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Extensional Rewriting with Sums
[chapter]
2007
Lecture Notes in Computer Science
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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
2015
International Conference on Typed Lambda Calculus and Applications
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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]
1994
Lecture Notes in Computer Science
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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]
2020
Lecture Notes in Computer Science
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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]
2010
Lecture Notes in Computer Science
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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
1996
Theoretical Computer Science
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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
2007
Journal of computer and system sciences (Print)
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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]
1999
Lecture Notes in Computer Science
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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
2011
Proceedings of the 2011 Joint EDBT/ICDT Ph.D. Workshop on - PhD '11
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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]
2004
arXiv
pre-print
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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
2015
2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
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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]
2015
arXiv
pre-print
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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
1986
Theoretical Computer Science
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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
2018
Science of Computer Programming
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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
1987
The Journal of Logic Programming
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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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