Accurate Step Counting

Starting with an evaluator for a language, an abstract machine for the same language can be mechanically derived using successive program transformations. This has relevance to studying both the space and time properties of programs because these can be estimated by counting transitions of the abstract machine and measuring the size of the additional data structures needed, such as environments and stacks. In this article we use this process to derive a function that accurately counts the number of steps required to evaluate expressions in a simple language.

Using a Generalisation Critic to find Bisimulations for Coinductive Proofs

Coinduction is a method of growing importance in reasoning about functional languages, due to the increasing prominence of lazy data structures. Through the use of bisimulations and proofs that bisimilarity is a congruence in various domains it can be used to prove the congruence of two processes. A coinductive proof requires a relation to be chosen which can be proved to be a bisimulation. We use proof planning to develop a heuristic method which automatically constucts a candidate relation. If this relation doesn't allow the proof to go through a proof critic analyses the reasons why it failed and modifies the relation accordingly. Several proof tools have been developed to aid coinductive proofs but all require user interaction. Crucially they require the user to supply an appropriate relation which the system can then prove to be a bisimulation.