An Abstract Interpretation Framework for Diagnosis and Verification of Timed Concurrent Constraint Languages

In this thesis, we propose a semantic framework for tccp based on abstract interpretation with the main purpose of formally verifying and debugging tccp programs. A key point for the efficacy of the resulting methodologies is the adequacy of the concrete semantics. Thus, in this thesis, much effort has been devoted to the development of a suitable small-step denotational semantics for the tccp language to start with. Our denotational semantics models precisely the small-step behavior of tccp and is suitable to be used within the abstract interpretation framework. Namely, it is defined in a compositional and bottom-up way, it is as condensed as possible (it does not contain redundant elements), and it is goal-independent (its calculus does not depend on the semantic evaluation of a specific initial agent). Another contribution of this thesis is the definition (by abstraction of our small-step denotational semantics) of a big-step denotational semantics that abstracts away from the information about the evolution of the state and keeps only the the first and the last (if it exists) state. We show that this big-step semantics is essentially equivalent to the input-output semantics. In order to fulfill our goal of formally validate tccp programs, we build different approximations of our small-step denotational semantics by using standard abstract interpretation techniques. In this way we obtain debugging and verification tools which are correct by construction. More specifically, we propose two abstract semantics that are used to formally debug tccp programs. The first one approximates the information content of tccp behavioral traces, while the second one approximates our small-step semantics with temporal logic formulas. By applying abstract diagnosis with these abstract semantics we obtain two fully-automatic verification methods for tccp.