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Fixing Incremental Computation: Derivatives of Fixpoints, and the Recursive Semantics of Datalog [article]

Mario Alvarez-Picallo, Alex Eyers-Taylor, Michael Peyton Jones, C.-H. Luke Ong
2018 arXiv   pre-print
Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based  ...  This allows us to perform incremental evaluation and maintenance of recursively defined functions with particular application to generalised Datalog programs.  ...  for their helpful comments on the manuscript.  ... 
arXiv:1811.06069v2 fatcat:fpsi73onfnbx7aovg53vcs6paa

Fixing Incremental Computation [chapter]

Mario Alvarez-Picallo, Alex Eyers-Taylor, Michael Peyton Jones, C.-H. Luke Ong
2019 Lecture Notes in Computer Science  
Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based  ...  This allows us to perform incremental evaluation and maintenance of recursively defined functions with particular application generalised Datalog programs.  ...  Section 6.2 lets us extend our derivative for the non-recursive semantics to a derivative for the recursive semantics, as well as letting us compute the fixpoints themselves incrementally.  ... 
doi:10.1007/978-3-030-17184-1_19 fatcat:hecsgwvbkrg4xnj2p5fdyn34z4

codeQuest: Scalable Source Code Queries with Datalog [chapter]

Elnar Hajiyev, Mathieu Verbaere, Oege de Moor
2006 Lecture Notes in Computer Science  
It combines two previous proposals, namely the use of logic programming and database systems. As the query language we use safe Datalog, which was originally introduced in the theory of databases.  ...  That provides just the right level of expressiveness; in particular recursion is indispensable for source code queries.  ...  Members of the Programming Tools Group at Oxford provided helpful feedback at all stages of this research.  ... 
doi:10.1007/11785477_2 fatcat:brh6r2kbafg2bjtfosrqfdzxii

Convergence of Datalog over (Pre-) Semirings [article]

Mahmoud Abo Khamis, Hung Q. Ngo, Reinhard Pichler, Dan Suciu, Yisu Remy Wang
2022 arXiv   pre-print
We consider an ordered semiring, define the semantics of a datalog program as a least fixpoint in this semiring, and study the number of steps required to reach that fixpoint, if ever.  ...  But modern big data systems require recursive computations beyond the Boolean space. In this paper we study the convergence of datalog when it is interpreted over an arbitrary semiring.  ...  ACKNOWLEDGMENTS Suciu and Wang were partially supported by NSF IIS 1907997 and NSF IIS 1954222. Pichler was supported by the Austrian Science Fund (FWF):P30930.  ... 
arXiv:2105.14435v3 fatcat:itw4fbn5ljdizbbwbhz6tyx54e

A Step Up in Expressiveness of Decidable Fixpoint Logics

Michael Benedikt, Pierre Bourhis, Michael Vanden Boom
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
Using automata, we show that the resulting logics have a decidable satisfiability problem, and provide a fine study of the complexity of satisfiability.  ...  Here we show that one of the main restrictions imposed in the past can be lifted, getting a richer decidable logic by allowing fixpoints in which the parameters of the fixpoint can be unguarded.  ...  Fragments of Datalog Datalog is a syntax for expressing the negation-free fragment of least fixpoint logic. It is heavily used to express database queries that involve some form of recursion.  ... 
doi:10.1145/2933575.2933592 dblp:conf/lics/BenediktBB16 fatcat:iofilouplngydidnz42r5dkpt4

Reusing and Modifying Rulebases by Predicate Substitution

Anthony J Bonner, Tomasz Imielinski
1997 Journal of computer and system sciences (Print)  
We provide a proof theory and a model theory for this language, including a fixpoint semantics.  ...  In addition, we show that substitution increases the expressive power of Datalog: not only does its data complexity increase from PTIME to EXPTIME, but substitution also allows large sets of Datalog rules  ...  This section puts that semantics into a form that is computationally tractable, and in which the minimal model is always finite.  ... 
doi:10.1006/jcss.1997.1456 fatcat:co6p45yvufaktpfdobkizqvl44

Extending the power of datalog recursion

Mirjana Mazuran, Edoardo Serra, Carlo Zaniolo
2012 The VLDB journal  
This monotonic extension greatly enhances the power of Datalog, while preserving (i) its declarative semantics and (ii) its amenability to efficient implementation via differential fixpoint and other optimization  ...  In fact, using a generalized notion of multiplicity called frequency, we show that diffusion models and page rank computations can be easily expressed and efficiently implemented using Datalog F S .  ...  the fixpoint operator, and in the first line, we have all 1s because the baseline is fixed to 1.  ... 
doi:10.1007/s00778-012-0299-1 fatcat:mf2jbhemqjaateedxvffa5njja

Incrementalizing lattice-based program analyses in Datalog

Tamás Szabó, Gábor Bergmann, Sebastian Erdweg, Markus Voelter
2018 Proceedings of the ACM on Programming Languages (PACMPL)  
To this end, we present a novel algorithm called DRed L that supports incremental maintenance of recursive lattice-value aggregation in Datalog.  ...  However, Datalog and other existing frameworks for incremental program analysis are limited in expressive power: They only support the powerset lattice as representation of analysis results, whereas many  ...  The second author was supported by the Hungarian Academy of Sciences, under grant LP2015-12 (http://mta.hu/lendulet) Lendület 2015 Research Group on Cyber-Physical Systems, and under the János Bolyai Research  ... 
doi:10.1145/3276509 fatcat:y4vhdozibrg4bl2memt76frhma

Semantics and Expressiveness Issues in Active Databases

Philippe Picouet, Victor Vianu
1998 Journal of computer and system sciences (Print)  
A formal framework is introduced for studying the semantics and expressiveness of active databases.  ...  Many thanks to Richard Hull, Eric Simon, and Jennifer Widom for very thorough and insightful comments on a draft of this paper.  ...  Acknowledgement: We thank Richard Hull for discussions on Heraclitus, and Eric Simon for discussions on ARDL and other active database systems.  ... 
doi:10.1006/jcss.1998.1567 fatcat:zweld73ibnetzhmgizhduajh44

Maintenance of Recursive Views [chapter]

Suzanne W. Dietrich
2017 Encyclopedia of Database Systems  
Without negation, a recursive Datalog program has a unique solution that corresponds to the theoretical fixpoint semantics or meaning of the logical specification.  ...  The view instance has reached a fixed point and will not change. When negation is introduced, the interaction of recursion and negation must be considered.  ...  As shown on the above deletion example, the DRed and PF algorithms both compute overestimates or approximations of tuples to be deleted from the recursive materialized view.  ... 
doi:10.1007/978-1-4899-7993-3_842-2 fatcat:fbblwrhi6ndjpdh75nbxr2x4nq

Formal semantics and high performance in declarative machine learning using Datalog

Jin Wang, Jiacheng Wu, Mingda Li, Jiaqi Gu, Ariyam Das, Carlo Zaniolo
2021 The VLDB journal  
We further provide specialized compilation and planning techniques for semi-naive fixpoint computation in the presence of aggregates and optimization strategies that are effective on diverse recursive  ...  This is achieved by introducing simple conditions under which the semantics of recursive programs is guaranteed to be equivalent to that of aggregate-stratified ones.  ...  as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.  ... 
doi:10.1007/s00778-021-00665-6 fatcat:v7pautergnevtovm2ff7zhobse

Change actions: from incremental computation to discrete derivatives [article]

Mario Alvarez-Picallo
2020 arXiv   pre-print
The goal of this thesis is threefold: first, to provide a general semantic setting for reasoning about incremental computation.  ...  Second, to establish and clarify the connection between derivatives in the incremental sense and derivatives in the analytic sense, that is to say, to provide a common definition of derivative of which  ...  Section 4.5.2 lets us extend our derivative for the non-recursive semantics to a derivative for the recursive semantics, as well as letting us compute the fixed points themselves incrementally.  ... 
arXiv:2002.05256v2 fatcat:o6zzymbz5rcgbgamuqve2fkyou

Nondeterministic, nonmonotonic logic databases

F. Giannotti, G. Manco, M. Nanni, D. Pedreschi
2001 IEEE Transactions on Knowledge and Data Engineering  
Also, we show how iterated fixpoint and stable model semantics can be combined to the purpose of clarifying the semantics of Datalog++ programs and supporting their efficient execution.  ...  AbstractÐWe consider in this paper an extension of Datalog with mechanisms for temporal, nonmonotonic, and nondeterministic reasoning, which we refer to as Datalog++.  ...  ACKNOWLEDGMENTS This paper is a revised, extended version of two extended abstracts [9] , [14] .  ... 
doi:10.1109/69.956102 fatcat:6pok6sdya5b7hmcv3egvihtxca

Hypothetical datalog: complexity and expressibility

Anthony J. Bonner
1990 Theoretical Computer Science  
One way to view this algorith is as a recursive procedure in which bottom-u fixpoint computations ccaar at each level of recursion. t each recursive rocedure applies the r ase to a differe olynomially  ...  many i;vels recursion and eat re computation runs in po~~~orn~~ w order to establis nds for the full logic of itions and deletions otion of Yb 'dase ~~t~~~~et~t~~n h T-operator.  ...  literals are computed, and the next fixpoint computation is begun.  ... 
doi:10.1016/0304-3975(90)90011-6 fatcat:v5hrycvxhbbifcoyxvhmczbyri

Win-move is coordination-free (sometimes)

Daniel Zinn, Todd J. Green, Bertram Ludäscher
2012 Proceedings of the 15th International Conference on Database Theory - ICDT '12  
In a recent paper by Hellerstein [15], a tight relationship was conjectured between the number of strata of a Datalog^ program and the number of "coordination stages" required for its distributed computation  ...  We show the surprising result that the query given by the well-founded semantics of the unstratifiable win-move program is coordination-free in some of the models we consider.  ...  to the number of rounds of the alternating fixpoint computation [14] , i.e., the number of coordination barriers would no longer be fixed for a given program (as for stratified Datalog ¬ ) but instead  ... 
doi:10.1145/2274576.2274588 dblp:conf/icdt/ZinnGL12 fatcat:dtdthuubtjbjhmuel7limzjjua
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