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 time and space 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 paper we will use this process to derive a function that accurately counts the number of steps required to evaluate expressions in a simple language, and illustrate this function with a range of examples.

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