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Cartesian closed 2-categories and permutation equivalence in higher-order rewriting

Tom Hirschowitz.

We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.

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Modules over monads and operational semantics (expanded version)

André Hirschowitz ; Tom Hirschowitz ; Ambroise Lafont.

This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition monads, thus covering new applications such as&nbsp;[&hellip;]

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A categorical framework for congruence of applicative bisimilarity in higher-order languages

Tom Hirschowitz ; Ambroise Lafont.

Applicative bisimilarity is a coinductive characterisation of observational equivalence in call-by-name lambda-calculus, introduced by Abramsky (1990). Howe (1996) gave a direct proof that it is a congruence, and generalised the result to all languages complying with a suitable format. We propose a&nbsp;[&hellip;]

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