This paper shows how to use Girard’s intuitionistic linear logic extended with arithmetic or other constraints to reason about pointer programs. More specifically, first, the paper defines the proof theory for ILC (Intuitionistic Linear logic with Constraints) and shows it is consistent via a proof of cut elimination. Second, inspired by prior work of O’Hearn, Reynolds and Yang, the paper explains how to interpret linear logical formulas as descriptions of a program store. Third, we define a simple imperative programming language with mutable references and arrays and give verification condition generation rules that produce assertions in ILC. Finally, we identify a fragment of ILC, ILC − , that is both decidable and closed under generation of verification conditions. In other words, if loop invariants are specified in ILC − , then the resulting verification conditions are also in ILC −. Since verification condition generation is syntax-directed, we obtain a decidable procedure for checking properties of pointer programs.

Abstract We have definitionally extended Isabelle/HOLCF to support axiomatic Haskell-style constructor classes. We have subsequently defined the functor and monad classes, together with their laws, and implemented state and resumption monad transformers as generic constructor class instances. This is a step towards our goal of giving modular denotational semantics for concurrent lazy functional programming languages, such as GHC Haskell. 1

Extended Static Checking (ESC) is a fully automated formal verification technique. Verification in ESC is achieved by translating programs and their specifications into verification conditions (VCs). Proof of a VC establishes the correctness of the program. The implementations of many seemingly simple algorithms are beyond the ability of traditional Extended Static Checking (ESC) tools to verify. Not being able to verify toy examples is often enough to turn users off of the idea of using formal methods. ESC4, the ESC component of the JML4 project, is able to verify many more kinds of methods in part because of its use of novel techniques which apply multiple theorem provers. In particular, we present Offline User-Assisted ESC (OUA-ESC), a new form of verification that lies between ESC and Full Static Program Verification (FSPV). ESC is generally quite efficient, as far as verification tools go, but it is still orders of magnitude slower than simple compilation. As can be imagined, proving VCs is computationally expensive: While small classes can be verified in seconds, verifying larger programs of 50 KLOC can take hours. To help address the added cost of using multiple provers and this lack of scalability, we present the multi-threaded version of ESC4 and its distributed prover back-end.

TPHOLs conference covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification. There were 42 papers submitted to TPHOLs 2004 in the full research category, each of which was refereed by at least 3 reviewers selected by the program committee. Of these submissions, 21 were accepted for presentation at the conference and publication in volume 3223 of Springer’s Lecture Notes in Computer Science series. In keeping with longstanding tradition, TPHOLs 2004 also offered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief introductory talk and then discuss their work at a poster

This thesis has three interrelated goals: The main goal is an analysis of Czech clitics, units of grammar on the borderline between morphology and syntax with rather peculiar ordering properties both relative to the whole clause and to each other. We examine the actual set of clitics, their rather rigid ordering properties, and finally the properties of so-called clitic climbing. The analysis evaluates previous research, but it also provides new insights, especially in the position of the clitic cluster and in the constraints on clitic climbing. We show that many of the constraints regarding position of the clitic cluster suggested in previous research do not hold. We also argue that cases when clitics do not follow the first constituent are in fact not exceptions in clitic placement but instead unusual frontings. The second goal is the development of a framework within Higher Order Grammar (HOG) supporting a transparent and modular treatment of word order. Unlike previous versions of HOG, we work with signs (containing phonological, syntactic and potentially other information) as actual objects of the grammar. Apart from that, we build on the simplicity and elegance of the pre-formal part of the linearization framework within Head-driven Phrase Structure Grammar. Finally, the third objective is to test the result of the second goal by applying it on the results of