Thu 19 Jan 2023 10:45 - 11:10 at Avenue34 - Semantics I Chair(s): Neel Krishnaswami

We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting
relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based
systems, refining cornerstone results of rewriting theory (such as Newman’s Lemma, Church-Rosser Theorem,
and critical pair-like lemmas) to a metric and quantitative setting. To avoid distance trivialisation and lack of
confluence issues, we introduce non-expansive, linear term rewriting systems, and then generalise the latter
to the novel class of graded term rewriting systems. These systems make quantitative rewriting modal and
context-sensitive, this way endowing rewriting with coeffectful behaviours.

Thu 19 Jan

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10:20 - 12:00
Semantics IPOPL at Avenue34
Chair(s): Neel Krishnaswami University of Cambridge
10:20
25m
Talk
A Type-Based Approach to Divide-and-Conquer Recursion in Coq
POPL
Pedro da Costa Abreu Junior Purdue University, Benjamin Delaware Purdue University, Alex Hubers University of Iowa, Christa Jenkins University of Iowa, J. Garrett Morris University of Iowa, Aaron Stump University of Iowa
DOI
10:45
25m
Talk
Elements of Quantitative RewritingVirtual
POPL
Francesco Gavazzo University of Pisa, Cecilia Di Florio University of Bologna
DOI
11:10
25m
Talk
The Geometry of Causality: Multi-token Geometry of Interaction and Its Causal Unfolding
POPL
Simon Castellan University of Rennes; Inria; CNRS; IRISA, Pierre Clairambault Université Aix-Marseille; Université de Toulon; CNRS; LIS
DOI
11:35
25m
Talk
Deconstructing the Calculus of Relations with Tape Diagrams
POPL
Filippo Bonchi University of Pisa, Alessandro Di Giorgio University of Pisa, Alessio Santamaria University of Pisa; University of Sussex
DOI