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- W205488546 abstract "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 lambda calculi with logic-friendly features (e.g., induction principles, dependent types) for paradox-free inference over fine-grained properties, while being more restrictive in modeling computations. In this dissertation, we design and implement a language called Nax that embraces benefits of both. Nax accepts all recursive datatypes, thus, allowing the same flexibility of defining recursive datatypes as in functional languages. Nax supports a number of Mendler-style recursion schemes that can express various kinds of recursive computations and also guarantee termination. Nax supports term-indexed types to support specifications of fine-grained properties. In addition, Nax supports a conservative extension of Hindley--Milner type inference. The theoretical contributions of this dissertation include theories for Mendler-style recursion schemes and term-indexed types, which we developed to establish strong normalization and logical consistency of Nax." @default.
- W205488546 created "2016-06-24" @default.
- W205488546 creator A5069304896 @default.
- W205488546 date "2000-01-01" @default.
- W205488546 modified "2023-09-26" @default.
- W205488546 title "The Nax Language: Unifying Functional Programming and Logical Reasoning in a Language based on Mendler-style Recursion Schemes and Term-indexed Types" @default.
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- W205488546 doi "https://doi.org/10.15760/etd.2086" @default.
- W205488546 hasPublicationYear "2000" @default.
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