On TLA

We describe the Temporal Logic of Actions (TLA) from a logical perspective. After giving the syntax and semantics of TLA, we discuss some methods for representing reactive systems in TLA and study veriication rules. 1 The L in TLA The Temporal Logic of Actions (TLA) is a variant of temporal logic, designed for the speciication and veriication of reactive systems in terms of their actions. In this paper we describe TLA from a logical perspective; our description of TLA has three aspects: 1. As a logic, TLA has a precise syntax and semantics. We deene these in the next section. Our intent is not to develop a new TLA, but rather to explain and to reene Lamport's deenition of TLA 19]. 2. Like HOL 13] and other logics, TLA can serve for representing reac-tive systems in several styles. In particular, a speciication may describe concurrent steps as interleaved or simultaneous; communication between components may be synchronous or asynchronous. We discuss a few styles in section 3. 3. Proofs in TLA rely on basic rules of temporal logic, rules for reenement, and rules for composition. We state the principal rules in sections 4 and 5. Following 7, 8], we show that some of them arise from general logical (or algebraic) considerations, largely independent of the details of TLA This paper is a self-contained presentation of TLA. It is however not a survey, in that it includes technical novelties and in that it is far from comprehensive. Lamport's original work on TLA 19] provides much additional, useful material, and in particular some motivation for the TLA approach and a proof system for TLA. Other papers discuss mechanical veriication in TLA 11, 16], reenement and composition 6, 4], real-time systems and hybrid systems 5, 18, 12], and medium-size examples 20]. There are also works on PTLA 1, 29], a propositional logic based on a preliminary version of TLA. Finally, the logic TLR has many similarities with TLA 28].