TITLE

Chapter 1: Proving Termination Using Dependent Types: the Case of Xor-Terms

AUTHOR(S)
Monin, Jean-François; Courant, Judicaël
PUB. DATE
September 2007
SOURCE
Trends in Functional Programming Volume 7;2007, Vol. 7, p1
SOURCE TYPE
Book
DOC. TYPE
Book Chapter
ABSTRACT
We study a normalization function in an algebra of terms quotiented by an associative, commutative and involutive operator (logical xor). This study is motivated by the formal verification of cryptographic systems, relying on a normalization function for xor-terms. Such a function is easy to define using general recursion. However, as it is to be used in a type theoretic proof assistant, we also need a proof of its termination. Instead of using a mixture of various rewriting orderings, we follow an approach involving the power of Type Theory with dependent types. The results are to be applied in the proof of the security API described in [14].
ACCESSION #
31422019

 

Related Articles

  • A jump inversion theorem for the enumeration jump. Soskov, I.N. // Archive for Mathematical Logic;2000, Vol. 39 Issue 6, p417 

    Abstract. We prove a jump inversion theorem for the enumeration jump and a minimal pair type theorem for the enumeration reducibilty. As an application some results of Selman, Case and Ash are obtained.

  • Sessions of the seminar 'Algebra i Logika'.  // Algebra & Logic;Sep2012, Vol. 51 Issue 4, p372 

    The article offers a list of academic papers about algebra and logic presented at the extended sessions of the seminar at the Mal'tsev Readings Conference on October 11-14, 2011.

  • SESSIONS OF THE SEMINAR 'ALGEBRA i LOGIKA'.  // Algebra & Logic;Nov2012, Vol. 51 Issue 5, p448 

    The article offers a list of academic papers on algebra and logic presented at the 2012 sessions of a seminar.

  • RSL volume 7 issue 2 Cover and Front matter.  // Review of Symbolic Logic;Jun2014, Vol. 7 Issue 2, pf1 

    The front cover of the journal "Review of Symbolic Logic" is presented along with the editors and subscription information.

  • RSL volume 7 issue 2 Cover and Back matter.  // Review of Symbolic Logic;Jun2014, Vol. 7 Issue 2, pb1 

    The back cover of the journal "Review of Symbolic Logic" is presented along with information for contributors.

  • Jacquette on Grelling's Paradox. Ketland, Jeffrey // Analysis;Jul2005, Vol. 65 Issue 3, p258 

    The article focuses on Grelling's Paradox that reappears in type theory, and thus that type theory, or higher-order logic, is inconsistent. The author of this article maintains in what follows that type theory, although it appears tailor-made to solve the problem, does not actually forestall...

  • Relations Versus Functions at the Foundations of Logic: Type-Theoretic Considerations. OPPENHEIMER, PAUL E.; ZALTA, EDWARD N. // Journal of Logic & Computation;Apr2011, Vol. 21 Issue 2, p351 

    Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. In contrast, Whitehead and Russell reduced an important part of mathematics to logic by defining functions in...

  • Type-theoretic logic with an operational account of intensionality. Fox, Chris; Lappin, Shalom // Synthese;Mar2015, Vol. 192 Issue 3, p563 

    We formulate a Curry-typed logic with fine-grained intensionality within Turner's typed predicate logic. This allows for an elegant presentation of a theory that corresponds to Fox and Lappin's property theory with curry typing, but without the need for a federation of languages. We then...

  • Visions of Henkin. Manzano, María; Alonso, Enrique // Synthese;Jul2015, Vol. 192 Issue 7, p2123 

    Leon Henkin (1921-2006) was not only an extraordinary logician, but also an excellent teacher, a dedicated professor and an exceptional person. The first two sections of this paper are biographical, discussing both his personal and academic life. In the last section we present three aspects of...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics