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Fixed-Point Constraints for Nominal Equational Unification
2018
International Conference on Rewriting Techniques and Applications
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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]
2020
arXiv
pre-print
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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
2019
Logical Methods in Computer Science
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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]
2016
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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
2020
Electronical Notes in Theoretical Computer Science
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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
2008
ACM Transactions on Programming Languages and Systems
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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]
2021
Lecture Notes in Computer Science
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_\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
2011
Logical Methods in Computer Science
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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
2021
The Quantitative Methods for Psychology
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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
2012
European Physical Journal C: Particles and Fields
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2012 pre-print arXiv:1205.3073v1 fatcat:b4o2ggveg5a4bessf65k4fhjeu
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
1999
Social Science Research Network
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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
2019
Sustainability
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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
2017
Electronical Notes in Theoretical Computer Science
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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
2010
Logic Journal of the IGPL
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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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