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A Rewriting Logic Approach to Type Inference [chapter]

Chucky Ellison, Traian Florin Şerbănuţă, Grigore Roşu
2009 Lecture Notes in Computer Science  
The proposed approach is exemplified by defining the Hindley-Milner polymorphic type inferencer W as a rewrite logic theory and using this definition to obtain a type inferencer by executing it in a rewriting  ...  Meseguer and Ros , u proposed rewriting logic semantics (RLS) as a programing language definitional framework that unifies operational and algebraic denotational semantics.  ...  In contrast to term rewriting, which is just a method of computation, rewriting logic is a computational logic built upon equational logic, proposed by Meseguer [25] as a logic for true concurrency.  ... 
doi:10.1007/978-3-642-03429-9_10 fatcat:v5zmfibm5jerhpmxtcw4xn6hgq

Rewriting, Inference, and Proof [chapter]

Natarajan Shankar
2010 Lecture Notes in Computer Science  
We discuss a range of issues at the intersection of rewriting and inference. How can other inference procedures be combined with rewriting? Can rewriting be used to describe inference procedures?  ...  We discuss these problems in the context of our ongoing effort to use PVS as a metatheoretic framework to construct a proof kernel for justifying the claims of theorem provers, rewriters, model checkers  ...  Inference systems can be represented using rewriting logic.  ... 
doi:10.1007/978-3-642-16310-4_1 fatcat:vqoukc27wnhtrdsvcr2hymspt4

Static type inference in a dynamically typed language

Alex Aiken, Brian Murphy
1991 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '91  
We use a non-standard approach to type inference because our requirements|using type information in the optimization of functional programs|di er substantially from those of other type systems.  ...  The essential elements of the system are a type language based on regular trees and a type inference logic that implements an abstract interpretation of the operational semantics of FL.  ...  It is also a pleasure to thank Carl Gunter, John Mitchell, Uday Reddy, Moshe Vardi, Jennifer Widom, John Williams, and Ed Wimmers for their comments on earlier versions of this paper.  ... 
doi:10.1145/99583.99621 dblp:conf/popl/AikenM91 fatcat:rirdu7zptzf75k5m7zndjryvdy

Pure Type Systems in Rewriting Logic: Specifying Typed Higher-Order Languages in a First-Order Logical Framework [chapter]

Mark-Oliver Stehr, José Meseguer
2004 Lecture Notes in Computer Science  
Furthermore, we use rewriting logic itself to give a formal operational description of type checking, that directly serves as an efficient type checking algorithm.  ...  More precisely, we apply membership equational logic, the equational sublogic of rewriting logic, to specify pure type systems as they can be found in the literature and also a new variant of pure type  ...  Acknowledgements Support for this work by DARPA and NASA (Contract NAS2-98073), by Office of Naval Research (Contract N00014-96-C-0114), by National Science Foundation Grant (CCR-9633363), and by a DAAD  ... 
doi:10.1007/978-3-540-39993-3_16 fatcat:67pi5kbczbae3iqakokze2j4t4


Leo Bachmair, Jieh Hsiang
1991 Journal of symbolic computation  
Another completion-based approach, to first-order theorem proving, uses a convergent rewrite system for Boolean expressions to convert first-order formulas into a normal form based on conjunction and exclusive  ...  For instance, reduction orderings, a key concept in term rewriting, have been used to develop improved versions, both in terms of efficiency and completeness, of resolution/paramodulation type deduction  ...  For researchers interested in other aspects of rewriting and its applications, we recommend the survey, Rewrite Systems by N. Dershowitz and J.-P.  ... 
doi:10.1016/s0747-7171(08)80129-0 fatcat:524cajbdfze73njq3r7nknovmy

MetaPRL – A Modular Logical Environment [chapter]

Jason Hickey, Aleksey Nogin, Robert L. Constable, Brian E. Aydemir, Eli Barzilay, Yegor Bryukhov, Richard Eaton, Adam Granicz, Alexei Kopylov, Christoph Kreitz, Vladimir N. Krupski, Lori Lorigo (+3 others)
2003 Lecture Notes in Computer Science  
The MetaPRL system combines the properties of an interactive LCF-style tactic-based proof assistant, a logical framework, a logical programming environment, and a formal methods programming toolkit.  ...  MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group.  ...  Figure 1 ( A ) A Syntax definitions define the language of a logic. (B) Inference rules define the primitive inferences of a logic.  ... 
doi:10.1007/10930755_19 fatcat:nker4ros75gvzpadxblbenbsky

Special issue on structural operational semantics

Rob van Glabbeek, Peter D. Mosses
2009 Information and Computation  
to a given semantic equivalence, are ensured.  ...  It also contains papers about the SOS of programming languages, focussing on bialgebraic semantics, co-inductive and bi-inductive forms of big-step SOS, the relationship to rewriting logic semantics, and  ...  A rewriting logic approach to operational semantics, by Traian FlorinŞerbȃnu¸tȃ, Grigore Rosu and José Meseguer, shows how rewriting logic semantics can be used as a computational logic framework for semantic  ... 
doi:10.1016/j.ic.2008.10.006 fatcat:gf7cgan5t5hpdflmz7b3vmhxmi

Reconstruction of Z3's Bit-Vector Proofs in HOL4 and Isabelle/HOL [chapter]

Sascha Böhme, Anthony C. J. Fox, Thomas Sewell, Tjark Weber
2011 Lecture Notes in Computer Science  
The authors are grateful to Nikolaj Bjørner and Leonardo de Moura for their help with Z3.  ...  For rewrite, we first try a simplification-based approach, expressing many word operations in terms of !!  ...  Theorems are implemented as an abstract data type, and the only way to construct new theorems is through a fixed set of functions (corresponding to the underlying logic's axiom schemata and inference rules  ... 
doi:10.1007/978-3-642-25379-9_15 fatcat:gesxkp2cm5girliosyngzyuwmi

Effective theorem proving for hardware verification [chapter]

D. Cyrluk, S. Rajan, N. Shankar, M. K. Srivas
1995 Lecture Notes in Computer Science  
We describe an approach for enhancing the effectiveness of theorem provers for hardware verification through the use of efficient automatic procedures for rewriting, arithmetic and equality reasoning,  ...  This approach is contrasted with approaches based on tactics or batch-oriented theorem proving.  ...  Sam Owre answered a number of questions regarding PVS and also proofread the paper.  ... 
doi:10.1007/3-540-59047-1_50 fatcat:zwwryahpejavfleqthleuefjjq

Maude as a formal meta-tool [chapter]

M. Clavel, F. Durán, S. Eker, J. Meseguer, M. O. Stehr
1999 Lecture Notes in Computer Science  
This paper explains how the reflective logical framework of rewriting logic can be used, in conjunction with an efficient reflective implementation such as the Maude language, to design formal meta-tools  ...  These challenges could be answered by adequate formal meta-tools that, when given the specification of a formal inference system, generate an efficient inference engine, and when given a specification  ...  to Rewriting Logic, all of which are important experiments discussed in this paper.  ... 
doi:10.1007/3-540-48118-4_39 fatcat:fefrfcvcafb2lih3jqxqudyacm

Equational Logic and Rewriting [chapter]

Claude Kirchner, Hélène Kirchner
2014 Handbook of the History of Logic  
Handbook-History-Logic-Computation-EquationalLogic Handbook-History-Logic-Computation-Rewriting  ...  approaches: • From 1935 to 1970, the theory and model settings main period, studying equational logics and their models, with the development of data types and algebraic specification languages; • From  ...  Since rewriting logic is reflective, strategy semantics can be defined inside the rewriting logic by rewrite rules at the meta-level. This is the approach followed by Maude in [32, 112] .  ... 
doi:10.1016/b978-0-444-51624-4.50006-x fatcat:eqtvr66m65eula7otl7fr6ppaa

Proof Certificates for Equality Reasoning

Zakaria Chihani, Dale Miller
2016 Electronical Notes in Theoretical Computer Science  
We shall illustrate the flexibility of this approach by showing how to formally define (and check) rewriting proofs of a variety of designs.  ...  The kinds of inference rules and decision procedures that one writes for proofs involving equality and rewriting are rather different from proofs that one might write in first-order logic using, say, sequent  ...  We choose this latter approach to equality in this paper.  ... 
doi:10.1016/j.entcs.2016.06.007 fatcat:kl3wk3vzoffsllajv2b72ub5bq

Page 2921 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
The goal of this paper is to provide a relatively gentle introduction to rewriting logic, and to paint in broad strokes the main research di- rections that have been pursued since its introduction in 1990  ...  Because of this ecumenical neutrality, rewriting logic has, from a logical viewpoint, good properties as a logical framework, in which many other logics can be naturally represented.  ... 

Formalizing Operational Semantic Specifications in Logic

Dale Miller
2009 Electronical Notes in Theoretical Computer Science  
Another approach to specification uses pieces of the syntax of logic-formulas, terms, types, and proofs-directly as elements of computation.  ...  Furthermore, binary clauses can be seen as a degenerative form of multiset rewriting: placing binary clauses within linear logic allows for rich forms of multiset rewriting which, in turn, provides a modular  ...  I would like to thank Andrew Gacek for providing several useful comments on an earlier draft of this paper.  ... 
doi:10.1016/j.entcs.2009.07.020 fatcat:ykrzxwjdb5glrkfrfwe5rbyfye

Page 2820 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
Summary: “Type inference can be phrased as constraint-solving over types.  ...  We then present a theory of order-sorted term rewriting and show that the key results for unsorted rewriting extend to sort-decreasing rewriting.  ... 
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