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 // Copyright (c) 2018, the Dart project authors. Please see the AUTHORS file // for details. All rights reserved. Use of this source code is governed by a // BSD-style license that can be found in the LICENSE file. /// @assertion Instantiate to bound then computes an actual type argument list /// for [G] as follows: /// /// Let [Ui],[1] be [Si], for all [i] in [1 .. k]. (This is the "current value" /// of the bound for type variable [i], at step [1]; in general we will /// consider the current step, [m], and use data for that step, e.g., the bound /// [Ui],[m], to compute the data for step [m + 1]). /// /// Let [-->m] be a relation among the type variables [X1 .. Xk] such that /// [Xp -->m Xq] iff [Xq] occurs in [Up],[m] (so each type variable is related /// to, that is, depends on, every type variable in its bound, possibly /// including itself). Let [==>m] be the transitive closure of [-->m]. For each /// [m], let [Ui],[m+1], for [i] in [1 .. k], be determined by the following /// iterative process: /// /// 1. If there exists a [j] in [1 .. k] such that [Xj ==>m X0j] (that is, if /// the dependency graph has a cycle) let [M1 .. Mp] be the strongly connected /// components (SCCs) with respect to [-->m] (that is, the maximal subsets of /// [X1 .. Xk] where every pair of variables in each subset are related in both /// directions by [==>m]; note that the SCCs are pairwise disjoint; also, they /// are uniquely defined up to reordering, and the order does not matter). Let /// [M] be the union of [M1 .. Mp] (that is, all variables that participate in /// a dependency cycle). Let [i] be in [1 .. k]. If [Xi] does not belong to [M] /// then [Ui,m+1 = Ui,m]. Otherwise there exists a [q] such that [Xi] belongs /// to [Mq]; [Ui,m+1] is then obtained from [Ui,m] by replacing every covariant /// occurrence of a variable in [Mq] by [dynamic], and replacing every /// contravariant occurrence of a variable in [Mq] by [Null]. /// /// 2. Otherwise, (if no dependency cycle exists) let [j] be the lowest number /// such that [Xj] occurs in [Up,m] for some [p] and [Xj -/->m Xq] for all [q] /// in [1..k] (that is, [Uj,m] is closed, that is, the current bound of [Xj] /// does not contain any type variables; but [Xj] is being depended on by the /// bound of some other type variable). Then, for all [i] in [1 .. k], [Ui,m+1] /// is obtained from [Ui,m] by replacing every covariant occurrence of [Xj] by /// [Uj,m], and replacing every contravariant occurrence of [Xj] by [Null]. /// /// 3. Otherwise, (when no dependencies exist) terminate with the result /// []. /// /// @description Checks that trying to declare [class A>], /// [class B?>] causes error: /// /// In order to allow the use of `A` in the bound in `B`, we must show that /// `X` satisfies the bound on the type parameter of `A`, i.e., we must show /// `X <: A`. But the constraint on `X` in `B` is actually `X <: A?`, and /// that is satisfied by `X == Null`, and it is not true that `Null <: A`, /// which is a counterexample to the claim that we can show `X <: A`. /// /// The point is that we need to show that `X <: A?` implies `X <: A`, and /// we know we can never prove that because we have a counterexample. /// /// There is no such problem in `C`: In that case we need to show that /// `X <: C?` implies `X <: C?`, which is immediate. /// /// The underlying requirement is that the type in the bound (like `A` and /// `C`) must be well-bounded, just like any other type, based on whatever we /// know about the involved types. In this situation the declared bounds of type /// parameters is the only thing we know about those type parameters, so we need /// to show that the declared bounds suffice to show that the type is /// well-bounded. For instance, in `C` we need to show that the bound in `C` /// suffices to show the bound in `C`; but in `B` we need to show that the bound /// in `B` suffices to show the bound in `A` (and it doesn't, so `B` is an /// error). /// /// @author iarkh@unipro.ru class A> {} class B?> {} // ^ // [analyzer] unspecified // [cfe] unspecified class C?> {} main() { }