arXiv subjects

Jake Masters

Publications and source records attributed to Jake Masters.

3 recordsLinked to original sources

arXiv2026

Mixed Choice Multiparty Session Types, Precisely

A precise (sound and complete) subtyping relation $\leq$ specifies that $T'$ is a subtype of $T$ if and only if a program of type $T'$ can always safely replace a program of type $T$ without compromising the safety of a larger program. This paper formulates and proves preciseness of subtyping for mixed choice multiparty session types with session delegation, creation, and interleaving. We prove soundness by developing the first general type system for a full mixed choice multiparty session $\pi$-calculus. To prove completeness, we introduce the three-party lock, which is a minimal and general form of liveness error for handling interleaved sessions, and we establish a new proof technique based on a construction of scheduler processes which enable exhaustive detection for all failures of the subtyping relation. We then extend the preciseness results to a family of mixed choice multiparty session types. Algorithms for checking (1) subtyping and (2) safety, deadlock-freedom, and liveness of typing contexts are fully implemented and optimised to run in quadratic time with respect to the size of the state space and typing context, and have been evaluated with (mixed choice) case studies from the literature.

cs.LO↗

arXiv2025

Logic of Sets with Atoms

Orbit-finite models of computation generalise the standard models of computation, to allow computation over infinite objects that are finite up to symmetries on atoms, denoted by $\mathbb{A}$. Set theory with atoms is used to reason about these objects. Recent work assumes that $\mathbb{A}$ is countable and that the symmetries are the automorphisms of a structure on $\mathbb{A}$. We study this set theory to understand generalisations of this approach. We show that: this construction is well-defined and sufficiently expressive; and that automorphism groups are adequate. Certain uncountable structures appear similar to countable structures, suggesting that the theory of orbit-finite constructions may apply to these uncountable structures. We prove results guaranteeing that the theory of symmetries of two structures are equal. Let: $PM(\mathcal{A})$ be the universe of symmetries induced by adding atoms in bijection with $\mathcal{A}$ and considering the symmetric universe; $\underline{\mathcal{A}}$ be the image of $\mathcal{A}$ on the atoms; and $\phi ^{PM(\mathcal{A})}$ be the relativisation of $\phi$ to $PM(\mathcal{A})$. We prove that all symmetric universes of equality atoms have theory $Th(PM(\left\langle \mathbb{N}\right\rangle))$. We prove that for structures $\mathcal{A}$, `nicely' covered by a set of cardinality $\kappa$, there is a structure $\mathcal{B}\equiv\mathcal{A}$ of size $\kappa$ such that for all formulae $\phi(x)$ in one variable, \begin{equation*} ZFC\vdash \phi(\underline{\mathcal{A}})^{PM(\mathcal{A})}\leftrightarrow\phi(\underline{\mathcal{B}})^{PM(\mathcal{B})} \end{equation*}

math.LO↗

arXiv2025

Asynchronous Global Protocols, Precisely: Full Proofs

Asynchronous multiparty session types are a type-based framework which ensure the compatibility of components in a distributed system by checking compliance against a specified global protocol. We propose a top-down approach, starting with the global protocol which is then projected into a set of local specifications. Next, we use an asynchronous refinement relation, precise asynchronous multiparty subtyping, to enable local specifications to be optimised by permuting actions within individual asynchronous components. This supports local reasoning, as each component can be independently developed and refined in isolation, before being integrated into a larger system. We show that this methodology guarantees both type soundness and liveness of the collection of optimised components. In this article, we first propose new operational semantics of global protocols which capture sound optimisations in the context of asynchronous message-passing. Next we define an asynchronous association between global protocols and a set of optimised local types. Thirdly, we prove, for the first time, the correctness of the most expressive endpoint projection in the literature, coinductive full merging projection. We then show the main theorems of this article: soundness and completeness of the operational correspondence of the asynchronous association. As a consequence, the association acts as an invariant that can be used to transfer key theorems from the bottom-up system to the top-down system. In particular, we used this to prove type soundness, session-fidelity, deadlock-freedom and liveness of the collection of optimised endpoints.

cs.PL↗