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Projections for infinitary rewriting [article]

Carlos Lombardi, Alejandro Ríos, Roel de Vrijer
2016 arXiv   pre-print
We extend this characterisation to infinitary rewriting and also refine it, by describing precisely the role that structural equivalence plays in the development of the notion of projection.  ...  Again, the foundation is a characterisation of projections for finitary rewriting described in Terese, Section 8.7.  ...  Results and discussion We give a definition of projections for infinitary rewriting, which extends and refines that given in [15] for the finitary case.  ... 
arXiv:1605.07808v2 fatcat:qpbljrsylzbdlp7oduoirhi7iy

Relating Structure and Power: Extended Version [article]

Samson Abramsky, Nihil Shah
2021 arXiv   pre-print
depth for the modal unfolding comonad.  ...  Moreover, the coalgebras for these indexed comonads can be used to characterize key combinatorial parameters: tree-depth for the Ehrenfeucht-Fraisse comonad, tree-width for the pebbling comonad, and synchronization-tree  ...  For all finite structures A, B, A → B iff B |= Q A . We now consider a number of rewrite rules on formulas: (R1) Associative-Commutative-Identity rewriting of conjunctions (R2) ∃v.  ... 
arXiv:2010.06496v7 fatcat:gx35xqxu2nb6dllwb52vxyf73q

Gradual Type Theory (Extended Version) [article]

Max S. New, Daniel R. Licata, Amal Ahmed
2018 arXiv   pre-print
For example, uniqueness principles for gradual type connectives show that if the βη laws hold for a connective, then casts between that connective must be equivalent to the lazy cast semantics.  ...  While existing gradual type soundness theorems for these languages aim to show that type-based reasoning is preserved when moving from the fully static setting to a gradual one, these theorems do not imply  ...  We thank Ron Garcia, Kenji Maillard and Gabriel Scherer for helpful discussions about this work. We thank the anonymous reviewers for helpful feedback on this article.  ... 
arXiv:1811.02440v1 fatcat:6vp4p5xmm5c2hhxpfcuyjch22e

From Symmetric Pattern-Matching to Quantum Control (Extended Version) [article]

Amr Sabry and Benoît Valiron and Juliana Kaizer Vizzotto
2018 arXiv   pre-print
We additionally give an operational semantics for the quantum language in the spirit of algebraic lambda-calculi and illustrate its expressiveness by modeling several common unitary operations.  ...  We then extend this language to the closed quantum domain (without measurements) by allowing linear combinations of terms and restricting fixpoints to structurally recursive fixpoints whose termination  ...  This technical report is an extended version of a paper accepted for publication in the proceedings of FoSSaCS'18 [17] .  ... 
arXiv:1804.00952v1 fatcat:6vqoeruysjdl3j22ycrcxbxogm

Interpolation and Amalgamation for Arrays with MaxDiff (Extended Version) [article]

Silvio Ghilardi and Alessandro Gianola and Deepak Kapur
2021 arXiv   pre-print
It is known from the literature that a diff operation is required for the theory of arrays in order to enjoy the Craig interpolation property at the quantifier-free level.  ...  Our maxdiff operation significantly increases the level of expressivity; however, obtaining interpolation results for the resulting theory becomes a surprisingly hard task.  ...  This project implements an interpolation algorithm for the theory of arrays extended with the diff operator by computing a reduction from the ARD theory to the theory of T O ∪ EUF and calling an interpolation  ... 
arXiv:2010.07082v2 fatcat:hww3ty45ezb5fcugezxaz7ek4i

Verification of Generalized Inconsistency-Aware Knowledge and Action Bases (Extended Version) [article]

Diego Calvanese, Marco Montali, Ario Santoso
2015 arXiv   pre-print
for standard KABs.  ...  Recently, KABs have been extended to manage inconsistency, with ad-hoc verification techniques geared towards specific semantics.  ...  FP7-318338, and by the UNIBZ internal project KENDO (Knowledge-driven ENterprise Distributed cOmputing).  ... 
arXiv:1504.08108v2 fatcat:cn44vyecfjdkxnv66krr7xipeq

Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory (Extended Version) [article]

Yannick Forster, Dominik Kirst, Dominik Wehr
2020 arXiv   pre-print
We contribute a reusable Coq library for first-order logic containing all results covered in this paper.  ...  Section Specification In general, we find that Coq provides the ideal grounds for mechanising projects like ours.  ...  Autosubst could of course be extended with a mode using setoid rewriting instead of appealing to functional extensionality, and if willing to waive the tool support, one can manually mechanise first-order  ... 
arXiv:2006.04399v1 fatcat:bhlqgibfbrborl6nkicbwjaibu

Unique Normal Forms in Infinitary Weakly Orthogonal Rewriting

Joerg Endrullis, Clemens Grabmayer, Dimitri Hendriks, Jan Willem Klop, Vincent Van Oostrom, Marc Herbstritt
2010 International Conference on Rewriting Techniques and Applications  
We present some contributions to the theory of infinitary rewriting for weakly orthogonal term rewrite systems, in which critical pairs may occur provided they are trivial.  ...  By translating this example, we show that UN ∞ also fails for the infinitary λβη-calculus.  ...  for orthogonal infinite CRSs require fully-extendedness, see [4] .  ... 
doi:10.4230/lipics.rta.2010.85 dblp:conf/rta/EndrullisGHKO10 fatcat:on4p6o7evjbzzhrbwvzr2hb27i

Extended term rewriting systems [chapter]

Jan Willem Klop, Roel Vrijer
1991 Lecture Notes in Computer Science  
In this paper we will consider some extensions of the usual term rewrite format, namely: term rewriting with conditions, infmi~y term rewriting and term rewriting with bound variables.  ...  We thank Aart Middeldorp and Vincent van Oostrom for carefully reading the manuscript and suggesting improvements.  ...  Discussions with Fer-Jan de Vries, who pointed out some shortcomings in an earlier version concerning Section 1, are gratefully acknowledged.  ... 
doi:10.1007/3-540-54317-1_79 fatcat:g7vqrgyaafabtgesdd2mvgihnq

On the adequacy of graph rewriting for simulating term rewriting

J. R. Kennaway, J. W. Klop, M. R. Sleep, F. J. de Vries
1994 ACM Transactions on Programming Languages and Systems  
Neither proof extends immediately to the infinitary case.  ...  There- fore, we seek to formulate a restricted version of infinitary term rewriting for which the unraveling of finite cyclic graph rewrite systems will yield an adequate mapping.  ...  Adequacy can therefore be expected to hold only for orthogonal systems of rewrite rules which are Church-l? osser for transfinite term reduction, that is, the almost noncollapsing systems.  ... 
doi:10.1145/177492.177577 fatcat:7eyaob6drfh3tkukuinorwzauy

Infinitary Combinatory Reduction Systems

Jeroen Ketema, Jakob Grue Simonsen
2011 Information and Computation  
In particular, for fully-extended, left-linear iCRSs we prove the well-known compression property, and for orthogonal iCRSs we prove that (1) if a set of redexes U has a complete development, then all  ...  We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting.  ...  Acknowledgments The authors extend their thanks to the anonymous referees for their diligent work and many comments that have led to substantial improvements in the readability of the paper.  ... 
doi:10.1016/j.ic.2011.01.007 fatcat:b54kclljc5fc5kxqpndfahjgea

Highlights in infinitary rewriting and lambda calculus

Jörg Endrullis, Dimitri Hendriks, Jan Willem Klop
2012 Theoretical Computer Science  
We present some highlights from the emerging theory of infinitary rewriting, both for first-order term rewriting systems and λ-calculus.  ...  In the first section we introduce the framework of infinitary rewriting for first-order rewrite systems, so without bound variables.  ...  The generalisation of PML to its infinitary version PML ∞ is straightforward.  ... 
doi:10.1016/j.tcs.2012.08.018 fatcat:ulhkxwoambaj3pjimztxxlz6jm

Infinitary Combinatory Reduction Systems [chapter]

Jeroen Ketema, Jakob Grue Simonsen
2005 Lecture Notes in Computer Science  
In particular, for fully-extended, left-linear iCRSs we prove the well-known compression property, and for orthogonal iCRSs we prove that (1) if a set of redexes U has a complete development, then all  ...  We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting.  ...  Acknowledgments The authors extend their thanks to the anonymous referees for their diligent work and many comments that have led to substantial improvements in the readability of the paper.  ... 
doi:10.1007/978-3-540-32033-3_32 fatcat:utgdfhexefhyhnl2yftwei5uqy

Unique Normal Forms in Infinitary Weakly Orthogonal Term Rewriting [article]

Joerg Endrullis, Clemens Grabmayer, Dimitri Hendriks, Jan Willem Klop
2009 arXiv   pre-print
The theory of finite and infinitary term rewriting is extensively developed for orthogonal rewrite systems, but to a lesser degree for weakly orthogonal rewrite systems.  ...  We start with a refinement of the by now classical Compression Lemma, as a tool for establishing infinitary confluence, and hence the property of unique infinitary normal forms, for the case of weakly  ...  We want to thank Vincent van Oostrom for many helpful remarks and pointers to work on weakly orthogonal TRSs.  ... 
arXiv:0911.1009v1 fatcat:hbtdceo5xjc3tarn6ucg6uuehy

Infinitary Term Rewriting for Weakly Orthogonal Systems: Properties and Counterexamples

Jörg Endrullis, Clemens Grabmayer, Dimitri Hendriks, Jan Willem Klop, Vincent Oostrom, Christopher Lynch
2014 Logical Methods in Computer Science  
We present some contributions to the theory of infinitary rewriting for weakly orthogonal term rewrite systems, in which critical pairs may occur provided they are trivial.  ...  By translating this example, we show that this property also fails for the infinitary lambda-beta-eta-calculus.  ...  Introduction While the theory of infinitary term rewriting is well-developed for orthogonal rewrite systems, much less is known about infinitary rewriting in non-orthogonal systems, in which critical pairs  ... 
doi:10.2168/lmcs-10(2:7)2014 fatcat:d37jizefc5envdltvbou7tfuim
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