On Role Logic

We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of first-order logic in lambda calculus, and a simple rule for implicit arguments of unary and binary predicates. The unrestricted version of role logic has the expressive power of first-order logic with transitive closure. Using a syntactic restriction on role logic formulas, we identify a natural fragment RL^2 of role logic. We show that the RL^2 fragment has the same expressive power as two-variable logic with counting C^2 and is therefore decidable. We present a translation of an imperative language into the decidable fragment RL^2, which allows compositional verification of programs that manipulate relational structures. In addition, we show how RL^2 encodes boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor

A type- and scope-safe universe of syntaxes with binding: their semantics and proofs

Almost every programming language's syntax includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of alpha-equivalence, capture-avoiding substitution, typing contexts, runtime environments, and so on. In the past, implementing and reasoning about programming languages required careful handling to maintain the correct behaviour of bound variables. Modern programming languages include features that enable constraints like scope safety to be expressed in types. Nevertheless, the programmer is still forced to write the same boilerplate over again for each new implementation of a scope safe operation (e.g., renaming, substitution, desugaring, printing, etc.), and then again for correctness proofs. We present an expressive universe of syntaxes with binding and demonstrate how to (1) implement scope safe traversals once and for all by generic programming; and (2) how to derive properties of these traversals by generic proving. Our universe description, generic traversals and proofs, and our examples have all been formalised in Agda and are available in the accompanying material available online at https://github.com/gallais/generic-syntax

Feat: Functional Enumeration of Algebraic Types

In mathematics, an enumeration of a set S is a bijective function from (an initial segment of) the natural numbers to S. We define "functional enumerations" as efficiently computable such bijections. This paper describes a theory of functional enumeration and provides an algebra of enumerations closed under sums, products, guarded recursion and bijections. We partition each enumerated set into numbered, finite subsets. We provide a generic enumeration such that the number of each part corresponds to the size of its values (measured in the number of constructors). We implement our ideas in a Haskell library called testing-feat, and make the source code freely available. Feat provides efficient "random access" to enumerated values. The primary application is property-based testing, where it is used to define both random sampling (for example QuickCheck generators) and exhaustive enumeration (in the style of SmallCheck). We claim that functional enumeration is the best option for automatically generating test cases from large groups of mutually recursive syntax tree types. As a case study we use Feat to test the pretty-printer of the Template Haskell library (uncovering several bugs)

Gauge field marginal of an Abelian Higgs model

We study the gauge field marginal of an Abelian Higgs model with Villain action defined on a 2D lattice in finite volume. Our first main result, which holds for gauge theories on arbitrary finite graphs and does not assume that the structure group is Abelian, is a loop expansion of the Radon--Nikodym derivative of the law of the gauge field marginal with respect to that of the pure gauge theory. This expansion is similar to the one of Seiler but holds in greater generality and uses a different graph theoretic approach. Furthermore, we show ultraviolet stability for the gauge field marginal of the model in a fixed gauge. More specifically, we show that moments of the H{ö}lder--Besov-type norms introduced in arXiv:1808.09196 are bounded uniformly in the lattice spacing. This latter result relies on a quantitative diamagnetic inequality that in turn follows from the loop expansion and elementary properties of Gaussian random variables

The C Object System: Using C as a High-Level Object-Oriented Language

The C Object System (Cos) is a small C library which implements high-level concepts available in Clos, Objc and other object-oriented programming languages: uniform object model (class, meta-class and property-metaclass), generic functions, multi-methods, delegation, properties, exceptions, contracts and closures. Cos relies on the programmable capabilities of the C programming language to extend its syntax and to implement the aforementioned concepts as first-class objects. Cos aims at satisfying several general principles like simplicity, extensibility, reusability, efficiency and portability which are rarely met in a single programming language. Its design is tuned to provide efficient and portable implementation of message multi-dispatch and message multi-forwarding which are the heart of code extensibility and reusability. With COS features in hand, software should become as flexible and extensible as with scripting languages and as efficient and portable as expected with C programming. Likewise, Cos concepts should significantly simplify adaptive and aspect-oriented programming as well as distributed and service-oriented computingComment: 18

Subheap-Augmented Garbage Collection

Automated memory management avoids the tedium and danger of manual techniques. However, as no programmer input is required, no widely available interface exists to permit principled control over sometimes unacceptable performance costs. This dissertation explores the idea that performance-oriented languages should give programmers greater control over where and when the garbage collector (GC) expends effort. We describe an interface and implementation to expose heap partitioning and collection decisions without compromising type safety. We show that our interface allows the programmer to encode a form of reference counting using Hayes\u27 notion of key objects. Preliminary experimental data suggests that our proposed mechanism can avoid high overheads suffered by tracing collectors in some scenarios, especially with tight heaps. However, for other applications, the costs of applying subheaps---in human effort and runtime overheads---remain daunting

HW-SW co-design techniques for modern programming languages

Modern programming languages raise the level of abstraction, hide the details of computer systems from programmers, and provide many convenient features. Such strong abstraction from the details of computer systems with runtime support of many convenient features increases the productivity of programmers. Such benefits, however, come with performance overheads. First, many of modern programming languages use a dynamic type system which incurs overheads of profiling program execution and generating specialized codes in the middle of execution. Second, such specialized codes constantly add overheads of dynamic type checks. Third, most of modern programming languages use automatic memory management which incurs memory overheads due to metadata and delayed reclamation as well as execution time overheads due to garbage collection operations. This thesis makes three contributions to address the overheads of modern programming languages. First, it describes the enhancements to the compiler of dynamic scripting languages necessary to enable sharing of compilation results across executions. These compilers have been developed with little consideration for reusing optimization efforts across executions since it is considered difficult due to dynamic nature of the languages. As a first step toward enabling the reuse of compilation results of dynamic scripting languages, it focuses on inline caching (IC) which is one of the fundamental optimization techniques for dynamic type systems. Second, it describes a HW-SW co-design technique to further improve IC operations. While the first proposal focuses on expensive IC miss handling during JavaScript initialization, the second proposal accelerates IC hit operations to improve the overall performance. Lastly, it describes how to exploit common sharing patterns of programs to reduce overheads of reference counting for garbage collection. It minimizes atomic operations in reference counting by biasing each object to a specific thread