A Special Case of Schematic Syntactic Unification

Cerna, David M.

doi:10.1109/synasc54541.2021.00024

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“…The required unification procedure should unify terms containing infinitely many variables that each occur finitely many times. This type of unification was first discussed in [14,15] and partially solved in [12]; a sufficient condition for unifiability was given. In this work we provide both a necessary and sufficient condition for unifiability of simple linear loops with a finite depth term checkable in finite time.…”

Section: Introductionmentioning

confidence: 99%

Higher-order pattern generalization modulo equational theories

Cerna

Kutsia

2020

Math. Struct. Comp. Sci.

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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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Section: Introductionmentioning

confidence: 99%