Typed self-evaluation via intensional type functions

Matt Brown, J. Palsberg
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引用次数: 9

Abstract

Many popular languages have a self-interpreter, that is, an interpreter for the language written in itself. So far, work on polymorphically-typed self-interpreters has concentrated on self-recognizers that merely recover a program from its representation. A larger and until now unsolved challenge is to implement a polymorphically-typed self-evaluator that evaluates the represented program and produces a representation of the result. We present Fωμi, the first λ-calculus that supports a polymorphically-typed self-evaluator. Our calculus extends Fω with recursive types and intensional type functions and has decidable type checking. Our key innovation is a novel implementation of type equality proofs that enables us to define a versatile representation of programs. Our results establish a new category of languages that can support polymorphically-typed self-evaluators.
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通过内涵类型函数进行类型自我评价
许多流行的语言都有一个自解释器,也就是说,一个为自己编写的语言的解释器。到目前为止,关于多态类型自解释器的工作主要集中在仅仅从程序的表示中恢复程序的自识别器上。一个更大的、迄今尚未解决的挑战是实现一个多态类型的自求值器,它对表示的程序求值,并生成结果的表示。我们提出了Fωμi,这是第一个支持多态型自求值器的λ-微积分。我们的微积分用递归类型和内蕴类型函数扩展了Fω,并具有可判定的类型检查。我们的关键创新是类型相等证明的新颖实现,它使我们能够定义程序的通用表示。我们的结果建立了一个新的语言类别,可以支持多态类型的自评估器。
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