POPL 2026
Sun 11 - Sat 17 January 2026 Rennes, France
Tue 13 Jan 2026 12:06 - 12:28 at Belvédère - Metatheory Chair(s): Cyril Cohen

Step-indexing, handled through the \emph{later modality} $\triangleright P$, plays a key role in many techniques for program verification. A key challenge in proofs is the \emph{later elimination problem}, i.e., turning $\triangleright P$ into $P$. Later elimination cannot be done unconditionally, and is traditionally linked one-to-one to the physical steps the program performs in the operational semantics, which often caused restrictions in proofs. Recently various techniques (\emph{flexible step indexing} and \emph{later credits}) have been proposed to remedy this restriction.

Unfortunately, there currently exist many variations of these techniques with different subsets of features and proof rules. Integrating these techniques into a domain-specific program logic also requires non-trivial proof engineering of the meta theory. In this paper we aim to consolidate this situation by introducing the new \emph{physical step modality}—a modular building block for step-indexing program logics. We demonstrate that our modality can be integrated into various projects in the Iris eco-system (Actris, RefinedRust, Perennial, Trillium) and both eases the proof engineering of the meta theory, and enables new and/or more concise proof rules that these projects previously did not support. All our results are mechanized in the Rocq prover.

Tue 13 Jan

Displayed time zone: Brussels, Copenhagen, Madrid, Paris change

11:00 - 12:50
MetatheoryCPP at Belvédère
Chair(s): Cyril Cohen Inria, CNRS, ENS Lyon, UCBL, LIP
11:00
22m
Talk
Can we formalise type theory intrinsically without any compromise? A case study in Cubical Agda
CPP
Liang-Ting Chen Academia Sinica, Fredrik Nordvall Forsberg University of Strathclyde, Tzu-Chun Tsai Academia Sinica
DOI Pre-print
11:22
22m
Talk
Formalization of a Proof Calculus for Incremental Linearization for Satisfiability Modulo Nonlinear Arithmetic and Transcendental Functions
CPP
Tomaz Mascarenhas Universidade Federal de Minas Gerais, Harun Khan Stanford University, Abdalrhman Mohamed Stanford University, Andrew Reynolds University of Iowa, Haniel Barbosa Universidade Federal de Minas Gerais, Clark Barrett Stanford University, Cesare Tinelli University of Iowa
11:44
22m
Talk
Mechanizing Synthetic Tait Computability in Istari
CPP
Runming Li Carnegie Mellon University, Yue Yao Carnegie Mellon University, Robert Harper Carnegie Mellon University
DOI
12:06
22m
Talk
Building Blocks for Step-Indexed Program Logics
CPP
Thomas Somers Radboud University Nijmegen, Jonas Kastberg Hinrichsen Aalborg University, Lennard Gäher MPI-SWS, Robbert Krebbers Radboud University Nijmegen