Abstract: Problems and Results in Unification and Type Search

Type search is the problem of finding a complete typing derivation in some typed calculus for a term with incomplete type information. Type search has been considered for a variety of typed calculi, e.g., the simply-typed lambda-calculus, System F, F_omega, and variations of these systems. For each typed calculus, the problem is considered for various amounts of type information, e.g., no information, the final type and types of free variables, types of all variables, etc. Each combination of calculus, type system, and amount of type information is a distinct type search problem. Various forms of unification have been used for analyzing type search problems, both in devising algorithms for performing type search and in proving some type search problems to be undecidable. This talk describes various ways in which the undecidability of unification problems has been used to prove the undecidability of type search problems.