Predicates, temporal logic, and simulations
We present an integrated theory of predicates, temporal logic, and simulations, developed using the mechanical theorem prover HOL. Both the predicate-based formulation of temporal logic and the formal theory of simulations have been investigated before in the context of HOL. What is new here is the study of the interaction between the two. In particular, we develop a formal theory of simulations in which certain kinds of temporal properties of the simulating program can be translated into those of the simulated program. Thus, if the simulated program is hard to reason about but the simulating program is easy to reason about, then our theory enables us to perform as much reasoning as possible about the “easy” program and then translate the results back to the “hard” program. The translatable temporal properties include many useful liveness properties.
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