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@40281:   datatype variance = COVARIANT | CONTRAVARIANT | INVARIANT
wenzelm@40281:   val infer_types: Proof.context -> (string -> typ option) -> (indexname -> typ option) ->
wenzelm@40281:     term list -> term list
wenzelm@40281: end;
wenzelm@40281: 
wenzelm@40281: structure Subtyping =
wenzelm@40281: struct
wenzelm@40281: 
wenzelm@40281: (** coercions data **)
wenzelm@40281: 
wenzelm@40281: datatype variance = COVARIANT | CONTRAVARIANT | INVARIANT
wenzelm@40281: 
wenzelm@40281: datatype data = Data of
wenzelm@40282:   {coes: term Symreltab.table,  (*coercions table*)
wenzelm@40282:    coes_graph: unit Graph.T,  (*coercions graph*)
wenzelm@40282:    tmaps: (term * variance list) Symtab.table};  (*map functions*)
wenzelm@40281: 
wenzelm@40281: fun make_data (coes, coes_graph, tmaps) =
wenzelm@40281:   Data {coes = coes, coes_graph = coes_graph, tmaps = tmaps};
wenzelm@40281: 
wenzelm@40281: structure Data = Generic_Data
wenzelm@40281: (
wenzelm@40281:   type T = data;
wenzelm@40281:   val empty = make_data (Symreltab.empty, Graph.empty, Symtab.empty);
wenzelm@40281:   val extend = I;
wenzelm@40281:   fun merge
wenzelm@40281:     (Data {coes = coes1, coes_graph = coes_graph1, tmaps = tmaps1},
wenzelm@40281:       Data {coes = coes2, coes_graph = coes_graph2, tmaps = tmaps2}) =
wenzelm@40281:     make_data (Symreltab.merge (op aconv) (coes1, coes2),
wenzelm@40281:       Graph.merge (op =) (coes_graph1, coes_graph2),
wenzelm@40281:       Symtab.merge (eq_pair (op aconv) (op =)) (tmaps1, tmaps2));
wenzelm@40281: );
wenzelm@40281: 
wenzelm@40281: fun map_data f =
wenzelm@40281:   Data.map (fn Data {coes, coes_graph, tmaps} =>
wenzelm@40281:     make_data (f (coes, coes_graph, tmaps)));
wenzelm@40281: 
wenzelm@40281: fun map_coes f =
wenzelm@40281:   map_data (fn (coes, coes_graph, tmaps) =>
wenzelm@40281:     (f coes, coes_graph, tmaps));
wenzelm@40281: 
wenzelm@40281: fun map_coes_graph f =
wenzelm@40281:   map_data (fn (coes, coes_graph, tmaps) =>
wenzelm@40281:     (coes, f coes_graph, tmaps));
wenzelm@40281: 
wenzelm@40281: fun map_coes_and_graph f =
wenzelm@40281:   map_data (fn (coes, coes_graph, tmaps) =>
wenzelm@40281:     let val (coes', coes_graph') = f (coes, coes_graph);
wenzelm@40281:     in (coes', coes_graph', tmaps) end);
wenzelm@40281: 
wenzelm@40281: fun map_tmaps f =
wenzelm@40281:   map_data (fn (coes, coes_graph, tmaps) =>
wenzelm@40281:     (coes, coes_graph, f tmaps));
wenzelm@40281: 
wenzelm@40281: fun rep_data context = Data.get context |> (fn Data args => args);
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;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** utils **)
wenzelm@40281: 
wenzelm@40281: val is_param = Type_Infer.is_param
wenzelm@40281: val is_paramT = Type_Infer.is_paramT
wenzelm@40281: val deref = Type_Infer.deref
wenzelm@40281: fun mk_param i S = TVar (("?'a", i), S); (* TODO dup? see src/Pure/type_infer.ML *)
wenzelm@40281: 
wenzelm@40281: fun nameT (Type (s, [])) = s;
wenzelm@40281: fun t_of s = Type (s, []);
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;
wenzelm@40282: val is_compT = fn (Type (_, _ :: _)) => true | _ => false;
wenzelm@40281: val is_freeT = fn (TFree _) => true | _ => false;
wenzelm@40281: val is_fixedvarT = fn (TVar (xi, _)) => not (is_param xi) | _ => false;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40282: (* unification *)  (* TODO dup? needed for weak 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@40281:     val thy = ProofContext.theory_of ctxt;
wenzelm@40281:     val pp = Syntax.pp ctxt;
wenzelm@40281:     val arity_sorts = Type.arity_sorts pp (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@40281:             (Vartab.update_new (xi, 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@40281:           meets (Ts, Ss) (meet (deref tye T, S) tye_idx)
wenzelm@40281:       | meets _ tye_idx = tye_idx;
wenzelm@40281: 
wenzelm@40281:     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@40281:       (case pairself (`is_paramT o 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: val add_edge = Typ_Graph.add_edge_acyclic;
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@40282: fun new_imm_preds G Ts =
wenzelm@40281:   subtract (op =) Ts (distinct (op =) (maps (Typ_Graph.imm_preds G) Ts));
wenzelm@40282: fun new_imm_succs G Ts =
wenzelm@40281:   subtract op= Ts (distinct (op =) (maps (Typ_Graph.imm_succs G) Ts));
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (* Graph shortcuts *)
wenzelm@40281: 
wenzelm@40281: fun maybe_new_node s G = perhaps (try (Graph.new_node (s, ()))) G
wenzelm@40281: fun maybe_new_nodes ss G = fold maybe_new_node ss G
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** error messages **)
wenzelm@40281: 
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@40281:       in Term.subst_bounds (map Syntax.mark_boundT 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@40281: 
wenzelm@40281: fun inf_failed msg =
wenzelm@40281:   "Subtype inference failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n\n";
wenzelm@40281: 
wenzelm@40281: fun err_appl ctxt msg tye bs t T u U =
wenzelm@40281:   let val ([t', u'], [T', U']) = prep_output ctxt tye bs [t, u] [T, U]
wenzelm@40281:   in error (inf_failed msg ^ Type.appl_error (Syntax.pp ctxt) t' T' u' U' ^ "\n") end;
wenzelm@40281: 
wenzelm@40281: fun err_subtype ctxt msg tye (bs, t $ u, U, V, U') =
wenzelm@40281:   err_appl ctxt msg tye bs t (U --> V) u U';
wenzelm@40281: 
wenzelm@40281: fun err_list ctxt msg tye Ts =
wenzelm@40281:   let
wenzelm@40281:     val (_, Ts') = prep_output ctxt tye [] [] Ts;
wenzelm@40281:     val text = cat_lines ([inf_failed msg,
wenzelm@40281:       "Cannot unify a list of types that should be the same,",
wenzelm@40281:       "according to suptype dependencies:",
wenzelm@40281:       (Pretty.string_of (Pretty.list "[" "]" (map (Pretty.typ (Syntax.pp ctxt)) Ts')))]);
wenzelm@40281:   in
wenzelm@40281:     error text
wenzelm@40281:   end;
wenzelm@40281: 
wenzelm@40281: fun err_bound ctxt msg tye packs =
wenzelm@40281:   let
wenzelm@40281:     val pp = Syntax.pp ctxt;
wenzelm@40281:     val (ts, Ts) = fold
wenzelm@40281:       (fn (bs, t $ u, U, _, U') => fn (ts, Ts) =>
wenzelm@40281:         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@40281:     val text = cat_lines ([inf_failed msg, "Cannot fullfill subtype constraints:"] @
wenzelm@40281:         (map2 (fn [t, u] => fn [T, U] => Pretty.string_of (
wenzelm@40281:           Pretty.block [
wenzelm@40281:             Pretty.typ pp T, Pretty.brk 2, Pretty.str "<:", Pretty.brk 2, Pretty.typ pp U,
wenzelm@40281:             Pretty.brk 3, Pretty.str "from function application", Pretty.brk 2,
wenzelm@40281:             Pretty.block [Pretty.term pp t, Pretty.brk 1, Pretty.term pp u]]))
wenzelm@40281:         ts Ts))
wenzelm@40281:   in
wenzelm@40281:     error text
wenzelm@40281:   end;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** constraint generation **)
wenzelm@40281: 
wenzelm@40281: fun generate_constraints ctxt =
wenzelm@40281:   let
wenzelm@40281:     fun gen cs _ (Const (_, T)) tye_idx = (T, tye_idx, cs)
wenzelm@40281:       | gen cs _ (Free (_, T)) tye_idx = (T, tye_idx, cs)
wenzelm@40281:       | gen cs _ (Var (_, T)) tye_idx = (T, tye_idx, cs)
wenzelm@40281:       | gen cs bs (Bound i) tye_idx =
wenzelm@40281:           (snd (nth bs i handle Subscript => err_loose i), tye_idx, cs)
wenzelm@40281:       | gen cs bs (Abs (x, T, t)) tye_idx =
wenzelm@40281:           let val (U, tye_idx', cs') = gen cs ((x, T) :: bs) t tye_idx
wenzelm@40281:           in (T --> U, tye_idx', cs') end
wenzelm@40281:       | gen cs bs (t $ u) tye_idx =
wenzelm@40281:           let
wenzelm@40281:             val (T, tye_idx', cs') = gen cs bs t tye_idx;
wenzelm@40281:             val (U', (tye, idx), cs'') = gen cs' bs u tye_idx';
wenzelm@40281:             val U = mk_param idx [];
wenzelm@40281:             val V = mk_param (idx + 1) [];
wenzelm@40281:             val tye_idx''= strong_unify ctxt (U --> V, T) (tye, idx + 2)
wenzelm@40281:               handle NO_UNIFIER (msg, tye') => err_appl ctxt msg tye' bs t T u U;
wenzelm@40281:             val error_pack = (bs, t $ u, U, V, U');
wenzelm@40281:           in (V, tye_idx'', ((U', U), error_pack) :: cs'') end;
wenzelm@40281:   in
wenzelm@40281:     gen [] []
wenzelm@40281:   end;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (** constraint resolution **)
wenzelm@40281: 
wenzelm@40281: exception BOUND_ERROR of string;
wenzelm@40281: 
wenzelm@40281: fun process_constraints ctxt cs tye_idx =
wenzelm@40281:   let
wenzelm@40281:     val coes_graph = coes_graph_of (Context.Proof ctxt);
wenzelm@40281:     val tmaps = tmaps_of (Context.Proof ctxt);
wenzelm@40281:     val tsig = Sign.tsig_of (ProofContext.theory_of ctxt);
wenzelm@40281:     val pp = Syntax.pp ctxt;
wenzelm@40281:     val arity_sorts = Type.arity_sorts pp tsig;
wenzelm@40281:     val subsort = Type.subsort tsig;
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@40281: 
wenzelm@40282: 
wenzelm@40281:     (* check whether constraint simplification will terminate using weak unification *)
wenzelm@40282: 
wenzelm@40281:     val _ = fold (fn (TU, error_pack) => fn tye_idx =>
wenzelm@40281:       (weak_unify ctxt TU tye_idx handle NO_UNIFIER (msg, tye) =>
wenzelm@40281:         err_subtype ctxt ("Weak unification of subtype constraints fails:\n" ^ msg)
wenzelm@40281:           tye error_pack)) 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)
wenzelm@40281:               | INVARIANT => (cs, strong_unify ctxt constraint tye_idx
wenzelm@40281:                   handle NO_UNIFIER (msg, tye) => err_subtype ctxt msg tye error_pack));
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)));
wenzelm@40281:             val test_update = is_compT orf is_freeT orf is_fixedvarT;
wenzelm@40281:             val (ch, done') =
wenzelm@40281:               if not (null new) then ([],   done)
wenzelm@40281:               else split_cs (test_update o deref tye') done;
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@40281:             val args = map2 mk_param (idx upto idx + n - 1) (arity_sorts a S);
wenzelm@40281:             val tye' = Vartab.update_new (xi, Type(a, args)) tye;
wenzelm@40281:             val (ch, done') = split_cs (is_compT o 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@40281:               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*)
wenzelm@40281:         and eliminate TU error_pack done todo tye idx =
wenzelm@40281:           let
wenzelm@40281:             val [TVar (xi, S)] = filter is_paramT TU;
wenzelm@40281:             val [T] = filter_out 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@40281:             val (ch, done') = split_cs (test_update o deref tye') done;
wenzelm@40281:             val todo' = ch @ todo;
wenzelm@40281:           in
wenzelm@40281:             if subsort (S', S) (*TODO check this*)
wenzelm@40281:             then simplify done' todo' (tye', idx)
wenzelm@40281:             else err_subtype ctxt "Sort mismatch" tye error_pack
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@40281:               (case (deref tye T, deref tye U) of
wenzelm@40281:                 (Type (a, []), 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@40281:                   else err_subtype ctxt (a ^" is not a subtype of " ^ b) (fst tye_idx) error_pack
wenzelm@40281:               | (Type (a, Ts), Type (b, Us)) =>
wenzelm@40281:                   if a<>b then err_subtype ctxt "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@40281:                     exists is_paramT [T, U]
wenzelm@40281:                   then eliminate [T, U] error_pack done todo tye idx
wenzelm@40281:                   else if exists (is_freeT orf is_fixedvarT) [T, U]
wenzelm@40281:                   then err_subtype ctxt "Not eliminated free/fixed variables"
wenzelm@40281:                         (fst tye_idx) error_pack
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@40281: 
wenzelm@40281:     fun find_error_pack lower T' =
wenzelm@40281:       map snd (filter (fn ((T, U), _) => if lower then T' = U else T' = T) cs');
wenzelm@40281: 
wenzelm@40282:     fun unify_list (T :: Ts) tye_idx =
wenzelm@40281:       fold (fn U => fn tye_idx => strong_unify ctxt (T, U) tye_idx
wenzelm@40282:         handle NO_UNIFIER (msg, tye) => err_list ctxt msg tye (T :: Ts))
wenzelm@40281:       Ts tye_idx;
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@40281:       (if super then Graph.imm_succs else Graph.imm_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
wenzelm@40281:               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@40281:         fun fitting Ts S U = Type.of_sort tsig (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@40281:         fun restriction T = Type.of_sort tsig (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
wenzelm@40281:           [] => 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;
wenzelm@40281:             val (G'', tye_idx') = (add_edge (T, U) G', tye_idx)
wenzelm@40281:               handle Typ_Graph.CYCLES cycles =>
wenzelm@40281:                 let
wenzelm@40281:                   val (tye, idx) = fold unify_list cycles tye_idx
wenzelm@40281:                 in
wenzelm@40281:                   (*all cycles collapse to one node,
wenzelm@40281:                     because all of them share at least the nodes x and y*)
wenzelm@40281:                   collapse (tye, idx) (distinct (op =) (flat cycles)) G
wenzelm@40281:                 end;
wenzelm@40281:           in
wenzelm@40281:             build_graph G'' cs tye_idx'
wenzelm@40281:           end
wenzelm@40281:     and collapse (tye, idx) nodes G = (*nodes non-empty list*)
wenzelm@40281:       let
wenzelm@40281:         val T = hd nodes;
wenzelm@40281:         val P = new_imm_preds G nodes;
wenzelm@40281:         val S = new_imm_succs G nodes;
wenzelm@40281:         val G' = Typ_Graph.del_nodes (tl nodes) G;
wenzelm@40281:       in
wenzelm@40281:         build_graph G' (map (fn x => (x, T)) P @ map (fn x => (T, x)) S) (tye, idx)
wenzelm@40281:       end;
wenzelm@40281: 
wenzelm@40281:     fun assign_bound lower G key (tye_idx as (tye, _)) =
wenzelm@40281:       if is_paramT (deref tye key) then
wenzelm@40281:         let
wenzelm@40281:           val TVar (xi, S) = 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@40281:           val bound = map (deref tye) raw_bound;
wenzelm@40281:           val not_params = filter_out 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@40281:                 SOME (map nameT (filter_out is_paramT (map (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)
wenzelm@40281:                 handle BOUND_ERROR msg => err_bound ctxt msg tye (find_error_pack lower key))
wenzelm@40281:         in
wenzelm@40281:           (case assignment of
wenzelm@40281:             NONE => tye_idx
wenzelm@40281:           | SOME T =>
wenzelm@40281:               if is_paramT T then tye_idx
wenzelm@40281:               else if lower then (*upper bound check*)
wenzelm@40281:                 let
wenzelm@40281:                   val other_bound = map (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@40281:                   else err_bound ctxt ("Assigned simple type " ^ s ^
wenzelm@40281:                     " clashes with the upper bound of variable " ^
wenzelm@40281:                     Syntax.string_of_typ ctxt (TVar(xi, S))) tye (find_error_pack (not lower) key)
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@40281:           assign_alternating ts (filter (is_paramT o 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@40281:         val max_params = filter (is_paramT o 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@40281:         fold unify_list 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: 
wenzelm@40281: fun insert_coercions ctxt tye ts =
wenzelm@40281:   let
wenzelm@40281:     fun deep_deref T =
wenzelm@40281:       (case deref tye T of
wenzelm@40281:         Type (a, Ts) => Type (a, map deep_deref Ts)
wenzelm@40281:       | U => U);
wenzelm@40281: 
wenzelm@40281:     fun gen_coercion ((Type (a, [])), (Type (b, []))) =
wenzelm@40281:           if a = b
wenzelm@40281:           then Abs (Name.uu, Type (a, []), Bound 0)
wenzelm@40281:           else
wenzelm@40281:             (case Symreltab.lookup (coes_of (Context.Proof ctxt)) (a, b) of
wenzelm@40281:               NONE => raise Fail (a ^ " is not a subtype of " ^ b)
wenzelm@40281:             | SOME co => co)
wenzelm@40281:       | gen_coercion ((Type (a, Ts)), (Type (b, Us))) =
wenzelm@40281:           if a <> b
wenzelm@40281:           then raise raise Fail ("Different constructors: " ^ a ^ " and " ^ b)
wenzelm@40281:           else
wenzelm@40281:             let
wenzelm@40282:               fun inst t Ts =
wenzelm@40282:                 Term.subst_vars
wenzelm@40281:                   (((Term.add_tvar_namesT (fastype_of t) []) ~~ rev Ts), []) t;
wenzelm@40281:               fun sub_co (COVARIANT, TU) = gen_coercion TU
wenzelm@40281:                 | sub_co (CONTRAVARIANT, TU) = gen_coercion (swap TU);
wenzelm@40281:               fun ts_of [] = []
wenzelm@40282:                 | ts_of (Type ("fun", [x1, x2]) :: xs) = x1 :: x2 :: (ts_of xs);
wenzelm@40281:             in
wenzelm@40281:               (case Symtab.lookup (tmaps_of (Context.Proof ctxt)) a of
wenzelm@40281:                 NONE => raise Fail ("No map function for " ^ a ^ " known")
wenzelm@40281:               | SOME tmap =>
wenzelm@40281:                   let
wenzelm@40281:                     val used_coes = map sub_co ((snd tmap) ~~ (Ts ~~ Us));
wenzelm@40281:                   in
wenzelm@40281:                     Term.list_comb
wenzelm@40281:                       (inst (fst tmap) (ts_of (map fastype_of used_coes)), used_coes)
wenzelm@40281:                   end)
wenzelm@40281:             end
wenzelm@40281:       | gen_coercion (T, U) =
wenzelm@40281:           if Type.could_unify (T, U)
wenzelm@40281:           then Abs (Name.uu, T, Bound 0)
wenzelm@40281:           else raise Fail ("Cannot generate coercion from "
wenzelm@40281:             ^ Syntax.string_of_typ ctxt T ^ " to " ^ Syntax.string_of_typ ctxt U);
wenzelm@40281: 
wenzelm@40281:     fun insert _ (Const (c, T)) =
wenzelm@40281:           let val T' = deep_deref T;
wenzelm@40281:           in (Const (c, T'), T') end
wenzelm@40281:       | insert _ (Free (x, T)) =
wenzelm@40281:           let val T' = deep_deref T;
wenzelm@40281:           in (Free (x, T'), T') end
wenzelm@40281:       | insert _ (Var (xi, T)) =
wenzelm@40281:           let val T' = deep_deref T;
wenzelm@40281:           in (Var (xi, T'), T') end
wenzelm@40281:       | insert bs (Bound i) =
wenzelm@40281:           let val T = nth bs i handle Subscript =>
wenzelm@40281:             raise TYPE ("Loose bound variable: B." ^ string_of_int i, [], []);
wenzelm@40281:           in (Bound i, T) end
wenzelm@40281:       | insert bs (Abs (x, T, t)) =
wenzelm@40281:           let
wenzelm@40281:             val T' = deep_deref T;
wenzelm@40282:             val (t', T'') = insert (T' :: bs) t;
wenzelm@40281:           in
wenzelm@40281:             (Abs (x, T', t'), T' --> T'')
wenzelm@40281:           end
wenzelm@40281:       | insert bs (t $ u) =
wenzelm@40281:           let
wenzelm@40281:             val (t', Type ("fun", [U, T])) = insert bs t;
wenzelm@40281:             val (u', U') = insert bs u;
wenzelm@40281:           in
wenzelm@40281:             if U <> U'
wenzelm@40281:             then (t' $ (gen_coercion (U', U) $ u'), T)
wenzelm@40281:             else (t' $ 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@40281: fun infer_types ctxt const_type var_type raw_ts =
wenzelm@40281:   let
wenzelm@40281:     val (idx, ts) = Type_Infer.prepare ctxt const_type var_type raw_ts;
wenzelm@40281: 
wenzelm@40281:     fun gen_all t (tye_idx, constraints) =
wenzelm@40281:       let
wenzelm@40281:         val (_, tye_idx', constraints') = generate_constraints ctxt t tye_idx
wenzelm@40281:       in (tye_idx', constraints' @ constraints) end;
wenzelm@40281: 
wenzelm@40281:     val (tye_idx, constraints) = fold gen_all ts ((Vartab.empty, idx), []);
wenzelm@40281:     val (tye, _) = process_constraints ctxt constraints tye_idx;
wenzelm@40281:     val ts' = insert_coercions ctxt tye ts;
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@40281: fun coercion_infer_types ctxt =
wenzelm@40281:   infer_types ctxt
wenzelm@40281:     (try (Consts.the_constraint (ProofContext.consts_of ctxt)))
wenzelm@40281:     (ProofContext.def_type ctxt);
wenzelm@40281: 
wenzelm@40281: local
wenzelm@40281: 
wenzelm@40281: fun add eq what f = Context.>> (what (fn xs => fn ctxt =>
wenzelm@40281:   let val xs' = f ctxt xs in if eq_list eq (xs, xs') then NONE else SOME (xs', ctxt) end));
wenzelm@40281: 
wenzelm@40281: in
wenzelm@40281: 
wenzelm@40281: val _ = add (op aconv) (Syntax.add_term_check ~100 "coercions") coercion_infer_types;
wenzelm@40281: 
wenzelm@40281: end;
wenzelm@40281: 
wenzelm@40281: 
wenzelm@40281: (* interface *)
wenzelm@40281: 
wenzelm@40281: fun add_type_map map_fun context =
wenzelm@40281:   let
wenzelm@40281:     val ctxt = Context.proof_of context;
wenzelm@40281:     val t = singleton (Variable.polymorphic ctxt) (Syntax.read_term ctxt map_fun);
wenzelm@40281: 
wenzelm@40281:     fun err_str () = "\n\nthe general type signature for a map function is" ^
wenzelm@40281:       "\nf1 => f2 => ... => fn => C [x1, ..., xn] => C [x1, ..., xn]" ^
wenzelm@40281:       "\nwhere C is a constructor and fi is of type (xi => yi) or (yi => xi)";
wenzelm@40281: 
wenzelm@40281:     fun gen_arg_var ([], []) = []
wenzelm@40282:       | gen_arg_var ((T, T') :: Ts, (U, U') :: Us) =
wenzelm@40281:           if T = U andalso T' = U' then COVARIANT :: gen_arg_var (Ts, Us)
wenzelm@40281:           else if T = U' andalso T' = U then CONTRAVARIANT :: gen_arg_var (Ts, Us)
wenzelm@40281:           else error ("Functions do not apply to arguments correctly:" ^ err_str ())
wenzelm@40281:       | gen_arg_var (_, _) =
wenzelm@40281:           error ("Different numbers of functions and arguments\n" ^ err_str ());
wenzelm@40281: 
wenzelm@40281:     (* TODO: This function is only needed to introde the fun type map
wenzelm@40281:       function: "% f g h . g o h o f". There must be a better solution. *)
wenzelm@40281:     fun balanced (Type (_, [])) (Type (_, [])) = true
wenzelm@40281:       | balanced (Type (a, Ts)) (Type (b, Us)) =
wenzelm@40281:           a = b andalso forall I (map2 balanced Ts Us)
wenzelm@40281:       | balanced (TFree _) (TFree _) = true
wenzelm@40281:       | balanced (TVar _) (TVar _) = true
wenzelm@40281:       | balanced _ _ = false;
wenzelm@40281: 
wenzelm@40281:     fun check_map_fun (pairs, []) (Type ("fun", [T as Type (C, Ts), U as Type (_, Us)])) =
wenzelm@40281:           if balanced T U
wenzelm@40282:           then ((pairs, Ts ~~ Us), C)
wenzelm@40281:           else if C = "fun"
wenzelm@40281:             then check_map_fun (pairs @ [(hd Ts, hd (tl Ts))], []) U
wenzelm@40281:             else error ("Not a proper map function:" ^ err_str ())
wenzelm@40281:       | check_map_fun _ _ = error ("Not a proper map function:" ^ err_str ());
wenzelm@40281: 
wenzelm@40281:     val res = check_map_fun ([], []) (fastype_of t);
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: 
wenzelm@40281: fun add_coercion coercion context =
wenzelm@40281:   let
wenzelm@40281:     val ctxt = Context.proof_of context;
wenzelm@40281:     val t = singleton (Variable.polymorphic ctxt) (Syntax.read_term ctxt coercion);
wenzelm@40281: 
wenzelm@40281:     fun err_coercion () = error ("Bad type for coercion " ^
wenzelm@40281:         Syntax.string_of_term ctxt t ^ ":\n" ^
wenzelm@40281:         Syntax.string_of_typ ctxt (fastype_of t));
wenzelm@40281: 
wenzelm@40281:     val (Type ("fun", [T1, T2])) = fastype_of t
wenzelm@40281:       handle Bind => err_coercion ();
wenzelm@40281: 
wenzelm@40281:     val a =
wenzelm@40281:       (case T1 of
wenzelm@40281:         Type (x, []) => x
wenzelm@40281:       | _ => err_coercion ());
wenzelm@40281: 
wenzelm@40281:     val b =
wenzelm@40281:       (case T2 of
wenzelm@40281:         Type (x, []) => x
wenzelm@40281:       | _ => err_coercion ());
wenzelm@40281: 
wenzelm@40281:     fun coercion_data_update (tab, G) =
wenzelm@40281:       let
wenzelm@40281:         val G' = maybe_new_nodes [a, b] G
wenzelm@40281:         val G'' = Graph.add_edge_trans_acyclic (a, b) G'
wenzelm@40281:           handle Graph.CYCLES _ => error (a ^ " is already a subtype of " ^ b ^
wenzelm@40281:             "!\n\nCannot add coercion of type: " ^ a ^ " => " ^ b);
wenzelm@40281:         val new_edges =
wenzelm@40281:           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:         fun complex_coercion tab G (a, b) =
wenzelm@40281:           let
wenzelm@40281:             val path = hd (Graph.irreducible_paths G (a, b))
wenzelm@40281:             val path' = (fst (split_last path)) ~~ tl path
wenzelm@40281:           in Abs (Name.uu, Type (a, []),
wenzelm@40281:               fold (fn t => fn u => t $ u) (map (the o Symreltab.lookup tab) path') (Bound 0))
wenzelm@40281:           end;
wenzelm@40281: 
wenzelm@40281:         val tab' = fold
wenzelm@40281:           (fn pair => fn tab => Symreltab.update (pair, complex_coercion tab G_and_new pair) tab)
wenzelm@40281:           (filter (fn pair => pair <> (a, b)) new_edges)
wenzelm@40281:           (Symreltab.update ((a, b), t) tab);
wenzelm@40281:       in
wenzelm@40281:         (tab', G'')
wenzelm@40281:       end;
wenzelm@40281:   in
wenzelm@40281:     map_coes_and_graph coercion_data_update context
wenzelm@40281:   end;
wenzelm@40281: 
wenzelm@40281: val _ = Context.>> (Context.map_theory
wenzelm@40281:   (Attrib.setup (Binding.name "coercion") (Scan.lift Parse.term >>
wenzelm@40281:     (fn t => fn (context, thm) => (add_coercion t context, thm)))
wenzelm@40281:     "declaration of new coercions" #>
wenzelm@40281:   Attrib.setup (Binding.name "map_function") (Scan.lift Parse.term >>
wenzelm@40281:     (fn t => fn (context, thm) => (add_type_map t context, thm)))
wenzelm@40281:     "declaration of new map functions"));
wenzelm@40281: 
wenzelm@40281: end;