arXiv subjects

Stelios Tsampas

Publications and source records attributed to Stelios Tsampas.

At least 19 recordsLinked to original sources

arXiv2026

Towards a Higher-Order Bialgebraic Denotational Semantics

The bialgebraic abstract GSOS framework by Turi and Plotkin provides an elegant categorical approach to modelling the operational and denotational semantics of programming and process languages. In abstract GSOS, bisimilarity is always a congruence, and it coincides with denotational equivalence. This saves the language designer from intricate, ad-hoc reasoning to establish these properties. The bialgebraic perspective on operational semantics in the style of abstract GSOS has recently been extended to higher-order languages, preserving compositionality of bisimilarity. However, a categorical understanding of bialgebraic denotational semantics according to Turi and Plotkin's original vision has so far been missing in the higher-order setting. In the present paper, we develop a theory of adequate denotational semantics in higher-order abstract GSOS. The denotational models are parametric in an appropriately chosen semantic domain in the form of a locally final coalgebra for a behaviour bifunctor, whose construction is fully decoupled from the syntax of the language. Our approach captures existing accounts of denotational semantics such as semantic domains built via general step-indexing, previously introduced on a per-language basis, and is shown to be applicable to a wide range of different higher-order languages, e.g. simply typed and untyped languages, or languages with computational effects such as probabilistic or non-deterministic branching.

cs.PL↗

arXiv2026

Higher-order bialgebraic semantics

Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which provides off-the-shelf compositionality results for first-order languages, so far does not apply to higher-order languages. In the present work, we develop a theory of abstract GSOS specifications for higher-order languages, in effect transferring the core principles of Turi and Plotkin's framework to a higher-order setting. In our theory, the operational semantics of higher-order languages is represented by certain dinatural transformations that we term (pointed) higher-order GSOS laws. We give a general compositionality result that applies to all systems specified in this way and discuss how compositionality of combinatory logics and the lambda-calculus w.r.t. a strong variant of Abramsky's applicative bisimilarity are obtained as instances.

cs.LO↗

arXiv2026

Compositionality in Coalgebraic Trace Semantics

A key requirement on any well-behaved process language is its compositionality: behavioural equivalence of processes should be respected by the constructors of the language. Turi and Plotkin's abstract GSOS provides an elegant bialgebraic framework for modelling rule formats that guarantee compositionality from the outset. Their original results, however, are restricted to compositionality of strong bisimilarity, a rather fine-grained notion of process equivalence. In the present paper, we demonstrate that Turi and Plotkin's approach also applies to trace equivalence, which only observes external actions of processes. To this end, we revisit the general compositionality result of their original theory and present it in a refined form with regard to the required naturality conditions. This step makes abstract GSOS applicable over Kleisli categories and thereby enables reasoning about compositionality in the setting of coalgebraic trace semantics. As our main contribution, we introduce De Simone laws, a type of GSOS laws over Kleisli categories, and prove that their operational models are compositional for coalgebraic trace equivalence. This result recovers and explains compositionality of the well-known De Simone rule format for labelled transition systems in a natural categorical setting. As a further application, we derive from our general framework a novel De Simone-type format for probabilistic systems, compositional for probabilistic trace equivalence.

cs.LO↗

arXiv2026

Towards a Higher-Order Mathematical Operational Semantics

Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which has been successfully applied to obtain off-the-shelf compositionality results for first-order languages, so far does not apply to higher-order languages. In the present work, we develop a theory of abstract GSOS specifications for higher-order languages, in effect transferring the core principles of Turi and Plotkin's framework to a higher-order setting. In our theory, the operational semantics of higher-order languages is represented by certain dinatural transformations that we term pointed higher-order GSOS laws. We give a general compositionality result that applies to all systems specified in this way and discuss how compositionality of the SKI calculus and the $λ$-calculus w.r.t. a strong variant of Abramsky's applicative bisimilarity are obtained as instances.

cs.LO↗

arXiv2025

CRDT Emulation, Simulation, and Representation Independence

Conflict-free replicated data types (CRDTs) are distributed data structures designed for fault tolerance and high availability. CRDTs have historically been taxonomized into state-based CRDTs, in which replicas apply updates locally and periodically broadcast their state to other replicas over the network, and operation-based (or op-based) CRDTs, in which every state-updating operation is individually broadcast. In the literature, state-based and op-based CRDTs are considered equivalent due to the existence of algorithms that let them emulate each other, and verification techniques and results that apply to one kind of CRDT are said to apply to the other thanks to this equivalence. However, what it means for state-based and op-based CRDTs to emulate each other has never been made fully precise. Emulation is nontrivial since state-based and op-based CRDTs place different requirements on the underlying network with regard to both the causal ordering of message delivery, and the granularity of the messages themselves. We specify and formalize CRDT emulation in terms of simulation by modeling CRDTs and their interactions with the network as transition systems. We show that emulation can be understood as weak simulations between the transition systems of the original and emulating CRDT systems, thus closing a gap in the CRDT literature. We precisely characterize which properties of CRDT systems are preserved by our weak simulations, and therefore which properties can be said to be preserved by emulation algorithms. Finally, we leverage our emulation results to obtain a general representation independence result for CRDTs: intuitively, clients of a CRDT cannot tell whether they are interacting with a state-based or op-based CRDT in particular.

cs.PL↗

arXiv2025

Bialgebraic Reasoning on Stateful Languages

Reasoning about program equivalence in imperative languages is notoriously challenging, as the presence of states (in the form of variable stores) fundamentally increases the observational power of program terms. The key desideratum for any notion of equivalence is compositionality, guaranteeing that subprograms can be safely replaced by equivalent subprograms regardless of the context. To facilitate compositionality proofs and avoid boilerplate work, one would hope to employ the abstract bialgebraic methods provided by Turi and Plotkin's powerful theory of mathematical operational semantics (a.k.a. abstract GSOS) or its recent extension by Goncharov et al. to higher-order languages. However, multiple attempts to apply abstract GSOS to stateful languages have thus failed. We propose a novel approach to the operational semantics of stateful languages based on the formal distinction between readers (terms that expect an initial input store before being executed), and writers (running terms that have already been provided with a store). In contrast to earlier work, this style of semantics is fully compatible with abstract GSOS, and we can thus leverage the existing theory to obtain coinductive reasoning techniques. We demonstrate that our approach generates non-trivial compositionality results for stateful languages with first-order and higher-order store and that it flexibly applies to program equivalences at different levels of granularity, such as trace, cost, and natural equivalence.

cs.PL↗

arXiv2025

Big Steps in Higher-Order Mathematical Operational Semantics

Small-step and big-step operational semantics are two fundamental styles of structural operational semantics (SOS), extensively used in practice. The former one is more fine-grained and is usually regarded as primitive, as it only defines a one-step reduction relation between a given program and its direct descendant under an ambient evaluation strategy. The latter one implements, in a self-contained manner, such a strategy directly by relating a program to the net result of the evaluation process. The agreement between these two styles of semantics is one of the key pillars in operational reasoning on programs; however, such agreement is typically proven from scratch every time on a case-by-case basis. A general, abstract mathematical argument behind this agreement is up till now missing. We cope with this issue within the framework of higher-order mathematical operational semantics by providing an abstract categorical notion of big-step SOS, complementing the existing notion of abstract higher-order GSOS. Moreover, we introduce a general construction for deriving the former from the latter, and prove an abstract equivalence result between the two.

cs.LO↗

arXiv2025

Abstract Operational Methods for Call-by-Push-Value

Levy's call-by-push-value is a comprehensive programming paradigm that combines elements from functional and imperative programming, supports computational effects and subsumes both call-by-value and call-by-name evaluation strategies. In the present work, we develop modular methods to reason about program equivalence in call-by-push-value, and in fine-grain call-by-value, which is a popular lightweight call-by-value sublanguage of the former. Our approach is based on the fundamental observation that presheaf categories of sorted sets are suitable universes to model call-by-(push)-value languages, and that natural, coalgebraic notions of program equivalence such as applicative similarity and logical relations can be developed within. Starting from this observation, we formalize fine-grain call-by-value and call-by-push-value in the higher-order abstract GSOS framework, reduce their key congruence properties to simple syntactic conditions by leveraging existing theory and argue that introducing changes to either language incurs minimal proof overhead.

cs.PL↗

arXiv2024

Bialgebraic Reasoning on Higher-Order Program Equivalence

Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of the desired notion of equivalence. In the present paper we introduce a general construction of (step-indexed) logical relations at the level of Higher-Order Mathematical Operational Semantics, a highly parametric categorical framework for modeling the operational semantics of higher-order languages. Our main result asserts that for languages whose weak operational model forms a lax bialgebra, the logical relation is automatically sound for contextual equivalence. Our abstract theory is shown to instantiate to combinatory logics and $λ$-calculi with recursive types, and to different flavours of contextual equivalence.

cs.LO↗

arXiv2024

Logical Predicates in Higher-Order Mathematical Operational Semantics

We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are special cases of coalgebraic invariants on mixed-variance functors. We then introduce the notion of a locally maximal logical refinement of a given predicate, with a view to enabling inductive reasoning, and identify sufficient conditions on the overall setup in which locally maximal logical refinements canonically exist. Finally, we develop induction-up-to techniques that simplify inductive proofs via logical predicates on systems encoded as (certain classes of) higher-order GSOS laws by identifying and abstracting away from their boiler-plate part.

cs.LO↗

arXiv2023

Weak Similarity in Higher-Order Mathematical Operational Semantics

Higher-order abstract GSOS is a recent extension of Turi and Plotkin's framework of Mathematical Operational Semantics to higher-order languages. The fundamental well-behavedness property of all specifications within the framework is that coalgebraic strong (bi)similarity on their operational model is a congruence. In the present work, we establish a corresponding congruence theorem for weak similarity, which is shown to instantiate to well-known concepts such as Abramsky's applicative similarity for the lambda-calculus. On the way, we develop several techniques of independent interest at the level of abstract categories, including relation liftings of mixed-variance bifunctors and higher-order GSOS laws, as well as Howe's method.

cs.PL↗

arXiv2023

A Study on Indoor Noise Levels in a Set of School Buildings in Greece utilizing an IoT infrastructure

Monitoring noise pollution in urban areas in a more systematic manner has been gaining traction as a theme among the research community, especially with the rise of smart cities and the IoT. However, although it affects our everyday life in a profound way, monitoring indoor noise levels inside workplaces and public buildings has so far grabbed less of our attention. In this work, we report on noise levels data produced by an IoT infrastructure installed inside 5 school buildings in Greece. Our results indicate that such data can help to produce a more accurate picture of the conditions that students and educators experience every day, and also provide useful insights in terms of health risks and aural comfort.

cs.CY↗

arXiv2022

Stateful Structural Operational Semantics

Compositionality of denotational semantics is an important concern in programming semantics. Mathematical operational semantics in the sense of Turi and Plotkin guarantees compositionality, but seen from the point of view of stateful computation it applies only to very fine-grained equivalences that essentially assume unrestricted interference by the environment between any two statements. We introduce the more restrictive stateful SOS rule format for stateful languages. We show that compositionality of two more coarse-grained semantics, respectively given by assuming read-only interference or no interference between steps, remains an undecidable property even for stateful SOS. However, further restricting the rule format in a manner inspired by the cool GSOS formats of Bloom and van Glabbeek, we obtain the streamlined and cool stateful SOS formats, which respectively guarantee compositionality of the two more abstract equivalences.

cs.LO↗

arXiv2021

Abstract Congruence Criteria for Weak Bisimilarity

We introduce three general compositionality criteria over operational semantics and prove that, when all three are satisfied together, they guarantee weak bisimulation being a congruence. Our work is founded upon Turi and Plotkin's mathematical operational semantics and the coalgebraic approach to weak bisimulation by Brengos. We demonstrate each criterion with various examples of success and failure and establish a formal connection with the simply WB cool rule format of Bloom and van Glabbeek. In addition, we show that the three criteria induce lax models in the sense of Bonchi et al.

cs.LO↗

arXiv2021

Fully Abstract and Robust Compilation and How to Reconcile the Two, Abstractly

The most prominent formal criterion for secure compilation is full abstraction, the preservation and reflection of contextual equivalence. Recent work introduced robust compilation, defined as the preservation of robust satisfaction of hyperproperties, i.e., their satisfaction against arbitrary attackers. In this paper, we initially set out to compare these two approaches to secure compilation. To that end, we provide an exact description of the hyperproperties that are robustly satisfied by programs compiled with a fully abstract compiler, and show that they can be meaningless or trivial. We then propose a novel criterion for secure compilation formulated in the framework of Mathematical Operational Semantics (MOS), guaranteeing both full abstraction and the preservation of robust satisfaction of hyperproperties in a more sensible manner.

cs.PL↗

arXiv2021

CapablePtrs: Securely Compiling Partial Programs Using the Pointers-as-Capabilities Principle

Capability machines such as CHERI provide memory capabilities that can be used by compilers to provide security benefits for compiled code (e.g., memory safety). The existing C to CHERI compiler, for example, achieves memory safety by following a principle called "pointers as capabilities" (PAC). Informally, PAC says that a compiler should represent a source language pointer as a machine code capability. But the security properties of PAC compilers are not yet well understood. We show that memory safety is only one aspect, and that PAC compilers can provide significant additional security guarantees for partial programs: the compiler can provide security guarantees for a compilation unit, even if that compilation unit is later linked to attacker-provided machine code. As such, this paper is the first to study the security of PAC compilers for partial programs formally. We prove for a model of such a compiler that it is fully abstract. The proof uses a novel proof technique (dubbed TrICL, read trickle), which should be of broad interest because it reuses the whole-program compiler correctness relation for full abstraction, thus saving work. We also implement our scheme for C on CHERI, show that we can compile legacy C code with minimal changes, and show that the performance overhead of compiled code is roughly proportional to the number of cross-compilation-unit function calls.

cs.PL↗

arXiv2021

Experiences from Using LoRa and IEEE 802.15.4 for IoT-enabled Classrooms

Several networking technologies targeting the IoT application space currently compete within the smart city domain, both in outdoor and indoor deployments. However, up till now, there is no clear winner, and results from real-world deployments have only recently started to surface. In this paper, we present a comparative study of 2 popular IoT networking technologies, LoRa and IEEE 802.15.4, within the context of a research-oriented IoT deployment inside school buildings in Europe, targeting energy efficiency in education. We evaluate the actual performance of these two technologies in real-world settings, presenting a comparative study on the effect of parameters like the built environment, network quality, or data rate. Our results indicate that both technologies have their advantages, and while in certain cases both are perfectly adequate, in our use case LoRa exhibits a more robust behavior. Moreover, LoRa's characteristics make it a very good choice for indoor IoT deployments such as in educational buildings, and especially in cases where there are low bandwidth requirements.

cs.NI↗

arXiv2020

A categorical approach to secure compilation

We introduce a novel approach to secure compilation based on maps of distributive laws. We demonstrate through four examples that the coherence criterion for maps of distributive laws can potentially be a viable alternative for compiler security instead of full abstraction, which is the preservation and reflection of contextual equivalence. To that end, we also make use of the well-behavedness properties of distributive laws to construct a categorical argument for the contextual connotations of bisimilarity.

cs.PL↗