Behavioural aspects of term-rewriting systems

Imperial Users onl

Functional real-time programming: the language Ruth and its semantics

Real-time systems are amongst the most safety critical systems involving computer software and the incorrect functioning of this software can cause great damage, up to and including the loss of life. If seems sensible therefore to write real-time software in a way that gives us the best chance of correctly implementing specifications. Because of the high level of functional programming languages, their semantic simplicity and their amenability to formal reasoning and correctness preserving transformation it thus seems natural to use a functional language for this task. This thesis explores the problems of applying functional programming languages to real-time by defining the real-time functional programming language Ruth. The first part of the thesis concerns the identification of the particular problems associated with programming real-time systems. These can broadly be stated as a requirement that a real-time language must be able to express facts about time, a feature we have called time expressibility. The next stage is to provide time expressibility within a purely functional framework. This is accomplished by the use of timestamps on inputs and outputs and by providing a real-time clock as an input to Ruth programs. The final major part of the work is the construction of a formal definition of the semantics of Ruth to serve as a basis for formal reasoning and transformation. The framework within which the formal semantics of a real-time language are defined requires time expressibility in the same way as the real-time language itself. This is accomplished within the framework of domain theory by the use of specialised domains for timestamped objects, called herring-bone domains. These domains could be used as the basis for the definition of the semantics of any real-time language

Functional models of procedural programs

This thesis shows how any Procedural Programming notation may be modelled by a purely Functional notation and discusses the applications and implications of this modelling approach. Existing ad hoc modelling techniques are gathered together within a common framework. The thesis shows that these techniques break down when the state of computation for a procedural language Is not an environment mapping from identifiers to denotable values. A simple method for overcoming this difficulty is Introduced, demonstrating that models may be constructed for all procedural programming notations. The modelling approach allows the considerable body of functional reasoning techniques to be brought to bear In the analysis of procedural programs. The thesis Introduces a simple technique called "Abstraction Projection", with which the programmer may project a model onto a sub domain suitable for a particular analytic task. Abstraction Projection removes from the model all details irrelevant to the computation of values within this sub domain. The thesis also provides semantic definitions for the terms "Functional Language", "Procedural Language" and "Referential Transparency"

Functional programming and embedded systems.

Embedded computer systems seem to be the antithesis of functional language systems. Embedded systems are small, stand-alone, and are often forced to accept inelegant design compromises due to hardware cost. They run continuously and are reactive, that is, their primary goal is to monitor sensors and control effectors, using observed external events to trigger state-changing control actions. Yet this thesis describes how functional abstraction can tame the inelegance of embedded systems. Architectural compromises can be made in device drivers, programmed within the functional language, but a function-level interface is presented to the application programmer. Four modifications are introduced to a test-bed purely-functional language in order to facilitate embedded-systems programming: I/O register access; communicating processes; interrupts; and a real-time incremental garbage collector. Referential transparency is preserved. The conventional model of communicating processes is augmente..

Graphical application and visualization of lazy functional computation.

Mere academic toys or the tools of the future? Lazy functional programming languages have undoubted attractive properties. This thesis explores their potential, from the programmer's point of view, for implementing interactive and graphical applications to which they do not seem immediately suited. The discussion is centred round two example applications. One is a graphical design program based on an idea of the artist M. C. Escher. The thesis argues that the graphical user interface may be encapsulated in an "interpret " function that when applied by a mouse click to an interface of appropriate type yields the required behaviour. The second example is a monitoring interpreter for a functional language. The idea is that if the mechanics of the reduction are presented at a suitable level of abstraction, this may be used to give insight into what is going on. On the basis of this the programmer might modify the code so that a program runs more efficiently in terms of speed and memory requirements. Problems of displaying the reduction are addressed, and solutions proposed for overcoming these: displaying the graph as a spanning tree, to ensure planarity, with extra leave

A Functional Approach to Memory-Safe Operating Systems

Purely functional languages--with static type systems and dynamic memory management using garbage collection--are a known tool for helping programmers to reduce the number of memory errors in programs. By using such languages, we can establish correctness properties relating to memory-safety through our choice of implementation language alone. Unfortunately, the language characteristics that make purely functional languages safe also make them more difficult to apply in a low-level domain like operating systems construction. The low-level features that support the kinds of hardware manipulations required by operating systems are not typically available in memory-safe languages with garbage collection. Those that are provided may have the ability to violate memory- and type-safety, destroying the guarantees that motivate using such languages in the first place. This work demonstrates that it is possible to bridge the gap between the requirements of operating system implementations and the features of purely functional languages without sacrificing type- and memory-safety. In particular, we show that this can be achieved by isolating the potentially unsafe memory operations required by operating systems in an abstraction layer that is well integrated with a purely functional language. The salient features of this abstraction layer are that the operations it exposes are memory-safe and yet sufficiently expressive to support the implementation of realistic operating systems. The abstraction layer enables systems programmers to perform all of the low-level tasks necessary in an OS implementation, such as manipulating an MMU and executing user-level programs, without compromising the static memory-safety guarantees of programming in a purely functional language. A specific contribution of this work is an analysis of memory-safety for the abstraction layer by formalizing a meaning for memory-safety in the presence of virtual-memory using a novel application of noninterference security policies. In addition, we evaluate the expressiveness of the abstraction layer by implementing the L4 microkernel API, which has a flexible set of virtual memory management operations

Message-based functional operating systems

AbstractA scheme is described for writing nondeterministic programs in a functional language. The scheme is based on message passing between a number of expressions being evaluated in parallel. I suggest that is represents a significant improvement over previous methods employing a nondeterministic merge primitive, and overcomes numerous drawbacks in that approach