A generic complete dynamic logic for reasoning about purity and effects

Till Mossakowski (1, 2) , Lutz Schröder (1, 2) , Sergey Goncharov (1)

1 Safe and secure cognitive systems
2 Department of Computer Science

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 modelled 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.

Mots clés: Monads for effects; Dynamic logic; Observational equivalence; Completeness

Till Mossakowski, Lutz Schröder, Sergey Goncharov. A generic complete dynamic logic for reasoning about purity and effects. Formal Aspects of Computing, 2010, 22 (3), pp.363-384. ⟨10.1007/s00165-010-0153-4⟩. ⟨hal-00587601⟩