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- W3185736670 abstract "We give a formal treatment of simple type theories, such as the simply-typed λ-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional algebraic structure, one can further axiomatize second-order, variable-binding operators. This provides a syntax-independent representation of simple type theories. We describe multisorted second-order presentations, such as the presentation of the simply-typed λ-calculus, and their clone-theoretic algebras; free algebras on clones abstractly describe the syntax of simple type theories quotiented by equations such as β- and η-equality. We give a construction of free algebras and derive a corresponding induction principle, which facilitates syntax-independent proofs of properties such as adequacy and normalization for simple type theories. Working only with clones avoids some of the complexities inherent in presheaf-based frameworks for abstract syntax." @default.
- W3185736670 created "2021-08-02" @default.
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- W3185736670 date "2021-01-01" @default.
- W3185736670 modified "2023-09-26" @default.
- W3185736670 title "Abstract Clones for Abstract Syntax" @default.
- W3185736670 doi "https://doi.org/10.4230/lipics.fscd.2021.30" @default.
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