1,066 papers · page 3 of 54
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 compositionali…
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 g…
In physics and chemistry, quantum systems are typically modeled using energy constraints formulated as Hamiltonians. Investigations into such systems often focus on the evolution of the Hamiltonians under various initial conditions, an approach summarized as Adiabatic Quantum Com…
Initial semantics aims to model inductive structures and their properties, and to provide them with recursion principles respecting these properties. An ubiquitous example is the fold operator for lists. We are concerned with initial semantics that model languages with variable b…
We present a new design for an algebraic simplification library structured around concepts from universal algebra: theories, models, homomorphisms, and universal properties of free algebras and free extensions of algebras. The library's dependently typed interface guarantees that…
We introduce SecRef*, a secure compilation framework protecting stateful programs verified in F* against linked unverified code, with which the program dynamically shares ML-style mutable references. To ease program verification in this setting, we track which references are shar…
To study the semantics of a programming language, it is useful to consider different specification forms—e.g., a substitution-based small-step operational semantics and an environment-based interpreter—because they have mutually exclusive benefits. Developing these specifications…
The representation of functions in higher-order languages includes both the function’s code and an environment structure that captures the bindings of the function’s free variables. This paper explores caller-provided environments, where instead of packaging the entirety of a fun…
Multi-stage programming is a popular approach to typed meta-programming, reducing abstraction overhead and producing performant programs. However, the traditional quote-and-splice staging syntax, as introduced by Rowan Davies in 1996, can introduce complexities in managing expres…
We present a novel characterization of stable mergesort functions using relational parametricity, and show that it implies the functional correctness of mergesort. As a result, one can prove the correctness of several variations of mergesort (e.g., top-down, bottom-up, tail-recur…
It is well known that liveness properties cannot be proven using standard simulation arguments. This issue has been mitigated by extending standard notions of simulation for transition systems to fairness-preserving simulations for systems equipped with an additional fairness con…
Solutions to the longest increasing subsequence problem are typically implemented imperatively, relying on arrays for constant-time lookups and updates. Replacing these arrays with functional sequences allows a purely functional solution with the same asymptotic running time, but…
We construct a linear type system inside dependent type theory. For this, we equip the output type of a program with a bag containing copies of each of the input variables. We call the number of copies of an input variable its multiplicity. We then characterise a dependent type w…
Over the last 15 years, several popular systematic abstraction frameworks have emerged---frameworks that allow a static analysis to be derived by systematically transforming a concrete semantics. These frameworks guarantee computability of the resulting artifact by the applicatio…
Verifying graph algorithms has long been considered challenging in separation logic, mainly due to structural sharing between graph subcomponents. We show that these challenges can be effectively addressed by representing graphs as a partial commutative monoid (PCM), and by lever…
We present an algorithm that canonicalizes the algebraic representations of the topological semantics of machine knitting programs. Machine knitting is a staple technology of modern textile production where hundreds of mechanical needles are manipulated to form yarn into interloc…
Gradual typing has long been advocated as a means to bridge the gap between static and dynamic typing disciplines, enabling a range of use cases such as the gradual migration of existing dynamically typed code to more statically typed code, as well as making advanced static typin…
Normalization by evaluation (NbE) based on an untyped domain model is a convenient and powerful way to normalize terms to their βη normal forms. It enables a concise technical setup and simplicity for mechanization. Nevertheless, to date, untyped NbE has only been studied for cum…
The metatheory of dependent types has seen a lot of progress in recent years. In particular, the development of categorical gluing finally lets us work with semantic presentations of type theory (such as categories with families) to establish fundamental properties of type theory…
Many programs process lists by recursing in a wide variety of sequential and/or divide-and-conquer patterns. Reasoning about the correctness and completeness of these programs requires reasoning about the lengths of the lists, techniques for which are typically undecidable or at …