Inproceedings,
A generic complete dynamic logic for reasoning about purity and effects
Fundamental Approaches to Software Engineering (FASE 2008), volume 4961 of Lecture Notes in Computer Science, page 199-214. Springer, (2008)
Abstract
For a number of programming languages, among them Eiffel, C, Java and Ruby,
Hoare-style logics and dynamic logics have been developed. In these
logics, pre- and postconditions are typically formulated using
potentially effectful programs. In order to ensure that these pre- and
postconditions behave like logical formulae (that is, enjoy some kind of
referential transparency), a notion of purity is needed. Here, we
introduce a generic framework for reasoning about purity and effects.
Effects are modeled abstractly and axiomatically, using Moggi's idea of
encapsulation of effects as monads. We introduce a dynamic logic (from
which, as usual, a Hoare logic can be derived) whose logical
formulae are pure programs in a strong sense. We formulate a set
of proof rules for this logic, and prove it to be complete with respect
to a categorical semantics. Using dynamic logic, we then develop a
relaxed notion of purity which allows for observationally neutral
effects such writing on newly allocated memory.
