Many approaches to programming emphasize the use of interfaces. The basic idea is to decompose programs into modules and to specify how each module's interface behaves. This makes it easier to reason about programs because one can rely on a module's speci#cation rather than examining its implementation, which is more complicated.

This paper analyses a technique (called Gazing) for unfolding de nitions on the basis of a global plan built in an abstract space. Gazing's logical properties are studied inside a formal framework which relies on a more general theory of abstraction. Some experimental results con rming the theoretical ones are also presented.

An investigation was made of the characteristics of computer programming languages intended for the implementation of provably correct programs and of the characteristics of programs written in these languages. It was discovered that potential run time exceptions and the necessity of providing a rigorously correct implementation of exception handlers so dominate the potential control paths of programs written in verifiable languages that the usual code optimization techniques are ineffective. It was further discovered that the call intensive control structures of these programs, necessitated by verification constraints, also thwart optimization and lead to inefficient code. It is shown that theorems can be derived at potential exception sites which, if true, guarantee that the exception condition will never arise permitting removal of the exception path from the program’s flow graph. These theorems are proved using the automatic theorem prover which is part of the program verification system. Is is also shown that many of the routine calls contained in verifiable programs may be reduced in expense by converting parameters to global variables or eliminated completely by expanding the called routines at their call sites. Both the exception suppression and call reduction techniques reduce the complexity of the program’s call graph and facilitate conventional optimizations. Several examples are presented and the potential improvements in code size resulting from the application of these techniques are discussed.

Theorem Proving. In Proceedings of the 11th IJCAI. International Joint Conference on Artificial Intelligence, 1989. Also available as DAI Research Paper No 430, Dept. of Artificial Intelligence, Edinburgh.

by mathematics and recalls spending "hours just roaming around, sometimes working mathematics problems mentally" (Bledsoe 1976). When Woody was 12, his father died. It was a devastating blow both emotionally and financially. As Woody recalled, "We were poor before, but after papa died in January 1934, things got worse" (Bledsoe 1976). He and the rest of his brothers and sisters worked dreary 10-hour days to make ends meet. Woody ran away from home at 16. He found work in north Texas driving a tractor all night. After a month, he hopped a freight train to Colorado to visit his brother, who was working in a Civilian Conservation Corps camp. After a few weeks, he made his way to the south Texas town of Calliham, where he lived with some friends for a year. He graduated from high school during that year (1939). Woody then returned to live with his mother, who had moved to Norman, Oklahoma. He took a job as a dishwasher, working 12-hour days 7 days a week. He enrolled at the University o