2,199 papers · page 9 of 110
Dirac notation is widely used in quantum physics and quantum programming languages to define, compute and reason about quantum states. This paper considers Dirac notation from the perspective of automated reasoning. We prove two main results: first, the first-order theory of Dira…
Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to involve expressive Separation Logics (SLs) th…
Many of today’s message-passing systems not only require messages to be exchanged in a certain order but also to happen at a certain time or within a certain time window . Such correctness conditions are particularly prominent in Internet of Things (IoT) and real-time systems app…
We consider the formulation of a symbolic execution (SE) procedure for functional programs that interact with effectful, opaque libraries. Our procedure allows specifications of libraries and abstract data type (ADT) methods that are expressed in Linear Temporal Logic over Finite…
We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible, the state of the art requires user-provide…
E-graphs are a data structure to compactly represent a program space and reason about equality of program terms. E-graphs have been successfully applied to a number of domains, including program optimization and automated theorem proving. In many applications, however, it is nece…
Guarded Kleene Algebra with Tests (GKAT) provides a sound and complete framework to reason about trace equivalence between simple imperative programs. However, there are still several notable limitations. First, GKAT is completely agnostic with respect to the meaning of primitive…
Formal verification is a gold standard for building reliable computer systems. Certified systems in particular come with a formal specification, and a proof of correctness which can easily be checked by a third party. Unfortunately, verifying large-scale, heterogeneous systems re…
We propose a method for conducting algebraic program analysis (APA) incrementally in response to changes of the program under analysis. APA is a program analysis paradigm that consists of two distinct steps: computing a path expression that succinctly summarizes the set of progra…
Many programming languages need to check whether two recursive types are in a subtyping relation. Traditionally recursive types are modelled in two different ways: equi- or iso- recursive types. While efficient algorithms for subtyping equi-recursive types are well studied for si…
Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism(for concurrency, efficiency, or algorithmic de…
Datalog has gained prominence in program analysis due to its expressiveness and ease of use. Its generic fixpoint resolution algorithm over relational domains simplifies the expression of many complex analyses. The performance and scalability issues of early Datalog approaches ha…
We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic programming language corresponds to a graphon, an…
Parametricity is a property of the syntax of type theory implying, e.g., that there is only one function having the type of the polymorphic identity function. Parametricity is usually proven externally, and does not hold internally. Internalising it is difficult because once ther…
We introduce SCIO ⋆ , a formally secure compilation framework for statically verified programs performing input-output (IO). The source language is an F ⋆ subset in which a verified program interacts with its IO-performing context via a higher-order interface that includes refine…
While current bug detection techniques for concurrent software focus on unearthing low-level issues such as data races or deadlocks, they often fall short of discovering more intricate temporal behaviours that can arise even in the absence of such low-level issues. In this paper,…
Recent work has proposed a memory property for parallel programs, called disentanglement, and showed that it is pervasive in a variety of programs, written in different languages, ranging from C/C++ to Parallel ML, and showed that it can be exploited to improve the performance of…
We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one, based on the LFPL system of Martin Hofmann,…
JSON Schema is the de-facto standard schema language for JSON data. The language went through many minor revisions, but the most recent versions of the language, starting from Draft 2019-09, added two novel features, dynamic references and annotation-dependent validation, that ch…
Pushdown Vector Addition Systems with States (PVASS) consist of finitely many control states, a pushdown stack, and a set of counters that can be incremented and decremented, but not tested for zero. Whether the reachability problem is decidable for PVASS is a long-standing open …