Online Worldwide Seminar on Logic and Semantics (OWLS)

The seminar used to hold on Wednesdays at 2pm UTC (April 2020 - December 2021)

We're having a break!

OWLS has now been running for close to two years and has played an important role keeping the community connected in difficult times. As things slowly get back to normal, and with the zoom fatigue that has built up in the last year, the organizers feel that this is a good time to take a break from the weekly seminars. We might still organize some special edition seminars or revive the series later in the year!

Thanks for joining us and participating so actively!

Mailing list

The OWLS mailing list is still available. It will be used to inform people if the seminar was to resume. To subscribe, or manage an existing subscription, visit this link:

• https://lists.cam.ac.uk/mailman/listinfo/cl-owls

Messages will be sent from the address cl-owls@lists.cam.ac.uk.

Programme

Seminars used to take place on Wednesdays at 2pm UTC.

Seminars were about 45 minutes long including questions. Every other week, the seminar hosted a young researcher to present their work; these seminars are labelled OWLS-YR.

Here is the list of past seminars in reverse chronological order.

• 08 December 2021 (OWLS). Bart Jacobs, Radboud University, "The differences between Pearl's and Jeffrey's update rules in probabilistic learning" Chair: Pawel Sobocinski (video)

  Updating beliefs (also called conditioning) is an important technique in probabilistic reasoning. It may happen that the evidence for such conditioning is fuzzy, for instance when I'm 80% sure that I heard the alarm. In such situations there are two update rules, due to Pearl and to Jeffrey. They give wildly different outcomes and satisfy different mathematical (logical) properties. What makes this situation even more uncomfortable is that it is not clear when one should apply which rule. Bayesian probability plays an important role in modern cognition theory. An intriguing question is whether the human mind works according to Pearl or Jeffrey. This presentation puts all this in a mathematically precise perspective.

• 01 December 2021 (YR-OWLS). Ken Sakayori, University of Bologna, "Categorical Analysis of the π-calculus" Chair: Koko Muroya (video)

  In this talk, we investigate whether a categorical semantics can be given to the (non-session-typed) π-calculus in the same way that a cartesian closed category is a model of the λ-calculus. We show that an affirmative answer can be given under the assumption that special processes, called forwarders, behave as identities. This is shown by designing a variant of i/o-typed π-calculus and a categorical structure called compact closed Freyd category and establishing a correspondence between them. The correspondence is not ad-hoc in the sense that the definition of compact closed Freyd category is fairly standard: compact closed Freyd categories combine two well-known structures, namely, closed Freyd category and compact closed category. The correspondence, however, is not completely satisfactory because the assumption that "forwarders behave as identities" is questionable from the operational/behavioral viewpoint. Unfortunately, the statement that "forwarders behave as identities" is not valid for the majority of the conventional behavioral equivalences for the π-calculus. We examine and discuss if there are ways to validate the assumption by restricting the language or modifying the operational semantics. (Based on joint works with Takeshi Tsukada)

• 17 November 2021 (YR-OWLS). Dolav Nitay, "Learning of Structurally Unambiguous Probabilistic Grammars". Chair: Krishna S. (video)

  The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness results for learning context-free grammars in general, and probabilistic grammars in particular, most of the literature has concentrated on the second problem. In this work we address the first problem. We restrict attention to structurally unambiguous weighted context-free grammars (SUWCFG) and provide a query learning algorithm for structurally unambiguous probabilistic context-free grammars (SUPCFG). We show that SUWCFG can be represented using co-linear multiplicity tree automata (CMTA), and provide a polynomial learning algorithm that learns CMTAs. We show that the learned CMTA can be converted into a probabilistic grammar, thus providing a complete algorithm for learning a structurally unambiguous probabilistic context free grammar (both the grammar topology and the probabilistic weights) using structured membership queries and structured equivalence queries. A summarized version of this work was published at AAAI 21.

• 10 November 2021 (OWLS). Chris Heunen, University of Edinburgh, "Axioms for the category of Hilbert spaces". Chair: Alexandra Silva (video)

  We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure such as probabilities, convexity, complex numbers, continuity, or dimension. We'll discuss the axioms, sketch the proof of the theorem, and survey open questions, further directions, and context. (Based on joint work with Andre Kornell arxiv:2109.07418.)

• 03 November 2021 (YR-OWLS). Karoliina Lehtinen, Aix-Marseille University, "Good-for-games vs. history-determinism in quantitative automata". Chair: Charles Grellois (video)

  Automata models between determinism and nondeterminism can retain some of the algorithmic properties of deterministic automata while enjoying some of the expressiveness and succinctness of nondeterminism. In the setting of regular languages two such models -- namely good-for-games automata and history-deterministic automata -- coincide, and have known applications in reactive synthesis. In this talk, I discuss what happens when these notions are lifted to the quantitative setting. Perhaps surprisingly, the two automata models are no longer equivalent. This talk will explore the landscape of these automata classes and their applications to different quantitative synthesis problems.

• 20 October 2021 (YR-OWLS). Thejaswini Raghavan, University of Warwick, "The Strahler Number of a Parity Game and more". Chair: Charles Grellois (video)

  Solving parity games has been of great interest due to its unique complexity status. In this talk, we will look at "The Strahler number of a Parity game" and argue that it is a robust, and hence arguably natural, parameter as it coincides with its alternative version based on trees of progress measures and—remarkably—with the register number defined by Lehtinen (2018). We show that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices and linear in (d/2k)^k, where k is the Strahler number. One algorithm we obtain is by providing small Strahler Universal Trees. Since most known techniques for solving parity games can be viewed as a search for winning sets for the players with the help of universal trees, it makes sense to build faster algorithms parametrised by these trees. We will explore some algorithms where these trees are explicitly taken as input, and we compare their advantages and disadvantages. This talk is based primarily based on two works: 1) The Strahler Number of a Parity Game with Laure Daviaud and Marcin Jurdziński and 2) A Symmetric Attractor-Decomposition Lifting Algorithm for Parity Games with Marcin Jurdziński, Rémi Morvan and Pierre Ohlmann.

• 13 October 2021 (OWLS). Quentin Carbonneaux and Peter O'Hearn, Facebook, "Applying proof to a microkernel IPC mechanism". Chair: Alexandra Silva (video)

  Facebook is building a new microkernel operating system as part of its AR/VR strategy. This talk describes a project to apply software verification to a central part of the OS: the interpocess communication design. We use Iris, an implementation of concurrent separation logic in the Coq proof assistant, to verify two queue data structures used for IPC. The verification effort uncovered algorithmic simplifications as well as bugs in client code. The simplifications involve the removal of redundant operations in a performance-critical part of the kernel. The proof work was completed in person months, not years, by engineers with no prior familiarity with Iris. These findings are spurring further use of verification at Facebook.

• 14 July 2021. No seminar as ACT 2021 is taking place.
• 07 July 2021 (YR-OWLS). Clara Lacroce, McGill University, "Optimal Spectral-Norm Approximate Minimization". Chair: Nathanaël Fijalkow (video)

  I will present recent work in approximate minimization, done in collaboration with Borja Balle, Prakash Panangaden, Doina Precup and Guillaume Rabusseau. We address the approximate minimization problem for weighted finite automata (WFAs) with weights in $\R$, over a one-letter alphabet: to compute the best possible approximation of a WFA given a bound on the number of states. This work is grounded in Adamyan-Arov-Krein approximation theory, a remarkable collection of results on the approximation of Hankel operators. In addition to its intrinsic mathematical relevance, this theory has proven to be very effective for model reduction. We adapt these results to the framework of weighted automata over a one-letter alphabet. We provide theoretical guarantees and bounds on the quality of the approximation in the spectral and $\ell^2$ norm. We develop an algorithm, based on the properties of Hankel operators, that returns the optimal approximation in the spectral norm. Then, we study the approximate minimization problem of black boxes trained for language modelling of sequential data over a one-letter alphabet. We use the spectral norm to measure the distance between the black box and the WFA, and we provide theoretical guarantees to study the potentially infinite-rank Hankel matrix of the black box, without accessing the training data. Finally, we propose an algorithm returning an asymptotically-optimal approximation of the black box.

• 30 June 2021. No seminar as LICS 2021 is taking place.
• 23 June 2021 (YR-OWLS). Etienne Miquey, ENS Lyon, "Evidenced Frames: A Unifying Framework Broadening Realizability Models". Chair: Charles Grellois (video)

  Constructive foundations have for decades been built upon realizability models for higher-order logic and type theory. However, traditional realizability models have a rather limited notion of computation, which only supports non-termination and avoids many other commonly used effects. Work to address these limitations has typically overlaid structure on top of existing models, such as by using powersets to represent non-determinism, but kept the realizers themselves deterministic. On the other hand, the algebraic structure of existing realizability models taking into account effects in a more direct fashion (as is done in Krivine realizability for instance) is hard to analyze.

  In this work, we (Liron Cohen, Ross Tate & myself) alternatively address these limitations by making the structure underlying realizability models more flexible. To this end, we introduce evidenced frames: a general-purpose framework for building realizability models that support diverse effectful computations. We demonstrate that this flexibility permits models wherein the realizers themselves can be effectful, such as λ-terms that can manipulate state, reduce non-deterministically, or fail entirely. Beyond the broader notions of computation, we demonstrate that evidenced frames form a unifying framework for (realizability) models of higher-order dependent predicate logic. In particular, we prove that evidenced frames are complete with respect to these models, and that the existing completeness construction for implicative algebras—another foundational framework for realizability—factors through our simpler construction. As such, we conclude that evidenced frames offer an ideal domain for unifying and broadening realizability models.

• 16 June 2021 (OWLS). Ugo Dal Lago, University of Bologna "On Differential Program Semantics". Chair: Jamie Vicary (video)

  Traditionally, program semantics is centered around program equivalences and refinements, based on which verification and transformation techniques can be justified. More and more often, however, programs are substituted with approximately equivalent programs, or verified against imprecise specifications. Program semantics has started dealing with program differences only in recent years, through the interpretation of programs in metric spaces. We give a brief survey about the state of the art on metric program semantics, and on the inadequacy of metrics as a way to deal with program differences. We thus point at a few recent results on a new kind of differential program semantics in which differences are context-sensitive, thus richer in structure than mere numbers.

• 09 June 2021 (YR-OWLS). Adwait Godbole, University of California at Berkeley, "Verification of Parameterized Release-Acquire". Chair: Nathanaël Fijalkow

  Memory consistency models provide semantics to memory accesses of multiprocessor programs, sequential Consistency (SC) being a well known example. Weak Memory Models (WMMs) are relaxations of SC which provide weaker guarantees but allow for improved performance. Verification of safety properties has been shown to be a very hard problem from a complexity standpoint for many WMMs. Hence abstractions of such systems and, frameworks providing approximate results are of interest. This talk is based on the safety verification problem for Release-Acquire (RA) semantics, a popular fragment of C++11 that balances performance and programmability. The focus will be on the role of parameterization, which allows a program to be executed by arbitrarily many (apriori unknown number of) threads. This can be seen as a (conservative) over-approximation of actual system behaviour. I will talk about some general concepts, including a simplified semantics which we found to be useful in analysing parameterized RA systems. I will then discuss how one can refine the parameterized system with non-parameterized programs. The expressivity of allowed programs affects the hardness of the verification problem and I will talk about concrete algorithmic and complexity results for different program classes. To conclude I will give some extensions of these ideas to variant WMMs as well as avenues for future work.

  This is based on joint work with S.Krishna (IIT Bombay) and Roland Meyer (TU Braunshweig). An arxiv version can be found at https://arxiv.org/abs/2101.12123.

• 02 June 2021 (OWLS). Meena Mahajan, IMSc, HBNI, Chennai, "Refuting false QBFs with Merge Resolution". Chair: Pawel Sobocinski (video)

  Resolution is one of the most well-studied proof systems for proving classical propositional tautologies. It has naturally been the first-choice system to be built upon and generalised to obtain proof systems for quantified Boolean formulas QBFs. In this talk, I will briefly survey some resolution-based QBF proof system approaches, and then discuss the proof system MergeRes. This is the first QBF system where strategies are built into the proof, as opposed to being algorithmically extracted from them. I will describe how this approach, and the chosen way in MergeRes for representing the strategies, is double-edged: it gives MergeRes an exponential advantage over many resolution-based QBF proof systems while refuting certain formulas, but also leads to exponential lower bounds in MergeRes for some formulas that are easily refutable in other calculi.

  This is joint work with Olaf Beyersdorff, Joshua Blinkhorn, Tomáš Peitl, and Gaurav Sood, and has appeared at STACS 2019/JAR 2020 and FSTTCS 2020.

• 26 May 2021 (YR-OWLS). Gabriel Scherer, INRIA, "Normalization by realizability: a dependently typed pearl". Chair: Charles Grellois (video)

  The work to be presented is in collaboration with Pierre-Évariste Dagand and Lionel Rieg. It studies the computational content of the Fundamental Lemma of classical realizability for the simply-typed lambda-calculus with sums.

  (If you are unfamiliar with classical realizability, it might help to think of it as a unary logical relation with an elegant symmetric setup -- it originates in studies of classical logic. The talk will gently introduce classical realizability.)

  Two salient points of our presentation correspond to folklore ideas that we present as opinionated recommandations, to ourselves and others, of how to give a "modern" presentation of these questions (classical realizability, and in general studying the computational content of a proof device):

  1. We present classical realizablity as compilation to Curien-Herbelin style symmetric abstract machine calculi, instead of the Krivine Abstract machine, to represent realizers. Experts will recognize the polarized reduction rules of Munch-Maccagnoni.

  2. To present computation content, we are *not* using extraction of a program from a mathematical-style proof in a proof assistant. That beautiful approach rarely works and it generates ugly code. Instead we *write* the logical argument directly as a program in a dependently-typed (meta)language, and we think about the code we are writing.

• 19 May 2021 (OWLS).Mikołaj Bojańczyk, University of Warsaw, "Transducers as functional programs". Chair: Alexandra Silva (video)

  I will discuss how certain functions, e.g. string-to-string transducers, or tree-to-tree transducers, can be presented using primitives of functional programming languages, such as composition of functions, or monad operations on the underlying datatypes (lists or trees). If the primitives are chosen well, then we can get classes of functions known from automata theory, e.g. two-way automata as string-to-string transducers or monadic second-order transductions.

• 12 May 2021 (YR-OWLS). Masaki Waga, Kyoto University, "Online Quantitative Timed Pattern Matching with Semiring-Valued Weighted Automata". Chair: Koko Muroya (slides) (video)

  Monitoring of a signal plays an essential role in the runtime verification of cyber-physical systems. Qualitative timed pattern matching is one of the mathematical formulations of monitoring, which gives a Boolean verdict for each sub-signal according to the satisfaction of the given specification. There are two orthogonal directions of extension of qualitative timed pattern matching. One direction on the result is quantitative: what users want is often not a qualitative verdict but the quantitative measurement of the satisfaction of the specification. The other direction on the algorithm is online checking: the monitor returns some verdicts before obtaining the entire signal, which enables to monitor a running system. In this talk, we talk about a combination of these two extensions taking an automata-based approach. This is the first quantitative and online timed pattern matching algorithm to the best of our knowledge. More specifically, we employ what we call timed symbolic weighted automata to specify quantitative specifications to be monitored, and we obtain an online algorithm using the shortest distance of a weighted variant of the zone graph and dynamic programming. Moreover, our problem setting is semiring-based and therefore, general. Our experimental results confirm the scalability of our algorithm for specifications with a time-bound.

• 5 May 2021 (OWLS). Alessio Guglielmi, University of Bath, "Subatomic proof systems and decision trees". Chair: Jamie Vicary (slides)

  Joint work with Chris Barrett and Victoria Barrett

  Subatomic proof systems in deep inference exploit the idea that atoms can be seen as superpositions of values, for example, true and false. Adopting this point of view leads to some dramatic simplifications of proof systems and their proof theory, and this talk provides an example.

  A single, simple, linear inference shape, together with a certain notion of saturation, generates a proof system for a language of standard boolean operators augmented by decision trees. We prove cut-elimination and several other proof-theoretic results for this proof system. Moreover, the proof system provides cut-free proofs of Statman tautologies that are polynomial in the size of the tautologies, while standard proof systems only yield exponential cut-free proofs. The ideas are natural, simple, and mostly rely on two notions that appear to have very general applicability: projecting proofs around atoms and eversion of formulae.

  I could summarise the philosophy behind deep inference and subatomic proof theory as follows. We expand the class of proofs to make accessible better proofs for richer languages and to simplify the normalisation theory. One main reason for its success is deep inference's unique ability to deal with self-dual non-commutative operators, which is what atoms are when used as decision tree constructors.

  The talk does not assume previous knowledge of deep inference and focuses on the general concepts rather than the technicalities. More information about deep inference is at http://alessio.guglielmi.name/res/cos/.

• 28 April 2021 (YR-OWLS). Fabio Zanasi, UCL London, "The Logical Essentials of Machine Learning". Chair: Nathanaël Fijalkow (video)

  I will present recent and ongoing work (joint with G. Cruttwell, B. Gavranovic, N. Ghani, and P. Wilson) on providing semantic foundations to machine learning using the tools of logic, algebra and category theory. This framework provides a much needed unifying perspective on different training techniques for machine learning models, based on the categorical notion of lens. This abstract viewpoint does not only allow to study uniformly learning with neural networks, but also to extend these techniques to other, previously unexplored models, such as Boolean circuits.

• 21 April 2021 (OWLS). Andy Pitts, Cambridge, "Constructive Initial Algebra Semantics". (video) Chair: Pawel Sobocinski

  Initial algebras for endofunctors are a simple category-theoretic concept that has proved useful in computer science logic and semantics for explaining all sorts of inductive (and dually, coinductive) concepts. I will begin by recalling an old theorem of Adamek in classical set theory about constructing initial algebras via transfinite iteration. I will then describe a new version that works in constructive logic with a weak form of choice (the "weakly initial set of covers" axiom of van den Berg, Moerdijk and Palmgren). I will also try to explain why the constructive version is useful even from a classical point of view. This is joint work with Shaun Steenkamp.

• 14 April 2021 (YR-OWLS). Joshua Moerman, RWTH Aachen, "Weighted Register Automata". Chair: Nathanaël Fijalkow (video)

  Register automata are an extension of automata that deal with data, possibly from an infinite domain. Many algorithms from classical automata theory remain to work on deterministic register automata. However, the nondeterministic register automata are strictly more expression and some properties become undecidable. Motivated by a recent result that the subclass of unambiguous register automata has decidable equivalence, we investigate weighted register automata, the common generalisation of register automata and weighted automata. These include unambiguous register automata. We show that equivalence is also decidable for these automata. This improves the previous results in three ways: (a) we allow for more data domains; (b) the complexity is exponentially better; and (c) we allow automata with guessing. Most importantly, we feel that our main contribution is the development of the mathematical theory of so-called orbit-finitely spanned vector spaces, on which our decision procedure is based. In the talk I will mostly talk about these structures. This is joint work with Mikołaj Bojańczyk and Bartek Klin.

• 7 April 2021 (OWLS). Assia Mahboubi, Inria and Vrije Universiteit Amsterdam, "Mathematical Structures in Dependent Type Theory ". (video) Chair: Pawel Sobocinski

  The past decade has seen the advent of several large-scale digital libraries of formalised mathematics, written with the help of proof assistants. Most of these libraries are framed by hierarchies of formal algebraic structures. These structures play a similar role as Bourbaki's mathematical structures, codifying the mathematical language used throughout the library, its vocabulary and its notational apparatus. The latter hierarchies can also be seen as a formal-proof-engineering device, which organises inheritance and sharing between various interfaces.

  This talk will discuss the recent techniques proposed to design these hierarchies in proof assistants based on dependent type theory, the corresponding achievements, but also their pitfalls and limitations.

• 31 March 2021 (YR-OWLS). Tiziano Dalmonte, TU Wien, "Proof systems and countermodels for non-normal modal logics". (video) Chair: Charles Grellois

  Non-normal modal logics are called in this way because they do not validate some axioms or rules of the weakest normal modal logic K. They have been studied since the seminal works by C.I. Lewis, Lemmon, Kripke, Segerberg, Scott, and Montague, and are applied in many areas, such as deontic, epistemic, multi-agent, and probabilistic reasoning. In this talk I will present a bi-neighbourhood semantics for non-normal modal logics that generalizes their standard neighbourhood semantics. Then I will present two kinds of calculi, labelled and internal, that provide decision procedures for these logics and allow for the extraction of countermodels of non-valid formulas. Based on joint works with Nicola Olivetti, Björn Lellmann, Sara Negri, Elaine Pimentel, and Gian Luca Pozzato.

• 24 March 2021 (OWLS). Anca Muscholl, Université Bordeaux, "Learning sound negotiations". (video) Chair: Pawel Sobocinski

  Negotiations are a model of distributed computation related to workflow Petri nets. Deterministic sound negotiations turn out to be amenable to efficient analysis algorithms, and several verification questions can be answered in polynomial time. In this talk we show an efficient Angluin-style learning algorithm in this model.

  This is joint work with Igor Walukiewicz.

• 17 March 2021 (YR-OWLS). Pierre Ohlmann, Université de Paris, "Controlling a random population". Chair: S. Krishna (slides) (video)

  Bertrand et al. introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all agents to a target state? They showed that the problem is decidable and EXPTIME-complete in the adversarial setting, and posed as an open problem the stochastic setting, where the agent is represented by a Markov decision process. In this paper, we show that the stochastic control problem is decidable. Our solution makes significant uses of well quasi orders, of the max-flow min-cut theorem, and of the theory of regular cost functions. We introduce an intermediate problem of independent interest called the sequential flow problem, and study the complexity of solving it. Joint work with Thomas Colcombet and Nathanaël Fijalkow.

• 10 March 2021 (OWLS). Dale Miller, Inria-Saclay and LIX/Ecole Polytechnique, "A proof theory for model checking". (video) Chair: Pawel Sobocinski

  While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the emphasis of model checking is on establishing the truth of a property in a model, we rely on the proof-theoretic notion of additive inference rules, since such rules allow provability to directly describe truth conditions. Unfortunately, the additive treatment of quantifiers requires inference rules to have infinite sets of premises and the additive treatment of model descriptions provides no natural notion of state exploration. By employing a focused proof system, it is possible to construct large-scale, synthetic rules that also qualify as additive but contain elements of multiplicative inference. These additive synthetic rules -- essentially rules built from the description of a model -- allow direct treatment of state exploration. This proof-theoretic framework provides a natural treatment of reachability and non-reachability problems, as well as tabled-deduction, bisimulation, and winning strategies.

  This talk is based on a paper co-authored with Quentin Heath appearing in the Journal of Automated Reasoning, 2019.

  The slides are available here. The article on which the talk is based is here.

• 24 February 2021 (OWLS). Jorge Perez, University of Groningen, "Session Types and Higher-Order Concurrency". (video) Chair: Pawel Sobocinski

  (based on joint works with Alen Arslanagić, Dimitris Kouzapas, Erik Voogd, and Nobuko Yoshida)

  Session types are a type-based approach for ensuring correct message-passing programs. A session type specifies the protocol that each channel endpoint in aprogram should respect.

  Session types have been originally developed for processes in the pi-calculus, the paradigmatic calculus of interaction and concurrency. While there is substantial value in studying session types for the pi-calculus, it is also insightful to investigate them for programming calculi with a more direct link with (functional) programming languages. To this end, we have studied a core calculus for higher-order concurrency and sessions, called HO. HO is a compact blend of sessions and higher-order concurrency, in which the values exchanged by processes can only be abstractions (functions from names to processes).

  In this talk, I will overview two results on the expressivity of HO processes with session types. They show how session types not only delineate and enable encodings; they inform the techniques required to reason about their correctness properties. First, HO and the session pi-calculus are equally expressible: one language can be encoded into the other, up to tight behavioral equivalences. Second, there is a class of so-called minimal session types, which only covers protocols without sequential composition but is still expressive enough to encode all typable HO processes.

• 17 February 2021 (YR-OWLS). Benjamin Kaminski, University College London, "Quantitative Separation Logic". Chair: Nathanaël Fijalkow

  We present quantitative separation logic (QSL). In contrast to classical separation logic, QSL employs quantities which evaluate to real numbers instead of predicates which evaluate to Boolean values. The connectives of classical separation logic, separating conjunction and separating implication, are lifted from predicates to quantities. This extension is conservative: Both connectives are backward compatible to their classical analogs and obey the same laws, e.g. modus ponens, adjointness, etc. Furthermore, we present a weakest precondition calculus for quantitative reasoning about probabilistic pointer programs in QSL. This calculus is a conservative extension of both Ishtiaq's, O'Hearn's and Reynolds' separation logic for heap-manipulating programs and Kozen's / McIver and Morgan's weakest preexpectations for probabilistic programs. Our calculus preserves O'Hearn's frame rule, which enables local reasoning - a key principle of separation logic. Finally, we briefly touch upon open questions regarding lower bounds on weakest preexpectations and intensional completeness of our calculus.

• 3 February 2021 (YR-OWLS). Sonia Marin, University College London, "From axioms to synthetic inference rules via focusing". (video) Chair: C. Grellois

  Focusing is a general technique that was designed to improve proof search, but has since become increasingly relevant in structural proof theory. The essential idea is to identify and merge the non-deterministic choices in a proof. A focused proof is then given by the alternation of phases where invertible rules are applied eagerly (bottom-up) and phases where the other rules are confined and controlled. The focusing theorem, which asserts the completeness of focused proofs, delivers strong representational benefits. For instance, by ignoring the internal structure of the phases one obtains a well-behaved notion of ‘synthetic rule’ (e.g. they commute with cut-reduction steps). In this talk, we will present a careful study of a family of synthetic rules, the bipoles, giving a fresh view to an old problem: how to incorporate inference rules corresponding to axioms into proof systems for classical and intuitionistic logics. As different synthetic inference rules can be produced for the same axiom, we in fact unify and generalise previous approaches for transforming axioms into rules. This is joint work with Dale Miller, Elaine Pimentel, and Marco Volpe.

• 27 January 2021 (OWLS). Sam Staton, University of Oxford, "Names and probabilities". (video) Chair: Alexandra Silva

  One way of thinking of a “pure name” (or “guid") is as a random number, and so names are related to probability. It’s important to understand how some names can be private or secret, and this turns out to correspond to probabilistic concepts. I will talk about semantic models for higher-order programming with probabilities and for programming with names. I’ll show a model of probability that is also a good model of programming with names: it's fully abstract at first order.

  This talk will take us past the nu calculus, quasi Borel spaces, some bits of descriptive set theory and some non-parametric statistics. But it will be an introductory talk and I won’t assume familiarity with any of this. The talk will be partly based on our paper at POPL 2021, https://doi.org/10.1145/3434292, which is joint work with Marcin Sabok, Dario Stein and Michael Wolman.

• 20 January 2021 (YR-OWLS). Ori Lahav, School of Computer Science at Tel Aviv University, "What's Decidable about Causally Consistent Shared Memory?". Chair: Nathanaël Fijalkow (slides) (video)

  While causal consistency is one of the most fundamental consistency models weaker than sequential consistency, the decidability of safety verification for (finite-state) concurrent programs running under causally consistent shared-memories is still unclear. We establish the decidability of this problem for two standard and well-studied variants of causal consistency. To do so, for each of the variants, we develop an equivalent "lossy" operational semantics, and show that it constitutes a well-structured transition system, which enables decidable verification. The two novel semantics are based on similar key observations, which, we believe, may also be of independent use in the investigation of weakly consistent shared memory models and their verification. Interestingly, our results are in contrast to the undecidability of this problem under the Release/Acquire fragment of the C/C++11 memory model, which forms another variant of a causally consistent memory that, in terms of allowed outcomes, lies strictly between the two models we study. Nevertheless, all these variants coincide for write/write-race-free programs, which implies the decidability of verification for such programs under Release/Acquire.
  (Joint work with Udi Boker, partly presented at PLDI'20)

• 6 January 2021 (YR-OWLS). Sarah Winter, Université libre de Bruxelles, "Synthesizing computable functions from synchronous specifications". Chair: S. Krishna (slides) (video)

  Church's synthesis problem asks whether a synchronous specification from infinite words to infinite words can be realized by a synchronous function. We relax this requirement and ask whether a synchronous specification from infinite words to infinite words can be realized by a computable function, in other words, we simply ask whether a specification is implementable.
  This question has been previously studied by Holtmann et al. who showed that the problem is decidable (it was later shown to be EXPtime-complete) for synchronous specifications with total domain. We show that the question is EXPtime-complete for synchronous specifications with partial domain. A specification with partial domain is implementable if for every input sequence in its domain an output sequence can be computed that is correct w.r.t. the specification. A fundamental difference between the total and the partial domain setting is that, if the specification is implementable, in the former setting sequential transducers suffice to do so and in the latter setting a more powerful computation model is needed. We show that if a synchronous specification from infinite words to infinite words is implementable then a deterministic two-way transducer can compute an implementation.
  This is joint work with Emmanuel Filiot.

• 16 December 2020 (OWLS special Christmas edition). Moshe Vardi, Rice University, Lessons from COVID-19: Efficiency vs Resilience. Chair: Nathanaël Fijalkow (video)

  In both computer science and economics, efficiency is a cherished property. In computer science, the field of algorithms is almost solely focused on their efficiency. In economics, the main advantage of the free market is that it promises "economic efficiency." A major lesson from COVID-19 is that both fields have over-emphasized efficiency and under-emphasized resilience. I argue that resilience is a more important property than efficiency and discuss how the two fields can broaden their focus to make resilience a primary consideration. I will include a technical example, showing how we can shift the focus in strategic reasoning from efficiency to resilience.

• 9 December 2020 (OWLS). Derek Dreyer, MPI-SWS, "Turning Iris Up to Eleven: Next Steps in Higher-Order Separation Logic". (video) Chair: Alexandra Silva

  Iris is a framework for higher-order concurrent separation logic, implemented in the Coq proof assistant, which we have been developing since 2014. Originally designed for pedagogical purposes, Iris has grown into a ongoing, multi-institution project, with active collaborators at Aarhus University, BedRock Systems, Boston College, CNRS/LRI, Groningen University, INRIA, ITU Copenhagen, KU Leuven, Microsoft Research, MIT, MPI-SWS, NYU, Radboud University Nijmegen, Saarland University, and Vrije Universiteit Brussel, and over 35 published papers studying or deploying Iris for verification of complex programs and programming language meta-theory in Rust, Go, OCaml, Scala, and more (https://iris-project.org).

  In this talk, we will present two brand new -- and very different -- developments that have the potential to extend the reach of Iris even further. The first is a new *ownership-based refinement type system* for C, which supports *automated* verification of C programs while at the same time being *foundational* (producing Iris proofs in Coq). The second is a complete "remodeling" of Iris, replacing its original step-indexed model with a *transfinite* step-indexed model in order to make Iris suitable for verification of liveness properties.

  For this talk, we will not assume any prior knowledge of Iris. Rather, we will briefly review the distinguishing features of Iris, and then explain the key insights behind the aforementioned new developments -- and the problems they are solving -- at a high level of abstraction.

  The first new development is joint work with Michael Sammler, Rodolphe Lepigre, Robbert Krebbers, Kayvan Memarian, and Deepak Garg. The second is joint work with Simon Spies, Lennard Gäher, Daniel Gratzer, Joseph Tassarotti, Robbert Krebbers, and Lars Birkedal.

• 2 December 2020 (YR-OWLS). Maaike Zwart, University of Oxford, "Distributive Laws in the Boom Hierarchy". Chair: S. Krishna (slides) (video)

  During my PhD research I have studied distributive laws for monads, and developed various no-go theorems. These theorems prove that monads with certain algebraic properties cannot be composed with each other via a distributive law. In this talk I will focus on examples, and share the intuition that I have developed from my results. All the examples in this talk will be based on the Boom hierarchy, a hierarchy of data structures which lends itself perfectly for the study of monad compositions. Based on which monads in this hierarchy do and do not compose with each other via a distributive law, I will make predictions about the behaviour of monad compositions in general.

• 25 November 2020 (YR-OWLS). Francesco Gavazzo, University of Bologna, "Modal Reasoning = Metric Reasoning, via Lawvere". Chair: Charles Grellois (slides) (video)

  Mainstream formal analyses of software systems focus on extensional properties of program behaviour. Such properties ultimately deal with the input/output semantics of programs, this way giving information on what programs compute. There are several situations, however, where intensional properties of programs turn out to be crucial to ensure the correct behaviour of software systems. In these scenarios, one needs not only to know what output a program computes, but also how the program computes it. Typical examples of intensional aspects of computations include efficiency, resource usage, robustness with respect to errors, and privacy and security.

  In the last decades, these properties have been studied in isolation by means of type systems, denotational semantics, and operational techniques. More recently, uniform accounts of a large family of intensional aspects of computations (oftentimes referred to as coeffectful computations) have been proposed in terms of graded modal types and graded (co)monads.

  In this talk, I will present a general framework for studying operationally-based notions of program equivalence for languages with graded modal types. These notions of equivalence identify programs with the same intensional behaviour and thus allow for the intensional analysis of programs. The framework will be instantiated to study the intensional refinement of Abramsky's applicative bisimilarity (a coinductively-defined notion of equivalence for higher-order sequential languages) giving an abstract compositionality theorem generalising well-known results on intensional program behaviour such as Abadi's et al. Non-interference, Pfenning's Proof Irrelevance, and Reed and Pierce's Metric Preservation.

  Finally, a formal connection between the theory of intensional program equivalence and the theory of abstract program distance built on top of Lawvere's analysis of generalised metric spaces will be established, this way allowing for the transfer of results and techniques developed in the context of program metric to the realm of intensional analyses of languages with modal types.

• 18 November 2020 (OWLS). Joël Ouaknine, Max Planck Institute for Software Systems, "Holonomic Techniques, Periods, and Decision Problems". (video) Chair: Pawel Sobocinski

  Holonomic techniques have deep roots going back to Wallis, Euler, and Gauss, and have evolved in modern times as an important subfield of computer algebra, thanks in large part to the work of Zeilberger and others over the past three decades. In this talk, I will give an overview of the area, and in particular will present a select survey of known and original results on decision problems for holonomic sequences and functions. I will also discuss some surprising connections to the theory of periods and exponential periods, which are classical objects of study in algebraic geometry and number theory; in particular, I will relate the decidability of certain decision problems for holonomic sequences to deep conjectures about periods and exponential periods, notably those due to Kontsevich and Zagier.

  Parts of this talk will be based on the paper "On Positivity and Minimality for Second-Order Holonomic Sequences", https://arxiv.org/abs/2007.12282.

• 11 November 2020 (YR-OWLS). Abhisekh Sankaran, University of Cambridge, "Extension preservation in the finite and prefix classes of first order logic". Chair: Koko Muroya (slides) (video)

  It is well known that the classic Łoś-Tarski preservation theorem fails in the finite: there are first-order definable classes of finite structures closed under extensions which are not definable (in the finite) in the existential fragment of first-order logic. We strengthen this by constructing for every n, first-order definable classes of finite structures closed under extensions which are not definable with n quantifier alternations. The classes we construct are definable in the extension of Datalog with negation and indeed in the existential fragment of transitive-closure logic. This answers negatively an open question posed by Rosen and Weinstein.

• 4 November 2020 (OWLS). Orna Kupferman, Hebrew University, Examining Classical Graph-Theory Problems from the Viewpoint of Formal-Verification Methods. Chair: Alexandra Silva (slides) (video)

  The talk surveys a series of works that lift the rich semantics and structure of graphs, and the experience of the formal-verification community in reasoning about them, to classical graph-theoretical problems.

• 28 October 2020 (YR-OWLS). Sebastian Junges, UC Berkeley, "Finding Memoryless Policies in Partially Observable MDPs is 'Existential Theory of the Reals'-complete". Chair: Nathanaël Fijalkow (slides) (video)

  Partially observable Markov Decision Processes (POMDPs) are a prime model in sequential decision making. They are heavily studied in operations research, artificial intelligence and verification, to name a few. For POMDPs, a good policy reaches the target with probability at some threshold, and makes its decisions solely based on the previously made observations. Deciding whether a good policy exists is undecidable. One of the methods to solve instances of this reachability problem is to restrict the memory that the strategy may use. This approach is commonly taking, e.g., in reinforcement learning for POMDPs. In the first part of the talk, we consider memoryless strategies in POMDPs. and show that this problem is as hard as the feasibility problem in parametric Markov Chain (pMC) analysis.

  In the second part of the talk, we consider this feasibility problem for pMCs. Roughly, a pMC is a Markov chain with symbolic transitions. The feasibility problem asks: Do values for the symbols exist such that in the induced parameter-free Markov chain, a target state is reached with probability at least a half. We discuss the complexity landscape for variants of this decision problem. In particular, we establish that feasibility in pMCs is complete for the complexity class "existential theory of the reals” (ETR). Another example of an ETR-complete problem is deciding whether a multivariate polynomial has a real root. Together with the results of the first half of the talk, this establishes that deciding whether there exists a good memoryless policy in a POMDP is ETR-complete.

• 21 October 2020 (OWLS). Antonin Kucera, Masaryk University, "Efficient analysis of VASS termination complexity". Chair: Pawel Sobocinski (video)
• 14 October 2020 (YR-OWLS). Henning Basold, Universteit Leiden, "Coalgebraic Communication Protocols and Session Types". Chair: Koko Muroya (video)

  This is joint work with Alex Keizer and Jorge A. Pérez.

  Compositional methods are central to the development and verification of software systems. They allow to break down large systems into smaller components, while enabling reasoning about the behaviour of the composed system. For concurrent and communicating systems, compositional techniques based on *behavioural type systems* have received much attention. By abstracting communication protocols as types, these type systems can statically check that programs interact with channels according to a certain protocol, whether the intended messages are exchanged in a certain order. For this talk, we will put on our coalgebraic spectacles to investigate *session types*, a widely studied class of behavioral type systems. We will seek a syntax-free description of session-based concurrency as states of coalgebras. The result will be a description of type equivalence, duality, and subtyping relations in terms of canonical coinductive presentations. In turn, this coinductive presentation makes it possible to elegantly derive a decidable type system with subtyping for π-calculus processes, in which the states of a coalgebra will serve as channel protocols. Going full circle, we will also exhibit a coalgebra structure on an existing session type system, and show that the relations and type system resulting from our coalgebraic perspective agree with the existing ones.

• 7 October 2020 (OWLS). Andrej Bauer, University of Ljubljana, "Effects in the real world". Chair: Pawel Sobocinski (video)

  Joint work with Danel Ahman, University of Ljubljana.

  In modern languages, computational effects are often structured using monads or algebraic effects and handlers. These mechanisms excel at implementation of computational effects within the language itself. For instance, the familiar implementation of mutable state in terms of state-passing functions requires no native state, and can be implemented either as a monad or using handlers. One is naturally drawn to using these techniques also for dealing with actual effects, such as manipulation of native memory and access to hardware. These are represented inside the language as algebraic operations or a monad, but treated specially by the language's top-level runtime, which invokes corresponding operating system functionality. While this approach works in practice, one wishes that the ingenuity of the language implementors were better supported by a more flexible methodology with a sound theoretical footing.

  We address the issue by showing how to design a programming language based on runners of algebraic effects. We review runners, recast them as a programming construct, and present a calculus that captures the core ideas of programming with them. Through examples of runners we show how they capture both the interaction between the program and the external world, and encapsulation of programs in virtual environments that tightly control access to external resources and provide strong guarantees of proper resource finalization.

  We accompanied our work with a prototype programming language Coop (https://github.com/andrejbauer/coop) and a Haskell library for runners (https://github.com/danelahman/haskell-coop).

  References:

  • https://arxiv.org/abs/1910.11629
  • https://github.com/andrejbauer/coop
  • https://github.com/danelahman/haskell-coop
• 30 September 2020 (YR-OWLS). Ryoma Sin'ya, Akita University, "Asymptotic Approximation by Regular Languages". Chair: Koko Muroya (slides) (video) In this talk we will introduce a new property of formal languages called REG-measurability where REG is the class of regular languages. Intuitively, a language L is REG-measurable if there exists an infinite sequence of regular languages that ``converges'' to L. A language without REG-measurability has a complex shape in some sense so that it can not be approximated by regular languages.
  The motivation, why we have been interested in REG-measurability, originally came from the following conjecture posed by [Dömösi-Horvath-Ito 1991]: the set of all primitive words over a non-singleton alphabet is not context-free.
  We will describe that several context-free languages are REG-measurable (including languages with transcendental generating function and transcendental density, in particular), while a certain simple deterministic context-free language and the set of primitive words are REG-immeasurable in a strong sense. We will also discuss some open problems and future work.
  This talk is based on the following work: http://www.math.akita-u.ac.jp/~ryoma/misc/measure.pdf
• 23 September 2020 (OWLS). Anupam Das, University of Birmingham, "Cyclic proofs, Peano arithmetic, and Logical complexity". Chair: Jamie Vicary (video) Cyclic proof theory is an increasingly popular tool for (co)inductive reasoning in algebras, type systems, modal fixed point logics and predicate logics with inductive definitions. Understanding the relative power of cyclicity and induction constitutes one of the key questions traversing these areas. The setting of first-order arithmetic provides us with well understood delineations of proof theoretic expressivity, namely in terms of *logical complexity*, i.e. the number of quantifier alternations required for formulas occurring in a proof. We show that cyclic proofs in arithmetic are strictly more succinct than inductive ones in this sense, refining a recent result that cyclic arithmetic and Peano arithmetic are equivalent [Simpson '17] cf. also [Berardi & Tatsuta '17]. We give a converse result too, thus classifying the proof theoretic strength of cyclic arithmetic theories with restricted logical complexity. The former result is based on structural proof theoretic techniques, namely a form of cut-elimination, while the latter result requires us to adapt recent results on the reverse mathematics of omega-word automaton theory [Kołodziejczyk, Michalewski, Pradic & Skrzypczak '16] with classical proof theoretic methods. Given the uniformity of our approach, we are able to recover a metamathematical account of our cyclic theories too. As a result we partially resolve an open problem on the logical strength of McNaughton's theorem on determinisation of omega-word automata from [Kołodziejczyk, Michalewski, Pradic & Skrzypczak '16], by reduction to a form of Gödel incompleteness for cyclic theories. This talk is based on the following work: https://arxiv.org/abs/1807.10248.
  References:
  • [Berardi & Tatsuta '17] Equivalence of inductive definitions and cyclic proofs under arithmetic. Proceedings of LICS 2017.
  • [Kołodziejczyk, Michalewski, Pradic & Skrzypczak '16] The Logical Strength of Büchi's Decidability Theorem. Proceedings of CSL '16.
  • [Simpson '17] Cyclic Arithmetic Is Equivalent to Peano Arithmetic. Proceedings of FoSSaCS 2017.
• 9 September 2020 (OWLS). Filippo Bonchi, Universita di Pisa, "Functorial Semantics: from Lawvere to Carboni-Walters". Chair: Pawel Sobocinski (video) Various kinds of relational algebras have been studied since long time. The traditional approach consists in giving an algebraic theory, namely a signature and a set of equations. Unfortunately, the equations often turn out to be incomplete, unless one uses more sophisticated logics (e.g, Horn clauses). In this talk, we advocate the use of a different sort of algebra, where terms are not anymore trees but rather graphs. This has a clear categorical justification that can be clearly expressed by mean of functorial semantics by Lawvere. We start by gently introducing the Lawvere's approach and then explain its relational extension to Cartesian Bicategories by Carboni and Walters.
• 2 September 2020 (OWLS DEBATE), 3pm UTC. Panel: Brendan Fong, MIT; Nicole Immorlica, Microsoft Research; Delia Kesner, Université de Paris (IRIF); Benjamin Pierce, University of Pennsylvania; Thomas Schwentick, Technische Universität Dortmund; Moshe Vardi, Rice University. "Evolution or Revolution? The Future of Conferences in Theoretical Computer Science". Chair: Jamie Vicary (video)

  The entire community is invited to participate in a debate on the future of the conference system in theoretical computer science. This will provide a rare community-wide opportunity for us to discuss the strengths and weaknesses of our current system, and consider if we can do better. Questions will be asked by members of the audience, and answered by our panel members.

  The scope of the debate is all aspects of our publishing and community traditions, characterised by prestige earned mostly through publication in competitive conferences, and frequent local and international travel. Possible topics for discussion include the need to publish in conferences for career progression, which usually involves burning carbon; wasted reviewing effort when good papers are rejected from highly competitive conferences; the extent of our responsibility as a community to respond to climate change; alternative publishing models, like the journal-focussed system used in mathematics; high costs of conference travel and registration; virtual conference advantages, disadvantages and best practice; improving equality, diversity and access; consequences and response to COVID-19; and the role of professional bodies. These topics have many tight relationships, and need to be discussed together to gain a full understanding of the issues involved.

  Poll responses. Here are the results of the three anonymous polls that were held during the debate.

  1. Until recently, it was common for members of the TCS community to make regular flights. If COVID-19 can be resolved soon with a widely-available vaccine, should we try as a community to:
     • go back to our usual flight habits (i.e. flying several times per year) (2 responses, 3%)
     • continue regular flights, but at a substantially reduced frequency (i.e. flying a couple of times per year) (58 responses, 73%)
     • almost completely eliminate flights (i.e. flying a few times per career) (19 responses, 24%)
  2. Most researchers in TCS follow the "conference first" model, in which results are published first in a conference (either physical or virtual, and preferably high-status), and later on in a journal in expanded form. As a community, should we aim to:
     • continue this into the future (43 responses, 32%)
     • switch to a "journal first" model more like mathematics, changing the TCS conference system so presentation of a paper does not imply publication in an associated proceedings volume (91 responses, 68%)
  3. For the purposes of professional networking and scholarly communication in TCS, virtual conferences can be:
     • just as effective as physical conferences, or even more effective (28 responses, 20%)
     • less effective than physical conferences, but still reasonably effective (67 responses, 47%)
     • much less effective than physical conferences (48 responses, 34%)

  The following links provide further reading on topics related to the debate:

  • Antoine Amarilli, Thomas Colcombet, Hugo Férée and Thomas Schwentick (2020), "Pledge for Sustainable Research in Theoretical Computer Science"
  • Boaz Barak (2016), "Computer Science should Stay Young"
  • Lance Fortnow (2009), "Time for Computer Science to Grow Up"
  • Benjamin Pierce (2020), "Conferences in an Era of Expensive Carbon"
  • Moshe Vardi (2020), "Publish and Perish"

• 26 August 2020 (OWLS). Orna Grumberg, Technion - Israel Institute of Technology , "Automated Program Repair". Chair: Alexandra Silva (slides) (video) In the process of software development and maintenance, much efforts are invested in order to ensure that the product is as bug free as possible. Automating the repair process is highly desired. In this talk we present two approaches to automated program repair, based on formal methods. The first approach automatically repairs an erroneous program using a predefined set of mutations to the code (e.g., replacing ‘+’ with ‘-‘ ; ‘>’ with ‘<’, etc.). The repair algorithm goes through generate-validate iterations, which involve fault localization mechanism in order to disregard sets of unsuccessful repairs. The approach guarantees soundness and completeness with respect to a bounded notion of correctness. The second approach intertwines compositional Assume-Guarantee verification with repair. Automata learning is used for compositional verification. If an erroneous behavior is found, abduction assists in repairing the system by inferring new constraints that eliminate erroneous runs. Then, the verification proceeds for the repaired system. This is a joint work with: Hadar Frenkel, Corina Pasareanu, Bat-chen Rothenberg and Sarai Sheinvald.
• 12 August 2020 (OWLS). Javier Esparza, Technical University of Munich, "An Efficient Normalisation Procedure for Linear Temporal Logic". Chair: Pawel Sobocinski (video) In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a normal form for formulas of LTL with past operators, which Manna and Pnueli then used as the basis of their famous classification of temporal formulas. Some years later, Chang, Manna, and Pnueli built on this result to derive a similar normal form for the future fragment of LTL. Both normalisation procedures had a non-elementary worst-case blow-up, and followed an involved path from LTL formulas to counter-free automata to star-free regular expressions and back to LTL.
  
  We improve on both points. We present a purely syntactic normalisation procedure from LTL to LTL, with single exponential blow-up, that can be implemented in a few dozen lines of Standard ML code. As an application, we derive a simple algorithm to translate LTL into deterministic Rabin automata. The algorithm normalises the formula, translates it into a special very weak alternating automaton, and applies a simple determinisation procedure, valid only for these special automata.
  
  This is joint work with Salomon Sickert that appeared in LICS 2020
• 5 August 2020 (OWLS-YR). Umang Mathur, University of Illinois at Urbana Champaign, "Verification of Uninterpreted and Partially Interpreted Programs". Chair: Krishna. S (slides) (video) Uninterpreted programs are sequential programs with loops and recursion written over a first order vocabulary where the constant, function and predicate symbols used are completely uninterpreted. The input to an uninterpreted program is a first order structure which also determines the semantics of such a programs. The verification question in this setting asks if an uninterpreted a program meets all its assertions on all input structures. In this talk, I will discuss the decidability boundaries for the verification question of uninterpreted programs. In general, the problem is undecidable, but becomes decidable for a sub-class, called coherent uninterpreted programs. The decidability result is tight in that slightly relaxing the coherence criteria leads to undecidability. I will then discuss how the decidability result of coherent programs segue into more general classes of programs, called k-coherent programs (k is a natural number). Finally, I will discuss extensions to the verification question for partially interpreted programs, where the vocabulary is associated with an underlying first order theory and the inputs are those first order structures which are also models of this underlying theory.
• 29 July 2020 (OWLS). Tarmo Uustalu, Reykjavik University, "Interaction laws of monads and comonads". Chair: Jamie Vicary (slides) (video) We introduce and study functor-functor and monad-comonad interaction laws as mathematical objects to describe interaction of effectful computations with behaviors of effect-performing machines. Monad-comonad interaction laws are monoid objects of the monoidal category of functor-functor interaction laws. We show that, for suitable generalizations of the concepts of dual and Sweedler dual, the greatest functor resp. monad interacting with a given functor or comonad is its dual while the greatest comonad interacting with a given monad is its Sweedler dual. We relate monad-comonad interaction laws to stateful runners. We show that functor-functor interaction laws are Chu spaces over the category of endofunctors taken with the Day convolution monoidal structure. Hasegawa's glueing endows the category of these Chu spaces with a monoidal structure whose monoid objects are monad-comonad interaction laws.
  
  This is joint work with Shin-ya Katsumata (NII, Tokyo) and Exequiel Rivas (Inria, Paris).
• 22 July 2020 (OWLS-YR). Justin Hsu, University of Wisconsin–Madison, "A separation logic for probabilistic independence". Chair: Koko Muroya (slides) (video) Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods handle independence poorly, if at all. We propose a probabilistic separation logic PSL, where separation models probabilistic independence, based on a new, probabilistic model of the logic of bunched implications (BI). The program logic PSL is capable of verifying information-theoretic security of cryptographic constructions for several well-known tasks, including private information retrieval, oblivious transfer, secure multi-party addition, and simple oblivious RAM, while reasoning purely in terms of independence and uniformity. If time permits, we will also discuss ongoing work for reasoning about conditional independence.
• 15 July 2020 (OWLS). Christine Tasson, IRIF, Paris, "Towards a model of mixed linear and non-linear substitution." Chair: Alexandra Silva (slides) (video) A functional program is said to be linear when it uses exactly once its input. Linearity is useful to handle memory safely, single-use channels in concurrency, or quantum resources. Yet, we do not want all inputs to be linear and some of them can be used several times safely. Hence the need to understand what is a model of linear-non-linear substitution. Such settings appear naturally in differential lambda-calculus which is our initial motivation. We move from the usual categorical axiomatization of linear logic and lambda-calculus to the multicategorical axiomatisation, using profunctors and 2 monads to give account to linear and non-linear contexts. We present how to combine the linear and the non-linear 2 monads in order to model the linear-non-linear substitution. This is joint work with Martin Hyland.
• 1 July 2020 (OWLS-YR). Amina Doumane, CNRS, ENS de Lyon, "(Non)axiomatizability of positive relation algebras via graph homomorphisms". Chair: Charles Grellois (slides) (video) We study the equational theories of composition and intersection on binary relations, with or without their associated neutral elements (identity and full relation). Without these constants, the equational theory coincides with that of semilattice-ordered semigroups. We show that the equational theory is no longer finitely based when adding one or the other constant—contradicting a conjecture from the litterature. Our proofs exploit a characterisation in terms of graphs and graph homomorphisms, which we show how to adapt in order to capture standard equational theories over the considered signatures.
• 24 June 2020 (OWLS). Valeria Vignudelli, ENS Lyon, "Monads and Quantitative Equational Theories for Nondeterminism and Probability". Chair: Pawel Sobocinski (video) The monad of convex sets of probability distributions is a well-known tool for modelling the combination of nondeterministic and probabilistic computational effects. In this talk I will discuss theories allowing us to reason equationally about this monad, and applications to program verification. In order to reason about distances between programs combining nondeterminism and probabilities, the monad of convex sets of distributions can be lifted from the category of sets to the category of metric spaces. Using the framework of quantitative algebras, recently introduced by Mardare, Panangaden, and Plotkin, we derive an equational presentation of this monad on metric spaces. The main results I will present in this talk are based on collaborations with Filippo Bonchi, Matteo Mio, and Ana Sokolova.
• 17 June 2020 (OWLS-YR). Marie Fortin, University of Liverpool, "FO = FO3 for Linear Orders with Monotone Binary Relations" Chair: Nathanaël Fijalkow (slides) (video) It is well-known that linear orders have the 3-variable property, meaning that over linear orders, every monadic first-order formula with up to 3 free variables is equivalent to one that uses at most 3 variables in total. Over the years, this has been extended to richer classes of structures, such as real-time signals with the +1 relation, Mazurkiewicz traces, or message sequence charts. In this talk, I will present a unifying proof that generalizes those facts. It is based on star-free PDL, a variant of propositional dynamic logic that captures precisely the 3-variable fragment of first-order logic. More precisely, I will show that over structures consisting of one linear order and arbitrarily many binary relations satisfying some monotonicity conditions, star-free PDL has the same expressive power as full first-order logic. This implies that any class of such structures has the 3-variable property.
• 10 June 2020 (OWLS). Seminar cancelled in support of Black Lives Matter.
• 3 June 2020 (OWLS-YR). Dmitry Chistikov, University of Warwick, "Parikh's theorem from the complexity viewpoint". Chair: Krishna S. (video) (slides) Parikh's theorem (1961) connects two basic concepts in computer science, recursion and iteration. It states that commutative images of context-free and regular languages form the same family --- namely semilinear sets, or sets definable in Presburger arithmetic (the first-order logic of addition and order). This theorem has become a standard tool in the theory of verification, with many different proofs and extensions.
  In this talk, we will recall Parikh's theorem and look at it from the complexity viewpoint. Transformation from pushdown automata into finite automata incurs a description blowup, but how big does it need to be? We will look at context-free languages in general and at their subclass, one-counter languages, focusing in particular on lower bounds (hardness).
• 27 May 2020 (OWLS). Dexter Kozen, Cornell University, "Brzozowski derivatives as distributive laws". Chair: Alexandra Silva (slides) (video)
• 13 May 2020 (OWLS). Bartek Klin, Warsaw University, "Monadic monadic second order logic". Chair: Jamie Vicary (slides) (video) Monadic second order logic (MSO) is usually studied over specific kinds of structures, be it finite words, infinite words, finite or infinite trees, total orders of various shapes, etc. A monad is a notion of "a kind of structures" that covers these and many other examples. One can formulate an abstract definition of MSO for a generic monad. I will explain how this is done, and I will describe some conditions that a monad should satisfy to ensure a basic "sanity check": that every definable language is recognized by a finite algebra. (joint work with Mikołaj Bojańczyk and Julian Salamanca)
• 29 April 2020 (OWLS). Daniela Petrisan, University of Paris, "Combining probabilistic and non-deterministic choice via weak distributive laws" (video). Chair: Pawel Sobocinski
• 15 April 2020 (OWLS). Joost-Pieter Katoen, RWTH Aachen University, "Termination of probabilistic programs". Chair: Alexandra Silva (slides) (video) Program termination is a key question in program verification. This talk considers the termination of probabilistic programs, programs that can describe randomised algorithms and more recently received attention in machine learning. Probabilistic termination has several nuances and has some unexpected effects. Programs may diverge with zero probability; they almost-surely terminate (AST). Two AST-programs run in sequence may have an infinite expected run-time, though each of its constituents has a finite expected run-time. This talk will demystify the notions of probabilistic termination, its surprising effects, and its hardness ("degree of undecidability"). We will show a simple proof rule for deciding AST.
• 1 April 2020 (OWLS). Kevin Buzzard, Imperial College London, "Is HoTT the way to do mathematics?". Chair: Jamie Vicary (slides) (video) Homotopy type theory (HoTT) is a foundation for mathematics. Its origins are in work of Awodey, Warren and independently Voevodsky, an algebraic geometer who then changed area and proposed a new definition of equality between mathematical objects. Voevodsky was initially motivated by a desire to formally verify his own work on a computer. However after his unfortunate death in 2017 it was still not the case that any serious algebraic geometry recognisable to a classical algebraic geometer had been formalised in a HoTT computer system. Even in 2020 Grothendieck's original definition of a scheme (the fundamental building block of modern algebraic geometry) has only been formalised in Lean's Dependent Type Theory (DTT), and not in any HoTT system. In my talk, I will start by explaining Voevodsky's univalence axiom, the problems it solves and the problems it causes. I will then explain a basic mathematical question for which Voevodsky's axiom seems in theory like it might be helpful. I will finally talk about work of Ramon Fernandez Mir on formalising Grothendieck's original definition of a scheme in Lean's DTT system (without Voevodsky's axiom). Whether or not this can be done in a HoTT system is apparently an open problem, but one which is easily attackable, and I will finish by explaining my plan for attacking it.

Organizing committees

If you have any feedback about OWLS, feel free to get in touch with an organizer.

OWLS

• Alexandra Silva, University College London, UK
• Pawel Sobocinski, Tallinn University of Technology, Estonia
• Jamie Vicary, University of Cambridge, UK

OWLS-YR

• Nathanaël Fijalkow, CNRS, Laboratoire Bordelais de Recherche en Informatique, France
• Charles Grellois, Université Aix-Marseille, France
• S. Krishna, IIT Bombay, India
• Koko Muroya, RIMS, Kyoto University, Japan