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Lightweight integration of the Ergo theorem prover inside a proof assistant

Sylvain Conchon, Evelyne Contejean, Johannes Kanig, Stéphane Lescuyer
2007 Proceedings of the second workshop on Automated formal methods - AFM '07  
In order to make a sound integration in a proof assistant possible, Ergo is capable of generating proof traces for CC(X).  ...  Its core component is CC(X), a new combination scheme for the theory of uninterpreted symbols parameterized by a built-in theory X.  ...  The remainder of this paper focuses on the design of Ergo and attempts of integration in Coq.  ... 
doi:10.1145/1345169.1345176 fatcat:k6tzizy3lzciho5az7rmka2xu4

(Mathematical) Logic for Systems Biology (Invited Paper) [chapter]

Joëlle Despeyroux
2016 Lecture Notes in Computer Science  
The examples we have considered so far are very simple ones-coming with completely formal (interactive) proofs in Coq.  ...  We present two candidate logics (two modal extensions of linear logic, called HyLL and SELL), along with biological examples.  ...  Linear Logic and Focusing Literals are either atomic formulas (p) or their negations (p ⊥ ).  ... 
doi:10.1007/978-3-319-45177-0_1 fatcat:imfgsz4r4jdfdi5et7jkrw7gwy

Focusing and higher-order abstract syntax

Noam Zeilberger
2008 Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '08  
Focusing is a proof-search strategy, originating in linear logic, that elegantly eliminates inessential nondeterminism, with one byproduct being a correspondence between focusing proofs and programs with  ...  We describe how to translate the language and proof of type safety almost directly into Coq using HOAS, and finally, show how the system's modular design pays off in enabling a very simple extension with  ...  Finally, I am grateful to the coq-club mailing list for useful advice on Coq, and particularly to Xavier Leroy for explaining a cool trick for coding mutual induction principles.  ... 
doi:10.1145/1328438.1328482 dblp:conf/popl/Zeilberger08 fatcat:k7z24zxcpnh4hfqt2m33iaj4c4

Focusing and higher-order abstract syntax

Noam Zeilberger
2008 SIGPLAN notices  
Focusing is a proof-search strategy, originating in linear logic, that elegantly eliminates inessential nondeterminism, with one byproduct being a correspondence between focusing proofs and programs with  ...  We describe how to translate the language and proof of type safety almost directly into Coq using HOAS, and finally, show how the system's modular design pays off in enabling a very simple extension with  ...  Finally, I am grateful to the coq-club mailing list for useful advice on Coq, and particularly to Xavier Leroy for explaining a cool trick for coding mutual induction principles.  ... 
doi:10.1145/1328897.1328482 fatcat:xkiaq4eeezaqbb2zsd42vkgu2q

Enabling Automatic Certification of Online Auctions

Wei Bai, Emmanuel M. Tadjouddine, Yu Guo
2014 Electronic Proceedings in Theoretical Computer Science  
We have also used abstract interpretation to translate the auction's specifications from OWL-S, based on description logic, to COQ, based on typed lambda calculus, in order to enable automatic verification  ...  We have shown how these mechanisms can be formalised as semantic web services in OWL-S, a good enough expressive machine-readable formalism enabling software agents, to discover, invoke, and execute a  ...  We have focused on the specifications of auction mechanisms required to be machine-understandable and have proposed an OWL-S formalisation of the mechanisms.  ... 
doi:10.4204/eptcs.147.9 fatcat:picdy4iabreilleihyy6ucov2q

Practical Tactics for Separation Logic [chapter]

Andrew McCreight
2009 Lecture Notes in Computer Science  
We have implemented our tactics in the Coq proof assistant, applying them to a deep embedding of Cminor, a C-like intermediate language used by Leroy's verified CompCert compiler.  ...  We present a comprehensive set of tactics that make it practical to use separation logic in a proof assistant to verify partial correctness properties of complex pointer-intensive programs.  ...  Power and Webster [17] describe a deep embedding of linear logic in Coq along with a couple of very primitive tactics.  ... 
doi:10.1007/978-3-642-03359-9_24 fatcat:g3y7n7upafgdhcrgamtkaz7aue

Computational Logic for Biomedicine and Neurosciences [article]

Elisabetta de Maria, Joelle Despeyroux
2020 arXiv   pre-print
on linear logic.  ...  The studied properties and their proofs are formalized in a very expressive (non linear) inductive logic: the Calculus of Inductive Constructions (CIC).  ...  More precisely, in a "two-level approach", we shall use Linear Logic (LL) as the intermediate logic, formalised in CIC, which is a type theory implemented in the Coq Proof Assistant [9] .  ... 
arXiv:2007.07571v2 fatcat:ht73rdk57bhijnqak7qw2535ym

Code Formal Verification of Operation System

Yu Zhang, Yunwei Dong, Huo Hong, Fan Zhang
2010 International Journal of Computer Network and Information Security  
system kernel in C code level.  ...  We present a case study to the verification of real-world C systems code derived from an implementation of μC/OS -II in the end.  ...  Therefore, we use the weakest pre-predicate logic to calculus the pre-condition in Hoare logic. In this way, we can get pre-condition mechanically.  ... 
doi:10.5815/ijcnis.2010.02.02 fatcat:2xx46lr5grh4tb4hpulujdxh3q

A Coq Library for Verification of Concurrent Programs

Reynald Affeldt, Naoki Kobayashi
2008 Electronical Notes in Theoretical Computer Science  
In this paper, we propose a library that enables verification of realistic concurrent programs in the Coq proof assistant.  ...  This encoding is coupled with a specification language akin to spatial logics, including in particular a notion of fairness, which is important to write satisfactory specifications for realistic concurrent  ...  Coupet-Grimal [9] proposes an encoding of linear temporal logic in Coq.  ... 
doi:10.1016/j.entcs.2007.11.010 fatcat:3v5mtqlvu5dkpmsfyn5ftnob5a

ML Pattern-Matching, Recursion, and Rewriting: From FoCaLiZe to Dedukti [chapter]

Raphaël Cauderlier, Catherine Dubois
2016 Lecture Notes in Computer Science  
In the actual version, those proofs found by Zenon are verified by Coq.  ...  In this paper we propose to extend the FoCaLiZe compiler by a backend to the Dedukti language -a proof checker for Deduction modulo -in order to benefit from Zenon Modulo, an extension of Zenon for Deduction  ...  In FoCaLiZe backend to Coq, termination of recursive functions is achieved thanks to the high-level Function mechanism [12] .  ... 
doi:10.1007/978-3-319-46750-4_26 fatcat:3lcz3tnzsvejdlkvzpewkh4tty

Refinement to Certify Abstract Interpretations: Illustrated on Linearization for Polyhedra

Sylvain Boulmé, Alexandre Maréchal
2018 Journal of automated reasoning  
In order to help formal development, we propose a proof framework, embedded in Coq, that implements a refinement calculus.  ...  Our concern is the modular development of a certified static analyzer in the Coq proof assistant.  ...  Our Coq implementation, described in Section 4.2, has a different representation of K in order to mechanize refinement proofs.  ... 
doi:10.1007/s10817-018-9492-2 fatcat:bq2ztwbt5nhilesotkqanxsikq

Page 1410 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
Summary: “We consider the language obtained by mixing the model of regions and the propositional linear temporal logic.  ...  (English summary) Mechanizing and automating mathematics: in honor of N. G. de Bruijn. J. Automat. Reason. 29 (2002), no. 3-4, 309-336.  ... 

A Logical Framework for Systems Biology [article]

Elisabetta De Maria, Joelle Despeyroux, Amy Felty
2014 arXiv   pre-print
We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic.  ...  We formalize the proofs of these properties in the Coq Proof Assistant, with the help of a Lambda Prolog prover for partial automation of the proofs.  ...  The second author thanks François Fages, Sylvain Soliman, Alessandra Carbone, Vincent Danos, and Jean Krivine for fruitful discussions on various preliminary versions of the HyLL logic in view of its potential  ... 
arXiv:1404.5439v1 fatcat:ozovyfxkize7vfhojwzd2rti7u

A Logical Framework for Systems Biology [chapter]

Elisabetta de Maria, Joëlle Despeyroux, Amy P. Felty
2014 Lecture Notes in Computer Science  
We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic.  ...  We formalize the proofs of these properties in the Coq Proof Assistant, with the help of a Lambda Prolog prover for partial automation of the proofs. Proposition (Property 1, Version 1).  ...  Our aim is to find the logical essence of biochemical reactions.  ... 
doi:10.1007/978-3-319-10398-3_10 fatcat:d7evjgpf2jbnldjouh3budpzuq

A Focused Sequent Calculus Framework for Proof Search in Pure Type Systems

Stéphane Lengrand, Roy Dyckhoff, James McKinna, Henk Barendregt
2011 Logical Methods in Computer Science  
Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation  ...  We show how to make the logical rules of PTSC into a syntax-directed system PS for proof-search, by incorporating the conversion rules as in syntax-directed presentations of the PTS rules for type-checking  ...  linear logic [Gir87] .  ... 
doi:10.2168/lmcs-7(1:6)2011 fatcat:fto35brddvcupdepcvb7gz25dm
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