%0 Journal Article %1 MossakowskiEA09 %A Mossakowski, Till %A Schröder, Lutz %A Goncharov, Sergey %D 2010 %J Formal Aspects of Computing %K completeness logic monad purity side-effect soundness %N 3-4 %P 363-384 %T A Generic Complete Dynamic Logic for Reasoning about Purity and Effects %U http://dx.doi.org/10.1007/s00165-010-0153-4 %V 22 %X 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.

@article{MossakowskiEA09, 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 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.}, added-at = {2016-08-05T15:59:03.000+0200}, author = {Mossakowski, Till and Schr{\"o}der, Lutz and Goncharov, Sergey}, biburl = {https://www.bibsonomy.org/bibtex/2ee6e70722b94d12746fc4150a25cbad4/tillmo}, interhash = {35ea22a396d1ccb1ebdb1926c94a6671}, intrahash = {ee6e70722b94d12746fc4150a25cbad4}, issn = {0934-5043}, journal = {Formal Aspects of Computing}, keywords = {completeness logic monad purity side-effect soundness}, number = {3-4}, pages = {363-384}, pdfurl = {http://www.informatik.uni-bremen.de/~lschrode/papers/mdl-compl.pdf}, status = {Reviewed}, timestamp = {2016-08-05T15:59:03.000+0200}, title = {A Generic Complete Dynamic Logic for Reasoning about Purity and Effects}, url = {http://dx.doi.org/10.1007/s00165-010-0153-4}, volume = 22, year = 2010 }