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Satisfiability modulo theories: introduction and applications
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Domain-specific languages (DSLs) are useful for capturing and reusing engineering expertise. They can formalize industrial patterns and practices while increasing the scalability of verification, because input programs are written at a higher level of abstraction. However, engineering new DSLs with custom verification is a non-trivial task in its own right, and usually requires programming language, formal methods, and automated theorem proving expertise. In this tutorial we present FORMULA 2.0, which is formal framework for developing DSLs. FORMULA specifications are succinct descriptions of DSLs, and specifications can be immediately connected to state-of-the-art analysis engines without additional expertise. FORMULA provides: (1) succinct specifications of DSLs and compilers, (2) efficient compilation and execution of input programs, (3) program synthesis and compiler verification. We take a unique approach to provide these features: Specifications are written as strongly-typed open-world logic programs. These specifications are highly declarative and easily express rich synthesis / verification problems. Automated reasoning is enabled by efficient symbolic execution of logic programs into quantifier-free sub-problems, which are dispatched to the state-of-the-art SMT solver Z3. FORMULA has been applied within Microsoft to develop DSLs for verifiable device drivers and protocols. It has been used by the automotive / embedded systems industries for software / hardware co-design and design-space exploration under hard resource allocation constraints. It is being used to develop semantic specifications for complex cyber-physical systems.