Meta-level inference: two applications

We describe two uses of meta-level inference: to control the search for a proof; and to derive new control information, and illustrate them in the domain of algebraic equation solving. The derivation of control information is the main focus of the paper. It involves the proving of theorems in the Meta-Theory of Algebra. These proofs are guided by meta-meta-level inference. We are developing a meta-meta-language to describe formulae, and proof plans, and have built a program, IMPRESS, which uses these plans to build a proof. We describe one such proof plan in detail. IMPRESS will form part of a self-improving algebra system