Reusability and Dependent Types

Robin米尔纳创造了一个口号：良好类型的程序无法运行，宣传了类型函数式语言（如MLand Haskell）在使用类型捕捉运行时错误方面的优势。如今，我们可以并且希望走得更远：依赖类型编程利用了非常有表现力的类型系统的力量来提供更强大的功能，但也为软件开发提供了额外的支持，使用类型来指导开发过程。这可以从最近大量的语言提案中得到证明，这些提案的目标是利用依赖类型的力量，例如Haskell with GADT、Agda、Coq、Omega、Concoqtion、Guru、Ynot、Epigram等等。然而，表达型类型系统也有其代价：更具体的类型经常会降低代码的可重用性，而代码过于具体的实现类型可能不适合当前的应用。这种现象已经出现在ML和Haskell的传统Hindley-Milner风格系统中;它在依赖类型设置中变得更加普遍。幸运的是，一切都没有失去：依赖型的表达能力足够强，他们可以反思性地谈论自己，基于诺丁汉最近对依赖类型编程的研究并受其启发，（EPSRC EP/C512022/1）和容器类型（EPSRCEP/C511964/2）和牛津大学的数据类型通用编程（EPSRCGR/S27078/01，EP/E02128 X/1）我们计划探索依赖类型的潜力，以提供可重用和可靠的软件组件。为了实现这一点，我们打算探索两种替代方法--结构可重用性和设计可重用性--并在一个依赖类型的框架中表达这两种方法。我们的计划是构建扩展Epigram 2框架的新工具，使用容器类型研究底层理论，最重要的是建立新颖的编程模式和库。我们为诺丁汉的RA（彼得·莫里斯，他的博士学位为这项提议奠定了基础）和两名博士生（牛津和斯特拉斯克莱德各一名）寻求资金，以及设备，协调，旅行和异议（即研讨会和暑期学校）的适当支持。

Robin Milner coined the slogan well typed programs cannot gowrong , advertising the strength of typed functional languages like MLand Haskell in using types to catch runtime errors. Nowadays, we canand want to go further: dependently typed programming exploits thepower of very expressive type systems to deliver stronger guaranteesbut also additional support for software development, using types toguide the development process. This is witnessed by a recent surge oflanguage proposals with the goal to harness the power of dependenttypes, e.g. Haskell with GADTs, Agda, Coq, Omega, Concoqtion, Guru,Ynot, Epigram and so on.However, expressive type systems have their price: more specific typesfrequently reduce the reusability of code, whose too-specificimplementation type may not fit its current application. Thisphenomenon already shows up in the traditional Hindley-Milner styletype system of ML and Haskell; it becomes even more prevalent in adependently typed setting. Luckily, all is not lost: dependent typesare expressive enough that they can talk about themselvesreflectively, making meta-programming one of its potential killerapplications with the potential of combining expressive types andreusable software components.Based on and inspired by recent research at Nottingham on dependentlytyped programming (EPSRC EP/C512022/1) and container types (EPSRCEP/C511964/2) and at Oxford on datatype-generic programming (EPSRCGR/S27078/01, EP/E02128X/1) we plan to explore the potential ofdependent types to deliver reusable and reliable softwarecomponents. To achieve this, we intend to explore two alternativeroads - reusability by structure and reusability by design - andexpress both within a dependently typed framework. Our programme is tobuild new tools extending the Epigram 2 framework, investigate theunderlying theory using container types, and most importantlyestablish novel programming patterns and libraries. We seek fundingfor an RA at Nottingham (Peter Morris, whose PhD laid much of thegroundwork for this proposal), and two doctoral students (one each atOxford and Strathclyde), together with appropriate support forequipment, coordination, travel, and dissimination (i.e. a workshopand a summer school)