arXiv subjects

Alexander J. Summers

Publications and source records attributed to Alexander J. Summers.

16 recordsLinked to original sources

arXiv2025

Place Capability Graphs: A General-Purpose Model of Rust's Ownership and Borrowing Guarantees

Rust's novel type system has proved an attractive target for verification and program analysis tools, due to the rich guarantees it provides for controlling aliasing and mutability. However, fully understanding, extracting and exploiting these guarantees is subtle and challenging: existing models for Rust's type checking either support a smaller idealised language disconnected from real-world Rust code, or come with severe limitations in terms of precise modelling of Rust borrows, composite types storing them, function signatures and loops. In this paper, we present a novel model of Rust's type-checking called Place Capability Graphs, which lifts these limitations, and which can be directly calculated from the Rust compiler's own programmatic representations and analyses. We demonstrate that our model supports over 97% of Rust functions in the most popular public crates, and show its suitability as a general-purpose basis for verification and program analysis tools by developing promising new prototype versions of the existing Flowistry and Prusti tools.

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arXiv2024

Formal Foundations for Translational Separation Logic Verifiers (extended version)

Program verification tools are often implemented as front-end translations of an input program into an intermediate verification language (IVL) such as Boogie, GIL, Viper, or Why3. The resulting IVL program is then verified using an existing back-end verifier. A soundness proof for such a translational verifier needs to relate the input program and verification logic to the semantics of the IVL, which in turn needs to be connected with the verification logic implemented in the back-end verifiers. Performing such proofs is challenging due to the large semantic gap between the input and output programs and logics, especially for complex verification logics such as separation logic. This paper presents a formal framework for reasoning about translational separation logic verifiers. At its center is a generic core IVL that captures the essence of different separation logics. We define its operational semantics and formally connect it to two different back-end verifiers, which use symbolic execution and verification condition generation, resp. Crucially, this semantics uses angelic non-determinism to enable the application of different proof search algorithms and heuristics in the back-end verifiers. An axiomatic semantics for the core IVL simplifies reasoning about the front-end translation by performing essential proof steps once and for all in the equivalence proof with the operational semantics rather than for each concrete front-end translation. We illustrate the usefulness of our formal framework by instantiating our core IVL with elements of Viper and connecting it to two Viper back-ends as well as a front-end for concurrent separation logic. All our technical results have been formalized in Isabelle/HOL, including the core IVL and its semantics, the semantics of two back-ends for a subset of Viper, and all proofs.

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arXiv2024

Reasoning about Interior Mutability in Rust using Library-Defined Capabilities

Existing automated verification techniques for safe Rust code rely on the strong type-system properties to reason about programs, especially to deduce which memory locations do not change (i.e., are framed) across function calls. However, these type guarantees do not hold in the presence of interior mutability (e.g., when interacting with any concurrent data structure). As a consequence, existing verification techniques for safe code such as Prusti and Creusot are either unsound or fundamentally incomplete if applied to this setting. In this work, we present the first technique capable of automatically verifying safe clients of existing interiorly mutable types. At the core of our approach, we identify a novel notion of implicit capabilities: library-defined properties that cannot be expressed using Rust's types. We propose new annotations to specify these capabilities and a first-order logic encoding suitable for program verification. We have implemented our technique in a verifier called Mendel and used it to prove absence of panics in Rust programs that make use of popular standard-library types with interior mutability, including Rc, Arc, Cell, RefCell, AtomicI32, Mutex and RwLock. Our evaluation shows that these library annotations are useful for verifying usages of real-world libraries, and powerful enough to require zero client-side annotations in many of the verified programs.

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arXiv2024

Towards Trustworthy Automated Program Verifiers: Formally Validating Translations into an Intermediate Verification Language (extended version)

Automated program verifiers are typically implemented using an intermediate verification language (IVL), such as Boogie or Why3. A verifier front-end translates the input program and specification into an IVL program, while the back-end generates proof obligations for the IVL program and employs an SMT solver to discharge them. Soundness of such verifiers therefore requires that the front-end translation faithfully captures the semantics of the input program and specification in the IVL program, and that the back-end reports success only if the IVL program is actually correct. For a verification tool to be trustworthy, these soundness conditions must be satisfied by its actual implementation, not just the program logic it uses. In this paper, we present a novel validation methodology that, given a formal semantics for the input language and IVL, provides formal soundness guarantees for front-end implementations. For each run of the verifier, we automatically generate a proof in Isabelle showing that the correctness of the produced IVL program implies the correctness of the input program. This proof can be checked independently from the verifier, in Isabelle, and can be combined with existing work on validating back-ends to obtain an end-to-end soundness result. Our methodology based on forward simulation employs several modularisation strategies to handle the large semantic gap between the input language and the IVL, as well as the intricacies of practical, optimised translations. We present our methodology for the widely-used Viper and Boogie languages. Our evaluation shows that it is effective in validating the translations performed by the existing Viper implementation.

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arXiv2024

A Formal Model to Prove Instantiation Termination for E-matching-Based Axiomatisations (Extended Version)

SMT-based program analysis and verification often involve reasoning about program features that have been specified using quantifiers; incorporating quantifiers into SMT-based reasoning is, however, known to be challenging. If quantifier instantiation is not carefully controlled, then runtime and outcomes can be brittle and hard to predict. In particular, uncontrolled quantifier instantiation can lead to unexpected incompleteness and even non-termination. E-matching is the most widely-used approach for controlling quantifier instantiation, but when axiomatisations are complex, even experts cannot tell if their use of E-matching guarantees completeness or termination. This paper presents a new formal model that facilitates the proof, once and for all, that giving a complex E-matching-based axiomatisation to an SMT solver, such as Z3 or cvc5, will not cause non-termination. Key to our technique is an operational semantics for solver behaviour that models how the E-matching rules common to most solvers are used to determine when quantifier instantiations are enabled, but abstracts over irrelevant details of individual solvers. We demonstrate the effectiveness of our technique by presenting a termination proof for a set theory axiomatisation adapted from those used in the Dafny and Viper verifiers.

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arXiv2024

Resource Specifications for Resource-Manipulating Programs

Specifications for modular program verifiers are expressed as constraints on program states (e.g. preconditions) and relations on program states (e.g. postconditions). For programs whose domain is managing resources of any kind (e.g. cryptocurrencies), such state-based specifications must make explicit properties that a human would implicitly understand for free. For example, it's clear that depositing into your bank account will not change other balances, but classically this must be stated as a frame condition. As a result, classical specifications for resource-manipulating programs quickly become verbose and difficult to interpret, write and debug. In this paper, we present a novel methodology that extends a modular program verifier to support user-defined first-class resources, allowing resource-related operations and properties to be expressed directly and eliminating the need to reify implicit knowledge in the specifications. We implement our methodology as an extension of the program verifier Prusti, and use it to verify real-world smart contracts and a key part of a blockchain application. Our evaluation demonstrates that specifications written with our methodology are more concise and substantially simpler than specifications written purely in terms of program states.

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arXiv2022

Compositional Reasoning for Side-effectful Iterators and Iterator Adapters

Iteration is a programming operation that traditionally refers to visiting the elements of a data structure in sequence. However, modern programming systems such as Rust, Java, and C# generalise iteration far beyond the traditional use case. They allow iterators to be parameterised with (potentially side-effectful) closures and support the composition of iterators to form iterator chains, where each iterator in the chain consumes values from its predecessor and produces values for its successor. Such generalisations pose three major challenges for modular specification and verification of iterators and the client code using them: (1) How can parameterised iterators be specified modularly and their (accumulated) side effects reasoned about? (2) How can the behaviour of an iterator chain be derived from the specifications of its component iterators? (3) How can proofs about such iterators be automated? We present the first methodology for the modular specification and verification of advanced iteration idioms with side-effectful computations. It addresses the three challenges above using a combination of inductive two-state invariants, higher-order closure contracts, and separation logic-like ownership. We implement and our methodology in a state-of-the-art SMT-based Rust verifier. Our evaluation shows that our methodology is sufficiently expressive to handle advanced and idiomatic iteration idioms and requires modest annotation overhead.

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arXiv2022

REST: Integrating Term Rewriting with Program Verification (Extended Version)

We introduce REST, a novel term rewriting technique for theorem proving that uses online termination checking and can be integrated with existing program verifiers. REST enables flexible but terminating term rewriting for theorem proving by: (1) exploiting newly-introduced term orderings that are more permissive than standard rewrite simplification orderings; (2) dynamically and iteratively selecting orderings based on the path of rewrites taken so far; and (3) integrating external oracles that allow steps that cannot be justified with rewrite rules. Our REST approach is designed around an easily implementable core algorithm, parameterizable by choices of term orderings and their implementations; in this way our approach can be easily integrated into existing tools. We implemented REST as a Haskell library and incorporated it into Liquid Haskell's evaluation strategy, extending Liquid Haskell with rewriting rules. We evaluated our REST implementation by comparing it against both existing rewriting techniques and E-matching and by showing that it can be used to supplant manual lemma application in many existing Liquid Haskell proofs.

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arXiv2021

Rich Specifications for Ethereum Smart Contract Verification

Smart contracts are programs that execute inside blockchains such as Ethereum to manipulate digital assets. Since bugs in smart contracts may lead to substantial financial losses, there is considerable interest in formally proving their correctness. However, the specification and verification of smart contracts faces challenges that do not arise in other application domains. Smart contracts frequently interact with unverified, potentially adversarial outside code, which substantially weakens the assumptions that formal analyses can (soundly) make. Moreover, the core functionality of smart contracts is to manipulate and transfer resources; describing this functionality concisely requires dedicated specification support. Current reasoning techniques do not fully address these challenges, being restricted in their scope or expressiveness (in particular, in the presence of re-entrant calls), and offering limited means of expressing the resource transfers a contract performs. In this paper, we present a novel specification methodology tailored to the domain of smart contracts. Our specification constructs and associated reasoning technique are the first to enable: (1) sound and precise reasoning in the presence of unverified code and arbitrary re-entrancy, (2) modular reasoning about collaborating smart contracts, and (3) domain-specific specifications based on resources and resource transfers, which allow expressing a contract's behavior in intuitive and concise ways and exclude typical errors by default. We have implemented our approach in 2vyper, an SMT-based automated verification tool for Ethereum smart contracts written in the Vyper language, and demonstrated its effectiveness in succinctly capturing and verifying strong correctness guarantees for real-world contracts.

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arXiv2021

Formally Validating a Practical Verification Condition Generator (extended version)

A program verifier produces reliable results only if both the logic used to justify the program's correctness is sound, and the implementation of the program verifier is itself correct. Whereas it is common to formally prove soundness of the logic, the implementation of a verifier typically remains unverified. Bugs in verifier implementations may compromise the trustworthiness of successful verification results. Since program verifiers used in practice are complex, evolving software systems, it is generally not feasible to formally verify their implementation. In this paper, we present an alternative approach: we validate successful runs of the widely-used Boogie verifier by producing a certificate which proves correctness of the obtained verification result. Boogie performs a complex series of program translations before ultimately generating a verification condition whose validity should imply the correctness of the input program. We show how to certify three of Boogie's core transformation phases: the elimination of cyclic control flow paths, the (SSA-like) replacement of assignments by assumptions using fresh variables (passification), and the final generation of verification conditions. Similar translations are employed by other verifiers. Our implementation produces certificates in Isabelle, based on a novel formalisation of the Boogie language.

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arXiv2019

Local Reasoning for Global Graph Properties

Separation logics are widely used for verifying programs that manipulate complex heap-based data structures. These logics build on so-called separation algebras, which allow expressing properties of heap regions such that modifications to a region do not invalidate properties stated about the remainder of the heap. This concept is key to enabling modular reasoning and also extends to concurrency. While heaps are naturally related to mathematical graphs, many ubiquitous graph properties are non-local in character, such as reachability between nodes, path lengths, acyclicity and other structural invariants, as well as data invariants which combine with these notions. Reasoning modularly about such graph properties remains notoriously difficult, since a local modification can have side-effects on a global property that cannot be easily confined to a small region. In this paper, we address the question: What separation algebra can be used to avoid proof arguments reverting back to tedious global reasoning in such cases? To this end, we consider a general class of global graph properties expressed as fixpoints of algebraic equations over graphs. We present mathematical foundations for reasoning about this class of properties, imposing minimal requirements on the underlying theory that allow us to define a suitable separation algebra. Building on this theory we develop a general proof technique for modular reasoning about global graph properties over program heaps, in a way which can be integrated with existing separation logics. To demonstrate our approach, we present local proofs for two challenging examples: a priority inheritance protocol and the non-blocking concurrent Harris list.

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arXiv2019

Modular Verification of Heap Reachability Properties in Separation Logic

The correctness of many algorithms and data structures depends on reachability properties, that is, on the existence of chains of references between objects in the heap. Reasoning about reachability is difficult for two main reasons. First, any heap modification may affect an unbounded number of reference chains, which complicates modular verification, in particular, framing. Second, general graph reachability is not supported by SMT solvers, which impedes automatic verification. In this paper, we present a modular specification and verification technique for reachability properties in separation logic. For each method, we specify reachability only locally within the fragment of the heap on which the method operates. A novel form of reachability framing for relatively convex subheaps allows one to extend reachability properties from the heap fragment of a callee to the larger fragment of its caller, enabling precise procedure-modular reasoning. Our technique supports practically important heap structures, namely acyclic graphs with a bounded outdegree as well as (potentially cyclic) graphs with at most one path (modulo cycles) between each pair of nodes. The integration into separation logic allows us to reason about reachability and other properties in a uniform way, to verify concurrent programs, and to automate our technique via existing separation logic verifiers. We demonstrate that our verification technique is amenable to SMT-based verification by encoding a number of benchmark examples into the Viper verification infrastructure.

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arXiv2018

Permission Inference for Array Programs

Information about the memory locations accessed by a program is, for instance, required for program parallelisation and program verification. Existing inference techniques for this information provide only partial solutions for the important class of array-manipulating programs. In this paper, we present a static analysis that infers the memory footprint of an array program in terms of permission pre- and postconditions as used, for example, in separation logic. This formulation allows our analysis to handle concurrent programs and produces specifications that can be used by verification tools. Our analysis expresses the permissions required by a loop via maximum expressions over the individual loop iterations. These maximum expressions are then solved by a novel maximum elimination algorithm, in the spirit of quantifier elimination. Our approach is sound and is implemented; an evaluation on existing benchmarks for memory safety of array programs demonstrates accurate results, even for programs with complex access patterns and nested loops.

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arXiv2018

Automating Deductive Verification for Weak-Memory Programs

Writing correct programs for weak memory models such as the C11 memory model is challenging because of the weak consistency guarantees these models provide. The first program logics for the verification of such programs have recently been proposed, but their usage has been limited thus far to manual proofs. Automating proofs in these logics via first-order solvers is non-trivial, due to reasoning features such as higher-order assertions, modalities and rich permission resources. In this paper, we provide the first implementation of a weak memory program logic using existing deductive verification tools. We tackle three recent program logics: Relaxed Separation Logic and two forms of Fenced Separation Logic, and show how these can be encoded using the Viper verification infrastructure. In doing so, we illustrate several novel encoding techniques which could be employed for other logics. Our work is implemented, and has been evaluated on examples from existing papers as well as the Facebook open-source Folly library.

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arXiv2016

Automatic Verification of Iterated Separating Conjunctions using Symbolic Execution

In permission logics such as separation logic, the iterated separating conjunction is a quantifier denoting access permission to an unbounded set of heap locations. In contrast to recursive predicates, iterated separating conjunctions do not prescribe a structure on the locations they range over, and so do not restrict how to traverse and modify these locations. This flexibility is important for the verification of random-access data structures such as arrays and data structures that can be traversed in multiple ways such as graphs. Despite its usefulness, no automatic program verifier natively supports iterated separating conjunctions; they are especially difficult to incorporate into symbolic execution engines, the prevalent technique for building verifiers for these logics. In this paper, we present the first symbolic execution technique to support general iterated separating conjunctions. We propose a novel representation of symbolic heaps and flexible support for logical specifications that quantify over heap locations. Our technique exhibits predictable and fast performance despite employing quantifiers at the SMT level, by carefully controlling quantifier instantiations. It is compatible with other features of permission logics such as fractional permissions, recursive predicates, and abstraction functions. Our technique is implemented as an extension of the Viper verification infrastructure.

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arXiv2012

The Relationship Between Separation Logic and Implicit Dynamic Frames

Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In this paper, we precisely connect the semantics of these two logics. We define a logic whose syntax subsumes both that of a standard separation logic, and that of implicit dynamic frames as sub-syntaxes. We define a total heap semantics for our logic, and, for the separation logic subsyntax, prove it equivalent the standard partial heaps model. In order to define a semantics which works uniformly for both subsyntaxes, we define the novel concept of a minimal state extension, which provides a different (but equivalent) definition of the semantics of separation logic implication and magic wand connectives, while also giving a suitable semantics for these connectives in implicit dynamic frames. We show that our resulting semantics agrees with the existing definition of weakest pre-condition semantics for the implicit dynamic frames fragment. Finally, we show that we can encode the separation logic fragment of our logic into the implicit dynamic frames fragment, preserving semantics. For the connectives typically supported by tools, this shows that separation logic can be faithfully encoded in a first-order automatic verification tool (Chalice).

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