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A Type-Theoretic Foundation for Programming With Higher-Order Abstract Syntax and First-Class Substitutions

Overview Higher-Order Abstract Syntax (HOAS) is a simple, powerful technique for implementing object languages, since it directly supports common and tricky routines dealing with variables, such as capture-avoiding substitution and renaming. This is achieved by representing binders in the object-language via binders in the meta-language. However, enriching functional programming languages with direct support for HOAS has been a major challenge, because recursion over HOAS encodings requires one to traverse - abstractions and necessitates programming with open objects. The paper presents a novel type-theoretic foundation based on contextual modal types which allows one to recursively analyze open terms via higher-order pattern matching. By design, variables occurring in open terms can never escape their scope.

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Publisher
Association for Computing Machinery
File Format
PDF
Date Published
Jan 9, 2009
Format
White Papers
Topics
Programming Languages

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