Abstract

Full simply typed lambda calculus is the simply typed lambda calculus extended with product types and sum types. We propose a Kripke-style semantics for full simply typed lambda calculus. We then prove soundness and completeness of type assignment in full simply typed lambda calculus with respect to the proposed semantics. The key point in the proof of completeness is the notion of a canonical model.

中文翻译：

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完全简单键入的Lambda演算的Kripke风格语义和完整性

完全简单类型的lambda演算是用乘积类型和总和类型扩展的简单类型的lambda演算。我们为完全简单类型的lambda演算提出了一种Kripke风格的语义。然后，我们针对提出的语义在完全简单类型的lambda演算中证明类型分配的正确性和完整性。完整性证明的关键是规范模型的概念。