《鲁迪克》中的归纳类型和功能类型
Inductive and Functional Types in Ludics
摘要：
Ludics是一个逻辑框架，其中类型/公式由具有相同计算行为的术语集建模。本文研究了ludics中归纳数据类型和函数类型的表示。我们研究他们的结构后，游戏语义的方法。归纳类型被解释为至少不动点，我们证明了一个内部的完整性结果，给出了一个明确的建设这样的不动点。然后研究了ludics对归纳类型和功能类型的解释的相互作用性质。特别是，我们确定哪些高阶函数类型不能满足类型安全，我们给出了计算解释。
英文摘要：
Ludics is a logical framework in which types/formulas are modelled by sets of terms with the same computational behaviour. This paper investigates the representation of inductive data types and functional types in ludics. We study their structure following a game semantics approach. Inductive types are interpreted as least fixed points, and we prove an internal completeness result giving an explicit construction for such fixed points. The interactive properties of the ludics interpretation of inductive and functional types are then studied. In particular, we identify which higher-order functions types fail to satisfy type safety, and we give a computational explanation.
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