We now define the notion, already discussed, of an effectively calculable function of positive integers by identifying it with the notion of a recursive function of positive integers (or of a lambdadefinable function of positive integers). The phrase in parentheses refers to the apparatus which Church had developed to investigate this and other problems in the foundations of mathematics: the calculus of lambda conversion. Both the Thesis and the lambda calculus have been of seminal influence on the development of Computing Science. The main subject of this article is the lambda calculus but I will begin with a brief sketch of the emergence of the Thesis. The epistemological status of Church’s Thesis is not immediately clear from the above quotation and remains a matter of debate, as is explored in other papers of this volume. My own view, which I will state but not elaborate here, is that the thesis is empirical because it relies for its significance on a claim about what can be calculated by mechanisms. This becomes clearer in

Profiling tools, which measure and display the dynamic space and time behaviour of programs, are essential for identifying execution bottlenecks. A variety of such tools exist for conventional languages, but almost none for non-strict functional languages. There is a good reason for this: lazy evaluation means that the program is executed in an order which is not immediately apparent from the source code, so it is difficult to relate dynamically-gathered statistics back to the original source. This thesis examines the difficulties of profiling lazy higher-order functional languages and develops a profiling tool which overcomes them. It relates information about both the time and space requirements of the program back to the original source expressions identified by the programmer. Considerable attention is paid to the cost semantics with two abstract cost semantics, lexical scoping and evaluation scoping, being investigated. Experience gained from the two profiling schemes led to the d...

Two parallel implementations of a state-of-the-art ocean model are described and analyzed: one is written in the implicitly parallel language Id for the Monsoon multithreaded dataflow architecture, and the other in data parallel CM Fortran for the CM-5. The multithreaded programming model is inherently more expressive than the data parallel model. One goal of this study is to understand what, if any, are the performance penalties of multithreaded execution when implementing a program that is well suited for data parallel execution. To avoid technology and machine configuration issues, the two implementations are compared in terms of overhead cycles per required floating point operation. When simulating flows in complex geometries typical of ocean basins, the data parallel model only remains efficient if redundant computations are performed over land. The generality of the Id programming model allows one to easily and transparently implement a parallel code that computes only in the oce...

Profiling tools, which measure and display the dynamic space and time behaviour of programs, are essential for identifying execution bottlenecks. A variety of such tools exist for conventional languages, but almost none for non-strict functional languages. There is a good reason for this: lazy evaluation means that the program is executed in an order which is not immediately apparent from the source code, so it is difficult to relate dynamically-gathered statistics back to the original source. This thesis examines the difficulties of profiling lazy higher-order functional languages and develops a profiling tool which overcomes them. It relates information about both the time and space requirements of the program back to the original source expressions identified by the programmer. Considerable attention is paid to the cost semantics with two abstract cost semantics, lexical scoping and evaluation scoping, being investigated. Experience gained from the two profiling schemes led to the d...