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Programming Languages as Mathematical Theories
Abstract
That computer science is somehow a mathematical activity was a view held by many of the pioneers of the subject, especially those who were concerned with its foundations. At face value it might mean that the actual activity of programming is a mathematical one. Indeed, at least in some form, this has been held. But here we explore a different gloss on it. We explore the claim that programming languages are (semantically) mathematical theories. This will force us to discuss the normative nature of semantics, the nature of mathematical theories, the role of theoretical computer science and the relationship between semantic theory and language design.
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