Toward a verification logic for rewriting logic.

*(English)*Zbl 0966.68123
Bert, Didier (ed.) et al., Recent trends in algebraic development techniques. 14th international workshop, WADT ’99, Château de Bonas, France, September 15-18, 1999. Selected papers. Berlin: Springer. Lect. Notes Comput. Sci. 1827, 438-458 (2000).

Summary: This paper is an initial step in the development of a logic for verifying properties of programs in rewriting logic. Rewriting logic is primarily a logic of change, in which deduction corresponds directly to computation, and not a logic to talk about change in a more indirect and global manner, such as the different modal and temporal logics that can be found in the literature.

We start by defining a modal action logic (VLRL) in which rewrite rules are captured as actions. The main novelty of this logic is a topological modality associated with state constructors that allows us to reason about the structure of states, stating that the current state can be decomposed into regions satisfying certain properties. Then, on top of the modal logic, we define a temporal logic for reasoning about properties of the computations generated from rewrite theories, and demonstrate its potential by means of two simple examples.

For the entire collection see [Zbl 0947.00036].

We start by defining a modal action logic (VLRL) in which rewrite rules are captured as actions. The main novelty of this logic is a topological modality associated with state constructors that allows us to reason about the structure of states, stating that the current state can be decomposed into regions satisfying certain properties. Then, on top of the modal logic, we define a temporal logic for reasoning about properties of the computations generated from rewrite theories, and demonstrate its potential by means of two simple examples.

For the entire collection see [Zbl 0947.00036].