Reasoning Support Sample Clauses

Reasoning Support. ‌ To reason about Circus models, three complementary strategies are avail- able. The first one is via algebraic refinement laws. Such laws can be proved within the Isabelle/UTP CSP semantics and enable us to transform mecha- nised Circus models in a piecewise and stepwise manner. For proofs of the laws, we have implemented automatic tactics that transform a conjecture about processes and actions within Isabelle/UTP into a pure HOL predi- cate, eliminating all artefacts of our UTP predicate models, such as lenses and state spaces. Those tactics are called rel simp, rel auto and rel blast and are defined in a separate theory of Isabelle/UTP. They use principles of transfer [21] and interpretation [14]. Many refinement laws about CSP can be proved in this manner, including basic laws for communication prefixes, external choice, recursion and parallel composition. Once a refinement law is proved, it can be used to rewrite part of a Circus model. A refinement of the overall Circus specification in which the part is embedded is obtained exploiting monotonicity of the language constructs. We have proved various monotonicity laws. The approach described in [31] can be used to automate their application, using a tactic language as well as window inference techniques. We note that refinement is also applicable to prove, for instance, that a trace tr = (x0, x0, · · · , en ) is exhibited by a Circus model. This is by turning the ^ trace into a process T = e1 −→ e2 −→ · · · −→ en and then composing that process in parallel with the Circus model, synchronising on all events in the trace. The parallel composition has to be refined by T itself, which can be checed using step laws for communication prefixes. ±
Sample 1
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