The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to encompass classical second-order logic, by incorporating parametric polymorphism and existential types. The system is shown to enjoy good computational properties, such as type preservation, confluence, and strong normalization, which is established by means of a reducibility argument. We identify a syntactic restriction on proofs that characterizes exactly the intuitionistic fragment of second-order lambda-PRK, and we study canonicity results.
翻译:羊羔- PRK- 计算法是一种羊羔- PRK- 计算法,它利用证据和反驳概念的双重性来为古典命题逻辑提供计算解释。 在这项工作中,我们通过纳入参数多形态和存在类型,将羊羔- PRK- 二级逻辑扩展至包括经典逻辑。 该系统被证明享有良好的计算特性,如类型保存、组合和强大的正常化,这是通过可减少的论据建立的。 我们确定了对精确体现羊羔- PRK 二级直觉碎片的证明的综合限制,我们研究的可听性结果。