Unification problem in equational theories

1997 ◽  
Vol 33 (6) ◽  
pp. 874-899
Author(s):  
S. L. Kryvyi
Keyword(s):  
Equational Theories ◽  
Unification Problem

scholarly journals Extensions of unification modulo ACUI

2019 ◽  
Vol 30 (6) ◽  
pp. 597-626 ◽  
Author(s):  
Franz Baader ◽  
Pavlos Marantidis ◽  
Antoine Mottet ◽  
Alexander Okhotin
Keyword(s):  
Function Symbol ◽  
The Other ◽  
Binary Function ◽  
Worst Case ◽  
Case Complexity ◽  
Equational Theories ◽  
Other Hand ◽  
Worst Case Complexity ◽  
Finite Set ◽  
Unification Problem

AbstractThe theory ACUI of an associative, commutative, and idempotent binary function symbol + with unit 0 was one of the first equational theories for which the complexity of testing solvability of unification problems was investigated in detail. In this paper, we investigate two extensions of ACUI. On one hand, we consider approximate ACUI-unification, where we use appropriate measures to express how close a substitution is to being a unifier. On the other hand, we extend ACUI-unification to ACUIG-unification, that is, unification in equational theories that are obtained from ACUI by adding a finite set G of ground identities. Finally, we combine the two extensions, that is, consider approximate ACUI-unification. For all cases we are able to determine the exact worst-case complexity of the unification problem.

Type Inference: Some Results, Some Problems1

1993 ◽  
Vol 19 (1-2) ◽  
pp. 87-125
Author(s):  
Paola Giannini ◽  
Furio Honsell ◽  
Simona Ronchi Della Rocca
Keyword(s):  
Large Class ◽  
Higher Order ◽  
Type Inference ◽  
Principal Type ◽  
Open Problems ◽  
Inference Problem ◽  
Type Assignment ◽  
Unification Problem

In this paper we investigate the type inference problem for a large class of type assignment systems for the λ-calculus. This is the problem of determining if a term has a type in a given system. We discuss, in particular, a collection of type assignment systems which correspond to the typed systems of Barendregt’s “cube”. Type dependencies being shown redundant, we focus on the strongest of all, Fω, the type assignment version of the system Fω of Girard. In order to manipulate uniformly type inferences we give a syntax directed presentation of Fω and introduce the notions of scheme and of principal type scheme. Making essential use of them, we succeed in reducing the type inference problem for Fω to a restriction of the higher order semi-unification problem and in showing that the conditional type inference problem for Fω is undecidable. Throughout the paper we call attention to open problems and formulate some conjectures.

Theories with equational forking

2002 ◽  
Vol 67 (1) ◽  
pp. 326-340 ◽  
Author(s):  
Markus Junker ◽  
Ingo Kraus
Keyword(s):  
Symmetric Relation ◽  
Equational Theories

AbstractWe show that equational independence in the sense of Srour equals local non-forking. We then examine so-called almost equational theories where equational independence is a symmetric relation.

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