One or Nothing: Anti-unification over the Simply-Typed Lambda Calculus

Abstract

Investigations concerned with anti-unification (AU) over λ-terms have focused on developing algorithms that produce generalizations residing within well-studied fragments of the simply-typed λ-calculus. These fragments forbid the nesting of generalizations variables, restrict the structure of their arguments, and are unitary. We consider the case of nested generalization variables and show that this AU problem is nullary, even when the arguments to free variables are severely restricted.