Formal proof of SCHUR conjugate function

  • Authors:

  • Franck Butelle;Florent Hivert;Micaela Mayero;Frédéric Toumazet

  • Affiliations:

  • LIPN, UMR, Université Paris 13, Villetaneuse;LITIS, EA, Université de Rouen, Saint-Etienne-du-Rouvray;LIPN, UMR, Université Paris 13, Villetaneuse and LIP, INRIA Grenoble, Rhône-Alpes, UCBL, ENS Lyon, Lyon;LIGM, UMR, Université de Marne-la-Vallée

  • Venue:
  • AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
  • Year:
  • 2010

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Abstract

The main goal of our work is to formally prove the correctness of the key commands of the SCHUR software, an interactive program for calculating with characters of Lie groups and symmetric functions. The core of the computations relies on enumeration and manipulation of combinatorial structures. As a first "proof of concept", we present a formal proof of the conjugate function, written in C. This function computes the conjugate of an integer partition. To formally prove this program, we use the Frama-C software. It allows us to annotate C functions and to generate proof obligations, which are proved using several automated theorem provers. In this paper, we also draw on methodology, discussing on how to formally prove this kind of program.