This paper presents semantic specifications and correctness proofs for both on-line and offline partial evaluation of strict first-order functional programs. To do so, our strategy consists of defining a core semantics as a basis for the specification of three non-standard evaluations: instrumented evaluation, on-line and off-line partial evaluation. We then use the technique of logical relations to prove the correctness of both on-line and off-line partial evaluation semantics.

The contributions of this work are as follows:

1. We provide a uniform framework to defining and proving correct both on-line and off-line partial evaluation.

2. This work required a formal specification of on-line partial evaluation with polyvariant specialization. We define criteria for its correctness with respect to an instrumented standard semantics. As a by-product, on-line partial evaluation appears to be based on a fixpoint iteration process, just like binding-time analysis.

3. We show that binding-time analysis, the preprocessing phase of off-line partial evaluation, is an abstraction of on-line partial evaluation. Therefore, its correctness can be proved with respect to on-line partial evaluation, instead of with respect to the standard semantics, as is customarily done.

4. Based on the binding-time analysis, we formally derive the specialization semantics for off-line partial evaluation. This strategy ensures the correctness of the resulting semantics.

Monitoring semantics is a formal model of program execution which captures ‘monitoring activity’ as found in profilers, tracers, debuggers, etc. Beyond its theoretical interest, this formalism provides a new methodology for implementing a large family of source-level monitoring activities for sequential deterministic programming languages. In this article we explore the use of monitoring semantics in the specification and implementation of a variety of monitors: profilers, tracers, collecting interpreters, and, most importantly, interactive source-level debuggers. Although we consider such monitors only for (both strict and non-strict) functional languages, the methodology extends easily to imperative languages, since it begins with a continuation semantics specification.

In addition, using standard partial evaluation techniques as an optimization strategy, we show that the methodology forms a practical basis for building real monitors. Our system can be optimized at two levels of specialization: specializing the interpreter with respect to a monitor specification automatically yields an instrumented interpreter; further specializing this instrumented interpreter with respect to a source program yields an instrumented program, i.e. one in which the extra code to perform monitoring has been automatically embedded into the program.

Communication lifting is a program transformation that can be applied to a synchronous process network to restructure the network. This restructuring in theory improves sequential and parallel performance. The transformation has been formally specified and proved correct and it has been implemented as an automatic program transformation tool. This tool has been applied to a small set of programs consisting of synchronous process networks. For these networks communication lifting generates parallel programs that do not require locking. Measurements indicate performance gains in practice both with sequential and parallel evaluation. Communication lifting is a worthwhile optimization to be included in a compiler for a lazy functional language.

We present purely functional implementations of queues and double-ended queues (deques) requiring only O(1) time per operation in the worst case. Our algorithms are considerably simpler than previous designs with the same bounds. The inspiration for our approach is the incremental behaviour of certain functions on lazy lists.

We give a direct type-theoretic characterization of the basic mechanisms of object-oriented programming, including objects, methods, message passing, and subtyping, by introducing an explicit constructor for object types and suitable introduction, elimination, and equality rules. The resulting abstract framework provides a basis for justifying and comparing previous encodings of objects based on recursive record types (Cardelli, 1984; Cardelli, 1992; Bruce, 1994; Cook et al., 1990; Mitchell, 1990a) and encodings based on existential types (Pierce & Turner, 1994).

We introduce a λ-calculus notation which enables us to detect in a term, more β-redexes than in the usual notation. On this basis, we define an extended β-reduction which is yet a subrelation of conversion. The Church Rosser property holds for this extended reduction. Moreover, we show that we can transform generalised redexes into usual ones by a process called ‘term reshuffling’.