Physical Sciences and Mathematics Commons^™

The Nax Language: Unifying Functional Programming And Logical Reasoning In A Language Based On Mendler-Style Recursion Schemes And Term-Indexed Types, Ki Yung Ahn

Dissertations and Theses

Two major applications of lambda calculi in computer science are functional programming languages and mechanized reasoning systems (or, proof assistants). According to the Curry--Howard correspondence, it is possible, in principle, to design a unified language based on a typed lambda calculus for both logical reasoning and programming. However, the different requirements of programming languages and reasoning systems make it difficult to design such a unified language that provides both. Programming languages usually extend lambda calculi with programming-friendly features (e.g., recursive datatypes, general recursion) for supporting the flexibility to model various computations, while sacrificing logical consistency. Logical reasoning systems usually extend …