Quantum Separation Logic (QSL) has been proposed as an effective tool to improve the scalability of deductive reasoning for quantum programs. In QSL, separation is interpreted as disentanglement , and the frame rule brings a notion of entanglement-local specification (one that only talks about the qubits entangled with those acted upon by the program). In this paper, we identify two notions of locality unique to the quantum domain, and we construct a novel quantum separation logic, RapunSL , which is able to soundly reduce reasoning about superposition states to reasoning about pure states ( basis-locality ), and reasoning about mixed states arising from measurement to reasoning about pure states ( outcome-locality ). To do so, we introduce two connectives, linear combination and mixing, which together with separation provide a dramatic improvement in the scalability of reasoning, as we demonstrate on a series of challenging case studies.

Abstract We propose the Automata-based Multiparty Protocols framework (AMP) for top-down protocol development. The framework features a new very general formalism for global protocol specifications called Protocol State Machines (PSMs), Communicating State Machines (CSMs) as specifications for local participants, and a type system to check a $$\pi $$ π -calculus with session interleaving and delegation against the CSM specification. Moreover, we define a large class of PSMs, called “tame”, for which we provide a sound and complete PSPACE projection operation that computes a CSM describing the same protocol as a given PSM if one exists. We propose these components as a backwards-compatible new backend for frameworks in the style of Multiparty Session Types. In comparison to the latter, AMP offers a considerable improvement in expressivity, decoupling of the various components (e.g. projection and typing), and robustness (thanks to the complete projection).

We present BlueBell , a program logic for reasoning about probabilistic programs where unary and relational styles of reasoning come together to create new reasoning tools. Unary-style reasoning is very expressive and is powered by foundational mechanisms to reason about probabilistic behavior like independence and conditioning . The relational style of reasoning, on the other hand, naturally shines when the properties of interest compare the behavior of similar programs (e.g. when proving differential privacy) managing to avoid having to characterize the output distributions of the individual programs. So far, the two styles of reasoning have largely remained separate in the many program logics designed for the deductive verification of probabilistic programs. In BlueBell , we unify these styles of reasoning through the introduction of a new modality called “joint conditioning” that can encode and illuminate the rich interaction between conditional independence and relational liftings ; the two powerhouses from the two styles of reasoning.

There is an increasing body of literature proposing new and efficient persistent versions of concurrent data structures ensuring that a consistent state can be recovered after a power failure or a crash. Their correctness is typically stated in terms of durable linearizability (DL), which requires that individual library operations appear to be executed atomically in a sequence consistent with the real-time order and, moreover, that recovering from a crash return a state corresponding to a prefix of that sequence. Sadly, however, there are hardly any formal DL proofs, and those that do exist cover the correctness of rather simple persistent algorithms on specific (simplified) persistency models. In response, we propose a general, powerful, modular, and incremental proof technique that can be used to guide the development and establish DL. Our technique is (1) general , in that it is not tied to a specific persistency and/or consistency model, (2) powerful , in that it can handle the most advanced persistent algorithms in the literature, (3) modular , in that it allows the reuse of an existing linearizability argument, and (4) incremental , in that the additional requirements for establishing DL depend on the complexity of the algorithm to be verified. We illustrate this technique on various versions of a persistent set, leading to the link-free set of Zuriel et al.

Prior work on multi-language program verification has achieved impressive results, including the compositional verification of complex compilers. But the existing approaches to this problem impose a variety of restrictions on the overall structure of multi-language programs (e.g. fixing the source language, fixing the set of involved languages, fixing the memory model, or fixing the semantics of interoperation). In this paper, we explore the problem of how to avoid such global restrictions. Concretely, we present DimSum : a new, decentralized approach to multi-language semantics and verification, which we have implemented in the Coq proof assistant. Decentralization means that we can define and reason about languages independently from each other (as independent modules communicating via events), but also combine and translate between them when necessary (via a library of combinators). We apply DimSum to a high-level imperative language Rec (with an abstract memory model and function calls), a low-level assembly language Asm (with a concrete memory model, arbitrary jumps, and syscalls), and a mathematical specification language Spec. We evaluate DimSum on two case studies: an Asm library extending Rec with support for pointer comparison, and a coroutine library for Rec written in Asm. In both cases, we show how DimSum allows the Asm libraries to be abstracted to Rec-level specifications, despite the behavior of the Asm libraries not being syntactically expressible in Rec itself. We also verify an optimizing multi-pass compiler from Rec to Asm, showing that it is compatible with these Asm libraries.

Hypersafety properties of arity n are program properties that relate n traces of a program (or, more generally, traces of n programs). Classic examples include determinism, idempotence, and associativity. A number of relational program logics have been introduced to target this class of properties. Their aim is to construct simpler proofs by capitalizing on structural similarities between the n related programs. We propose an unexplored, complementary proof principle that establishes hyper-triples (i.e. hypersafety judgments) as a unifying compositional building block for proofs, and we use it to develop a Logic for Hyper-triple Composition (LHC), which supports forms of proof compositionality that were not achievable in previous logics. We prove LHC sound and apply it to a number of challenging examples.

The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions of Linear Logic and session types for concurrent processes, has settled the logical foundations of message-passing concurrency. Central to this approach is the resource consumption paradigm heralded by Linear Logic. In this paper, we investigate a new point in the design space of session type systems for message-passing concurrent programs. We identify O’Hearn and Pym’s Logic of Bunched Implications (BI) as a fruitful basis for an interpretation of the logic as a concurrent programming language. This leads to a treatment of non-linear resources that is radically different from existing approaches based on Linear Logic. We introduce a new π-calculus with sessions, called πBI; its most salient feature is a construct called spawn, which expresses new forms of sharing that are induced by structural principles in BI. We illustrate the expressiveness of πBI and lay out its fundamental theory: type preservation, deadlock-freedom, and weak normalization results for well-typed processes; an operationally sound and complete typed encoding of an affine λ-calculus; and a non-interference result for access of resources.

We present TaDA Live, a concurrent separation logic for reasoning compositionally about the termination of blocking fine-grained concurrent programs. The crucial challenge is how to deal with abstract atomic blocking : that is, abstract atomic operations that have blocking behaviour arising from busy-waiting patterns as found in, for example, fine-grained spin locks. Our fundamental innovation is with the design of abstract specifications that capture this blocking behaviour as liveness assumptions on the environment. We design a logic that can reason about the termination of clients that use such operations without breaking their abstraction boundaries, and the correctness of the implementations of the operations with respect to their abstract specifications. We introduce a novel semantic model using layered subjective obligations to express liveness invariants and a proof system that is sound with respect to the model. The subtlety of our specifications and reasoning is illustrated using several case studies.

We develop a theory of decidable inductive invariants for an infinite-state variant of the Applied pi-calculus, with applications to automatic verification of stateful cryptographic protocols with unbounded sessions/nonces. Since the problem is undecidable in general, we introduce depth-bounded protocols, a strict generalisation of a class from the literature, for which our decidable analysis is sound and complete. Our core contribution is a procedure to check that an invariant is inductive, which implies that every reachable configuration satisfies it. Our invariants can capture security properties like secrecy, can be inferred automatically, and represent an independently checkable certificate of correctness. We provide a prototype implementation and we report on its performance on some textbook examples.

We introduce a new class of security protocols with an unbounded number of sessions and unlimited fresh data for which the problem of secrecy is decidable. The only constraint we place on the class is a notion of depthboundedness. Precisely we prove that, restricted to messages of up to a given size, secrecy is decidable for all depthbounded processes. This decidable fragment of security protocols captures many real-world symmetric key protocols, including Needham-Schroeder Symmetric Key, Otway-Rees, and Yahalom.

First-order logic with the reachability predicate (FO[R]) is an important means of specification in system analysis. Its decidability status is known for some individual types of infinite-state systems such as pushdown (decidable) and vector addition systems (undecidable).