COALGEBRAIC LOGIC PROGRAMMING FOR TYPE INFERENCE: Parallelism and Corecursion for New Generation of Programming Languages

键入的主要目的是防止在程序运行期间发生执行错误。米尔纳正式提出了这一观点，指出“好类型的程序不会出错”。实际上，类型结构提供了减少程序员错误的基本技术。函数式语言发展的一个主要趋势是底层类型系统的表达能力的提高，例如，在依赖类型、类型类、广义代数类型(GADT)、依赖类型类和规范结构方面。Milner风格的可判定类型推理并不总是满足这样的扩展(例如，主体类型可能不再存在)，并且判定良好类型推理有时需要编译时类型推理之外的计算。新类型推理算法的实现包括各种一阶决策过程，特别是统一和逻辑编程(LP)、约束LP、嵌入交互策略(Coq的eAUTO)的LP以及补充重写的LP。最近，Gonthier等人提出了一个强有力的主张，即对于更丰富的类型系统，LP风格的类型推理比传统的策略驱动的证明开发更高效、更自然。第二个主要趋势是并行性：没有副作用使得并行计算子表达式变得容易。强大的函数组合抽象机制和高阶函数在并行化中起着重要的作用。三种主要的并行语言是EDEN(显式并行)、并行ML(隐式并行)和格拉斯哥并行Haskell(半显式并行)。控制并行性特别区别于函数式语言，在文献中很少将类型推理和并行性考虑在一起。随着类型推理变得越来越复杂并在整个程序开发中发挥更大的作用，顺序类型推理势必成为语言并行的瓶颈。我们新的协代数逻辑编程(CoALP)在一个算法中提供了额外的表达能力(协递归)和并行性。我们建议使用CoALP来代替目前在类型推理中使用的LP工具。随着协递归、并行和类型(函数式)编程方面的重大发展，这些不相交的社区已经变得至关重要：丰富的类型理论越来越依赖于新一代LP语言；协代数语义学已经在语言设计中产生了影响；并行语言方言在跨FP/LP编程范型应用公共技术方面具有巨大的潜力。这个项目在将三个社区的当地和国际合作者聚集在一起方面是独一无二的。该项目的支持者数量比言语更能说明我们议程的及时性。该项目将影响EPSRC战略计划的两个流：“编程语言和编译器”和“验证和正确性”。该项目在理论(自动证据搜索中产生的(Co)递归计算的协代数学研究)、实践(新语言CoALP的实现及其在类型推理工具中的嵌入)和方法论(混合协递归和并行)方面是新颖的。

The main goal of typing is to prevent the occurrence of execution errors during the running of a program. Milner formalised the idea, showing that ``well-typed programs cannot go wrong''. In practice, type structures provide a fundamental technique of reducing programmer errors. At their strongest, they cover most of the properties of interest to the verification community.A major trend in the development of functional languages is improvement in expressiveness of the underlying type system, e.g., in terms of Dependent Types, Type Classes, Generalised Algebraic Types (GADTs), Dependent Type Classes and Canonical Structures. Milner-style decidable type inference does not always suffice for such extensions (e.g. the principal type may no longer exist), and deciding well-typedness sometimes requires computation additional to compile-time type inference.Implementations of new type inference algorithms include a variety of first-order decision procedures, notably Unification and Logic Programming (LP), Constraint LP, LP embedded into interactive tactics (Coq's eauto), and LP supplemented by rewriting.Recently, a strong claim has been made by Gonthier et al that, for richer type systems, LP-style type inference is more efficient and natural than traditional tactic-driven proof development.A second major trend is parallelism: the absence of side-effects makes it easy to evaluate sub-expressions in parallel. Powerful abstraction mechanisms of function composition and higher-order functions play important roles in parallelisation. Three major parallel languages are Eden (explicit parallelism) Parallel ML (implicit parallelism) and Glasgow parallel Haskell (semi-explicit parallelism). Control parallelism in particular distinguishes functional languages.Type inference and parallelism are rarely considered together in the literature. As type inference becomes more sophisticated and takes a bigger role in the overall program development, sequential type inference is bound to become a bottle-neck for language parallelisation.Our new Coalgebraic Logic Programming (CoALP) offers both extra expressiveness (corecursion) and parallelism in one algorithm. We propose to use CoALP in place of LP tools currently used in type inference.With the mentioned major developments in Corecursion, Parallelism, and Typeful (functional) programming it has become vital for these disjoint communities to combine their efforts: enriched type theories rely more and more on the new generation of LP languages; coalgebraic semantics has become influential in language design; and parallel dialects of languages have huge potential in applying common techniques across the FP/LP programming paradigm. This project is unique in bringing together local and international collaborators working in the three communities. The number ofsupporters the project has speaks better than words about the timeliness of our agenda.The project will impact on two streams of EPSRC's strategic plan: "Programming Languages and Compilers" and "Verification and Correctness". The project is novel in aspects of Theory (coalgebraic study of (co)recursive computations arising in automated proof-search); Practice (implementation of the new language CoALP and its embedding in type-inference tools); and Methodology (Mixed corecursion and parallelism).