Reasoning about the garden of forking paths

Lazy evaluation is a powerful tool for functional programmers. It enables the concise expression of on-demand computation and a form of compositionality not available under other evaluation strategies. However, the stateful nature of lazy evaluation makes it hard to analyze a program's computational cost, either informally or formally. In this work, we present a novel and simple framework for formally reasoning about lazy computation costs based on a recent model of lazy evaluation: clairvoyant call-by-value. The key feature of our framework is its simplicity, as expressed by our definition of the clairvoyance monad. This monad is both simple to define (around 20 lines of Coq) and simple to reason about. We show that this monad can be effectively used to mechanically reason about the computational cost of lazy functional programs written in Coq.Comment: 28 pages, accepted by ICFP'2

Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Unfolding-based Partial Order Reduction

Partial order reduction (POR) and net unfoldings are two alternative methods to tackle state-space explosion caused by concurrency. In this paper, we propose the combination of both approaches in an effort to combine their strengths. We first define, for an abstract execution model, unfolding semantics parameterized over an arbitrary independence relation. Based on it, our main contribution is a novel stateless POR algorithm that explores at most one execution per Mazurkiewicz trace, and in general, can explore exponentially fewer, thus achieving a form of super-optimality. Furthermore, our unfolding-based POR copes with non-terminating executions and incorporates state-caching. Over benchmarks with busy-waits, among others, our experiments show a dramatic reduction in the number of executions when compared to a state-of-the-art DPOR.Comment: Long version of a paper with the same title appeared on the proceedings of CONCUR 201

First Class Copy & Paste

The Subtext project seeks to make programming fundamentally easier by altering the nature of programming languages and tools. This paper defines an operational semantics for an essential subset of the Subtext language. It also presents a fresh approach to the problems of mutable state, I/O, and concurrency.Inclusions reify copy & paste edits into persistent relationships that propagate changes from their source into their destination. Inclusions formulate a programming language in which there is no distinction between a programÂs representation and its execution. Like spreadsheets, programs are live executions within a persistent runtime, and programming is direct manipulation of these executions via a graphical user interface. There is no need to encode programs into source text.Mutation of state is effected by the computation of hypothetical recursive variants of the state, which can then be lifted into new versions of the state. Transactional concurrency is based upon queued single-threaded execution. Speculative execution of queued hypotheticals provides concurrency as a semantically transparent implementation optimization