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Automatic Generation of Simple Lemmas from Recursive Definitions Using Decision Procedures – Preliminary Report – [chapter]

Deepak Kapur, M. Subramaniam
2003 Lecture Notes in Computer Science  
Using nontrivial examples, it is shown how the method can be used to automatically generate many simple lemmas; these lemmas are likely to be found useful in automatically proving other nontrivial properties  ...  Using recent results on integrating induction schemes into decidable theories, a method for generating lemmas useful for reasoning about T -based function definitions is proposed.  ...  Acknowledgment: We thank Jürgen Giesl for collaborative work which triggered some of the ideas in this paper.  ... 
doi:10.1007/978-3-540-40965-6_9 fatcat:eeg4v6iebbcsdc7pzkzkftr7q4

A Domain-Specific Language for Incremental and Modular Design of Large-Scale Verifiably-Safe Flow Networks (Preliminary Report)

Azer Bestavros, Assaf Kfoury
2011 Electronic Proceedings in Theoretical Computer Science  
A prerequisite for a type theory is a formal semantics, i.e, a rigorous definition of the entities that qualify as feasible flows through the networks, possibly restricted to satisfy additional efficiency  ...  , the rules guarantee the properties are preserved as we build larger networks from smaller ones.  ...  We use a BNF definition to generate formal expressions, each being a formal description of a network.  ... 
doi:10.4204/eptcs.66.2 fatcat:iqouzfxk55dk5lvdlnw2detddq

Effective theorem proving for hardware verification [chapter]

D. Cyrluk, S. Rajan, N. Shankar, M. K. Srivas
1995 Lecture Notes in Computer Science  
These automatic procedures can be combined into general-purpose proof strategies that can efficiently automate a number of proofs including those of hardware correctness.  ...  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,  ...  The N-bit ripple-carry adder example comes from a PVS library for bit-vectors being developed by Rick Butler and Paul Miner of NASA.  ... 
doi:10.1007/3-540-59047-1_50 fatcat:zwwryahpejavfleqthleuefjjq

Formalising a Turing-Complete Choreographic Language in Coq [article]

Luís Cruz-Filipe and Fabrizio Montesi, Marco Peressotti
2021 arXiv   pre-print
With this effort, we show that theorem proving can be a very useful tool in the field of choreographic languages: besides the added degree of confidence that we get from a mechanised proof, the formalisation  ...  process led us to a significant simplification of the underlying theory.  ...  The induction principle automatically generated by Coq from the type definition is not strong enough for our purposes: the constructor for composition includes elements of type PRFunction inside a vector  ... 
arXiv:2102.02627v1 fatcat:76u6tg72ujahdlspfsduvtvspm

A decision procedure for satisfiability in separation logic with inductive predicates

James Brotherston, Carsten Fuhs, Juan A. Navarro Pérez, Nikos Gorogiannis
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
Our decision procedure is based on the computation of a certain fixed point from the definition of an inductive predicate, called its "base", that exactly characterises its satisfiability.  ...  Finally, we provide an implementation of our decision procedure, and analyse its performance both on a synthetically generated set of test formulas, and on a second test set harvested from the separation  ...  We wish to thank the anonymous reviewers for their valuable comments, which have helped us greatly in improving the presentation of the paper.  ... 
doi:10.1145/2603088.2603091 dblp:conf/csl/BrotherstonFPG14 fatcat:budlww4xpfav5bwnmcoy5idaey

Rewriting Induction + Linear Arithmetic = Decision Procedure [chapter]

Stephan Falke, Deepak Kapur
2012 Lecture Notes in Computer Science  
The proof method developed for inductive theorem proving couples (implicit) inductive reasoning with a decision procedure for the theory of linear integer arithmetic with (free) constructors.  ...  For these results, a class of term rewrite systems (TRSs) with built-in linear integer arithmetic is introduced and it is shown how these TRSs can be used in the context of inductive theorem proving.  ...  This may require techniques similar to [15, 16] which automatically generate suitable generalization lemmas that are needed for deciding validity.  ... 
doi:10.1007/978-3-642-31365-3_20 fatcat:wzgjgb7tv5gwvhuerw262bvr4e

Goal Translation for a Hammer for Coq (Extended Abstract)

Łukasz Czajka, Cezary Kaliszyk
2016 Electronic Proceedings in Theoretical Computer Science  
mechanism based on a Ben-Yelles-type algorithm combined with limited rewriting, congruence closure and a first-order generalization of the left rules of Dyckhoff's system LJT.  ...  Hammers are tools that provide general purpose automation for formal proof assistants.  ...  We thank the organizers of the First Coq Coding Sprint, especially Yves Bertot, for the help with implementing Coq export plugins.  ... 
doi:10.4204/eptcs.210.4 fatcat:aitngrbffvczxp2tc2bhcrlg6e

A certifying extraction with time bounds from Coq to call-by-value λ-calculus [article]

Yannick Forster, Fabian Kunze
2019 arXiv   pre-print
We provide three case studies: A universal L-term obtained as extraction from the Coq definition of a step-indexed self-interpreter for Ł, a many-reduction from solvability of Diophantine equations to  ...  We provide a plugin extracting Coq functions of simple polymorphic types to the (untyped) call-by-value λ-calculus L. The plugin is implemented in the MetaCoq framework and entirely written in Coq.  ...  Closed abstractions are called procedures and are the (only) normal forms of normalising, closed terms. L provides for recursion using a fixed-point operator: Lemma 1 (Fact 6 [12] ).  ... 
arXiv:1904.11818v2 fatcat:dj6vmkyumbfrvlifu3744gnfj4

A Certifying Extraction with Time Bounds from Coq to Call-By-Value Lambda Calculus

Yannick Forster, Fabian Kunze, Michael Wagner
2019 International Conference on Interactive Theorem Proving  
We provide three case studies: A universal L-term obtained as extraction from the Coq definition of a step-indexed self-interpreter for L, a many-reduction from solvability of Diophantine equations to  ...  We provide a plugin extracting Coq functions of simple polymorphic types to the (untyped) call-byvalue λ-calculus L. The plugin is implemented in the MetaCoq framework and entirely written in Coq.  ...  Closed abstractions are called procedures and are the (only) normal forms of normalising, closed terms. L provides for recursion using a fixed-point operator: Lemma 1 (Fact 6 [12] ).  ... 
doi:10.4230/lipics.itp.2019.17 dblp:conf/itp/0002K19 fatcat:6nikrg7iyzfb5dgntacfmdonay

Theory Exploration Powered by Deductive Synthesis [chapter]

Eytan Singher, Shachar Itzhaky
2021 Lecture Notes in Computer Science  
generation of a library of lemmas from a base set of inductive data types and recursive definitions.  ...  AbstractThis paper presents a symbolic method for automatic theorem generation based on deductive inference.  ...  Notably, this procedure cannot reason about recursive definitions since such reasoning routinely requires the use of induction.  ... 
doi:10.1007/978-3-030-81688-9_6 fatcat:6nzwbykqofftlciqg453veclia

Synthesizing Inductive Lemmas for Reasoning with First-Order Logic with Least Fixpoints [article]

Adithya Murali, Lucas Peña, Eion Blanchard, Christof Löding, P. Madhusudan
2021 arXiv   pre-print
In this paper, we undertake a foundational study of automatically finding proofs that use induction to reason in these logics.  ...  Recursively defined linked datastructures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) combined with  ...  Let us consider the simple case of a recursively defined unary predicate whose definition ( ) := lfp ( , ).  ... 
arXiv:2009.10207v2 fatcat:sbg75szo5rbxxkkhxvytrukjoe

Symbolic Graphs: Linear Solutions to Connectivity Related Problems

Raffaella Gentilini, Carla Piazza, Alberto Policriti
2007 Algorithmica  
Definition 4 (Scc-Closed Vertex Set) Given Boolean combinations of scc-closed sets are scc closed.  ...  The importance of symbolic data structures such as Ordered Binary Decision Diagrams (OBDD) is rapidly growing in many areas of Computer Science where the large dimensions of the input models is a challenging  ...  Preliminaries This section collects preliminary notions and notations, used in the rest of the paper, concerning graphs and connectivity.  ... 
doi:10.1007/s00453-007-9079-5 fatcat:gbrx2nuv2fbrlb2s5j2koax3vu

Automatic Sequences and Zip-Specifications [article]

Clemens Grabmayer and Joerg Endrullis and Dimitri Hendriks and Jan Willem Klop and Lawrence S. Moss
2012 arXiv   pre-print
The importance of zip-specifications resides in their intimate connection with automatic sequences. We establish a new and simple characterization of automatic sequences.  ...  We further obtain a natural extension of the class of automatic sequences, obtained by 'zip-mix' specifications that use zips of different arities in one specification.  ...  The following lemmas use the notation from Definition 72: Lemma 84.  ... 
arXiv:1201.3251v2 fatcat:oaijmegxvfbfzj6cpbqttx2lj4

Satisfiability Modulo Recursive Programs [chapter]

Philippe Suter, Ali Sinan Köksal, Viktor Kuncak
2011 Lecture Notes in Computer Science  
We present a semi-decision procedure for checking satisfiability of expressive correctness properties of recursive first-order functional programs.  ...  Our procedure is sound for counterexamples and for proofs of terminating functions.  ...  We thank Mirco Dotta and Swen Jacobs for preliminary versions of some of the benchmarks. We thank Panagiotis Manolios and J Strother Moore for discussions about ACL2.  ... 
doi:10.1007/978-3-642-23702-7_23 fatcat:msorndfrk5d4zj7pbcvxtssoxu

An overview of Rewrite Rule Laboratory (RRL) [chapter]

Deepak Kapur, Hantao Zhang
1989 Lecture Notes in Computer Science  
the use of formal methods in hardware and software design.  ...  We provide a brief historical account of development of RRL and its descendants, give an overview of the main capabilities of RRL and conclude with a discussion of applications of RRL.  ...  This is despite the fact that some of the lemmas are generated automatically using generalization and other heuristics implemented in RRL.  ... 
doi:10.1007/3-540-51081-8_138 fatcat:qwdmeuudbrhzjklqdzzgcxcp24
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