836
   399
        map_filter
wenzelm@40838
   400
          (fn (TU, pack) => if member (op =) pairs TU then SOME pack else NONE)
traytel@40836
   401
          cs'
traytel@40836
   402
      end;
wenzelm@40281
   403
wenzelm@40282
   404
    fun unify_list (T :: Ts) tye_idx =
traytel@40836
   405
      fold (fn U => fn tye_idx' => strong_unify ctxt (T, U) tye_idx') Ts tye_idx;
wenzelm@40281
   406
wenzelm@40281
   407
    (*styps stands either for supertypes or for subtypes of a type T
wenzelm@40281
   408
      in terms of the subtype-relation (excluding T itself)*)
wenzelm@40282
   409
    fun styps super T =
wenzelm@40281
   410
      (if super then Graph.imm_succs else Graph.imm_preds) coes_graph T
wenzelm@40281
   411
        handle Graph.UNDEF _ => [];
wenzelm@40281
   412
wenzelm@40282
   413
    fun minmax sup (T :: Ts) =
wenzelm@40281
   414
      let
wenzelm@40281
   415
        fun adjust T U = if sup then (T, U) else (U, T);
wenzelm@40281
   416
        fun extract T [] = T
wenzelm@40282
   417
          | extract T (U :: Us) =
wenzelm@40281
   418
              if Graph.is_edge coes_graph (adjust T U) then extract T Us
wenzelm@40281
   419
              else if Graph.is_edge coes_graph (adjust U T) then extract U Us
traytel@40836
   420
              else raise BOUND_ERROR "uncomparable types in type list";
wenzelm@40281
   421
      in
wenzelm@40281
   422
        t_of (extract T Ts)
wenzelm@40281
   423
      end;
wenzelm@40281
   424
wenzelm@40282
   425
    fun ex_styp_of_sort super T styps_and_sorts =
wenzelm@40281
   426
      let
wenzelm@40281
   427
        fun adjust T U = if super then (T, U) else (U, T);
wenzelm@40282
   428
        fun styp_test U Ts = forall
wenzelm@40281
   429
          (fn T => T = U orelse Graph.is_edge coes_graph (adjust U T)) Ts;
wenzelm@40281
   430
        fun fitting Ts S U = Type.of_sort tsig (t_of U, S) andalso styp_test U Ts
wenzelm@40281
   431
      in
wenzelm@40281
   432
        forall (fn (Ts, S) => exists (fitting Ts S) (T :: styps super T)) styps_and_sorts
wenzelm@40281
   433
      end;
wenzelm@40281
   434
wenzelm@40281
   435
    (* computes the tightest possible, correct assignment for 'a::S
wenzelm@40281
   436
       e.g. in the supremum case (sup = true):
wenzelm@40281
   437
               ------- 'a::S---
wenzelm@40281
   438
              /        /    \  \
wenzelm@40281
   439
             /        /      \  \
wenzelm@40281
   440
        'b::C1   'c::C2 ...  T1 T2 ...
wenzelm@40281
   441
wenzelm@40281
   442
       sorts - list of sorts [C1, C2, ...]
wenzelm@40281
   443
       T::Ts - non-empty list of base types [T1, T2, ...]
wenzelm@40281
   444
    *)
wenzelm@40282
   445
    fun tightest sup S styps_and_sorts (T :: Ts) =
wenzelm@40281
   446
      let
wenzelm@40281
   447
        fun restriction T = Type.of_sort tsig (t_of T, S)
wenzelm@40281
   448
          andalso ex_styp_of_sort (not sup) T styps_and_sorts;
wenzelm@40281
   449
        fun candidates T = inter (op =) (filter restriction (T :: styps sup T));
wenzelm@40281
   450
      in
wenzelm@40281
   451
        (case fold candidates Ts (filter restriction (T :: styps sup T)) of
traytel@40836
   452
          [] => raise BOUND_ERROR ("no " ^ (if sup then "supremum" else "infimum"))
wenzelm@40281
   453
        | [T] => t_of T
wenzelm@40281
   454
        | Ts => minmax sup Ts)
wenzelm@40281
   455
      end;
wenzelm@40281
   456
wenzelm@40281
   457
    fun build_graph G [] tye_idx = (G, tye_idx)
wenzelm@40282
   458
      | build_graph G ((T, U) :: cs) tye_idx =
wenzelm@40281
   459
        if T = U then build_graph G cs tye_idx
wenzelm@40281
   460
        else
wenzelm@40281
   461
          let
wenzelm@40281
   462
            val G' = maybe_new_typnodes [T, U] G;
wenzelm@40281
   463
            val (G'', tye_idx') = (add_edge (T, U) G', tye_idx)
wenzelm@40281
   464
              handle Typ_Graph.CYCLES cycles =>
wenzelm@40281
   465
                let
traytel@40836
   466
                  val (tye, idx) = 
traytel@40836
   467
                    fold 
traytel@40836
   468
                      (fn cycle => fn tye_idx' => (unify_list cycle tye_idx'
traytel@40836
   469
                        handle NO_UNIFIER (msg, tye) => 
traytel@40836
   470
                          err_bound ctxt 
traytel@40836
   471
                            (gen_msg err ("constraint cycle not unifiable" ^ msg)) (fst tye_idx)
traytel@40836
   472
                            (find_cycle_packs cycle)))
traytel@40836
   473
                      cycles tye_idx
wenzelm@40281
   474
                in
traytel@40836
   475
                  collapse (tye, idx) cycles G
traytel@40836
   476
                end
wenzelm@40281
   477
          in
wenzelm@40281
   478
            build_graph G'' cs tye_idx'
wenzelm@40281
   479
          end
traytel@40836
   480
    and collapse (tye, idx) cycles G = (*nodes non-empty list*)
wenzelm@40281
   481
      let
traytel@40836
   482
        (*all cycles collapse to one node,
traytel@40836
   483
          because all of them share at least the nodes x and y*)
traytel@40836
   484
        val nodes = (distinct (op =) (flat cycles));
traytel@40836
   485
        val T = Type_Infer.deref tye (hd nodes);
wenzelm@40281
   486
        val P = new_imm_preds G nodes;
wenzelm@40281
   487
        val S = new_imm_succs G nodes;
wenzelm@40281
   488
        val G' = Typ_Graph.del_nodes (tl nodes) G;
traytel@40836
   489
        fun check_and_gen super T' =
traytel@40836
   490
          let val U = Type_Infer.deref tye T';
traytel@40836
   491
          in
traytel@40836
   492
            if not (is_typeT T) orelse not (is_typeT U) orelse T = U
traytel@40836
   493
            then if super then (hd nodes, T') else (T', hd nodes)
traytel@40836
   494
            else 
traytel@40836
   495
              if super andalso 
traytel@40836
   496
                Graph.is_edge coes_graph (nameT T, nameT U) then (hd nodes, T')
traytel@40836
   497
              else if not super andalso 
traytel@40836
   498
                Graph.is_edge coes_graph (nameT U, nameT T) then (T', hd nodes)
traytel@40836
   499
              else err_bound ctxt (gen_msg err "cycle elimination produces inconsistent graph")
traytel@40836
   500
                    (fst tye_idx) 
traytel@40836
   501
                    (maps find_cycle_packs cycles @ find_error_pack super T')
traytel@40836
   502
          end;
wenzelm@40281
   503
      in
traytel@40836
   504
        build_graph G' (map (check_and_gen false) P @ map (check_and_gen true) S) (tye, idx)
wenzelm@40281
   505
      end;
wenzelm@40281
   506
wenzelm@40281
   507
    fun assign_bound lower G key (tye_idx as (tye, _)) =
wenzelm@40286
   508
      if Type_Infer.is_paramT (Type_Infer.deref tye key) then
wenzelm@40281
   509
        let
wenzelm@40286
   510
          val TVar (xi, S) = Type_Infer.deref tye key;
wenzelm@40281
   511
          val get_bound = if lower then get_preds else get_succs;
wenzelm@40281
   512
          val raw_bound = get_bound G key;
wenzelm@40286
   513
          val bound = map (Type_Infer.deref tye) raw_bound;
wenzelm@40286
   514
          val not_params = filter_out Type_Infer.is_paramT bound;
wenzelm@40282
   515
          fun to_fulfil T =
wenzelm@40281
   516
            (case sort_of T of
wenzelm@40281
   517
              NONE => NONE
wenzelm@40282
   518
            | SOME S =>
wenzelm@40286
   519
                SOME
wenzelm@40286
   520
                  (map nameT
wenzelm@40286
   521
                    (filter_out Type_Infer.is_paramT (map (Type_Infer.deref tye) (get_bound G T))),
wenzelm@40286
   522
                      S));
wenzelm@40281
   523
          val styps_and_sorts = distinct (op =) (map_filter to_fulfil raw_bound);
wenzelm@40281
   524
          val assignment =
wenzelm@40281
   525
            if null bound orelse null not_params then NONE
wenzelm@40281
   526
            else SOME (tightest lower S styps_and_sorts (map nameT not_params)
traytel@40836
   527
                handle BOUND_ERROR msg => 
traytel@40836
   528
                  err_bound ctxt (gen_msg err msg) tye (find_error_pack lower key))
wenzelm@40281
   529
        in
wenzelm@40281
   530
          (case assignment of
wenzelm@40281
   531
            NONE => tye_idx
wenzelm@40281
   532
          | SOME T =>
wenzelm@40286
   533
              if Type_Infer.is_paramT T then tye_idx
wenzelm@40281
   534
              else if lower then (*upper bound check*)
wenzelm@40281
   535
                let
wenzelm@40286
   536
                  val other_bound = map (Type_Infer.deref tye) (get_succs G key);
wenzelm@40281
   537
                  val s = nameT T;
wenzelm@40281
   538
                in
wenzelm@40281
   539
                  if subset (op = o apfst nameT) (filter is_typeT other_bound, s :: styps true s)
wenzelm@40281
   540
                  then apfst (Vartab.update (xi, T)) tye_idx
traytel@40836
   541
                  else err_bound ctxt (gen_msg err ("assigned simple type " ^ s ^
wenzelm@40281
   542
                    " clashes with the upper bound of variable " ^
traytel@40836
   543
                    Syntax.string_of_typ ctxt (TVar(xi, S)))) tye (find_error_pack (not lower) key)
wenzelm@40281
   544
                end
wenzelm@40281
   545
              else apfst (Vartab.update (xi, T)) tye_idx)
wenzelm@40281
   546
        end
wenzelm@40281
   547
      else tye_idx;
wenzelm@40281
   548
wenzelm@40281
   549
    val assign_lb = assign_bound true;
wenzelm@40281
   550
    val assign_ub = assign_bound false;
wenzelm@40281
   551
wenzelm@40281
   552
    fun assign_alternating ts' ts G tye_idx =
wenzelm@40281
   553
      if ts' = ts then tye_idx
wenzelm@40281
   554
      else
wenzelm@40281
   555
        let
wenzelm@40281
   556
          val (tye_idx' as (tye, _)) = fold (assign_lb G) ts tye_idx
wenzelm@40281
   557
            |> fold (assign_ub G) ts;
wenzelm@40281
   558
        in
traytel@40836
   559
          assign_alternating ts 
traytel@40836
   560
            (filter (Type_Infer.is_paramT o Type_Infer.deref tye) ts) G tye_idx'
wenzelm@40281
   561
        end;
wenzelm@40281
   562
wenzelm@40281
   563
    (*Unify all weakly connected components of the constraint forest,
wenzelm@40282
   564
      that contain only params. These are the only WCCs that contain
wenzelm@40281
   565
      params anyway.*)
wenzelm@40281
   566
    fun unify_params G (tye_idx as (tye, _)) =
wenzelm@40281
   567
      let
wenzelm@40286
   568
        val max_params =
wenzelm@40286
   569
          filter (Type_Infer.is_paramT o Type_Infer.deref tye) (Typ_Graph.maximals G);
wenzelm@40281
   570
        val to_unify = map (fn T => T :: get_preds G T) max_params;
wenzelm@40281
   571
      in
traytel@40836
   572
        fold 
traytel@40836
   573
          (fn Ts => fn tye_idx' => unify_list Ts tye_idx'
traytel@40836
   574
            handle NO_UNIFIER (msg, tye) => err_list ctxt (gen_msg err msg) (fst tye_idx) Ts)
traytel@40836
   575
          to_unify tye_idx
wenzelm@40281
   576
      end;
wenzelm@40281
   577
wenzelm@40281
   578
    fun solve_constraints G tye_idx = tye_idx
wenzelm@40281
   579
      |> assign_alternating [] (Typ_Graph.keys G) G
wenzelm@40281
   580
      |> unify_params G;
wenzelm@40281
   581
  in
wenzelm@40281
   582
    build_graph Typ_Graph.empty (map fst cs') tye_idx'
wenzelm@40281
   583
      |-> solve_constraints
wenzelm@40281
   584
  end;
wenzelm@40281
   585
wenzelm@40281
   586
wenzelm@40281
   587
wenzelm@40281
   588
(** coercion insertion **)
wenzelm@40281
   589
traytel@40836
   590
fun gen_coercion ctxt tye (T1, T2) =
traytel@40836
   591
  (case pairself (Type_Infer.deref tye) (T1, T2) of
traytel@40836
   592
    ((Type (a, [])), (Type (b, []))) =>
traytel@40836
   593
        if a = b
traytel@40836
   594
        then Abs (Name.uu, Type (a, []), Bound 0)
traytel@40836
   595
        else
traytel@40836
   596
          (case Symreltab.lookup (coes_of ctxt) (a, b) of
traytel@40836
   597
            NONE => raise Fail (a ^ " is not a subtype of " ^ b)
traytel@40836
   598
          | SOME co => co)
traytel@40836
   599
  | ((Type (a, Ts)), (Type (b, Us))) =>
traytel@40836
   600
        if a <> b
traytel@40836
   601
        then raise Fail ("Different constructors: " ^ a ^ " and " ^ b)
traytel@40836
   602
        else
traytel@40836
   603
          let
traytel@40836
   604
            fun inst t Ts =
traytel@40836
   605
              Term.subst_vars
traytel@40836
   606
                (((Term.add_tvar_namesT (fastype_of t) []) ~~ rev Ts), []) t;
traytel@40836
   607
            fun sub_co (COVARIANT, TU) = gen_coercion ctxt tye TU
traytel@40836
   608
              | sub_co (CONTRAVARIANT, TU) = gen_coercion ctxt tye (swap TU);
traytel@40836
   609
            fun ts_of [] = []
traytel@40836
   610
              | ts_of (Type ("fun", [x1, x2]) :: xs) = x1 :: x2 :: (ts_of xs);
traytel@40836
   611
          in
traytel@40836
   612
            (case Symtab.lookup (tmaps_of ctxt) a of
traytel@40836
   613
              NONE => raise Fail ("No map function for " ^ a ^ " known")
traytel@40836
   614
            | SOME tmap =>
traytel@40836
   615
                let
traytel@40836
   616
                  val used_coes = map sub_co ((snd tmap) ~~ (Ts ~~ Us));
traytel@40836
   617
                in
traytel@40836
   618
                  Term.list_comb
traytel@40836
   619
                    (inst (fst tmap) (ts_of (map fastype_of used_coes)), used_coes)
traytel@40836
   620
                end)
traytel@40836
   621
          end
traytel@40836
   622
  | (T, U) =>
traytel@40836
   623
        if Type.could_unify (T, U)
traytel@40836
   624
        then Abs (Name.uu, T, Bound 0)
traytel@40836
   625
        else raise Fail ("Cannot generate coercion from "
traytel@40836
   626
          ^ Syntax.string_of_typ ctxt T ^ " to " ^ Syntax.string_of_typ ctxt U));
traytel@40836
   627
wenzelm@40281
   628
fun insert_coercions ctxt tye ts =
wenzelm@40281
   629
  let
wenzelm@40281
   630
    fun insert _ (Const (c, T)) =
traytel@40836
   631
          let val T' = T;
wenzelm@40281
   632
          in (Const (c, T'), T') end
wenzelm@40281
   633
      | insert _ (Free (x, T)) =
traytel@40836
   634
          let val T' = T;
wenzelm@40281
   635
          in (Free (x, T'), T') end
wenzelm@40281
   636
      | insert _ (Var (xi, T)) =
traytel@40836
   637
          let val T' = T;
wenzelm@40281
   638
          in (Var (xi, T'), T') end
wenzelm@40281
   639
      | insert bs (Bound i) =
traytel@40836
   640
          let val T = nth bs i handle Subscript => err_loose i;
wenzelm@40281
   641
          in (Bound i, T) end
wenzelm@40281
   642
      | insert bs (Abs (x, T, t)) =
wenzelm@40281
   643
          let
traytel@40836
   644
            val T' = T;
wenzelm@40282
   645
            val (t', T'') = insert (T' :: bs) t;
wenzelm@40281
   646
          in
wenzelm@40281
   647
            (Abs (x, T', t'), T' --> T'')
wenzelm@40281
   648
          end
wenzelm@40281
   649
      | insert bs (t $ u) =
wenzelm@40281
   650
          let
traytel@40836
   651
            val (t', Type ("fun", [U, T])) = apsnd (Type_Infer.deref tye) (insert bs t);
wenzelm@40281
   652
            val (u', U') = insert bs u;
wenzelm@40281
   653
          in
traytel@40836
   654
            if can (fn TU => strong_unify ctxt TU (tye, 0)) (U, U')
traytel@40836
   655
            then (t' $ u', T)
traytel@40836
   656
            else (t' $ (gen_coercion ctxt tye (U', U) $ u'), T)
wenzelm@40281
   657
          end
wenzelm@40281
   658
  in
wenzelm@40281
   659
    map (fst o insert []) ts
wenzelm@40281
   660
  end;
wenzelm@40281
   661
wenzelm@40281
   662
wenzelm@40281
   663
wenzelm@40281
   664
(** assembling the pipeline **)
wenzelm@40281
   665
wenzelm@40281
   666
fun infer_types ctxt const_type var_type raw_ts =
wenzelm@40281
   667
  let
wenzelm@40281
   668
    val (idx, ts) = Type_Infer.prepare ctxt const_type var_type raw_ts;
wenzelm@40281
   669
traytel@40836
   670
    fun inf _ (t as (Const (_, T))) tye_idx = (t, T, tye_idx)
traytel@40836
   671
      | inf _ (t as (Free (_, T))) tye_idx = (t, T, tye_idx)
traytel@40836
   672
      | inf _ (t as (Var (_, T))) tye_idx = (t, T, tye_idx)
traytel@40836
   673
      | inf bs (t as (Bound i)) tye_idx =
traytel@40836
   674
          (t, snd (nth bs i handle Subscript => err_loose i), tye_idx)
traytel@40836
   675
      | inf bs (Abs (x, T, t)) tye_idx =
traytel@40836
   676
          let val (t', U, tye_idx') = inf ((x, T) :: bs) t tye_idx
traytel@40836
   677
          in (Abs (x, T, t'), T --> U, tye_idx') end
traytel@40836
   678
      | inf bs (t $ u) tye_idx =
traytel@40836
   679
          let
traytel@40836
   680
            val (t', T, tye_idx') = inf bs t tye_idx;
traytel@40836
   681
            val (u', U, (tye, idx)) = inf bs u tye_idx';
traytel@40836
   682
            val V = Type_Infer.mk_param idx [];
traytel@40836
   683
            val (tu, tye_idx'') = (t' $ u', strong_unify ctxt (U --> V, T) (tye, idx + 1))
traytel@40836
   684
              handle NO_UNIFIER (msg, tye') => 
traytel@40836
   685
                raise TYPE_INFERENCE_ERROR (err_appl_msg ctxt msg tye' bs t T u U);
traytel@40836
   686
          in (tu, V, tye_idx'') end;
wenzelm@40281
   687
traytel@40836
   688
    fun infer_single t (ts, tye_idx) = 
traytel@40836
   689
      let val (t, _, tye_idx') = inf [] t tye_idx;
traytel@40836
   690
      in (ts @ [t], tye_idx') end;
traytel@40836
   691
      
traytel@40836
   692
    val (ts', (tye, _)) = (fold infer_single ts ([], (Vartab.empty, idx))
traytel@40836
   693
      handle TYPE_INFERENCE_ERROR err =>     
traytel@40836
   694
        let
traytel@40836
   695
          fun gen_single t (tye_idx, constraints) =
traytel@40836
   696
            let val (_, tye_idx', constraints') = generate_constraints ctxt err t tye_idx
traytel@40836
   697
            in (tye_idx', constraints' @ constraints) end;
traytel@40836
   698
      
traytel@40836
   699
          val (tye_idx, constraints) = fold gen_single ts ((Vartab.empty, idx), []);
traytel@40836
   700
          val (tye, idx) = process_constraints ctxt err constraints tye_idx;
traytel@40836
   701
        in 
traytel@40836
   702
          (insert_coercions ctxt tye ts, (tye, idx))
traytel@40836
   703
        end);
wenzelm@40281
   704
wenzelm@40281
   705
    val (_, ts'') = Type_Infer.finish ctxt tye ([], ts');
wenzelm@40281
   706
  in ts'' end;
wenzelm@40281
   707
wenzelm@40281
   708
wenzelm@40281
   709
wenzelm@40281
   710
(** installation **)
wenzelm@40281
   711
wenzelm@40283
   712
(* term check *)
wenzelm@40283
   713
wenzelm@40281
   714
fun coercion_infer_types ctxt =
wenzelm@40281
   715
  infer_types ctxt
wenzelm@40281
   716
    (try (Consts.the_constraint (ProofContext.consts_of ctxt)))
wenzelm@40281
   717
    (ProofContext.def_type ctxt);
wenzelm@40281
   718
wenzelm@40283
   719
val add_term_check =
wenzelm@40283
   720
  Syntax.add_term_check ~100 "coercions"
wenzelm@40283
   721
    (fn xs => fn ctxt =>
wenzelm@40283
   722
      let val xs' = coercion_infer_types ctxt xs
wenzelm@40283
   723
      in if eq_list (op aconv) (xs, xs') then NONE else SOME (xs', ctxt) end);
wenzelm@40281
   724
wenzelm@40281
   725
wenzelm@40283
   726
(* declarations *)
wenzelm@40281
   727
wenzelm@40284
   728
fun add_type_map raw_t context =
wenzelm@40281
   729
  let
wenzelm@40281
   730
    val ctxt = Context.proof_of context;
wenzelm@40284
   731
    val t = singleton (Variable.polymorphic ctxt) raw_t;
wenzelm@40281
   732
wenzelm@40281
   733
    fun err_str () = "\n\nthe general type signature for a map function is" ^
wenzelm@40281
   734
      "\nf1 => f2 => ... => fn => C [x1, ..., xn] => C [x1, ..., xn]" ^
wenzelm@40281
   735
      "\nwhere C is a constructor and fi is of type (xi => yi) or (yi => xi)";
wenzelm@40281
   736
wenzelm@40281
   737
    fun gen_arg_var ([], []) = []
wenzelm@40282
   738
      | gen_arg_var ((T, T') :: Ts, (U, U') :: Us) =
wenzelm@40281
   739
          if T = U andalso T' = U' then COVARIANT :: gen_arg_var (Ts, Us)
wenzelm@40281
   740
          else if T = U' andalso T' = U then CONTRAVARIANT :: gen_arg_var (Ts, Us)
wenzelm@40281
   741
          else error ("Functions do not apply to arguments correctly:" ^ err_str ())
wenzelm@40281
   742
      | gen_arg_var (_, _) =
wenzelm@40281
   743
          error ("Different numbers of functions and arguments\n" ^ err_str ());
wenzelm@40281
   744
wenzelm@40281
   745
    (* TODO: This function is only needed to introde the fun type map
wenzelm@40281
   746
      function: "% f g h . g o h o f". There must be a better solution. *)
wenzelm@40281
   747
    fun balanced (Type (_, [])) (Type (_, [])) = true
wenzelm@40281
   748
      | balanced (Type (a, Ts)) (Type (b, Us)) =
wenzelm@40281
   749
          a = b andalso forall I (map2 balanced Ts Us)
wenzelm@40281
   750
      | balanced (TFree _) (TFree _) = true
wenzelm@40281
   751
      | balanced (TVar _) (TVar _) = true
wenzelm@40281
   752
      | balanced _ _ = false;
wenzelm@40281
   753
wenzelm@40281
   754
    fun check_map_fun (pairs, []) (Type ("fun", [T as Type (C, Ts), U as Type (_, Us)])) =
wenzelm@40281
   755
          if balanced T U
wenzelm@40282
   756
          then ((pairs, Ts ~~ Us), C)
wenzelm@40281
   757
          else if C = "fun"
wenzelm@40281
   758
            then check_map_fun (pairs @ [(hd Ts, hd (tl Ts))], []) U
wenzelm@40281
   759
            else error ("Not a proper map function:" ^ err_str ())
wenzelm@40281
   760
      | check_map_fun _ _ = error ("Not a proper map function:" ^ err_str ());
wenzelm@40281
   761
wenzelm@40281
   762
    val res = check_map_fun ([], []) (fastype_of t);
wenzelm@40281
   763
    val res_av = gen_arg_var (fst res);
wenzelm@40281
   764
  in
wenzelm@40281
   765
    map_tmaps (Symtab.update (snd res, (t, res_av))) context
wenzelm@40281
   766
  end;
wenzelm@40281
   767
wenzelm@40284
   768
fun add_coercion raw_t context =
wenzelm@40281
   769
  let
wenzelm@40281
   770
    val ctxt = Context.proof_of context;
wenzelm@40284
   771
    val t = singleton (Variable.polymorphic ctxt) raw_t;
wenzelm@40281
   772
wenzelm@40281
   773
    fun err_coercion () = error ("Bad type for coercion " ^
wenzelm@40281
   774
        Syntax.string_of_term ctxt t ^ ":\n" ^
wenzelm@40281
   775
        Syntax.string_of_typ ctxt (fastype_of t));
wenzelm@40281
   776
wenzelm@40840
   777
    val (T1, T2) = Term.dest_funT (fastype_of t)
wenzelm@40840
   778
      handle TYPE _ => err_coercion ();
wenzelm@40281
   779
wenzelm@40281
   780
    val a =
wenzelm@40281
   781
      (case T1 of
wenzelm@40281
   782
        Type (x, []) => x
wenzelm@40281
   783
      | _ => err_coercion ());
wenzelm@40281
   784
wenzelm@40281
   785
    val b =
wenzelm@40281
   786
      (case T2 of
wenzelm@40281
   787
        Type (x, []) => x
wenzelm@40281
   788
      | _ => err_coercion ());
wenzelm@40281
   789
wenzelm@40281
   790
    fun coercion_data_update (tab, G) =
wenzelm@40281
   791
      let
wenzelm@40281
   792
        val G' = maybe_new_nodes [a, b] G
wenzelm@40281
   793
        val G'' = Graph.add_edge_trans_acyclic (a, b) G'
wenzelm@40281
   794
          handle Graph.CYCLES _ => error (a ^ " is already a subtype of " ^ b ^
wenzelm@40281
   795
            "!\n\nCannot add coercion of type: " ^ a ^ " => " ^ b);
wenzelm@40281
   796
        val new_edges =
wenzelm@40281
   797
          flat (Graph.dest G'' |> map (fn (x, ys) => ys |> map_filter (fn y =>
wenzelm@40281
   798
            if Graph.is_edge G' (x, y) then NONE else SOME (x, y))));
wenzelm@40281
   799
        val G_and_new = Graph.add_edge (a, b) G';
wenzelm@40281
   800
wenzelm@40281
   801
        fun complex_coercion tab G (a, b) =
wenzelm@40281
   802
          let
wenzelm@40281
   803
            val path = hd (Graph.irreducible_paths G (a, b))
traytel@40836
   804
            val path' = fst (split_last path) ~~ tl path
wenzelm@40281
   805
          in Abs (Name.uu, Type (a, []),
wenzelm@40281
   806
              fold (fn t => fn u => t $ u) (map (the o Symreltab.lookup tab) path') (Bound 0))
wenzelm@40281
   807
          end;
wenzelm@40281
   808
wenzelm@40281
   809
        val tab' = fold
wenzelm@40281
   810
          (fn pair => fn tab => Symreltab.update (pair, complex_coercion tab G_and_new pair) tab)
wenzelm@40281
   811
          (filter (fn pair => pair <> (a, b)) new_edges)
wenzelm@40281
   812
          (Symreltab.update ((a, b), t) tab);
wenzelm@40281
   813
      in
wenzelm@40281
   814
        (tab', G'')
wenzelm@40281
   815
      end;
wenzelm@40281
   816
  in
wenzelm@40281
   817
    map_coes_and_graph coercion_data_update context
wenzelm@40281
   818
  end;
wenzelm@40281
   819
wenzelm@40283
   820
wenzelm@40283
   821
(* theory setup *)
wenzelm@40283
   822
wenzelm@40283
   823
val setup =
wenzelm@40283
   824
  Context.theory_map add_term_check #>
wenzelm@40284
   825
  Attrib.setup @{binding coercion}
wenzelm@40284
   826
    (Args.term >> (fn t => Thm.declaration_attribute (K (add_coercion t))))
wenzelm@40281
   827
    "declaration of new coercions" #>
traytel@40297
   828
  Attrib.setup @{binding coercion_map}
wenzelm@40284
   829
    (Args.term >> (fn t => Thm.declaration_attribute (K (add_type_map t))))
wenzelm@40283
   830
    "declaration of new map functions";
wenzelm@40281
   831
wenzelm@40281
   832
end;