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Co-induction Simply [chapter]

K. Rustan M. Leino, Michał Moskal
2014 Lecture Notes in Computer Science  
Co-induction is complicated to work with in interactive proof assistants and has had no previous support in dedicated program verifiers.  ...  , as well as letting users write co-inductive proofs.  ...  Acknowledgments During the course of this work, we have benefited from discussions with many colleagues who understand co-induction far better than we.  ... 
doi:10.1007/978-3-319-06410-9_27 fatcat:knloumszpbc7bb3scqs5acv46i

Co-inductive axiomatization of a synchronous language [chapter]

David Nowak, Jean -René Beauvais, Jean -Pierre Talpin
1998 Lecture Notes in Computer Science  
We investigate the use of a theorem prover, Coq, for the speci cation of in nite state systems and for the veri cation of co-inductive properties.  ...  Over the last decade, the increasing demand for the validation of safety critical systems lead to the development of domain-speci c programming languages (e.g. synchronous languages) and automatic veri  ...  Acknowledgments The authors wish to thank Eduardo Gim enez for the explanations he provided about the use of co-inductive types in Coq.  ... 
doi:10.1007/bfb0055148 fatcat:5ky4kjyuy5cf5e5jzbiqhutepu

Specification and Verification of a Steam-Boiler with Signal-Coq [chapter]

Mickaël Kerbœuf, David Nowak, Jean-Pierre Talpin
2000 Lecture Notes in Computer Science  
We investigate the use of a synchronous programming language, Signal, and of a proof assistant, Coq, for the speci cation and the veri cation of co-inductive properties of the well-known steam-boiler problem  ...  Over the last decade, the increasing demand for the validation of safety critical systems has led to the development of domain-speci c programming languages (e.g. synchronous languages) and automatic veri  ...  In 14], we have introduced a co-inductive semantics for the kernel of the language Signal and formalized it in the proof assistant Coq.  ... 
doi:10.1007/3-540-44659-1_22 fatcat:eb3gajnm6rd3rifpgtndqh45re

The use of proof plans to sum series [chapter]

Toby Walsh, Alex Nunes, Alan Bundy
1992 Lecture Notes in Computer Science  
The program was built to test the applicability of the proof planning search control technique in a domain of mathematics outwith induction. This experiment was successful.  ...  The series summing program extends previous work in this area and was built in a short time just by providing new series summing methods to our existing inductive theorem proving system Clam.  ...  The research reported in this paper was supported by SERC grant GR/F/71799, a SERC PostDoctoral Fellowship to the rst author and a SERC Senior Fellowship to the third author.  ... 
doi:10.1007/3-540-55602-8_175 fatcat:mnpvwypss5hptdwi2yqxztwkde

Mechanizing UNITY in Isabelle

Lawrence C. Paulson
2000 ACM Transactions on Computational Logic  
UNITY has been mechanized in higher-order logic using Isabelle, a proof assistant.  ...  A mechanical theory of unions of programs supports a degree of compositional reasoning.  ...  The set of states reachable in a UNITY program is defined inductively, as is the leads-to relation (Fig. 2 ). Isabelle provides powerful automatic tactics.  ... 
doi:10.1145/343369.343370 fatcat:gro7l35mcfatbjexqhbnq3h6nu

A Formal Executable Semantics of the JavaCard Platform [chapter]

Gilles Barthe, Guillaume Dufay, Line Jakubiec, Bernard Serpette, Simão Melo de Sousa
2001 Lecture Notes in Computer Science  
Moreover, we relate both components by giving a proof of correctness of the ByteCode Verifier. Both formalisations and proofs have been machined-checked using the proof assistant Coq.  ...  We present a formal executable specification of two crucial JavaCard platform components, namely the Java Card Virtual Machine (JCVM) and the ByteCode Verifier (BCV).  ...  Simão Sousa is partially supported by a grant from the Portuguese Fundação para a Ciencia e a Technologia under grant SFRH/BD/790/2000.  ... 
doi:10.1007/3-540-45309-1_20 fatcat:yavcygfipfahfgcdzan2s5oud4

A Hybrid Encoding of Howe's Method for Establishing Congruence of Bisimilarity

Alberto Momigliano, Simon J. Ambler, Roy L. Crole
2002 Electronical Notes in Theoretical Computer Science  
We give a short description of Hybrid, a new tool for interactive theorem proving, which was introduced in [4].  ...  It provides a form of Higher Order Abstract Syntax (HOAS) combined consistently with induction and coinduction.  ...  proof by co-induction.  ... 
doi:10.1016/s1571-0661(04)80506-1 fatcat:haiddmou5beupn2vrxzzrhtzxu

Mechanizing a proof by induction of process algebra specifications in higher order logic [chapter]

Monica Nesi
1992 Lecture Notes in Computer Science  
In this paper, we describe an attempt to mechanize a proof by mathematical induction of the correctness of a simple buffer.  ...  When dealing with inductively defined systems, correctness proofs of different specifications of the same system cannot be accomodated in a framework based on finite state automata.  ...  I am especially grateful to Mike Gordon, Tom Melham, Sara Kalvala, Brian Graham, John Van Tassel, John Harrison and Richard Boulton for their advice on mechanization in HOL.  ... 
doi:10.1007/3-540-55179-4_28 fatcat:4vvtbq4xkbcaxmftyjiaebyvue

Touring the MetaCoq Project (Invited Paper)

Matthieu Sozeau
2021 Electronic Proceedings in Theoretical Computer Science  
However, proof assistant implementations themselves are seldom verified, although they take a major share of the trusted code base in any such certification effort.  ...  the following artefacts: a specification of Coq's syntax and type theory, the Polymorphic Cumulative Calculus of (Co)-Inductive Constructions (PCUIC); a monad for the manipulation of raw syntax and interaction  ...  Ideally, this last step should also be verified: we present a verified erasure procedure ( §5) that takes a COQ environment and definition and produces a program in an (untyped) weak call-by-value λ -calculus  ... 
doi:10.4204/eptcs.337.2 fatcat:vkzxls6psredfkeo7xwazecbpa

Tool Integration for Reasoned Programming [chapter]

Andrew Ireland
2008 Lecture Notes in Computer Science  
We argue for the importance of tool integration in achieving the Program Verifier Grand Challenge.  ...  In particular, we argue for what we call strong integration, i.e. a co-operative style of interaction between tools.  ...  Using a theorem prover, ESC/Java can verify that a program is free of run-time exceptions. In general, annotations are required in order to support the theorem proving.  ... 
doi:10.1007/978-3-540-69149-5_45 fatcat:uey2thy64zfw3fcnbgm5o4cqhm

On the Strong Co–induction in Coq [chapter]

J. L. Freire Nistal, A. Blanco Ferro, Victor M. Gulías, E. Freire Brañas
2003 Lecture Notes in Computer Science  
In order to improve usability, most of the proofs are given in a general frame of partial order relations and not only in the specific complete lattice of a power-set.  ...  In this paper, we provide a library in Coq containing intuitionistic proofs of some facts that are on the basis of formal verification tools such as Model Checking or Theorem Proving: the Reduction Lemma  ...  The system automatically extracts the constructive contents of proofs as an executable ML program that permits the development of programs consistent with their specification.  ... 
doi:10.1007/978-3-540-45210-2_26 fatcat:zgz555vr55d6xnar65ignxqi7y

Multi-level Meta-reasoning with Higher-Order Abstract Syntax [chapter]

Alberto Momigliano, Simon J. Ambler
2003 Lecture Notes in Computer Science  
To further exhibit the flexibility of our system, we modify the target language with a notion of non-well-founded closure, inspired by Milner & Tofte [19] and formally verify via co-induction a subject  ...  proving and principles of (co)induction.  ...  Acknowledgments This paper has benefited from referees comments and discussions with Roy Crole, Dale Miller, Frank Pfenning, Carsten Schürmann and Amy Felty, who kindly made available to us the Coq proof  ... 
doi:10.1007/3-540-36576-1_24 fatcat:ckjjrrjcvraunl6yspkenkaccm

A verification tool for ERLANG

Lars–Åke Fredlund, Dilian Gurov, Thomas Noll, Mads Dam, Thomas Arts, Gennady Chugunov
2003 International Journal on Software Tools for Technology Transfer (STTT)  
EVT is essentially a classical proof assistant, or theorem-proving tool, requiring users to intervene in the proof process at crucial steps such as stating program invariants.  ...  However, the tool offers considerable support for automatic proof discovery through higher-level tactics tailored to the particular task of the verification of Erlang programs.  ...  relation between induction and co-induction variables a well-founded one.  ... 
doi:10.1007/s100090100071 fatcat:2p62i2rsdzb5jjs3f4j66znykq

Algebraic Model Checking

Peter Padawitz
2010 Electronic Communications of the EASST  
Besides realizing and integrating state-of-the-art proof and computation rules the system admits the co/algebraic specification of the models to be checked in terms of rewrite rules and functional-logic  ...  programs.  ...  Expander2 records each interactive proof in this way and also generates a proof term consisting of commands whose execution repeats the proof automatically.  ... 
doi:10.14279/tuj.eceasst.26.359 dblp:journals/eceasst/Padawitz10 fatcat:zcjxkwkhbzad7iikbnytzzr5ru

Synthesis from Examples: Interaction Models and Algorithms

Sumit Gulwani
2012 2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  
Examples are often a natural way to specify various computational artifacts such as programs, queries, and sequences.  ...  Synthesizing such artifacts from example based specifications has various applications in the domains of enduser programming and intelligent tutoring systems.  ...  Synthesis of algebraic proof problems that are similar in structure to a given example proof problem [19] .  ... 
doi:10.1109/synasc.2012.69 dblp:conf/synasc/Gulwani12 fatcat:he7lehjn6feutgjq475vkxqtuu
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