Higher-order pattern generalization modulo equational theories
David M. Cerna,Temur Kutsia +1 more
TL;DR: A sound and complete algorithm which takes two lambda terms and computes their equational generalizations in the form of higher-order patterns is developed and the notion of optimal solution is defined.
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Abstract: Abstract We consider anti-unification for simply typed lambda terms in theories defined by associativity, commutativity, identity (unit element) axioms and their combinations and develop a sound and complete algorithm which takes two lambda terms and computes their equational generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of such generalizations contains finitely many elements. We define the notion of optimal solution and investigate special restrictions of the problem for which the optimal solution can be computed in linear or polynomial time.
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Citations
Unital Anti-Unification: Type and Algorithms
David M. Cerna,Temur Kutsia +1 more
- 01 Jan 2020
TL;DR: This work proves that when the term signature contains at least two unital functions, anti-unification is of the nullary type, and addresses the problems of establishing generalization type and designing anti- Uniflcation algorithms.
12
One or Nothing: Anti-unification over the Simply-Typed Lambda Calculus
18 Jul 2022
TL;DR: In this paper , it was shown that the anti-unification problem is nullary (using capture-avoiding substitutions), even when the arguments to free variables are severely restricted.
Anti-unification and Generalization: A Survey
01 Feb 2023
TL;DR: A survey of AU research and its applications can be found in this article and a general framework for categorizing existing and future developments is presented in Section 2.2.1. But without a systematic study of the concept nor surveys of existing work, investigations often resort to developing application specific methods that existing approaches may cover.
1
Nominal Anti-Unification with Atom-Variables.
Manfred Schmidt-Schauß,Daniele Nantes-Sobrinho +1 more
1
References
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The Lambda Calculus. Its Syntax and Semantics
Henk Barendregt
- 30 Apr 2012
TL;DR: In this article, the Lambda-Calculus has been studied as a theory of composition and reduction, and the theory of reduction has been used to construct models of Lambda Theories.
2.9K
A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification
TL;DR: This paper presents a logic programming language, called L, that also contains both function variables and A-abstractions, but certain restriction are placed on occurrences of function variables, so an implementation of LA does not need to implement full higher-order unification.
A modular order-sorted equational generalization algorithm
TL;DR: This work extends the known untyped generalization algorithm to an order-sorted typed setting with sorts, subsorts, and subtype polymorphism, and extends it to work modulo equational theories, where function symbols can obey any combination of associativity, commutativity, and identity axioms.
59
Anti-unification for Unranked Terms and Hedges
TL;DR: A complete and minimal algorithm to compute least general generalizations for unranked terms and hedges that may contain term and hedge variables is designed and improved by restricting possible alternatives permitted in the generalizations.