Invariant Generation through Strategy Iteration in Succinctly Represented Control Flow Graphs

We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables. More specifically, we study the problem of performing static analysis by abstract interpretation using template linear constraint domains. Such invariants can be obtained by Kleene iterations that are, in order to guarantee termination, accelerated by widening operators. In many cases, however, applying this form of extrapolation leads to invariants that are weaker than the strongest inductive invariant that can be expressed within the abstract domain in use. Another well-known source of imprecision of traditional abstract interpretation techniques stems from their use of join operators at merge nodes in the control flow graph. The mentioned weaknesses may prevent these methods from proving safety properties. The technique we develop in this article addresses both of these issues: contrary to Kleene iterations accelerated by widening operators, it is guaranteed to yield the strongest inductive invariant that can be expressed within the template linear constraint domain in use. It also eschews join operators by distinguishing all paths of loop-free code segments. Formally speaking, our technique computes the least fixpoint within a given template linear constraint domain of a transition relation that is succinctly expressed as an existentially quantified linear real arithmetic formula. In contrast to previously published techniques that rely on quantifier elimination, our algorithm is proved to have optimal complexity: we prove that the decision problem associated with our fixpoint problem is in the second level of the polynomial-time hierarchy.Comment: 35 pages, conference version published at ESOP 2011, this version is a CoRR version of our submission to Logical Methods in Computer Scienc

Discourse-pragmatic variation in Paris French and London English: Insights from general extenders

This paper examines the use of general extenders (GEs), such as and stuff in English and et tout in French, in Paris French and London English. We aim to compare the social and the linguistic conditioning of extender use in the two languages, discuss the different kinds of spread in the two cities and reflect on the specificity of discourse-pragmatic variation. The study shows that GE forms as well as frequencies vary across factors such as gender, age and ethnicity, while some variants also appear to be grammaticalising and acquiring new pragmatic functions. The analysis includes a comparison of different age groups, and finds that different types of generational change may be occurring in both languages. In London, forms such as and stuff and and that diverge along ethnic lines, whereas in Paris et tout is becoming the dominant variant across the board. While different variants in both languages are indirectly associated with different social categories, they perform similar pragmatic functions such as hedging, marking solidarity and appealing to common knowledge between the speaker and the interlocutor(s)

Presenting and predicating lower events

The effects of different forms of predication have been insightfully (and almost exclusively) studied for 'simple' cases of predication, of which the 'presentational sentence' is maybe the paradigm instantiation. It is the aim of this paper to show that thc same kind of effects as well as in fact the same kind of structures are present at embedded levels in thematically and otherwise more complex structures. Beyond presentational sentences, 'unaccusative' experiencing constructions involving a dative subject, 'double object constructions' and - to a lesser extent - spraylload constructions are discussed. For all of these, it is argued that they comprise a predication encoding the ascription of a transient temporal property to a location. On this basis, a proposal is made as to how the scope asymmetry between the two arguments involved in the colistructions can be explained. Furthermore, a proposal is made as to how what has been called 'argument shift' is motivated

The effect of negative polarity items on inference verification

The scalar approach to negative polarity item (NPI) licensing assumes that NPIs are allowable in contexts in which the introduction of the NPI leads to proposition strengthening (e.g., Kadmon & Landman 1993, Krifka 1995, Lahiri 1997, Chierchia 2006). A straightforward processing prediction from such a theory is that NPI’s facilitate inference verification from sets to subsets. Three experiments are reported that test this proposal. In each experiment, participants evaluated whether inferences from sets to subsets were valid. Crucially, we manipulated whether the premises contained an NPI. In Experiment 1, participants completed a metalinguistic reasoning task, and Experiments 2 and 3 tested reading times using a self-paced reading task. Contrary to expectations, no facilitation was observed when the NPI was present in the premise compared to when it was absent. In fact, the NPI significantly slowed down reading times in the inference region. Our results therefore favor those scalar theories that predict that the NPI is costly to process (Chierchia 2006), or other, nonscalar theories (Giannakidou 1998, Ladusaw 1992, Postal 2005, Szabolcsi 2004) that likewise predict NPI processing cost but, unlike Chierchia (2006), expect the magnitude of the processing cost to vary with the actual pragmatics of the NPI

No value restriction is needed for algebraic effects and handlers

We present a straightforward, sound Hindley-Milner polymorphic type system for algebraic effects and handlers in a call-by-value calculus, which allows type variable generalisation of arbitrary computations, not just values. This result is surprising. On the one hand, the soundness of unrestricted call-by-value Hindley-Milner polymorphism is known to fail in the presence of computational effects such as reference cells and continuations. On the other hand, many programming examples can be recast to use effect handlers instead of these effects. Analysing the expressive power of effect handlers with respect to state effects, we claim handlers cannot express reference cells, and show they can simulate dynamically scoped state

Heavy Hands, Magic, and Scene-Reading Traps

This is one of a series of articles in which I examine errors that philosophers of language may be led to make if already prone to exaggerating the rôle compositional semantics can play in explaining how we communicate, whether by expressing propositions with our words or by merely implying them. In the present article, I am concerned less with “pragmatic contributions” to the propositions we express—contributions some philosophers seem rather desperate to deny the existence or ubiquity of—than I am with certain types of traps that those who exaggerate the rôle of semantic convention and underestimate the rôle of pragmatic inference are apt to fall into

On past participle agreement in transitive clauses in French

This paper provides a Minimalist analysis of past participle agreement in French in transitive clauses. Our account posits that the head v of vP in such structures carries an (accusativeassigning) structural case feature which may apply (with or without concomitant agreement) to case-mark a clause-mate object, the subject of a defective complement clause, or an intermediate copy of a preposed subject in spec-CP. In structures where a goal is extracted from vP (e.g. via wh-movement) v also carries an edge feature, and may also carry a specificity feature and a set of (number and gender) agreement features. We show how these assumptions account for agreement of a participle with a preposed specific clausemate object or defective-clause subject, and for the absence of agreement with an embedded object, with the complement of an impersonal verb, and with the subject of an embedded (finite or nonfinite) CP complement. We also argue that the absence of agreement marking (in expected contexts) on the participles faitmade and laissélet in infinitive structures is essentially viral in nature. Finally, we claim that obligatory participle agreement with reflexive and reciprocal objects arises because the derivation of reflexives involves A-movement and concomitant agreement