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Lifting is a well known technique in resolution theorem proving, logic programming, and term rewriting. In this paper we formulate lifting as an efficiency-motivated program transformation applicable to a wide variety of nondeterministic procedures. This formulation allows the immediate lifting of complex procedures, such as the Davis-Putnam algorithm, which are otherwise difficult to lift. We treat both classical lifting, which is based on unification, and various closely related program transformations which we also call lifting transformations. These nonclassical lifting transformations are closely related to constraint techniques in logic programming, resolution, and term rewriting.

We analyse the semantics of aspect-oriented extensions to functional languages by presenting compositional translations of these primitives into languages with traditional notions of state and control. As a first step, we examine an existing semantic description of aspects which allows the labelling of program points. We show that a restriction of these semantics to aspects which do not preempt the execution of code can be fully abstractly translated into a functional calculus with higher order references, but that removing this restriction requires a notion of exception handling to be added to the target language in order to yield a sound semantics. Next, we proceed to show that abandoning the labelling technique, and consequently relaxing the so-called ``obliviousness'' property of aspectual languages, allows preemptive aspects to be included in the general references model without the need for exceptions. This means that the game model of general references is inherited by the aspect calculus. The net result is a clean semantic description of aspect-orientation, which mirrors recently published techniques for their implementation, and thereby provides theoretical justification for these systems. The practical validity of our semantics is demonstrated by implementing extensions to the basic calculus in Standard ML, and showing how a number of useful aspect-oriented features can be expressed using general references alone. Our theoretical methodology closely follows the proof structure that often appears in the game semantics literature, and therefore provides an operational perspective on notions such as ``bad variables'' and factorisation theorems.

This thesis presents TransLucid, a low-level, purely declarative, intensional programming language. Built on a simple algebra and with just a small number of primitives, TransLucid programs define arbitrary dimensional infinite data structures, which are then queried to produce results. The formal foundations of TransLucid come from the work in intensional logic by Montague and Scott. The background chapters give a history of intensional logic and its predecessors in the Western world, as well as a history of intensional programming and Lucid, the first intensional programming language. The semantics of TransLucid are fully specified in the form of operational semantics. Three levels of semantics are given, in increasing order of efficiency, with the sequential warehouse semantics, the most efficient, being presented together with a proof that any expression will be evaluated by only examining relevant dimensions in the current context. The language is then extended in three important ways, by adding versioned identifiers, (declarative) side-effects and timestamped equations and demands. Adding versioned identifiers to TransLucid enriches the expressiveness of the language and allows the encoding of a variety of programming paradigms, ranging from manipulating large data-cubes to pattern-matching. Adding side-effects supports one of the main reasons for TransLucid: namely, to provide a target language, together with a methodology, for translating the main programming paradigms, thus creating a uniform end platform that can be the focus for optimisation and program verification. A translation of imperative programs into TransLucid is given. Timestamped equations and demands enable TransLucid to become a language for synchronous programming in real-time systems, as well as allowing runtime updates to a program's equations. The language TransLucid represents a decisive advance in declarative programming. It has applications in many fields of computer science and opens up exciting new avenues of research.

This thesis presents TransLucid, a low-level, purely declarative, intensional programming language. Built on a simple algebra and with just a small number of primitives, TransLucid programs define arbitrary dimensional infinite data structures, which are then queried to produce results. The formal foundations of TransLucid come from the work in intensional logic by Montague and Scott. The background chapters give a history of intensional logic and its predecessors in the Western world, as well as a history of intensional programming and Lucid, the first intensional programming language. The semantics of TransLucid are fully specified in the form of operational semantics. Three levels of semantics are given, in increasing order of efficiency, with the sequential warehouse semantics, the most efficient, being presented together with a proof that any expression will be evaluated by only examining relevant dimensions in the current context. The language is then extended in three important ways, by adding versioned identifiers, (declarative) side-effects and timestamped equations and demands. Adding versioned identifiers to TransLucid enriches the expressiveness of the language and allows the encoding of a variety of programming paradigms, ranging from manipulating large data-cubes to pattern-matching. Adding side-effects supports one of the main reasons for TransLucid: namely, to provide a target language, together with a methodology, for translating the main programming paradigms, thus creating a uniform end platform that can be the focus for optimisation and program verification. A translation of imperative programs into TransLucid is given. Timestamped equations and demands enable TransLucid to become a language for synchronous programming in real-time systems, as well as allowing runtime updates to a program's equations. The language TransLucid represents a decisive advance in declarative programming. It has applications in many fields of computer science and opens up exciting new avenues of research.