Abstract

We explore some foundational issues in the development of a theory of intensional semantics. A programming language may be given a variety of semantics, differing in the level of abstraction; one generally chooses the semantics at an abstraction level appropriate for reasoning about a particular kind of program property. Extensional semantics are typically appropriate for proving properties such as partial correctness, but an intensional semantics at a lower abstraction level is required in order to reason about computation strategy and thereby support reasoning about intensional aspects of behavior such as order of evaluation and efficiency. It is obviously desirable to be able to establish sensible relationships between two semantics for the same language, and we seek a general category-theoretic framework that permits this. Beginning with an "extensional" category, whose morphisms we can think of as functions of some kind, we model a notion of computation as a comonad with certain e...

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