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Extensional Rewriting with Sums [chapter]

Sam Lindley
2007 Lecture Notes in Computer Science  
Inspired by recent work on normalisation by evaluation for sums, we propose a normalising and confluent extensional rewriting theory for the simply-typed λ-calculus extended with sum types.  ...  As a corollary of confluence we obtain decidability for the extensional equational theory of simply-typed λ-calculus extended with sum types.  ...  We have proposed a confluent extensional rewriting theory for simply-typed lambda-calculus extended with sums. The key contribution is confluence and decidability for a conventional rewriting theory.  ... 
doi:10.1007/978-3-540-73228-0_19 fatcat:ie6kqmgtn5cprkpishzdu3wtdq

Multi-Focusing on Extensional Rewriting with Sums

Gabriel Scherer, Marc Herbstritt
2015 International Conference on Typed Lambda Calculus and Applications  
We propose a logical justification for the rewriting-based equivalence procedure for simply-typed lambda-terms with sums of Lindley [Lin07].  ...  Lindley's rewriting closely corresponds to preemptive rewriting [CMS08], a technical device used in the meta-theory of maximal multi-focus.  ...  Extensional rewriting with sums. In TLCA, pages 255-271, 2007. MS07 Dale Miller and Alexis Saurin. From proofs to focused proofs: A modular proof of focalization in linear logic.  ... 
doi:10.4230/lipics.tlca.2015.317 dblp:conf/tlca/Scherer15 fatcat:epwdawnvgjhxpojczyrb56cqq4

Combining first order algebraic rewriting systems, recursion and extensional lambda calculi [chapter]

Roberto Cosmo, Delia Kesner
1994 Lecture Notes in Computer Science  
We show that con uence and normalization are modular properties for the combination of left-linear algebraic rewriting systems with typed lambda calculi enriched with expansive extensional rules for and  ...  It is well known that con uence and strong normalization are preserved when combining left-linear algebraic rewriting systems with the simply typed lambda calculus.  ...  rewriting system (but this simple observation does not hold in the presence of conditional rules).  ... 
doi:10.1007/3-540-58201-0_90 fatcat:a3s3jyrjbrggzhu22f73vcz4ve

Deciding the Word Problem for Ground Identities with Commutative and Extensional Symbols [chapter]

Franz Baader, Deepak Kapur
2020 Lecture Notes in Computer Science  
In addition, we investigate a variant of extensionality that is more appropriate for commutative function symbols, but which raises the complexity of the word problem to coNP.  ...  We show that decidability in P is preserved if we also assume that certain function symbols f are extensional in the sense that f (s1, . . . , sn) ≈ f (t1, . . . , tn) implies s1 ≈ t1, . . . , sn ≈ tn.  ...  Our goal is, however, to deal both with the ground identities in E and with commutativity by rewriting.  ... 
doi:10.1007/978-3-030-51074-9_10 fatcat:7o3g6hd3wvejzbelngkci4dzyq

Inductive Consequences in the Calculus of Constructions [chapter]

Daria Walukiewicz-Chrząszcz, Jacek Chrząszcz
2010 Lecture Notes in Computer Science  
Extending the calculus of constructions with rewriting would greatly improve the efficiency of proof assistants such as Coq.  ...  However the positive answer can be recovered when the notion of inductive consequences is modified by allowing a certain form of functional extensionality.  ...  Fortunately, the sum of the constructor subterm with the rewrite relation generated by rules accepted by HORPO is always well-founded [17] .  ... 
doi:10.1007/978-3-642-14052-5_31 fatcat:u7kk462xend3tb3q3tcntf74r4

Combining algebraic rewriting, extensional lambda calculi, and fixpoints

Roberto Di Cosmo, Delia Kesner
1996 Theoretical Computer Science  
We show that confluence and strong normalization are modular properties for the combination of algebraic rewriting systems with typed lambda calculi enriched with expansive extensional rules for q and  ...  It is well known that confluence and strong normalization are preserved when combining algebraic rewriting systems with the simply typed lambda calculus.  ...  We have also shown how to deal in full generality with fixpoint combinators: confluence is preserved under very permissive hypotheses, so that for many interesting calculi it is now possible to focus on  ... 
doi:10.1016/s0304-3975(96)00121-1 fatcat:3wj6hg4vobfxzoxumonlv3gvva

View disassembly: A rewrite that extracts portions of views

Parke Godfrey, Jarek Gryz
2007 Journal of computer and system sciences (Print)  
The problem is NP-hard with respect to the number of unfoldings to remove, but not with respect to the size (complexity) of the view definition.  ...  Furthermore, we show that these cover-completion rewrites are preferable to absolutely optimal rewrites in many ways.  ...  We call such a rewrite a globally optimal rewrite, since it is smallest with respect to all possible rewrites.  ... 
doi:10.1016/j.jcss.2007.03.002 fatcat:pjkwsxg7cvgmfenkapjs4wz5tq

View Disassembly [chapter]

Parke Godfrey, Jarek Gryz
1999 Lecture Notes in Computer Science  
We explore a new form of view rewrite called view disassembly. The objective is to rewrite views in order to \remove" certain sub-views (or unfoldings) of the view.  ...  We show that the optimal rewrites for disassembled views is at least NP-hard. However, we provide good news too. We provide an approximation algorithm that has much better run-time behavior.  ...  However, this rewrite is not compact; in fact, there can be an exponential number of extensional unfoldings with respect to the size of the view's AND/OR tree.  ... 
doi:10.1007/3-540-49257-7_26 fatcat:6nyabyym7jgxlejmsu5zuzvsvi

Access control to materialized views

Sarah Nait Bahloul, Emmanuel Coquery, Mohand-Saïd Hacid
2011 Proceedings of the 2011 Joint EDBT/ICDT Ph.D. Workshop on - PhD '11  
In this context, issues related to confidentiality, integrity and availability of the data arise with a crucial importance, whether in economic, legal or medical domains.  ...  We are investigating this problem by resorting to an adaptation of query rewriting techniques. We choose to express fine-grained access control through authorization views.  ...  ., sum of sales). This framework should also be extended to accommodate materialized views with aggregate functions.  ... 
doi:10.1145/1966874.1966878 dblp:conf/edbt/BahloulCH11 fatcat:uiy2qhimtndgzceiyupwfexgum

ΣΠ-polycategories, additive linear logic, and process semantics [article]

C. A. Pastro
2004 arXiv   pre-print
Poly-sums and poly-products The purpose of this section is to show that the polycategory EP A has sums and products. We begin by defining sums and products of extensional processes.  ...  We will now work with the sum; the dual properties hold for the product. Note that it still must be shown that what we have defined as the "sum" is actually a sum.  ...  The dual rewrite, if there is one, is indicated in (1)-(2) obvious.  ... 
arXiv:math/0312422v2 fatcat:ydfkknc6qrdunb3dl5nxw3dqga

Polarised Intermediate Representation of Lambda Calculus with Sums

Guillaume Munch-Maccagnoni, Gabriel Scherer
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
The theory of the -calculus with extensional sums is more complex than with only pairs and functions.  ...  As an application, we can deduce a syntax-directed algorithm to decide the equivalence of normal forms in the simplytyped -calculus with sums, and justify it with our intermediate calculus.  ...  extensional sums.  ... 
doi:10.1109/lics.2015.22 dblp:conf/lics/Munch-Maccagnoni15 fatcat:rsuvx3pj35ec3of7xax5nzuv4e

Category Theory in Coq 8.5 [article]

Amin Timany, Bart Jacobs
2015 arXiv   pre-print
of rewrite.  ...  Although dualities behave nicely (in the aforemen-tioned sense), working with dual definitions is not always as smooth. This is especially evident in rewriting equalities.  ... 
arXiv:1505.06430v1 fatcat:tfwf2q2jzfbh3l6ejez3icjz7u

Partial evaluation and ω-completeness of algebraic specifications

Jan Heering
1986 Theoretical Computer Science  
Suppose P(x, y) is a program with two arguments, whose first argument has a known value c, but whose second argument is not yet known.  ...  evaluation amounts to 'making maximal use of incomplete information'., In this paper a precise meaning is given to this notion in the context of equational logic, initial algebra specification, and term rewriting  ...  Acknowledgment While writing this paper we had helpful discussions with Jan Bergstra, Paul Klint, Jan Willem Klop, and Ed Kuijpers.  ... 
doi:10.1016/0304-3975(86)90173-8 fatcat:65upbig66vbpdoph6y4qzburvq

Encoding TLA + into unsorted and many-sorted first-order logic

Stephan Merz, Hernán Vanzetto
2018 Science of Computer Programming  
The translation, based on encoding techniques such as boolification, injection of unsorted expressions into sorted languages, term rewriting, and abstraction, is the core component of a back-end prover  ...  In short, termination depends on the existence of extensionality rewriting rules for each kind of non-basic expression that abstract may catch.  ...  We define the embedding µ of an expression e as the sum of the coefficients W(e| p ) for every position p in e: µ(e) ∆ = W(e| 1 ) + . . . + W(e| n ).  ... 
doi:10.1016/j.scico.2017.09.004 fatcat:fvibuppmabaaxe6jebvjddkq24

Logic programming and digital circuit analysis

W.F. Clocksin
1987 The Journal of Logic Programming  
Our annealing schedule is to alternate (phase-l) rewrites at any cost with (phase-2) rewrites at strictly decreasing cost.  ...  The modules and connections of a circuit are represented extensionally, with no syntactic relationship between them.  ... 
doi:10.1016/0743-1066(87)90022-7 fatcat:eb33rt2za5g47f2nt5ww4xv33i
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