Fixpoint constructions in focused orthogonality models of linear logic
Orthogonality is a notion based on the duality between programs and their environments used to determine when they can be safely combined. For instance, it is a powerful tool to establish termination properties in classical formal systems. It was given a general treatment with the concept of orthogo...
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Published in | Electronic Notes in Theoretical Informatics and Computer Science Vol. 3 - Proceedings of... |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
23.11.2023
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Abstract | Orthogonality is a notion based on the duality between programs and their
environments used to determine when they can be safely combined. For instance,
it is a powerful tool to establish termination properties in classical formal
systems. It was given a general treatment with the concept of orthogonality
category, of which numerous models of linear logic are instances, by Hyland and
Schalk. This paper considers the subclass of focused orthogonalities. We
develop a theory of fixpoint constructions in focused orthogonality categories.
Central results are lifting theorems for initial algebras and final coalgebras.
These crucially hinge on the insight that focused orthogonality categories are
relational fibrations. The theory provides an axiomatic categorical framework
for models of linear logic with least and greatest fixpoints of types. We
further investigate domain-theoretic settings, showing how to lift bifree
algebras, used to solve mixed-variance recursive type equations, to focused
orthogonality categories. |
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AbstractList | Orthogonality is a notion based on the duality between programs and their
environments used to determine when they can be safely combined. For instance,
it is a powerful tool to establish termination properties in classical formal
systems. It was given a general treatment with the concept of orthogonality
category, of which numerous models of linear logic are instances, by Hyland and
Schalk. This paper considers the subclass of focused orthogonalities. We
develop a theory of fixpoint constructions in focused orthogonality categories.
Central results are lifting theorems for initial algebras and final coalgebras.
These crucially hinge on the insight that focused orthogonality categories are
relational fibrations. The theory provides an axiomatic categorical framework
for models of linear logic with least and greatest fixpoints of types. We
further investigate domain-theoretic settings, showing how to lift bifree
algebras, used to solve mixed-variance recursive type equations, to focused
orthogonality categories. |
Author | Galal, Zeinab Jafarrahmani, Farzad Fiore, Marcelo |
Author_xml | – sequence: 1 givenname: Marcelo surname: Fiore fullname: Fiore, Marcelo – sequence: 2 givenname: Zeinab surname: Galal fullname: Galal, Zeinab – sequence: 3 givenname: Farzad surname: Jafarrahmani fullname: Jafarrahmani, Farzad |
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Title | Fixpoint constructions in focused orthogonality models of linear logic |
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