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Syntax and Handlers for Operations with Scopes

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We propose a model of syntax with scoped operations, which are relevant to calculi with algebraic operations and handlers. A scoped operation (such as “catch” used to handle exceptions) encompasses pieces of syntax that, unlike arguments of algebraic operations, do not commute with global substitution. In this setting, a handler can be understood as an interpretation of a scoped operation. We propose two equivalent categorical models. One arises from the initial-algebra semantics in the category of endofunctors, generalising Ghani et al.’s monad of explicit substitutions, while the other arises from algebras over a category of indexed objects, in the style of Fiore et ’s formalisation of syntax with binders using algebras over presheaves.

Joint work with Tom Schrijvers, Nicolas Wu, and Mauro Jaskelioff.

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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