wenzelm@40281: (*  Title:      Tools/subtyping.ML
wenzelm@40281:     Author:     Dmitriy Traytel, TU Muenchen
wenzelm@40281: 
wenzelm@40281: Coercive subtyping via subtype constraints.
wenzelm@40281: *)
wenzelm@40281: 
wenzelm@40281: signature SUBTYPING =
wenzelm@40281: sig
wenzelm@40939:   val coercion_enabled: bool Config.T
wenzelm@40284:   val add_type_map: term -> Context.generic -> Context.generic
wenzelm@40284:   val add_coercion: term -> Context.generic -> Context.generic
traytel@45059:   val print_coercions: Proof.context -> unit
wenzelm@40283:   val setup: theory -> theory
wenzelm@40281: end;
wenzelm@40281: 
wenzelm@40283: structure Subtyping: SUBTYPING =
wenzelm@40281: struct
wenzelm@40281: 
wenzelm@40281: (** coercions data **)
wenzelm@40281: 
traytel@41353: datatype variance = COVARIANT | CONTRAVARIANT | INVARIANT | INVARIANT_TO of typ;
traytel@51327: datatype coerce_arg = PERMIT | FORBID | LEAVE
wenzelm@40281: 
wenzelm@40281: datatype data = Data of
traytel@45060:   {coes: (term * ((typ list * typ list) * term list)) Symreltab.table,  (*coercions table*)
traytel@45060:    (*full coercions graph - only used at coercion declaration/deletion*)
traytel@45060:    full_graph: int Graph.T,
wenzelm@52432:    (*coercions graph restricted to base types - for efficiency reasons stored in the context*)
traytel@45060:    coes_graph: int Graph.T,
traytel@51319:    tmaps: (term * variance list) Symtab.table,  (*map functions*)
traytel@51327:    coerce_args: coerce_arg list Symtab.table  (*special constants with non-coercible arguments*)};
wenzelm@40281: 
traytel@51319: fun make_data (coes, full_graph, coes_graph, tmaps, coerce_args) =
traytel@51319:   Data {coes = coes, full_graph = full_graph, coes_graph = coes_graph,
traytel@51319:     tmaps = tmaps, coerce_args = coerce_args};
wenzelm@40281: 
traytel@45935: fun merge_error_coes (a, b) =
traytel@45935:   error ("Cannot merge coercion tables.\nConflicting declarations for coercions from " ^
traytel@45935:     quote a ^ " to " ^ quote b ^ ".");
traytel@45935: 
traytel@45935: fun merge_error_tmaps C =
traytel@45935:   error ("Cannot merge coercion map tables.\nConflicting declarations for the constructor " ^
traytel@45935:     quote C ^ ".");
traytel@45935: 
traytel@51319: fun merge_error_coerce_args C =
wenzelm@55303:   error ("Cannot merge tables for constants with coercion-invariant arguments.\n" ^
wenzelm@55303:     "Conflicting declarations for the constant " ^ quote C ^ ".");
traytel@51319: 
wenzelm@40281: structure Data = Generic_Data
wenzelm@40281: (
wenzelm@40281:   type T = data;
traytel@51319:   val empty = make_data (Symreltab.empty, Graph.empty, Graph.empty, Symtab.empty, Symtab.empty);
wenzelm@40281:   val extend = I;
wenzelm@40281:   fun merge
traytel@51319:     (Data {coes = coes1, full_graph = full_graph1, coes_graph = coes_graph1,
traytel@51319:       tmaps = tmaps1, coerce_args = coerce_args1},
traytel@51319:       Data {coes = coes2, full_graph = full_graph2, coes_graph = coes_graph2,
traytel@51319:         tmaps = tmaps2, coerce_args = coerce_args2}) =
traytel@45060:     make_data (Symreltab.merge (eq_pair (op aconv)
traytel@45060:         (eq_pair (eq_pair (eq_list (op =)) (eq_list (op =))) (eq_list (op aconv))))
traytel@45935:         (coes1, coes2) handle Symreltab.DUP key => merge_error_coes key,
traytel@45060:       Graph.merge (op =) (full_graph1, full_graph2),
wenzelm@40281:       Graph.merge (op =) (coes_graph1, coes_graph2),
traytel@45935:       Symtab.merge (eq_pair (op aconv) (op =)) (tmaps1, tmaps2)
traytel@51319:         handle Symtab.DUP key => merge_error_tmaps key,
traytel@51319:       Symtab.merge (eq_list (op =)) (coerce_args1, coerce_args2)
traytel@51319:         handle Symtab.DUP key => merge_error_coerce_args key);
wenzelm@40281: );
wenzelm@40281: 
wenzelm@40281: fun map_data f =
traytel@51319:   Data.map (fn Data {coes, full_graph, coes_graph, tmaps, coerce_args} =>
traytel@51319:     make_data (f (coes, full_graph, coes_graph, tmaps, coerce_args)));
wenzelm@40281: 
wenzelm@40281: fun map_coes f =
traytel@51319:   map_data (fn (coes, full_graph, coes_graph, tmaps, coerce_args) =>
traytel@51319:     (f coes, full_graph, coes_graph, tmaps, coerce_args));
wenzelm@40281: 
wenzelm@40281: fun map_coes_graph f =
traytel@51319:   map_data (fn (coes, full_graph, coes_graph, tmaps, coerce_args) =>
traytel@51319:     (coes, full_graph, f coes_graph, tmaps, coerce_args));
wenzelm@40281: 
traytel@45060: fun map_coes_and_graphs f =
traytel@51319:   map_data (fn (coes, full_graph, coes_graph, tmaps, coerce_args) =>
traytel@45060:     let val (coes', full_graph', coes_graph') = f (coes, full_graph, coes_graph);
traytel@51319:     in (coes', full_graph', coes_graph', tmaps, coerce_args) end);
wenzelm@40281: 
wenzelm@40281: fun map_tmaps f =
traytel@51319:   map_data (fn (coes, full_graph, coes_graph, tmaps, coerce_args) =>
traytel@51319:     (coes, full_graph, coes_graph, f tmaps, coerce_args));
traytel@51319: 
traytel@51319: fun map_coerce_args f =
traytel@51319:   map_data (fn (coes, full_graph, coes_graph, tmaps, coerce_args) =>
traytel@51319:     (coes, full_graph, coes_graph, tmaps, f coerce_args));
wenzelm@40281: 
wenzelm@40285: val rep_data = (fn Data args => args) o Data.get o Context.Proof;
wenzelm@40281: 
wenzelm@40281: val coes_of = #coes o rep_data;
wenzelm@40281: val coes_graph_of = #coes_graph o rep_data;
wenzelm@40281: val tmaps_of = #tmaps o rep_data;
traytel@51319: val coerce_args_of = #coerce_args o rep_data;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** utils **)
wenzelm@40281: 
wenzelm@46614: fun restrict_graph G = Graph.restrict (fn x => Graph.get_node G x = 0) G;
traytel@45060: 
wenzelm@40281: fun nameT (Type (s, [])) = s;
wenzelm@40281: fun t_of s = Type (s, []);
wenzelm@40286: 
wenzelm@40281: fun sort_of (TFree (_, S)) = SOME S
wenzelm@40281:   | sort_of (TVar (_, S)) = SOME S
wenzelm@40281:   | sort_of _ = NONE;
wenzelm@40281: 
wenzelm@40281: val is_typeT = fn (Type _) => true | _ => false;
traytel@41353: val is_stypeT = fn (Type (_, [])) => true | _ => false;
wenzelm@40282: val is_compT = fn (Type (_, _ :: _)) => true | _ => false;
wenzelm@40281: val is_freeT = fn (TFree _) => true | _ => false;
wenzelm@40286: val is_fixedvarT = fn (TVar (xi, _)) => not (Type_Infer.is_param xi) | _ => false;
traytel@41353: val is_funtype = fn (Type ("fun", [_, _])) => true | _ => false;
traytel@51335: 
traytel@51335: fun mk_identity T = Abs (Name.uu, T, Bound 0);
traytel@43591: val is_identity = fn (Abs (_, _, Bound 0)) => true | _ => false;
wenzelm@40281: 
traytel@45060: fun instantiate t Ts = Term.subst_TVars
traytel@45060:   ((Term.add_tvar_namesT (fastype_of t) []) ~~ rev Ts) t;
traytel@45060: 
wenzelm@55303: exception COERCION_GEN_ERROR of unit -> string * Buffer.T;
traytel@54584: 
wenzelm@55303: infixr ++>  (*composition with deferred error message*)
wenzelm@55303: fun (err : unit -> string * Buffer.T) ++> s =
wenzelm@55303:   err #> apsnd (Buffer.add s);
traytel@54584: 
wenzelm@55303: fun eval_err err =
wenzelm@55303:   let val (s, buf) = err ()
wenzelm@55303:   in s ^ Markup.markup Markup.text_fold (Buffer.content buf) end;
traytel@54584: 
wenzelm@55303: fun eval_error err = error (eval_err err);
traytel@45060: 
traytel@45060: fun inst_collect tye err T U =
traytel@45060:   (case (T, Type_Infer.deref tye U) of
traytel@54584:     (TVar (xi, _), U) => [(xi, U)]
traytel@45060:   | (Type (a, Ts), Type (b, Us)) =>
wenzelm@55303:       if a <> b then eval_error err else inst_collects tye err Ts Us
wenzelm@55303:   | (_, U') => if T <> U' then eval_error err else [])
traytel@45060: and inst_collects tye err Ts Us =
traytel@45060:   fold2 (fn T => fn U => fn is => inst_collect tye err T U @ is) Ts Us [];
traytel@45060: 
wenzelm@40281: 
traytel@40836: (* unification *)
wenzelm@40281: 
wenzelm@40281: exception NO_UNIFIER of string * typ Vartab.table;
wenzelm@40281: 
wenzelm@40281: fun unify weak ctxt =
wenzelm@40281:   let
wenzelm@42361:     val thy = Proof_Context.theory_of ctxt;
wenzelm@42386:     val arity_sorts = Type.arity_sorts (Context.pretty ctxt) (Sign.tsig_of thy);
wenzelm@40281: 
wenzelm@40282: 
wenzelm@40281:     (* adjust sorts of parameters *)
wenzelm@40281: 
wenzelm@40281:     fun not_of_sort x S' S =
wenzelm@40281:       "Variable " ^ x ^ "::" ^ Syntax.string_of_sort ctxt S' ^ " not of sort " ^
wenzelm@40281:         Syntax.string_of_sort ctxt S;
wenzelm@40281: 
wenzelm@40281:     fun meet (_, []) tye_idx = tye_idx
wenzelm@40281:       | meet (Type (a, Ts), S) (tye_idx as (tye, _)) =
wenzelm@40281:           meets (Ts, arity_sorts a S handle ERROR msg => raise NO_UNIFIER (msg, tye)) tye_idx
wenzelm@40281:       | meet (TFree (x, S'), S) (tye_idx as (tye, _)) =
wenzelm@40281:           if Sign.subsort thy (S', S) then tye_idx
wenzelm@40281:           else raise NO_UNIFIER (not_of_sort x S' S, tye)
wenzelm@40281:       | meet (TVar (xi, S'), S) (tye_idx as (tye, idx)) =
wenzelm@40281:           if Sign.subsort thy (S', S) then tye_idx
wenzelm@40281:           else if Type_Infer.is_param xi then
wenzelm@40286:             (Vartab.update_new
wenzelm@40286:               (xi, Type_Infer.mk_param idx (Sign.inter_sort thy (S', S))) tye, idx + 1)
wenzelm@40281:           else raise NO_UNIFIER (not_of_sort (Term.string_of_vname xi) S' S, tye)
wenzelm@40281:     and meets (T :: Ts, S :: Ss) (tye_idx as (tye, _)) =
wenzelm@40286:           meets (Ts, Ss) (meet (Type_Infer.deref tye T, S) tye_idx)
wenzelm@40281:       | meets _ tye_idx = tye_idx;
wenzelm@40281: 
wenzelm@55301:     val weak_meet = if weak then fn _ => I else meet;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281:     (* occurs check and assignment *)
wenzelm@40281: 
wenzelm@40281:     fun occurs_check tye xi (TVar (xi', _)) =
wenzelm@40281:           if xi = xi' then raise NO_UNIFIER ("Occurs check!", tye)
wenzelm@40281:           else
wenzelm@40281:             (case Vartab.lookup tye xi' of
wenzelm@40281:               NONE => ()
wenzelm@40281:             | SOME T => occurs_check tye xi T)
wenzelm@40281:       | occurs_check tye xi (Type (_, Ts)) = List.app (occurs_check tye xi) Ts
wenzelm@40281:       | occurs_check _ _ _ = ();
wenzelm@40281: 
wenzelm@40281:     fun assign xi (T as TVar (xi', _)) S env =
wenzelm@40281:           if xi = xi' then env
wenzelm@40281:           else env |> weak_meet (T, S) |>> Vartab.update_new (xi, T)
wenzelm@40281:       | assign xi T S (env as (tye, _)) =
wenzelm@40281:           (occurs_check tye xi T; env |> weak_meet (T, S) |>> Vartab.update_new (xi, T));
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281:     (* unification *)
wenzelm@40281: 
wenzelm@40281:     fun show_tycon (a, Ts) =
wenzelm@40281:       quote (Syntax.string_of_typ ctxt (Type (a, replicate (length Ts) dummyT)));
wenzelm@40281: 
wenzelm@40281:     fun unif (T1, T2) (env as (tye, _)) =
wenzelm@40286:       (case pairself (`Type_Infer.is_paramT o Type_Infer.deref tye) (T1, T2) of
wenzelm@40281:         ((true, TVar (xi, S)), (_, T)) => assign xi T S env
wenzelm@40281:       | ((_, T), (true, TVar (xi, S))) => assign xi T S env
wenzelm@40281:       | ((_, Type (a, Ts)), (_, Type (b, Us))) =>
wenzelm@40281:           if weak andalso null Ts andalso null Us then env
wenzelm@40281:           else if a <> b then
wenzelm@40281:             raise NO_UNIFIER
wenzelm@40281:               ("Clash of types " ^ show_tycon (a, Ts) ^ " and " ^ show_tycon (b, Us), tye)
wenzelm@40281:           else fold unif (Ts ~~ Us) env
wenzelm@40281:       | ((_, T), (_, U)) => if T = U then env else raise NO_UNIFIER ("", tye));
wenzelm@40281: 
wenzelm@40281:   in unif end;
wenzelm@40281: 
wenzelm@40281: val weak_unify = unify true;
wenzelm@40281: val strong_unify = unify false;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (* Typ_Graph shortcuts *)
wenzelm@40281: 
wenzelm@40281: fun get_preds G T = Typ_Graph.all_preds G [T];
wenzelm@40281: fun get_succs G T = Typ_Graph.all_succs G [T];
wenzelm@40281: fun maybe_new_typnode T G = perhaps (try (Typ_Graph.new_node (T, ()))) G;
wenzelm@40281: fun maybe_new_typnodes Ts G = fold maybe_new_typnode Ts G;
wenzelm@44338: fun new_imm_preds G Ts =  (* FIXME inefficient *)
wenzelm@44338:   subtract (op =) Ts (distinct (op =) (maps (Typ_Graph.immediate_preds G) Ts));
wenzelm@44338: fun new_imm_succs G Ts =  (* FIXME inefficient *)
wenzelm@44338:   subtract (op =) Ts (distinct (op =) (maps (Typ_Graph.immediate_succs G) Ts));
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (* Graph shortcuts *)
wenzelm@40281: 
wenzelm@55301: fun maybe_new_node s G = perhaps (try (Graph.new_node s)) G;
wenzelm@55301: fun maybe_new_nodes ss G = fold maybe_new_node ss G;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** error messages **)
wenzelm@40281: 
traytel@54584: fun gen_err err msg =
wenzelm@55303:   err ++> ("\nNow trying to infer coercions globally.\n\nCoercion inference failed" ^
wenzelm@55303:     (if msg = "" then "" else ":\n" ^ msg) ^ "\n");
traytel@45060: 
traytel@54584: val gen_msg = eval_err oo gen_err
traytel@40836: 
wenzelm@40281: fun prep_output ctxt tye bs ts Ts =
wenzelm@40281:   let
wenzelm@40281:     val (Ts_bTs', ts') = Type_Infer.finish ctxt tye (Ts @ map snd bs, ts);
wenzelm@40281:     val (Ts', Ts'') = chop (length Ts) Ts_bTs';
wenzelm@40281:     fun prep t =
wenzelm@40281:       let val xs = rev (Term.variant_frees t (rev (map fst bs ~~ Ts'')))
wenzelm@49660:       in Term.subst_bounds (map Syntax_Trans.mark_bound_abs xs, t) end;
wenzelm@40281:   in (map prep ts', Ts') end;
wenzelm@40281: 
wenzelm@40281: fun err_loose i = error ("Loose bound variable: B." ^ string_of_int i);
wenzelm@42383: 
traytel@40836: fun unif_failed msg =
traytel@40836:   "Type unification failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n\n";
wenzelm@42383: 
traytel@40836: fun err_appl_msg ctxt msg tye bs t T u U () =
wenzelm@55301:   let val ([t', u'], [T', U']) = prep_output ctxt tye bs [t, u] [T, U] in
wenzelm@55301:     (unif_failed msg ^ Type.appl_error ctxt t' T' u' U' ^ "\n\n",
wenzelm@55303:       Buffer.empty |> Buffer.add "Coercion Inference:\n\n")
wenzelm@55301:   end;
wenzelm@40281: 
traytel@54584: fun err_list ctxt err tye Ts =
wenzelm@55303:   let val (_, Ts') = prep_output ctxt tye [] [] Ts in
wenzelm@55303:     eval_error (err ++>
wenzelm@55303:       ("\nCannot unify a list of types that should be the same:\n" ^
wenzelm@55303:         Pretty.string_of (Pretty.list "[" "]" (map (Syntax.pretty_typ ctxt) Ts'))))
wenzelm@40281:   end;
wenzelm@40281: 
traytel@54584: fun err_bound ctxt err tye packs =
wenzelm@40281:   let
wenzelm@40281:     val (ts, Ts) = fold
wenzelm@40281:       (fn (bs, t $ u, U, _, U') => fn (ts, Ts) =>
traytel@40836:         let val (t', T') = prep_output ctxt tye bs [t, u] [U', U]
wenzelm@40282:         in (t' :: ts, T' :: Ts) end)
wenzelm@40281:       packs ([], []);
wenzelm@55303:     val msg =
wenzelm@55303:       Pretty.string_of (Pretty.big_list "Cannot fulfil subtype constraints:"
traytel@45060:         (map2 (fn [t, u] => fn [T, U] =>
wenzelm@40281:           Pretty.block [
wenzelm@42383:             Syntax.pretty_typ ctxt T, Pretty.brk 2, Pretty.str "<:", Pretty.brk 2,
wenzelm@42383:             Syntax.pretty_typ ctxt U, Pretty.brk 3,
wenzelm@42383:             Pretty.str "from function application", Pretty.brk 2,
traytel@45060:             Pretty.block [Syntax.pretty_term ctxt (t $ u)]])
wenzelm@55303:           ts Ts));
wenzelm@55303:   in eval_error (err ++> ("\n" ^ msg)) end;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** constraint generation **)
wenzelm@40281: 
traytel@51319: fun update_coerce_arg ctxt old t =
traytel@51319:   let
traytel@51319:     val mk_coerce_args = the_default [] o Symtab.lookup (coerce_args_of ctxt);
traytel@51319:     fun update _ [] = old
traytel@51327:       | update 0 (coerce :: _) = (case coerce of LEAVE => old | PERMIT => true | FORBID => false)
traytel@51319:       | update n (_ :: cs) = update (n - 1) cs;
traytel@51319:     val (f, n) = Term.strip_comb (Type.strip_constraints t) ||> length;
traytel@51319:   in
traytel@51319:     update n (case f of Const (name, _) => mk_coerce_args name | _ => [])
traytel@51319:   end;
traytel@51319: 
traytel@40836: fun generate_constraints ctxt err =
wenzelm@40281:   let
traytel@51319:     fun gen _ cs _ (Const (_, T)) tye_idx = (T, tye_idx, cs)
traytel@51319:       | gen _ cs _ (Free (_, T)) tye_idx = (T, tye_idx, cs)
traytel@51319:       | gen _ cs _ (Var (_, T)) tye_idx = (T, tye_idx, cs)
traytel@51319:       | gen _ cs bs (Bound i) tye_idx =
wenzelm@43278:           (snd (nth bs i handle General.Subscript => err_loose i), tye_idx, cs)
traytel@51319:       | gen coerce cs bs (Abs (x, T, t)) tye_idx =
traytel@51319:           let val (U, tye_idx', cs') = gen coerce cs ((x, T) :: bs) t tye_idx
wenzelm@40281:           in (T --> U, tye_idx', cs') end
traytel@51319:       | gen coerce cs bs (t $ u) tye_idx =
wenzelm@40281:           let
traytel@51319:             val (T, tye_idx', cs') = gen coerce cs bs t tye_idx;
traytel@51319:             val coerce' = update_coerce_arg ctxt coerce t;
traytel@51319:             val (U', (tye, idx), cs'') = gen coerce' cs' bs u tye_idx';
wenzelm@40286:             val U = Type_Infer.mk_param idx [];
wenzelm@40286:             val V = Type_Infer.mk_param (idx + 1) [];
traytel@45060:             val tye_idx'' = strong_unify ctxt (U --> V, T) (tye, idx + 2)
traytel@41353:               handle NO_UNIFIER (msg, _) => error (gen_msg err msg);
wenzelm@40281:             val error_pack = (bs, t $ u, U, V, U');
wenzelm@52432:           in
traytel@51319:             if coerce'
traytel@51319:             then (V, tye_idx'', ((U', U), error_pack) :: cs'')
traytel@51319:             else (V,
traytel@51319:               strong_unify ctxt (U, U') tye_idx''
traytel@51319:                 handle NO_UNIFIER (msg, _) => error (gen_msg err msg),
traytel@51319:               cs'')
traytel@51319:           end;
wenzelm@40281:   in
traytel@51319:     gen true [] []
wenzelm@40281:   end;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** constraint resolution **)
wenzelm@40281: 
wenzelm@40281: exception BOUND_ERROR of string;
wenzelm@40281: 
traytel@40836: fun process_constraints ctxt err cs tye_idx =
wenzelm@40281:   let
wenzelm@42388:     val thy = Proof_Context.theory_of ctxt;
wenzelm@42388: 
wenzelm@40285:     val coes_graph = coes_graph_of ctxt;
wenzelm@40285:     val tmaps = tmaps_of ctxt;
wenzelm@42388:     val arity_sorts = Type.arity_sorts (Context.pretty ctxt) (Sign.tsig_of thy);
wenzelm@40281: 
wenzelm@40281:     fun split_cs _ [] = ([], [])
wenzelm@40282:       | split_cs f (c :: cs) =
wenzelm@40281:           (case pairself f (fst c) of
wenzelm@40281:             (false, false) => apsnd (cons c) (split_cs f cs)
wenzelm@40281:           | _ => apfst (cons c) (split_cs f cs));
wenzelm@42383: 
traytel@41353:     fun unify_list (T :: Ts) tye_idx =
wenzelm@42383:       fold (fn U => fn tye_idx' => strong_unify ctxt (T, U) tye_idx') Ts tye_idx;
wenzelm@40281: 
wenzelm@40282: 
wenzelm@40281:     (* check whether constraint simplification will terminate using weak unification *)
wenzelm@40282: 
traytel@41353:     val _ = fold (fn (TU, _) => fn tye_idx =>
traytel@41353:       weak_unify ctxt TU tye_idx handle NO_UNIFIER (msg, _) =>
traytel@40836:         error (gen_msg err ("weak unification of subtype constraints fails\n" ^ msg))) cs tye_idx;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281:     (* simplify constraints *)
wenzelm@40282: 
wenzelm@40281:     fun simplify_constraints cs tye_idx =
wenzelm@40281:       let
wenzelm@40281:         fun contract a Ts Us error_pack done todo tye idx =
wenzelm@40281:           let
wenzelm@40281:             val arg_var =
wenzelm@40281:               (case Symtab.lookup tmaps a of
wenzelm@40281:                 (*everything is invariant for unknown constructors*)
wenzelm@40281:                 NONE => replicate (length Ts) INVARIANT
wenzelm@40281:               | SOME av => snd av);
wenzelm@40281:             fun new_constraints (variance, constraint) (cs, tye_idx) =
wenzelm@40281:               (case variance of
wenzelm@40281:                 COVARIANT => (constraint :: cs, tye_idx)
wenzelm@40281:               | CONTRAVARIANT => (swap constraint :: cs, tye_idx)
traytel@41353:               | INVARIANT_TO T => (cs, unify_list [T, fst constraint, snd constraint] tye_idx
wenzelm@42383:                   handle NO_UNIFIER (msg, _) =>
traytel@54584:                     err_list ctxt (gen_err err
traytel@54584:                       ("failed to unify invariant arguments w.r.t. to the known map function\n" ^
traytel@54584:                         msg))
traytel@45060:                       (fst tye_idx) (T :: Ts))
wenzelm@40281:               | INVARIANT => (cs, strong_unify ctxt constraint tye_idx
wenzelm@42383:                   handle NO_UNIFIER (msg, _) =>
traytel@51248:                     error (gen_msg err ("failed to unify invariant arguments\n" ^ msg))));
wenzelm@40281:             val (new, (tye', idx')) = apfst (fn cs => (cs ~~ replicate (length cs) error_pack))
wenzelm@40281:               (fold new_constraints (arg_var ~~ (Ts ~~ Us)) ([], (tye, idx)));
traytel@49142:             val test_update = is_typeT orf is_freeT orf is_fixedvarT;
wenzelm@40281:             val (ch, done') =
traytel@51246:               done
traytel@51246:               |> map (apfst (pairself (Type_Infer.deref tye')))
traytel@51246:               |> (if not (null new) then rpair []  else split_cs test_update);
wenzelm@40281:             val todo' = ch @ todo;
wenzelm@40281:           in
wenzelm@40281:             simplify done' (new @ todo') (tye', idx')
wenzelm@40281:           end
wenzelm@40281:         (*xi is definitely a parameter*)
wenzelm@40281:         and expand varleq xi S a Ts error_pack done todo tye idx =
wenzelm@40281:           let
wenzelm@40281:             val n = length Ts;
wenzelm@40286:             val args = map2 Type_Infer.mk_param (idx upto idx + n - 1) (arity_sorts a S);
wenzelm@40281:             val tye' = Vartab.update_new (xi, Type(a, args)) tye;
wenzelm@40286:             val (ch, done') = split_cs (is_compT o Type_Infer.deref tye') done;
wenzelm@40281:             val todo' = ch @ todo;
wenzelm@40281:             val new =
wenzelm@40281:               if varleq then (Type(a, args), Type (a, Ts))
wenzelm@40286:               else (Type (a, Ts), Type (a, args));
wenzelm@40281:           in
wenzelm@40281:             simplify done' ((new, error_pack) :: todo') (tye', idx + n)
wenzelm@40281:           end
wenzelm@40281:         (*TU is a pair of a parameter and a free/fixed variable*)
traytel@41353:         and eliminate TU done todo tye idx =
wenzelm@40281:           let
wenzelm@40286:             val [TVar (xi, S)] = filter Type_Infer.is_paramT TU;
wenzelm@40286:             val [T] = filter_out Type_Infer.is_paramT TU;
wenzelm@40281:             val SOME S' = sort_of T;
wenzelm@40281:             val test_update = if is_freeT T then is_freeT else is_fixedvarT;
wenzelm@40281:             val tye' = Vartab.update_new (xi, T) tye;
wenzelm@40286:             val (ch, done') = split_cs (test_update o Type_Infer.deref tye') done;
wenzelm@40281:             val todo' = ch @ todo;
wenzelm@40281:           in
wenzelm@42388:             if Sign.subsort thy (S', S) (*TODO check this*)
wenzelm@40281:             then simplify done' todo' (tye', idx)
traytel@40836:             else error (gen_msg err "sort mismatch")
wenzelm@40281:           end
wenzelm@40281:         and simplify done [] tye_idx = (done, tye_idx)
wenzelm@40281:           | simplify done (((T, U), error_pack) :: todo) (tye_idx as (tye, idx)) =
wenzelm@40286:               (case (Type_Infer.deref tye T, Type_Infer.deref tye U) of
traytel@45060:                 (T1 as Type (a, []), T2 as Type (b, [])) =>
wenzelm@40281:                   if a = b then simplify done todo tye_idx
wenzelm@40281:                   else if Graph.is_edge coes_graph (a, b) then simplify done todo tye_idx
wenzelm@55303:                   else
wenzelm@55303:                     error (gen_msg err (quote (Syntax.string_of_typ ctxt T1) ^
wenzelm@55303:                       " is not a subtype of " ^ quote (Syntax.string_of_typ ctxt T2)))
wenzelm@40281:               | (Type (a, Ts), Type (b, Us)) =>
wenzelm@55303:                   if a <> b then
wenzelm@55303:                     error (gen_msg err "different constructors") (fst tye_idx) error_pack
wenzelm@40281:                   else contract a Ts Us error_pack done todo tye idx
wenzelm@40282:               | (TVar (xi, S), Type (a, Ts as (_ :: _))) =>
wenzelm@40281:                   expand true xi S a Ts error_pack done todo tye idx
wenzelm@40282:               | (Type (a, Ts as (_ :: _)), TVar (xi, S)) =>
wenzelm@40281:                   expand false xi S a Ts error_pack done todo tye idx
wenzelm@40281:               | (T, U) =>
wenzelm@40281:                   if T = U then simplify done todo tye_idx
wenzelm@40282:                   else if exists (is_freeT orf is_fixedvarT) [T, U] andalso
wenzelm@40286:                     exists Type_Infer.is_paramT [T, U]
traytel@41353:                   then eliminate [T, U] done todo tye idx
wenzelm@40281:                   else if exists (is_freeT orf is_fixedvarT) [T, U]
traytel@40836:                   then error (gen_msg err "not eliminated free/fixed variables")
wenzelm@40282:                   else simplify (((T, U), error_pack) :: done) todo tye_idx);
wenzelm@40281:       in
wenzelm@40281:         simplify [] cs tye_idx
wenzelm@40281:       end;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281:     (* do simplification *)
wenzelm@40282: 
wenzelm@40281:     val (cs', tye_idx') = simplify_constraints cs tye_idx;
wenzelm@42383: 
wenzelm@42383:     fun find_error_pack lower T' = map_filter
traytel@40836:       (fn ((T, U), pack) => if if lower then T' = U else T' = T then SOME pack else NONE) cs';
wenzelm@42383: 
wenzelm@42383:     fun find_cycle_packs nodes =
traytel@40836:       let
traytel@40836:         val (but_last, last) = split_last nodes
traytel@40836:         val pairs = (last, hd nodes) :: (but_last ~~ tl nodes);
traytel@40836:       in
traytel@40836:         map_filter
wenzelm@40838:           (fn (TU, pack) => if member (op =) pairs TU then SOME pack else NONE)
traytel@40836:           cs'
traytel@40836:       end;
wenzelm@40281: 
wenzelm@40281:     (*styps stands either for supertypes or for subtypes of a type T
wenzelm@40281:       in terms of the subtype-relation (excluding T itself)*)
wenzelm@40282:     fun styps super T =
wenzelm@44338:       (if super then Graph.immediate_succs else Graph.immediate_preds) coes_graph T
wenzelm@40281:         handle Graph.UNDEF _ => [];
wenzelm@40281: 
wenzelm@40282:     fun minmax sup (T :: Ts) =
wenzelm@40281:       let
wenzelm@40281:         fun adjust T U = if sup then (T, U) else (U, T);
wenzelm@40281:         fun extract T [] = T
wenzelm@40282:           | extract T (U :: Us) =
wenzelm@40281:               if Graph.is_edge coes_graph (adjust T U) then extract T Us
wenzelm@40281:               else if Graph.is_edge coes_graph (adjust U T) then extract U Us
traytel@40836:               else raise BOUND_ERROR "uncomparable types in type list";
wenzelm@40281:       in
wenzelm@40281:         t_of (extract T Ts)
wenzelm@40281:       end;
wenzelm@40281: 
wenzelm@40282:     fun ex_styp_of_sort super T styps_and_sorts =
wenzelm@40281:       let
wenzelm@40281:         fun adjust T U = if super then (T, U) else (U, T);
wenzelm@40282:         fun styp_test U Ts = forall
wenzelm@40281:           (fn T => T = U orelse Graph.is_edge coes_graph (adjust U T)) Ts;
wenzelm@55301:         fun fitting Ts S U = Sign.of_sort thy (t_of U, S) andalso styp_test U Ts;
wenzelm@40281:       in
wenzelm@40281:         forall (fn (Ts, S) => exists (fitting Ts S) (T :: styps super T)) styps_and_sorts
wenzelm@40281:       end;
wenzelm@40281: 
wenzelm@40281:     (* computes the tightest possible, correct assignment for 'a::S
wenzelm@40281:        e.g. in the supremum case (sup = true):
wenzelm@40281:                ------- 'a::S---
wenzelm@40281:               /        /    \  \
wenzelm@40281:              /        /      \  \
wenzelm@40281:         'b::C1   'c::C2 ...  T1 T2 ...
wenzelm@40281: 
wenzelm@40281:        sorts - list of sorts [C1, C2, ...]
wenzelm@40281:        T::Ts - non-empty list of base types [T1, T2, ...]
wenzelm@40281:     *)
wenzelm@40282:     fun tightest sup S styps_and_sorts (T :: Ts) =
wenzelm@40281:       let
wenzelm@42388:         fun restriction T = Sign.of_sort thy (t_of T, S)
wenzelm@40281:           andalso ex_styp_of_sort (not sup) T styps_and_sorts;
wenzelm@40281:         fun candidates T = inter (op =) (filter restriction (T :: styps sup T));
wenzelm@40281:       in
wenzelm@40281:         (case fold candidates Ts (filter restriction (T :: styps sup T)) of
traytel@40836:           [] => raise BOUND_ERROR ("no " ^ (if sup then "supremum" else "infimum"))
wenzelm@40281:         | [T] => t_of T
wenzelm@40281:         | Ts => minmax sup Ts)
wenzelm@40281:       end;
wenzelm@40281: 
wenzelm@40281:     fun build_graph G [] tye_idx = (G, tye_idx)
wenzelm@40282:       | build_graph G ((T, U) :: cs) tye_idx =
wenzelm@40281:         if T = U then build_graph G cs tye_idx
wenzelm@40281:         else
wenzelm@40281:           let
wenzelm@40281:             val G' = maybe_new_typnodes [T, U] G;
traytel@45059:             val (G'', tye_idx') = (Typ_Graph.add_edge_acyclic (T, U) G', tye_idx)
wenzelm@40281:               handle Typ_Graph.CYCLES cycles =>
wenzelm@40281:                 let
wenzelm@42383:                   val (tye, idx) =
wenzelm@42383:                     fold
traytel@40836:                       (fn cycle => fn tye_idx' => (unify_list cycle tye_idx'
wenzelm@42383:                         handle NO_UNIFIER (msg, _) =>
wenzelm@42383:                           err_bound ctxt
traytel@54584:                             (gen_err err ("constraint cycle not unifiable\n" ^ msg)) (fst tye_idx)
traytel@40836:                             (find_cycle_packs cycle)))
traytel@40836:                       cycles tye_idx
wenzelm@40281:                 in
traytel@40836:                   collapse (tye, idx) cycles G
traytel@40836:                 end
wenzelm@40281:           in
wenzelm@40281:             build_graph G'' cs tye_idx'
wenzelm@40281:           end
traytel@40836:     and collapse (tye, idx) cycles G = (*nodes non-empty list*)
wenzelm@40281:       let
traytel@40836:         (*all cycles collapse to one node,
traytel@40836:           because all of them share at least the nodes x and y*)
traytel@40836:         val nodes = (distinct (op =) (flat cycles));
traytel@40836:         val T = Type_Infer.deref tye (hd nodes);
wenzelm@40281:         val P = new_imm_preds G nodes;
wenzelm@40281:         val S = new_imm_succs G nodes;
wenzelm@46665:         val G' = fold Typ_Graph.del_node (tl nodes) G;
traytel@40836:         fun check_and_gen super T' =
traytel@40836:           let val U = Type_Infer.deref tye T';
traytel@40836:           in
traytel@40836:             if not (is_typeT T) orelse not (is_typeT U) orelse T = U
traytel@40836:             then if super then (hd nodes, T') else (T', hd nodes)
wenzelm@42383:             else
wenzelm@42383:               if super andalso
traytel@40836:                 Graph.is_edge coes_graph (nameT T, nameT U) then (hd nodes, T')
wenzelm@42383:               else if not super andalso
traytel@40836:                 Graph.is_edge coes_graph (nameT U, nameT T) then (T', hd nodes)
wenzelm@55303:               else
wenzelm@55303:                 err_bound ctxt (gen_err err "cycle elimination produces inconsistent graph")
wenzelm@55303:                   (fst tye_idx)
wenzelm@55303:                   (maps find_cycle_packs cycles @ find_error_pack super T')
traytel@40836:           end;
wenzelm@40281:       in
traytel@40836:         build_graph G' (map (check_and_gen false) P @ map (check_and_gen true) S) (tye, idx)
wenzelm@40281:       end;
wenzelm@40281: 
wenzelm@40281:     fun assign_bound lower G key (tye_idx as (tye, _)) =
wenzelm@40286:       if Type_Infer.is_paramT (Type_Infer.deref tye key) then
wenzelm@40281:         let
wenzelm@40286:           val TVar (xi, S) = Type_Infer.deref tye key;
wenzelm@40281:           val get_bound = if lower then get_preds else get_succs;
wenzelm@40281:           val raw_bound = get_bound G key;
wenzelm@40286:           val bound = map (Type_Infer.deref tye) raw_bound;
wenzelm@40286:           val not_params = filter_out Type_Infer.is_paramT bound;
wenzelm@40282:           fun to_fulfil T =
wenzelm@40281:             (case sort_of T of
wenzelm@40281:               NONE => NONE
wenzelm@40282:             | SOME S =>
wenzelm@40286:                 SOME
wenzelm@40286:                   (map nameT
wenzelm@42405:                     (filter_out Type_Infer.is_paramT
wenzelm@42405:                       (map (Type_Infer.deref tye) (get_bound G T))), S));
wenzelm@40281:           val styps_and_sorts = distinct (op =) (map_filter to_fulfil raw_bound);
wenzelm@40281:           val assignment =
wenzelm@40281:             if null bound orelse null not_params then NONE
wenzelm@40281:             else SOME (tightest lower S styps_and_sorts (map nameT not_params)
traytel@54584:                 handle BOUND_ERROR msg => err_bound ctxt (gen_err err msg) tye
wenzelm@55301:                   (maps (find_error_pack (not lower)) raw_bound));
wenzelm@40281:         in
wenzelm@40281:           (case assignment of
wenzelm@40281:             NONE => tye_idx
wenzelm@40281:           | SOME T =>
wenzelm@40286:               if Type_Infer.is_paramT T then tye_idx
wenzelm@40281:               else if lower then (*upper bound check*)
wenzelm@40281:                 let
wenzelm@40286:                   val other_bound = map (Type_Infer.deref tye) (get_succs G key);
wenzelm@40281:                   val s = nameT T;
wenzelm@40281:                 in
wenzelm@40281:                   if subset (op = o apfst nameT) (filter is_typeT other_bound, s :: styps true s)
wenzelm@40281:                   then apfst (Vartab.update (xi, T)) tye_idx
wenzelm@55303:                   else
wenzelm@55303:                     err_bound ctxt
wenzelm@55303:                       (gen_err err
wenzelm@55303:                         (Pretty.string_of (Pretty.block
wenzelm@55303:                           [Pretty.str "assigned base type", Pretty.brk 1,
wenzelm@55303:                             Pretty.quote (Syntax.pretty_typ ctxt T), Pretty.brk 1,
wenzelm@55303:                             Pretty.str "clashes with the upper bound of variable", Pretty.brk 1,
wenzelm@55303:                             Syntax.pretty_typ ctxt (TVar (xi, S))])))
wenzelm@55303:                       tye
wenzelm@55303:                       (maps (find_error_pack lower) other_bound)
wenzelm@40281:                 end
wenzelm@40281:               else apfst (Vartab.update (xi, T)) tye_idx)
wenzelm@40281:         end
wenzelm@40281:       else tye_idx;
wenzelm@40281: 
wenzelm@40281:     val assign_lb = assign_bound true;
wenzelm@40281:     val assign_ub = assign_bound false;
wenzelm@40281: 
wenzelm@40281:     fun assign_alternating ts' ts G tye_idx =
wenzelm@40281:       if ts' = ts then tye_idx
wenzelm@40281:       else
wenzelm@40281:         let
wenzelm@40281:           val (tye_idx' as (tye, _)) = fold (assign_lb G) ts tye_idx
wenzelm@40281:             |> fold (assign_ub G) ts;
wenzelm@40281:         in
wenzelm@42383:           assign_alternating ts
traytel@40836:             (filter (Type_Infer.is_paramT o Type_Infer.deref tye) ts) G tye_idx'
wenzelm@40281:         end;
wenzelm@40281: 
wenzelm@40281:     (*Unify all weakly connected components of the constraint forest,
wenzelm@40282:       that contain only params. These are the only WCCs that contain
wenzelm@40281:       params anyway.*)
wenzelm@40281:     fun unify_params G (tye_idx as (tye, _)) =
wenzelm@40281:       let
wenzelm@40286:         val max_params =
wenzelm@40286:           filter (Type_Infer.is_paramT o Type_Infer.deref tye) (Typ_Graph.maximals G);
wenzelm@40281:         val to_unify = map (fn T => T :: get_preds G T) max_params;
wenzelm@40281:       in
wenzelm@42383:         fold
traytel@40836:           (fn Ts => fn tye_idx' => unify_list Ts tye_idx'
traytel@54584:             handle NO_UNIFIER (msg, _) => err_list ctxt (gen_err err msg) (fst tye_idx) Ts)
traytel@40836:           to_unify tye_idx
wenzelm@40281:       end;
wenzelm@40281: 
wenzelm@40281:     fun solve_constraints G tye_idx = tye_idx
wenzelm@40281:       |> assign_alternating [] (Typ_Graph.keys G) G
wenzelm@40281:       |> unify_params G;
wenzelm@40281:   in
wenzelm@40281:     build_graph Typ_Graph.empty (map fst cs') tye_idx'
wenzelm@40281:       |-> solve_constraints
wenzelm@40281:   end;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** coercion insertion **)
wenzelm@40281: 
traytel@45060: fun gen_coercion ctxt err tye TU =
traytel@45060:   let
traytel@45060:     fun gen (T1, T2) = (case pairself (Type_Infer.deref tye) (T1, T2) of
traytel@45060:         (T1 as (Type (a, [])), T2 as (Type (b, []))) =>
traytel@45060:             if a = b
traytel@51335:             then mk_identity T1
traytel@45060:             else
traytel@45060:               (case Symreltab.lookup (coes_of ctxt) (a, b) of
wenzelm@55303:                 NONE =>
wenzelm@55303:                   raise COERCION_GEN_ERROR (err ++>
wenzelm@55303:                     (Pretty.string_of o Pretty.block)
wenzelm@55303:                       [Pretty.quote (Syntax.pretty_typ ctxt T1), Pretty.brk 1,
wenzelm@55303:                         Pretty.str "is not a subtype of", Pretty.brk 1,
wenzelm@55303:                         Pretty.quote (Syntax.pretty_typ ctxt T2)])
traytel@45060:               | SOME (co, _) => co)
traytel@45102:       | (T1 as Type (a, Ts), T2 as Type (b, Us)) =>
traytel@45060:             if a <> b
traytel@45060:             then
traytel@45060:               (case Symreltab.lookup (coes_of ctxt) (a, b) of
traytel@45060:                 (*immediate error - cannot fix complex coercion with the global algorithm*)
wenzelm@55303:                 NONE =>
wenzelm@55303:                   eval_error (err ++>
wenzelm@55304:                     ("No coercion known for type constructors: " ^
wenzelm@55304:                       quote (Proof_Context.markup_type ctxt a) ^ " and " ^
wenzelm@55304:                       quote (Proof_Context.markup_type ctxt b)))
traytel@45060:               | SOME (co, ((Ts', Us'), _)) =>
traytel@45060:                   let
traytel@45060:                     val co_before = gen (T1, Type (a, Ts'));
traytel@45060:                     val coT = range_type (fastype_of co_before);
wenzelm@55303:                     val insts =
wenzelm@55303:                       inst_collect tye (err ++> "Could not insert complex coercion")
wenzelm@55303:                         (domain_type (fastype_of co)) coT;
traytel@45060:                     val co' = Term.subst_TVars insts co;
traytel@45060:                     val co_after = gen (Type (b, (map (typ_subst_TVars insts) Us')), T2);
traytel@45060:                   in
traytel@45060:                     Abs (Name.uu, T1, Library.foldr (op $)
traytel@45060:                       (filter (not o is_identity) [co_after, co', co_before], Bound 0))
traytel@45060:                   end)
traytel@45060:             else
traytel@45060:               let
traytel@51335:                 fun sub_co (COVARIANT, TU) = (SOME (gen TU), NONE)
traytel@51335:                   | sub_co (CONTRAVARIANT, TU) = (SOME (gen (swap TU)), NONE)
traytel@51335:                   | sub_co (INVARIANT, (T, _)) = (NONE, SOME T)
traytel@51335:                   | sub_co (INVARIANT_TO T, _) = (NONE, NONE);
traytel@45060:                 fun ts_of [] = []
traytel@45060:                   | ts_of (Type ("fun", [x1, x2]) :: xs) = x1 :: x2 :: (ts_of xs);
traytel@45060:               in
traytel@45060:                 (case Symtab.lookup (tmaps_of ctxt) a of
traytel@45102:                   NONE =>
traytel@45102:                     if Type.could_unify (T1, T2)
traytel@51335:                     then mk_identity T1
wenzelm@55303:                     else
wenzelm@55303:                       raise COERCION_GEN_ERROR
wenzelm@55304:                         (err ++>
wenzelm@55304:                           ("No map function for " ^ quote (Proof_Context.markup_type ctxt a)
wenzelm@55304:                             ^ " known"))
traytel@51335:                 | SOME (tmap, variances) =>
traytel@45060:                     let
traytel@51335:                       val (used_coes, invarTs) =
traytel@51335:                         map_split sub_co (variances ~~ (Ts ~~ Us))
traytel@51335:                         |>> map_filter I
traytel@51335:                         ||> map_filter I;
traytel@51335:                       val Tinsts = ts_of (map fastype_of used_coes) @ invarTs;
traytel@45060:                     in
traytel@45060:                       if null (filter (not o is_identity) used_coes)
traytel@51335:                       then mk_identity (Type (a, Ts))
traytel@51335:                       else Term.list_comb (instantiate tmap Tinsts, used_coes)
traytel@45060:                     end)
traytel@45060:               end
traytel@45060:       | (T, U) =>
traytel@45060:             if Type.could_unify (T, U)
traytel@51335:             then mk_identity T
wenzelm@55303:             else raise COERCION_GEN_ERROR (err ++>
wenzelm@55303:               (Pretty.string_of o Pretty.block)
wenzelm@55303:                [Pretty.str "Cannot generate coercion from", Pretty.brk 1,
wenzelm@55303:                 Pretty.quote (Syntax.pretty_typ ctxt T), Pretty.brk 1,
wenzelm@55303:                 Pretty.str "to", Pretty.brk 1,
wenzelm@55303:                 Pretty.quote (Syntax.pretty_typ ctxt U)]));
traytel@45060:   in
traytel@45060:     gen TU
traytel@45060:   end;
traytel@40836: 
traytel@45060: fun function_of ctxt err tye T =
traytel@45060:   (case Type_Infer.deref tye T of
traytel@45060:     Type (C, Ts) =>
traytel@45060:       (case Symreltab.lookup (coes_of ctxt) (C, "fun") of
wenzelm@55304:         NONE =>
wenzelm@55304:           eval_error (err ++> ("No complex coercion from " ^
wenzelm@55304:             quote (Proof_Context.markup_type ctxt C) ^ " to " ^
wenzelm@55304:             quote (Proof_Context.markup_type ctxt "fun")))
traytel@45060:       | SOME (co, ((Ts', _), _)) =>
traytel@45060:         let
traytel@45060:           val co_before = gen_coercion ctxt err tye (Type (C, Ts), Type (C, Ts'));
traytel@45060:           val coT = range_type (fastype_of co_before);
wenzelm@55303:           val insts =
wenzelm@55303:             inst_collect tye (err ++> "Could not insert complex coercion")
wenzelm@55303:               (domain_type (fastype_of co)) coT;
traytel@45060:           val co' = Term.subst_TVars insts co;
traytel@45060:         in
traytel@45060:           Abs (Name.uu, Type (C, Ts), Library.foldr (op $)
traytel@45060:             (filter (not o is_identity) [co', co_before], Bound 0))
traytel@45060:         end)
wenzelm@55303:   | T' =>
wenzelm@55303:       eval_error (err ++>
wenzelm@55303:         (Pretty.string_of o Pretty.block)
wenzelm@55303:          [Pretty.str "No complex coercion from", Pretty.brk 1,
wenzelm@55304:           Pretty.quote (Syntax.pretty_typ ctxt T'), Pretty.brk 1,
wenzelm@55304:           Pretty.str "to", Pretty.brk 1, Proof_Context.pretty_type ctxt "fun"]));
traytel@45060: 
traytel@45060: fun insert_coercions ctxt (tye, idx) ts =
wenzelm@40281:   let
traytel@45060:     fun insert _ (Const (c, T)) = (Const (c, T), T)
traytel@45060:       | insert _ (Free (x, T)) = (Free (x, T), T)
traytel@45060:       | insert _ (Var (xi, T)) = (Var (xi, T), T)
wenzelm@40281:       | insert bs (Bound i) =
wenzelm@43278:           let val T = nth bs i handle General.Subscript => err_loose i;
wenzelm@40281:           in (Bound i, T) end
wenzelm@40281:       | insert bs (Abs (x, T, t)) =
traytel@45060:           let val (t', T') = insert (T :: bs) t;
traytel@45060:           in (Abs (x, T, t'), T --> T') end
wenzelm@40281:       | insert bs (t $ u) =
wenzelm@40281:           let
traytel@45060:             val (t', Type ("fun", [U, T])) = apsnd (Type_Infer.deref tye) (insert bs t);
wenzelm@40281:             val (u', U') = insert bs u;
wenzelm@40281:           in
traytel@40836:             if can (fn TU => strong_unify ctxt TU (tye, 0)) (U, U')
traytel@40836:             then (t' $ u', T)
wenzelm@55303:             else (t' $ (gen_coercion ctxt (K ("", Buffer.empty)) tye (U', U) $ u'), T)
wenzelm@40281:           end
wenzelm@40281:   in
wenzelm@40281:     map (fst o insert []) ts
wenzelm@40281:   end;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** assembling the pipeline **)
wenzelm@40281: 
wenzelm@42398: fun coercion_infer_types ctxt raw_ts =
wenzelm@40281:   let
wenzelm@42405:     val (idx, ts) = Type_Infer_Context.prepare ctxt raw_ts;
wenzelm@40281: 
traytel@51319:     fun inf _ _ (t as (Const (_, T))) tye_idx = (t, T, tye_idx)
traytel@51319:       | inf _ _ (t as (Free (_, T))) tye_idx = (t, T, tye_idx)
traytel@51319:       | inf _ _ (t as (Var (_, T))) tye_idx = (t, T, tye_idx)
traytel@51319:       | inf _ bs (t as (Bound i)) tye_idx =
wenzelm@43278:           (t, snd (nth bs i handle General.Subscript => err_loose i), tye_idx)
traytel@51319:       | inf coerce bs (Abs (x, T, t)) tye_idx =
traytel@51319:           let val (t', U, tye_idx') = inf coerce ((x, T) :: bs) t tye_idx
traytel@40836:           in (Abs (x, T, t'), T --> U, tye_idx') end
traytel@51319:       | inf coerce bs (t $ u) tye_idx =
traytel@40836:           let
traytel@51319:             val (t', T, tye_idx') = inf coerce bs t tye_idx;
traytel@51319:             val coerce' = update_coerce_arg ctxt coerce t;
traytel@51319:             val (u', U, (tye, idx)) = inf coerce' bs u tye_idx';
traytel@40836:             val V = Type_Infer.mk_param idx [];
traytel@40836:             val (tu, tye_idx'') = (t' $ u', strong_unify ctxt (U --> V, T) (tye, idx + 1))
wenzelm@42383:               handle NO_UNIFIER (msg, tye') =>
traytel@45060:                 let
traytel@45060:                   val err = err_appl_msg ctxt msg tye' bs t T u U;
traytel@45060:                   val W = Type_Infer.mk_param (idx + 1) [];
traytel@45060:                   val (t'', (tye', idx')) =
traytel@45060:                     (t', strong_unify ctxt (W --> V, T) (tye, idx + 2))
traytel@45060:                       handle NO_UNIFIER _ =>
traytel@45060:                         let
wenzelm@55303:                           val err' = err ++> "Local coercion insertion on the operator failed:\n";
traytel@45060:                           val co = function_of ctxt err' tye T;
traytel@51319:                           val (t'', T'', tye_idx'') = inf coerce bs (co $ t') (tye, idx + 2);
traytel@45060:                         in
traytel@45060:                           (t'', strong_unify ctxt (W --> V, T'') tye_idx''
wenzelm@55303:                             handle NO_UNIFIER (msg, _) => eval_error (err' ++> msg))
traytel@45060:                         end;
wenzelm@55303:                   val err' = err ++>
traytel@54584:                     ((if t' aconv t'' then ""
wenzelm@55303:                       else "Successfully coerced the operator to a function of type:\n" ^
wenzelm@55303:                         Syntax.string_of_typ ctxt
wenzelm@55303:                           (the_single (snd (prep_output ctxt tye' bs [] [W --> V]))) ^ "\n") ^
wenzelm@55303:                      (if coerce' then "Local coercion insertion on the operand failed:\n"
wenzelm@55303:                       else "Local coercion insertion on the operand disallowed:\n"));
traytel@45060:                   val (u'', U', tye_idx') =
wenzelm@52432:                     if coerce' then
traytel@51319:                       let val co = gen_coercion ctxt err' tye' (U, W);
traytel@51319:                       in inf coerce' bs (if is_identity co then u else co $ u) (tye', idx') end
traytel@51319:                     else (u, U, (tye', idx'));
traytel@45060:                 in
traytel@45060:                   (t'' $ u'', strong_unify ctxt (U', W) tye_idx'
wenzelm@55303:                     handle NO_UNIFIER (msg, _) => raise COERCION_GEN_ERROR (err' ++> msg))
traytel@45060:                 end;
traytel@40836:           in (tu, V, tye_idx'') end;
wenzelm@40281: 
wenzelm@42383:     fun infer_single t tye_idx =
traytel@51319:       let val (t, _, tye_idx') = inf true [] t tye_idx
traytel@40938:       in (t, tye_idx') end;
wenzelm@42383: 
traytel@40938:     val (ts', (tye, _)) = (fold_map infer_single ts (Vartab.empty, idx)
traytel@45060:       handle COERCION_GEN_ERROR err =>
traytel@40836:         let
traytel@40836:           fun gen_single t (tye_idx, constraints) =
traytel@45060:             let val (_, tye_idx', constraints') =
wenzelm@55303:               generate_constraints ctxt (err ++> "\n") t tye_idx
traytel@40836:             in (tye_idx', constraints' @ constraints) end;
wenzelm@42383: 
traytel@40836:           val (tye_idx, constraints) = fold gen_single ts ((Vartab.empty, idx), []);
wenzelm@55303:           val (tye, idx) = process_constraints ctxt (err ++> "\n") constraints tye_idx;
wenzelm@42383:         in
traytel@45060:           (insert_coercions ctxt (tye, idx) ts, (tye, idx))
traytel@40836:         end);
wenzelm@40281: 
wenzelm@40281:     val (_, ts'') = Type_Infer.finish ctxt tye ([], ts');
wenzelm@40281:   in ts'' end;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** installation **)
wenzelm@40281: 
wenzelm@40283: (* term check *)
wenzelm@40283: 
wenzelm@42616: val coercion_enabled = Attrib.setup_config_bool @{binding coercion_enabled} (K false);
wenzelm@40939: 
wenzelm@40283: val add_term_check =
wenzelm@45429:   Syntax_Phases.term_check ~100 "coercions"
wenzelm@42402:     (fn ctxt => Config.get ctxt coercion_enabled ? coercion_infer_types ctxt);
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40283: (* declarations *)
wenzelm@40281: 
wenzelm@40284: fun add_type_map raw_t context =
wenzelm@40281:   let
wenzelm@40281:     val ctxt = Context.proof_of context;
wenzelm@40284:     val t = singleton (Variable.polymorphic ctxt) raw_t;
wenzelm@40281: 
traytel@45059:     fun err_str t = "\n\nThe provided function has the type:\n" ^
wenzelm@42383:       Syntax.string_of_typ ctxt (fastype_of t) ^
traytel@45059:       "\n\nThe general type signature of a map function is:" ^
traytel@41353:       "\nf1 => f2 => ... => fn => C [x1, ..., xn] => C [y1, ..., yn]" ^
traytel@45059:       "\nwhere C is a constructor and fi is of type (xi => yi) or (yi => xi).";
wenzelm@42383: 
traytel@41353:     val ((fis, T1), T2) = apfst split_last (strip_type (fastype_of t))
wenzelm@47060:       handle List.Empty => error ("Not a proper map function:" ^ err_str t);
wenzelm@42383: 
wenzelm@40281:     fun gen_arg_var ([], []) = []
traytel@51335:       | gen_arg_var (Ts, (U, U') :: Us) =
traytel@41353:           if U = U' then
traytel@51335:             if null (Term.add_tvarsT U []) then INVARIANT_TO U :: gen_arg_var (Ts, Us)
traytel@51335:             else if Term.is_TVar U then INVARIANT :: gen_arg_var (Ts, Us)
traytel@51335:             else error ("Invariant xi and yi should be variables or variable-free:" ^ err_str t)
traytel@51335:           else
traytel@51335:             (case Ts of
traytel@51335:               [] => error ("Different numbers of functions and variant arguments\n" ^ err_str t)
traytel@51335:             | (T, T') :: Ts =>
traytel@51335:               if T = U andalso T' = U' then COVARIANT :: gen_arg_var (Ts, Us)
traytel@51335:               else if T = U' andalso T' = U then CONTRAVARIANT :: gen_arg_var (Ts, Us)
traytel@51335:               else error ("Functions do not apply to arguments correctly:" ^ err_str t));
wenzelm@40281: 
traytel@41353:     (*retry flag needed to adjust the type lists, when given a map over type constructor fun*)
traytel@41353:     fun check_map_fun fis (Type (C1, Ts)) (Type (C2, Us)) retry =
traytel@41353:           if C1 = C2 andalso not (null fis) andalso forall is_funtype fis
traytel@41353:           then ((map dest_funT fis, Ts ~~ Us), C1)
traytel@41353:           else error ("Not a proper map function:" ^ err_str t)
traytel@41353:       | check_map_fun fis T1 T2 true =
traytel@41353:           let val (fis', T') = split_last fis
traytel@41353:           in check_map_fun fis' T' (T1 --> T2) false end
traytel@41353:       | check_map_fun _ _ _ _ = error ("Not a proper map function:" ^ err_str t);
wenzelm@40281: 
traytel@41353:     val res = check_map_fun fis T1 T2 true;
wenzelm@40281:     val res_av = gen_arg_var (fst res);
wenzelm@40281:   in
wenzelm@40281:     map_tmaps (Symtab.update (snd res, (t, res_av))) context
wenzelm@40281:   end;
wenzelm@40281: 
traytel@45060: fun transitive_coercion ctxt tab G (a, b) =
traytel@45059:   let
traytel@45060:     fun safe_app t (Abs (x, T', u)) =
traytel@45060:       let
traytel@45060:         val t' = map_types Type_Infer.paramify_vars t;
traytel@45060:       in
traytel@45060:         singleton (coercion_infer_types ctxt) (Abs(x, T', (t' $ u)))
traytel@45060:       end;
traytel@45059:     val path = hd (Graph.irreducible_paths G (a, b));
traytel@45059:     val path' = fst (split_last path) ~~ tl path;
traytel@45059:     val coercions = map (fst o the o Symreltab.lookup tab) path';
traytel@45060:     val trans_co = singleton (Variable.polymorphic ctxt)
traytel@51335:       (fold safe_app coercions (mk_identity dummyT));
traytel@45060:     val (Ts, Us) = pairself (snd o Term.dest_Type) (Term.dest_funT (type_of trans_co))
traytel@45060:   in
traytel@45060:     (trans_co, ((Ts, Us), coercions))
traytel@45059:   end;
traytel@45059: 
wenzelm@40284: fun add_coercion raw_t context =
wenzelm@40281:   let
wenzelm@40281:     val ctxt = Context.proof_of context;
wenzelm@40284:     val t = singleton (Variable.polymorphic ctxt) raw_t;
wenzelm@40281: 
wenzelm@55303:     fun err_coercion () =
wenzelm@55303:       error ("Bad type for a coercion:\n" ^
traytel@45059:         Syntax.string_of_term ctxt t ^ " :: " ^
wenzelm@40281:         Syntax.string_of_typ ctxt (fastype_of t));
wenzelm@40281: 
wenzelm@40840:     val (T1, T2) = Term.dest_funT (fastype_of t)
wenzelm@40840:       handle TYPE _ => err_coercion ();
wenzelm@40281: 
traytel@45060:     val (a, Ts) = Term.dest_Type T1
traytel@45060:       handle TYPE _ => err_coercion ();
wenzelm@40281: 
traytel@45060:     val (b, Us) = Term.dest_Type T2
traytel@45060:       handle TYPE _ => err_coercion ();
wenzelm@40281: 
traytel@45060:     fun coercion_data_update (tab, G, _) =
wenzelm@40281:       let
traytel@45060:         val G' = maybe_new_nodes [(a, length Ts), (b, length Us)] G
wenzelm@40281:         val G'' = Graph.add_edge_trans_acyclic (a, b) G'
traytel@45059:           handle Graph.CYCLES _ => error (
traytel@45060:             Syntax.string_of_typ ctxt T2 ^ " is already a subtype of " ^
traytel@45060:             Syntax.string_of_typ ctxt T1 ^ "!\n\nCannot add coercion of type: " ^
traytel@45059:             Syntax.string_of_typ ctxt (T1 --> T2));
wenzelm@40281:         val new_edges =
wenzelm@49560:           flat (Graph.dest G'' |> map (fn ((x, _), ys) => ys |> map_filter (fn y =>
wenzelm@40281:             if Graph.is_edge G' (x, y) then NONE else SOME (x, y))));
wenzelm@40281:         val G_and_new = Graph.add_edge (a, b) G';
wenzelm@40281: 
wenzelm@40281:         val tab' = fold
traytel@45059:           (fn pair => fn tab =>
traytel@45060:             Symreltab.update (pair, transitive_coercion ctxt tab G_and_new pair) tab)
wenzelm@40281:           (filter (fn pair => pair <> (a, b)) new_edges)
traytel@45060:           (Symreltab.update ((a, b), (t, ((Ts, Us), []))) tab);
wenzelm@40281:       in
traytel@45060:         (tab', G'', restrict_graph G'')
wenzelm@40281:       end;
wenzelm@40281:   in
traytel@45060:     map_coes_and_graphs coercion_data_update context
wenzelm@40281:   end;
wenzelm@40281: 
traytel@45059: fun delete_coercion raw_t context =
traytel@45059:   let
traytel@45059:     val ctxt = Context.proof_of context;
traytel@45059:     val t = singleton (Variable.polymorphic ctxt) raw_t;
traytel@45059: 
wenzelm@55303:     fun err_coercion the =
wenzelm@55303:       error ("Not" ^
traytel@45059:         (if the then " the defined " else  " a ") ^ "coercion:\n" ^
traytel@45059:         Syntax.string_of_term ctxt t ^ " :: " ^
traytel@45059:         Syntax.string_of_typ ctxt (fastype_of t));
traytel@45059: 
traytel@45059:     val (T1, T2) = Term.dest_funT (fastype_of t)
traytel@45059:       handle TYPE _ => err_coercion false;
traytel@45059: 
traytel@54584:     val (a, _) = dest_Type T1
traytel@45060:       handle TYPE _ => err_coercion false;
traytel@45059: 
traytel@54584:     val (b, _) = dest_Type T2
traytel@45060:       handle TYPE _ => err_coercion false;
traytel@45059: 
traytel@45059:     fun delete_and_insert tab G =
traytel@45059:       let
traytel@45059:         val pairs =
traytel@45060:           Symreltab.fold (fn ((a, b), (_, (_, ts))) => fn pairs =>
traytel@45059:             if member (op aconv) ts t then (a, b) :: pairs else pairs) tab [(a, b)];
traytel@45059:         fun delete pair (G, tab) = (Graph.del_edge pair G, Symreltab.delete_safe pair tab);
traytel@45059:         val (G', tab') = fold delete pairs (G, tab);
wenzelm@49564:         fun reinsert pair (G, xs) =
wenzelm@49564:           (case Graph.irreducible_paths G pair of
wenzelm@49564:             [] => (G, xs)
wenzelm@49564:           | _ => (Graph.add_edge pair G, (pair, transitive_coercion ctxt tab' G' pair) :: xs));
traytel@45059:         val (G'', ins) = fold reinsert pairs (G', []);
traytel@45059:       in
traytel@45060:         (fold Symreltab.update ins tab', G'', restrict_graph G'')
traytel@45059:       end
traytel@45059: 
wenzelm@55303:     fun show_term t =
wenzelm@55303:       Pretty.block [Syntax.pretty_term ctxt t,
wenzelm@55303:         Pretty.str " :: ", Syntax.pretty_typ ctxt (fastype_of t)];
traytel@45059: 
traytel@45060:     fun coercion_data_update (tab, G, _) =
wenzelm@55303:       (case Symreltab.lookup tab (a, b) of
wenzelm@55303:         NONE => err_coercion false
wenzelm@55303:       | SOME (t', (_, [])) =>
wenzelm@55303:           if t aconv t'
wenzelm@55303:           then delete_and_insert tab G
wenzelm@55303:           else err_coercion true
wenzelm@55303:       | SOME (t', (_, ts)) =>
wenzelm@55303:           if t aconv t' then
wenzelm@55303:             error ("Cannot delete the automatically derived coercion:\n" ^
traytel@45059:               Syntax.string_of_term ctxt t ^ " :: " ^
wenzelm@55303:               Syntax.string_of_typ ctxt (fastype_of t) ^ "\n\n" ^
wenzelm@55303:               Pretty.string_of
wenzelm@55303:                 (Pretty.big_list "Deleting one of the coercions:" (map show_term ts)) ^
traytel@45059:               "\nwill also remove the transitive coercion.")
wenzelm@55303:           else err_coercion true);
traytel@45059:   in
traytel@45060:     map_coes_and_graphs coercion_data_update context
traytel@45059:   end;
traytel@45059: 
traytel@45059: fun print_coercions ctxt =
traytel@45059:   let
traytel@45060:     fun separate _ [] = ([], [])
wenzelm@52432:       | separate P (x :: xs) = (if P x then apfst else apsnd) (cons x) (separate P xs);
traytel@45060:     val (simple, complex) =
traytel@45060:       separate (fn (_, (_, ((Ts, Us), _))) => null Ts andalso null Us)
traytel@45060:         (Symreltab.dest (coes_of ctxt));
wenzelm@52432:     fun show_coercion ((a, b), (t, ((Ts, Us), _))) =
wenzelm@52432:       Pretty.item [Pretty.block
wenzelm@52432:        [Syntax.pretty_typ ctxt (Type (a, Ts)), Pretty.brk 1,
wenzelm@52432:         Pretty.str "<:", Pretty.brk 1,
wenzelm@52432:         Syntax.pretty_typ ctxt (Type (b, Us)), Pretty.brk 3,
wenzelm@52432:         Pretty.block
wenzelm@52432:          [Pretty.keyword "using", Pretty.brk 1,
wenzelm@52432:           Pretty.quote (Syntax.pretty_term ctxt t)]]];
wenzelm@52432: 
wenzelm@52432:     val type_space = Proof_Context.type_space ctxt;
wenzelm@52432:     val tmaps =
wenzelm@52432:       sort (Name_Space.extern_ord ctxt type_space o pairself #1)
wenzelm@52432:         (Symtab.dest (tmaps_of ctxt));
wenzelm@53539:     fun show_map (c, (t, _)) =
wenzelm@52432:       Pretty.block
wenzelm@53539:        [Name_Space.pretty ctxt type_space c, Pretty.str ":",
wenzelm@52432:         Pretty.brk 1, Pretty.quote (Syntax.pretty_term ctxt t)];
traytel@45059:   in
wenzelm@52432:    [Pretty.big_list "coercions between base types:" (map show_coercion simple),
wenzelm@52432:     Pretty.big_list "other coercions:" (map show_coercion complex),
wenzelm@52432:     Pretty.big_list "coercion maps:" (map show_map tmaps)]
wenzelm@52432:   end |> Pretty.chunks |> Pretty.writeln;
traytel@45059: 
traytel@45059: 
traytel@51319: (* theory setup *)
wenzelm@40283: 
traytel@51319: val parse_coerce_args =
traytel@51327:   Args.$$$ "+" >> K PERMIT || Args.$$$ "-" >> K FORBID || Args.$$$ "0" >> K LEAVE
wenzelm@40283: 
wenzelm@40283: val setup =
wenzelm@40283:   Context.theory_map add_term_check #>
wenzelm@40284:   Attrib.setup @{binding coercion}
wenzelm@40284:     (Args.term >> (fn t => Thm.declaration_attribute (K (add_coercion t))))
wenzelm@40281:     "declaration of new coercions" #>
traytel@45059:   Attrib.setup @{binding coercion_delete}
traytel@45059:     (Args.term >> (fn t => Thm.declaration_attribute (K (delete_coercion t))))
traytel@45059:     "deletion of coercions" #>
traytel@40297:   Attrib.setup @{binding coercion_map}
wenzelm@40284:     (Args.term >> (fn t => Thm.declaration_attribute (K (add_type_map t))))
traytel@51319:     "declaration of new map functions" #>
traytel@51319:   Attrib.setup @{binding coercion_args}
traytel@51319:     (Args.const false -- Scan.lift (Scan.repeat1 parse_coerce_args) >>
traytel@51319:       (fn spec => Thm.declaration_attribute (K (map_coerce_args (Symtab.update spec)))))
traytel@51319:     "declaration of new constants with coercion-invariant arguments";
wenzelm@40281: 
traytel@45059: 
traytel@45059: (* outer syntax commands *)
traytel@45059: 
traytel@45059: val _ =
wenzelm@52432:   Outer_Syntax.improper_command @{command_spec "print_coercions"}
wenzelm@52432:     "print information about coercions"
wenzelm@52432:     (Scan.succeed (Toplevel.keep (print_coercions o Toplevel.context_of)));
traytel@45059: 
wenzelm@40281: end;