This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages. It extends recent work in game semantics, in which programs are interpreted as strategies for computation by interaction with an environment. Abramsky has suggested that an intensional hierarchy of computational features such as state, and their fully abstract models, can be captured as violations of the constraints on strategies in the basic functional model. Non-local control flow is shown to fit into this framework as the violation of strong and weak ‘bracketing ’ conditions, related to linear behaviour. The language µPCF (Parigot’s λµ with constants and recursion) is adopted as a simple basis for higher-type, sequential computation with access to the flow of control. A simple operational semantics for both call-by-name and call-by-value evaluation is described. It is shown that dropping the bracketing condition on games models of PCF yields fully abstract models of µPCF.

We show how to translate the region calculus of Tofte and Talpin, a typed lambda calculus that can statically delimit the lifetimes of objects, into an extension of the polymorphic lambda calculus called F # . We give a denotational semantics of F # , and use it to give a simple and abstract proof of the correctness of memory deallocation. 1 Introduction Implementations of modern programming languages divide dynamically allocated memory into two parts. The stack is used for data that has a simple last-in, first-out lifetime determined by block structure; the other part (often called the heap) is used for data whose lifetime extends beyond the scope of program blocks. The heap is periodically "garbage collected" to reclaim memory that is no longer needed. Tofte and Talpin's region calculus [23] attempts to unify these two styles of memory management. The region calculus divides memory into regions, and provides a local scoping mechanism for those regions. Every value created by the pro...

Abstract. Perhaps surprisingly, there are infinite sets that admit mechanical exhaustive search in finite time. We investigate three related questions: What kinds of infinite sets admit mechanical exhaustive search in finite time? How do we systematically build such sets? How fast can exhaustive search over infinite sets be performed? Keywords. Higher-type computability and complexity, Kleene–Kreisel functionals, PCF, Haskell, topology. 1.

A number of authors have exported domain-theoretic techniques from denotational semantics to the operational study of contextual equivalence and order. We further develop this, and, moreover, we additionally export topological techniques. In particular, we work with an operational notion of compact set and show that total programs with values on certain types are uniformly continuous on compact sets of total elements. We apply this and other conclusions to prove the correctness of non-trivial programs that manipulate infinite data. What is interesting is that the development applies to sequential programming languages, in addition to languages with parallel features. 1

ion, Totality and PCF Gordon Plotkin Abstract Inspired by a question of Riecke, we consider the interaction of totality and full abstraction, asking whether full abstraction holds for Scott's model of cpos and continuous functions if one restricts to total programs and total observations. The answer is negative, as there are distinct operational and denotational notions of totality. However, when two terms are each total in both senses then they are totally equivalent operationally iff they are totally equivalent in the Scott model. Analysing further, we consider sequential and parallel versions of PCF and several models: Scott's model of continuous functions, Milner's fully abstract model of PCF and their effective submodels. We investigate how totality differs between these models. Some apparently rather difficult open problems arise, essentially concerning whether the sequential and parallel versions of PCF have the same expressive power, in the sense of total equivale...

This thesis contains three parts. The first part presents contributions in the fields of domain-specific language design, runtime system design, and static program analysis, the second part presents contributions in the field of control synthesis, and finally the third part presents contributions in the field of denotational semantics.

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The partial real line is an extension of the Euclidean real line with partial real numbers, which has been used to model exact real number computation in the programming language Real PCF. We introduce induction principles and recursion schemes for the partial unit interval, which allow us to verify that Real PCF programs meet their specification. They resemble the so-called Peano axioms for natural numbers. The theory is based on a domain-equation-like presentation of the partial unit interval. The principles are applied to show that Real PCF is universal in the sense that all computable elements of its universe of discourse are definable. These elements include higher-order functions such as integration operators. Keywords: Induction, coinduction, exact real number computation, domain theory, Real PCF, universality. Introduction The partial real line is the domain of compact real intervals ordered by reverse inclusion [28,21]. The idea is that singleton intervals represent total rea...

We introduce a computationally adequate metric model of PCF, based on the fact that the category of non-expansive maps of complete bounded ultrametric spaces is cartesian closed. The model captures certain temporal aspects of higher-type computation and contains both extensional and intensional functions. We show that Scott’s model arises as its extensional collapse. The intensional aspects of the metric model are illustrated via a Gödel-number-free version of Kleene’s T-predicate.

We present a process semantics for the purely additive fragment of linear logic in which formulas denote protocols and (equivalence classes of) proofs denote multi-channel concurrent processes. The polycategorical model induced by this process semantics is shown to be equivalent to the free polycategory based on the syntax (i.e., it is full and faithfully complete). This establishes that the additive fragment of linear logic provides a semantics of concurrent processes. Another property of this semantics is that it gives a canonical representation of proofs in additive linear logic.