@InProceedings{MossakowskiEA08b,
  author = {Till Mossakowski and Lutz Schr{\"o}der and Sergey Goncharov},
  title = { A generic complete dynamic logic for reasoning about purity and effects},
  year = {2008},
  editor = {J. Fiadeiro and P. Inverardi},
  booktitle = {Fundamental Approaches to Software Engineering (FASE 2008)},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  volume = {4961},
  pages = {199-214},
  keywords = {dynamic logic pure function monad observational purity completeness},
  url = {http://dx.doi.org/10.1007/978-3-540-78743-3_15},
  comment = { <a href = "http://www.informatik.uni-bremen.de/~till/papers/purity-effects.pdf"> [preprint] </a>},
  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.},
}