一句话：提出 F≤b，为有界量化提供隐式多态与类型推断，并证明其可靠、完备且可判定，已在 Abella 中机器化验证。
主流面向对象语言的类型系统支持子类型与有界量化，但针对有界量化的类型推断研究较少；局部类型推断虽被广泛采用，却对 bounded quantification 有重要限制且规范复杂。本文提出 kernel F≤ 的变体 F≤b，引入隐式多态：其声明式系统基于可判定高阶多态的双向类型与贪婪隐式实例化，使程序只需少量类型标注，并可省略类型参数；需要时也支持显式类型应用以处理 impredicative 实例化。作者证明 F≤b 相对 kernel F≤ 完备，其算法系统可靠、完备且可判定，并在 Abella 证明助手中机器化验证全部结果。
Mainstream object-oriented programming languages such as Java, Scala, C#, or TypeScript have polymorphic type systems with subtyping and bounded quantification. Bounded quantification, despite being a pervasive and widely used feature, has attracted little research work on type-inference algorithms to support it. A notable exception is local type inference, which is the basis of most current implementations of type inference for mainstream languages. However, support for bounded quantification in local type inference has important restrictions, and its non-algorithmic specification is complex. In this paper, we present a variant of kernel F ≤ , which is the canonical calculus with bounded quantification, with implicit polymorphism. Our variant, called F ≤ b , comes with a declarative and an algorithmic formulation of the type system. The declarative type system is based on previous work on bidirectional typing for predicative higher-rank polymorphism and a greedy approach to implicit instantiation. This allows for a clear declarative specification where programs require few type annotations and enables implicit polymorphism where applications omit type parameters. Just as local type inference, explicit type applications are also available in F ≤ b if desired. This is useful to deal with impredicative instantiations, which would not be allowed otherwise in F ≤ b . Due to the support for impredicative instantiations, we can obtain a completeness result with respect to kernel F ≤ , showing that all the well-typed kernel F ≤ programs can type-check in F ≤ b . The corresponding algorithmic version of the type system is shown to be sound, complete, and decidable. All the results have been mechanically formalized in the Abella theorem prover.
@article{paperbot1832,
title = {Greedy Implicit Bounded Quantification},
author = {Chen Cui and Shengyi Jiang and Bruno C. d. S. Oliveira},
journal = {Proceedings of the ACM on Programming Languages},
volume = {7},
number = {OOPSLA2},
year = {2023},
doi = {10.1145/3622871}
}