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

arXiv: https://arxiv.org/abs/2207.08918 · HTML: https://mlsanity.com/paper/2207.08918/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2022.

## Built on by (most cited first, 1 of 1)

- [Anti-unification and Generalization: A Survey](https://mlsanity.com/paper/2302.00277/) (2023)

## Abstract (arXiv)

Generalization techniques have many applications, including template construction, argument generalization, and indexing. Modern interactive provers can exploit advancement in generalization methods over expressive type theories to further develop proof generalization techniques and other transformations. So far, investigations concerned with anti-unification (AU) over λ-terms and similar type theories have focused on developing algorithms for well-studied variants. These variants forbid the nesting of generalization variables, restrict the structure of their arguments, and are textitunitary. Extending these methods to more expressive variants is important to applications. We consider the case of nested generalization variables and show that the AU problem is textitnullary (using textitcapture-avoiding substitutions), even when the arguments to free variables are severely restricted.