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Fixed-Point Constraints for Nominal Equational Unification

Mauricio Ayala-Rincón, Maribel Fernández, Daniele Nantes-Sobrinho, Michael Wagner
2018 International Conference on Rewriting Techniques and Applications  
We propose a new axiomatisation of the alpha-equivalence relation for nominal terms, based on a primitive notion of fixed-point constraint.  ...  This gives rise to a new notion of nominal unification, where solutions for unification problems are pairs of a fixed-point context and a substitution.  ...  For instance, checking whether [a]s ≈ α [b]t reduces to checking 7:2 Fixed-Point Constraints for Nominal Equational Unification whether s ≈ α (b a) · t and a#t.  ... 
doi:10.4230/lipics.fscd.2018.7 dblp:conf/rta/Ayala-RinconFN18 fatcat:i2v4hes4srdvdoyvmxs7grvocq

On Nominal Syntax and Permutation Fixed Points [article]

Mauricio Ayala-Rincón, Maribel Fernández, Daniele Nantes-Sobrinho
2020 arXiv   pre-print
We propose a new axiomatisation of the alpha-equivalence relation for nominal terms, based on a primitive notion of fixed-point constraint.  ...  This gives rise to a new notion of nominal unification, where solutions for unification problems are pairs of a fixed-point context and a substitution.  ...  Solving nominal C-unification problems via fixed-point constraints. In this section we propose an approach to nominal unification modulo commutativity via the notion of fixed-point constraints.  ... 
arXiv:1902.08345v4 fatcat:l3wpoq2xirgubpcwhddrxsdh7u

On Nominal Syntax and Permutation Fixed Points

Mauricio Ayala-Rincón, Maribel Fernández, Daniele Nantes-Sobrinho
2019 Logical Methods in Computer Science  
We propose a new axiomatisation of the alpha-equivalence relation for nominal terms, based on a primitive notion of fixed-point constraint.  ...  This gives rise to a new notion of nominal unification, where solutions for unification problems are pairs of a fixed-point context and a substitution.  ...  Solving nominal C-unification problems via fixed-point constraints. In this section we propose an approach to nominal unification modulo commutativity via the notion of fixed-point constraints.  ... 
doi:10.23638/lmcs-16(1:19)2020 fatcat:nxayfkgbvbeklitsv2rahbh3ga

Nominal Unification of Higher Order Expressions with Recursive Let [article]

Manfred Schmidt-Schauß and Temur Kutsia and Jordi Levy and Mateu Villaret
2016 arXiv   pre-print
We also explore specializations like nominal letrec-matching for plain expressions and for DAGs and determine the complexity of corresponding unification problems.  ...  A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time.  ...  Conclusion and Future Research We constructed a nominal letrec unification algorithm, several nominal letrec matching algorithms for variants, which all run in nondeterministic polynomial time.  ... 
arXiv:1608.03771v1 fatcat:igd5ptbomfdihfxmc3q6gbtila

Nominal Unification and Matching of Higher Order Expressions with Recursive Let [article]

Manfred Schmidt-Schauß and Temur Kutsia and Jordi Levy and Mateu Villaret and Yunus Kutz
2022 arXiv   pre-print
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in nondeterministic polynomial time.  ...  In addition we prove that there is a guessing strategy for nominal unification with letrec and atom-variable that is a trade-off between exponential growth and non-determinism.  ...  We omit failure rules, since these obviously follow from the nominal matching algorithm.  ... 
arXiv:2102.08146v4 fatcat:6m6lzbidl5fp5p27ut4csmafee

On Solving Nominal Disunification Constraints

Mauricio Ayala-Rincón, Maribel Fernández, Daniele Nantes-Sobrinho, Deivid Val
2020 Electronical Notes in Theoretical Computer Science  
In the nominal setting, unification problems consist of equational questions (s ≈α ? t) considered under freshness constraints (a# ?  ...  In addition to equational and freshness constraints, nominal disunification problems include also nominal disunification constraints (s ≈α ?  ...  with negated equations and apply our results to more general unification theories (for instance, AC and AC1-nominal unification problems).  ... 
doi:10.1016/j.entcs.2020.02.002 fatcat:emhxyw3vyfenvpheqnbrsgbb7a

Nominal logic programming

James Cheney, Christian Urban
2008 ACM Transactions on Programming Languages and Systems  
Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we  ...  Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence  ...  His support for me and this work has been unyielding. My other committee members, Robert Constable and Geri Gay, have also been very supportive.  ... 
doi:10.1145/1387673.1387675 fatcat:longqgnr75aktkwdy56eeyu4ne

Nominal Equational Problems [chapter]

Mauricio Ayala-Rincón, Maribel Fernández, Daniele Nantes-Sobrinho, Deivid Vale
2021 Lecture Notes in Computer Science  
_\alpha t$$ s ≈ α t , freshness constraints $$a\#t$$ a # t and their negations: $$s \not \approx _\alpha t$$ s ≉ α t and "Equation missing", where $$a$$ a is an atom and $$s, t$$ s , t nominal terms.  ...  With a particular strategy for rule application, the simplification process terminates and thus specifies an algorithm to solve nominal equational problems.  ...  As future work, we aim to investigate the purely equational approach to nominal syntax via the formulation of freshness constraints using fixed-point equations with the N-quantifier [21] , as well as  ... 
doi:10.1007/978-3-030-71995-1_2 fatcat:2mawpakhx5eanfleie67etcdpe

Constraint solving in non-permutative nominal abstract syntax

Matthew Lakin, Mitchell Wand
2011 Logical Methods in Computer Science  
In this paper we present a novel algorithm for solving constraints over a simple variant of nominal abstract syntax which we call non-permutative.  ...  Nominal abstract syntax is a popular first-order technique for encoding, and reasoning about, abstract syntax involving binders. Many of its applications involve constraint solving.  ...  Acknowledgements The author would like to thank Andrew Pitts for invaluable discussions on the subject matter of this paper, as well as Paul Blain Levy and an anonymous reviewer for help debugging proofs  ... 
doi:10.2168/lmcs-7(3:6)2011 fatcat:yyar7ud4uzbcdgbhft354dnpmq

A note on the interpretation and simulation of reparameterized intercepts in constrained versions of the nominal response model

Carl F. Falk
2021 The Quantitative Methods for Psychology  
This is a brief expository paper on reparameterized intercepts under constrained variants of the nominal response model, including the generalized partial credit and partial credit models.  ...  We give examples of how intercepts may be easily generated for Monte Carlo simulation studies, including a brief study to increase generalizability and explore limitations of a recently developed information  ...  These values are transformed into intercepts for calculation of Equation (2).  ... 
doi:10.20982/tqmp.17.4.p345 fatcat:73d74dpnifch3dtwbs3qhz7ueq

Update on the Pyramid Scheme

Tom Banks, T. J. Torres
2012 European Physical Journal C: Particles and Fields  
There are 3 different singlet fields, and a new strongly coupled gauge theory, so the constraints of perturbative unification are quite different.  ...  The models share much with the NMSSM, in particular, enhanced tree level contributions to the Higgs mass and a preference for small tan β.  ...  The F term equations for the fields L, B,B fix these fields in terms of M and leave over an M dependent superpotential gB +gB = 2 gg(M 3 − 1).  ... 
doi:10.1140/epjc/s10052-012-2185-9 fatcat:ava4epeqf5dlrgscqextitapu4

Monetary Union, Asymmetric Productivity Shocks and Fiscal Insurance: An Analytical Discussion of Welfare Issues

Kenneth M. Kletzer
1999 Social Science Research Network  
This paper argues that the benefits of fiscal insurance for allocative efficiency may be increased little by monetary unification.  ...  with resource allocation under a flexible nominal exchange rate regime.  ...  Equation 25 is derived by adding bonds nominally-indexed to each currency to the household budget constraint, equation 1.  ... 
doi:10.2139/ssrn.137333 fatcat:7adza6f2vrdlpap43rvepc4n6a

A Robust Fuzzy Optimization Model for Closed-Loop Supply Chain Networks Considering Sustainability

Xin Zhang, Gang Zhao, Yingxiu Qi, Botang Li
2019 Sustainability  
An efficient and effective supply chain network is of vital importance for improving customer satisfaction, optimizing the allocation of resources, and increasing profitability.  ...  The numerical example contains five candidate points for establishing plants, six candidate points for constructing distribution centers, 10 fixed customer points, five potential locations for collection  ...  Equation (33) is the carbon caps constraint.  ... 
doi:10.3390/su11205726 fatcat:htjcewqakjakthaop7o2yvbika

A Formalisation of Nominal α -equivalence with A and AC Function Symbols

Mauricio Ayala-Rincón, Washington de Carvalho-Segundo, Maribel Fernández, Daniele Nantes-Sobrinho
2017 Electronical Notes in Theoretical Computer Science  
This development is a first step towards verification of nominal matching, unification and narrowing algorithms modulo equational theories in general.  ...  A formalisation of soundness of the notion of α-equivalence in nominal abstract syntax modulo associative (A) and associative-commutative (AC) equational theories is described.  ...  Adequate manipulation of bound variables was a main motivation for the development of Nominal Logic [20] and other formal developments including, nominal unification [2, 9, 19, 25, 26] , that is, unification  ... 
doi:10.1016/j.entcs.2017.04.003 fatcat:ym72phsunrfizivtroo2khivgy

First-order unification using variable-free relational algebra

E. J. G. Arias, J. Lipton, J. Marino, P. Nogueira
2010 Logic Journal of the IGPL  
In this paper we adapt the framework and develop the missing piece, an algorithm for deciding equality constraint problems in the Herbrand domain, being this equivalent to the classical first-order unification  ...  Second, other constraint problems can be accommodated, for example, existential quantification in the logic can be interpreted as a new operation formalizing renaming apart.  ...  Acknowledgements We thank the anonymous referees for their insightful comments.  ... 
doi:10.1093/jigpal/jzq011 fatcat:mg7jrsa43zejlcjhb4oanwq4i4
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