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Context Unification and Traversal Equations
[chapter]

2001
*
Lecture Notes in Computer Science
*

This is done reducing

doi:10.1007/3-540-45127-7_14
fatcat:jgdadztljjaanhir4743jswy2e
*context**unification*to solvability of*traversal**equations*(a kind of word*unification*modulo certain permutations)*and*then, reducing*traversal**equations*to word*equations*with regular ...*Context**unification*was originally defined by H. Comon in ICALP'92, as the problem of finding a unifier for a set of*equations*containing first-order variables*and**context*variables. ... Bonet for her valuable comments*and*suggestions,*and*all the anonymous referees. ...##
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On the relation between Context and Sequence Unification

2010
*
Journal of symbolic computation
*

Both Sequence

doi:10.1016/j.jsc.2009.07.001
fatcat:kubunxx7czg5lmkk4a27hiycci
*and**Context**Unification*generalize the same problem: Word*Unification*. ...*Context**Unification*deals with the same problem for ranked terms involving*context*variables,*and*has applications in computational linguistics*and*program transformation. ... That proof was based on the use of*traversals*of terms,*and*on*traversal**equations*. These*traversal**equations*were reduced to word*equations*with regular constraints. ...##
###
Source-Tracking Unification
[chapter]

2003
*
Lecture Notes in Computer Science
*

Such a framework is useful for diagnosing

doi:10.1007/978-3-540-45085-6_39
fatcat:56ievgbgqnfcxhbo5hx56bd66m
*unification*-based systems, including debugging of type errors in programs*and*the generation of success*and*failure proofs in logic programming. ... We propose a path-based framework for deriving*and*simplifying source-tracking information for firstorder term*unification*in the empty theory. ... be*traversed*in either direction. ...##
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Source-tracking unification

2005
*
Information and Computation
*

Such a framework is useful for diagnosing

doi:10.1016/j.ic.2004.10.013
fatcat:sg4x4pzierg3tgrqefcq5bchce
*unification*-based systems, including debugging of type errors in programs*and*the generation of success*and*failure proofs in logic programming. ... We propose a path-based framework for deriving*and*simplifying source-tracking information for firstorder term*unification*in the empty theory. ... be*traversed*in either direction. ...##
###
Page 1309 of Mathematical Reviews Vol. , Issue 2003B
[page]

2003
*
Mathematical Reviews
*

This is done by reducing

*context**unification*to solvability of*traversal**equations*(a kind of word*unification*modulo certain permuta- tions),*and*then reducing*traversal**equations*to word*equations*with ... “In this paper, we prove that, if the so-called rank-bound conjec- ture is true, then the*context**unification*problem is decidable. ...##
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Page 4109 of Mathematical Reviews Vol. , Issue 94g
[page]

1994
*
Mathematical Reviews
*

Difference match- ing allows us to use rippling in other

*contexts*, e.g.,*equational*, inequational,*and*propositional reasoning. ... (D-MNCH; Munich)*Unification*in the union of disjoint*equational*theories: combining decision procedures. ...##
###
Traversable wormholes supported by cosmic accelerated expanding equations of state
[article]

2006
*
arXiv
*
pre-print

Chaplygin gas,

arXiv:gr-qc/0611150v1
fatcat:p4m54q6se5aofd65wkl6mi3lva
*and*the van der Waals quintessence*equation*of state. ... We explore the possibility that*traversable*wormholes be supported by specific*equations*of state responsible for the present accelerated expansion of the Universe, namely, phantom energy, the generalized ... [2] [3] [4] Secondly, the generalized Chaplygin gas (GCG) is a candidate for the*unification*of dark energy*and*dark matter,*and*is parametrized by an exotic*equation*of state given by p ch = −A/ρ α ...##
###
Page 22 of Computational Linguistics Vol. 26, Issue 4
[page]

2000
*
Computational Linguistics
*

Assuming instead that a recursive

*traversal*of the QLF is involved, then this particular*unification**equation*will be formed*and*solved entirely within the scope of the lambda binding x. ... john,y), but in this expression, y really is free*and*so we do not have a valid*equation*. ...##
###
Practical Higher-Order Pattern Unification with On-the-Fly Raising
[chapter]

2005
*
Lecture Notes in Computer Science
*

An important characteristic of such problems is that they are given by

doi:10.1007/11562931_28
fatcat:6tr7ribftjb4ppsvtfxsf4zvbq
*equations*appearing under a prefix of alternating universal*and*existential quantifiers. ... Higher-order pattern*unification*problems arise often in computations carried out within systems such as Twelf, λProlog*and*Isabelle. ... Acknowledgements This work began while the first author was on a sabbatical visit to the Protheo group at LORIA*and*INRIA, Nancy*and*the Comete*and*Parsifal groups at Ecole Polytechnique*and*INRIA, Saclay ...##
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TRAVERSABLE WORMHOLES SUPPORTED BY COSMIC ACCELERATED EXPANDING EQUATIONS OF STATE

2008
*
The Eleventh Marcel Grossmann Meeting
*

Chaplygin gas,

doi:10.1142/9789812834300_0359
fatcat:rlokxbxrvzfujlb3xu6d5hhkqu
*and*the van der Waals quintessence*equation*of state. ... We explore the possibility that*traversable*wormholes be supported by specific*equations*of state responsible for the present accelerated expansion of the Universe, namely, phantom energy, the generalized ... [2] [3] [4] Secondly, the generalized Chaplygin gas (GCG) is a candidate for the*unification*of dark energy*and*dark matter,*and*is parametrized by an exotic*equation*of state given by p ch = −A/ρ α ...##
###
Unification and Matching on Compressed Terms
[article]

2010
*
arXiv
*
pre-print

The present paper is the result of an investigation on term

arXiv:1003.1632v1
fatcat:wjvugw56y5g3vkpz6lmq2opctq
*unification**and*matching when the terms given as input are represented using different compression mechanisms for terms such as dags*and*Singleton ... For first-order*unification**and*matching polynomial time algorithms are presented, each of them improving previous results for those problems. ... The*context*matching problem is a particular case of*context**unification*where one of the sides of each*equation*in ∆ is ground. ...##
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Page 8490 of Mathematical Reviews Vol. , Issue 2002K
[page]

2002
*
Mathematical Reviews
*

programs (154-168); Jordi Levy

*and*Mateu Villaret,*Context*uni- fication*and**traversal**equations*(169-184); Sébastien Limet, Pierre Réty*and*Helmut Seidl, Weakly regular relations*and*applications (185 ... , Goal-directed E-*unification*(231-245); Michio Oyamaguchi*and*Yoshikatsu Ohta, The*unification*prob- lem for confluent right-ground term rewriting systems (246-260); Femke van Raamsdonk, On termination ...##
###
Processing Textbook-Style Matrices
[chapter]

2006
*
Lecture Notes in Computer Science
*

Given an underspecified matrix containing ellipses

doi:10.1007/11618027_8
fatcat:o4luat3vyvfvpl7lvesusxm4kq
*and*fill symbols, our algorithm extracts the semantic information contained. ... We present an algorithm that provides the interface between the textbook style representation of matrix expressions*and*their concrete interpretation as formal mathematical objects. ... Each edge in the graph will carry two weights: the horizontal cost of*traversing*the edge*and*the vertical cost of*traversing*it. ...##
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Linear Second-Order Unification and Context Unification with Tree-Regular Constraints
[chapter]

2000
*
Lecture Notes in Computer Science
*

Linear Second-Order Uni cation

doi:10.1007/10721975_11
fatcat:sjdoatbovvafhj2rgbm5kqv5z4
*and**Context*Uni cation are closely related problems. However, their equivalence was never formally proved. ... We comment on the possibility that linear second-order uni cation is decidable, if*context*uni cation is,*and*how to get rid of the tree-regular constraints. ... Bonet*and*all the anonymous referees for their helpful comments on the paper. ...##
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Optimizing Higher-Order Pattern Unification
[chapter]

2003
*
Lecture Notes in Computer Science
*

The presented modal framework explains a number of features of the current implementation of higher-order

doi:10.1007/978-3-540-45085-6_40
fatcat:t3c2cnvthrd7zfggww3kxrfsle
*unification*in Twelf*and*provides insight into several optimizations. ... This allows us to justify optimizations to pattern*unification*such as linearization, which eliminates many unnecessary occurs-checks. ... The main efficiency problem in pattern*unification*lies in treating this last case. In particular, we must*traverse*the term M . ...
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