A Unifying Approach to Recursive and Co-recursive Definitions

  • Pietro Di Gianantonio
  • Marino Miculan
Conference paper

DOI: 10.1007/3-540-39185-1_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2646)
Cite this paper as:
Di Gianantonio P., Miculan M. (2003) A Unifying Approach to Recursive and Co-recursive Definitions. In: Geuvers H., Wiedijk F. (eds) Types for Proofs and Programs. TYPES 2002. Lecture Notes in Computer Science, vol 2646. Springer, Berlin, Heidelberg

Abstract

In type theory based logical frameworks, recursive and co-recursive definitions are subject to syntactic restrictions that ensure their termination and productivity. These restrictions however greately decrease the expressive power of the language. In this work we propose a general approach for systematically defining fixed points for a broad class of well given recursive definition. This approach unifies the ones based on well-founded order to the ones based on complete metrics and contractive functions, thus allowing for mixed recursive/corecursive definitions. The resulting theory, implemented in the Coq proof assistant, is quite simple and hence it can be used broadly with a small, sustainable overhead on the user.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Pietro Di Gianantonio
    • 1
  • Marino Miculan
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità di UdineUdineITALY

Personalised recommendations