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Generalization techniques have many applications, such as templateconstruction, argument generalization, and indexing. Modern interactive proverscan exploit advancement in generalization methods over expressive-type theoriesto further develop proof generalization techniques and other transformations.So far, investigations concerned with anti-unification (AU) over lambda termsand similar type theories have focused on developing algorithms forwell-studied variants. These variants forbid the nesting of generalizationvariables, restrict the structure of their arguments, and are unitary.Extending these methods to more expressive variants is important toapplications. We consider the case of nested generalization variables and showthat the AU problem is nullary (using capture-avoiding substitutions), evenwhen the arguments to free variables are severely restricted.

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