A strictly linear subatomic proof system
V Barrett, A Guglielmi, B Ralph - CSL 2025-33rd EACSL Annual …, 2025 - inria.hal.science
We present a subatomic deep-inference proof system for a conservative extension of
propositional classical logic with decision trees that is strictly linear. In a strictly linear …
propositional classical logic with decision trees that is strictly linear. In a strictly linear …
Directed equality with dinaturality
A Laretto, F Loregian, N Veltri - arXiv preprint arXiv:2409.10237, 2024 - arxiv.org
We show how dinaturality plays a central role in the interpretation of directed type theory
where types are interpreted as (1-) categories and directed equality is represented by $\hom …
where types are interpreted as (1-) categories and directed equality is represented by $\hom …
Composing dinatural transformations: Towards a calculus of substitution
G McCusker, A Santamaria - Journal of Pure and Applied Algebra, 2021 - Elsevier
Dinatural transformations, which generalise the ubiquitous natural transformations to the
case where the domain and codomain functors are of mixed variance, fail to compose in …
case where the domain and codomain functors are of mixed variance, fail to compose in …
Coends of higher arity
F Loregian, E de Oliveira Santos - Applied Categorical Structures, 2022 - Springer
We specialise a recently introduced notion of generalised dinaturality for functors T:(C op)
p× C q→ D to the case where the domain (resp., codomain) is constant, obtaining notions of …
p× C q→ D to the case where the domain (resp., codomain) is constant, obtaining notions of …
[引用][C] A Calculus of Substitution for Dinatural Transformations. I.
G McCusker, A Santamaria - arXiv preprint arXiv:2007.07576, 2020