reasoning, trace semantics. Parallel computers have not yet had the expected impact on mainstream computing. Parallelism adds a level of complexity to the programming task that makes it very error-prone. Moreover, a large variety ofvery di erent parallel architectures exists. Porting an implementation from one machine to another may require substantial changes. This thesis addresses some of these problems by developing a formal basis for the design of parallel programs in form of a re nement calculus. The calculus allows the stepwise formal derivation of an abstract, low-level implementation from a trusted, high-level speci cation. The calculus thus helps structuring and documenting the development process. Portability is increased, because the introduction of a machine-dependent feature can be located in the re nement tree. Development e orts above this point in the tree are independent of that feature and are thus reusable. Moreover, the discovery of new, possibly more

This note summarises my understanding to date of two closely-related theories for dealing with “bulk ” data types: the Bird-Meertens formalism (henceforth abbreviated to BMF) and its extension in categorical data types (CDT). I've been led to this study for two reasons: as interesting formalisms for program derivation in their own right, and as a possible basis for defining useful operations for shared abstract data types. In this note I cover all the essential ideas I've found so far, and include a bibliography of the theories. Overview specifications using a small number of higher-order constructs. Functions are expressed as combinations of functions over data structures, avoiding the explicit use of recursion. This both simplifies proofs of correctness and allows the possibility for efficient (possibly parallel) implementation of the combination operators over a range of data types. A small-scale theory leads to potentially large-scale applications. The theory does not, however, start from a standpoint of immediate mechanisation. To do so, in Bird and Meertens ' view, would severely limit the many ways in which an

One problem of parallel computing is that parallel computers vary greatly in architecture so that a program written to run efficiently on a particular architecture, when porting to a different architecture, would often need to be changed and adapted substantially in order to run with reasonable performance on the target architecture. Porting with performance is, hence, labour-intensive and costly. A method of parallel programming using the Bird-Meertens Formalism where programs are formulated as compositions of (mainly) higher order functions on some data type in the data parallel functional style has been proposed as a solution. The library of (mainly) higher-order functions in which all communication and parallelism in a program is embedded could (it is argued) be implemented efficiently on different parallel architectures. This gives the advantage of portability between different architectures with reasonable and predictable performance without change in program source. ...