The ICS Decision Procedures for Embedded Deduction

Automated theorem proving... linear arithmetic, and lists. The ground (i.e., quantifier-free) fragment of many combinations is decidable when the fully quantified combination is not, and practical experience indicates that automation of the ground case is adequate for most applications. Practical experience also suggests several other desiderata for an effective deductive service. Some applications (e.g., construction of abstractions) invoke their deductive service a huge number of times in the course of a single calculation, so that performance of the service must be very good. Other applications such as proof search explore many variations on a formula (i.e., alternately asserting and denying various combinations of its premises), so the deductive service should not examine individual formulas in isolation, but should provide a rich application programming interface that supports incremental assertion, retraction, and querying of formulas. Other applications such as test case generation..