Interface specifications should express program properties in a formal, declarative, and implementation-independent way. To achieve implementation-independency, interface specifications have to support data abstraction. Program verification should enable to prove implementations correct w.r.t. such interface specifications. The presented work bridges the gap between existing specification and verification techniques for object-oriented programs. The integration is done within a formal framework for interface specifications and programming language semantics. Interface specification techniques are enhanced to support the specification of data structure sharing and destructive updating of shared variables. These extensions are necessary for the specification of real life software libraries. Moreover this generalization is needed for intermediate steps in correctness proofs. For verification, Hoare logic is extended to capture recursive classes and subtyping. Based on this extended logic, techniques are presented for proving typing properties, class and method invariants. The new

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Abstract. Landin’s SECD machine was the first abstract machine for applicative expressions, i.e., functional programs. Landin’s J operator was the first control operator for functional languages, and was specified by an extension of the SECD machine. We present a family of evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continuation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lockstep with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We also identify that the dump component of the SECD machine is managed in a callee-save way. The caller-save counterpart of the modernized SECD machine precisely corresponds to Thielecke’s doublebarrelled continuations and to Felleisen’s encoding of J in terms of call/cc. We then variously characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present several reduction semantics for applicative expressions

Abstract Nondeterminism is a pervasive phenomenon in computation. Often it arises as an emergent property of a complex system, typically as the result of contention for access to shared resources. In such circumstances, we cannot always know, in advance, exactly what will happen. In other circumstances, nondeterminism is explicitly introduced as a means of abstracting away from implementation details such as precise command scheduling and control flow. However, the kind of behaviours exhibited by nondeterministic computations can be extremely subtle in comparison to those of their deterministic counterparts and reasoning about such programs is notoriously tricky as a result. It is therefore important to develop semantic tools to improve our understanding of, and aid our reasoning about, such nondeterministic programs. In this thesis, we extend the framework of game semantics to encompass nondeterministic computation. Game semantics is a relatively recent development in denotational semantics; its main novelty is that it views a computation not as a static entity, but rather as a dynamic process of interaction. This perspective makes the theory well-suited to modelling many aspects of computational processes: the original use of game semantics in modelling the simple functional language PCF has subsequently been extended to handle more complex control structures such as references and continuations.

This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational semantics of PCF induced by an interpretation; (standard) Scott model, adequacy, weak adequacy and its proof (by a computability predicate) Domain Theory up to SFP and Scott domains; non full abstraction of the standard model, definability of compact elements and full abstraction for PCFP (PCF + parallel or), properties of order-extensional (continuous) models of PCF, Milner's model and Mulmuley's construction (excluding proofs) Additional topics (time permitting): results on pure simply-typed lambda calculus, Friedman 's Completeness Theorem, minimal model, logical relations and definability, undecidability of lambda definability (excluding proof), dI-domains and stable functions Homepa...

Machines and Recursive Definitions 2.1 Abstract Machines The best-known model of mechanical computation is (still) the first, introduced by Turing [18], and after half a century of study, few doubt the truth of the fundamental Church-Turing Thesis : A function f : N # N on the natural numbers (or, more generally, on strings from a finite alphabet) is computable in principle exactly when it can be computed by a Turing Machine. The Church-Turing Thesis grounds proofs of undecidability and it is essential for the most important applications of logic. On the other hand, it cannot be argued seriously that Turing machines model faithfully all algorithms on the natural numbers. If, for example, we code the input n in binary (rather than unary) notation, then the time needed for the computation of f(n) can sometimes be considerably shortened; and if we let the machine use two tapes rather than one, then (in some cases) we may gain a quadratic speedup of the computation, see [8]. This mea...

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interpretation and fixed-point computation . . . 71 5.1.2 The time-stamping technique . . . . . . . . . . . . . . . . 72 5.2 The time-stamps-based approximation algorithm . . . . . . . . . 73 5.2.1 A class of recursive equations . . . . . . . . . . . . . . . . 73 5.2.2 The intuition behind time stamps . . . . . . . . . . . . . 74 5.3 A formalization of the time-stamps-based algorithm . . . . . . . 75 5.3.1 State-passing recursive equations . . . . . . . . . . . . . . 75 5.3.2 Correctness . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.3.3 Complexity estimates . . . . . . . . . . . . . . . . . . . . 78 5.4 An extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Appendix 5.A Operational specification . . . . . . . . . . . . . . . . . 81 6 Static Transition Compression 85 6.2 Source and target languages . . . . . . . . . . . . . . . . . . . . . 86 6.2.1 An unstructured target language . . . . . . . . . . . . . . 86 6.2.2 A structured source language . . . . . . . . . . . . . . . . 86 6.3 A context-insensitive translation . . . . . . . . . . . . . . . . . . 87 6.3.4 Chains of jumps . . . . . . . . . . . . . . . . . . . . . . . 91 6.4 Context awareness . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6.4.1 Continuations and duplication . . . . . . . . . . . . . . . 92 6.4.2 Towards the right thing . . . . . . . . . . . . . . . . . . . 92 6.5 A context-sensitive translation . . . . . . . . . . . . . . . . . . . 93 6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

The work in this thesis has been carried out under the auspices of the research school IPA (Institute for Programming research and Algorithmics).vrije universiteit Böhm-Like Trees for Rewriting academisch proefschrift ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus prof.dr. T. Sminia, in het openbaar te verdedigen ten overstaan van de promotiecommissie van de faculteit der Exacte Wetenschappen op maandag 20 maart 2006 om 15.45 uur in de aula van de universiteit, De Boelelaan 1105 door

Lambda-lifting and lambda-dropping respectively transform a blockstructured functional program into recursive equations and vice versa.