Equational Logic of Recursive Program Schemes

  • John G. Mersch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3629)


In this paper we present FLRS, a sound and complete equational logic for proving the equivalence of recursive program schemes. We use extended versions of the Solution Theorems from [1] and [2] to provide coalgebraic semantics to recursive program schemes. We end the paper with a proof that FLRS is complete with respect to the coalgebraic semantics.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aczel, P., Adámek, J., Milius, S., Velebil, J.: Infinite trees and completely iterative theories: A coalgebraic view. Theoretical Computer Science 300, 1–45 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Milius, S., Moss, L.S.: The category theoretic solution of recursive program schemes (2004), preprint available at
  3. 3.
    Guessarian, I.: Algebraic Semantics. LNCS, vol. 99. Springer, Heidelberg (1981)zbMATHGoogle Scholar
  4. 4.
    Courcelle, B.: Fundamental properties of infinite trees. Theoretical Computer Science 25, 95–169 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Moss, L.S.: Recursion and corecursion have the same equational logic. Theoretical Computer Science 294, 233–267 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hurkens, A.J.C., McArthur, M., Moschovakis, Y.N., Moss, L.S., Whitney, G.T.: The logic of recursive equations. The Journal of Symbolic Logic 63, 451–478 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Moschovakis, Y.N.: The formal language of recursion. The Journal of Symbolic Logic 54, 1216–1252 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Mersch, J.G.: Equational Logic of Recursive Program Schemes. PhD thesis, Indiana University (2004)Google Scholar
  9. 9.
    Moss, L.S.: Parametric corecursion. Theoretical Computer Science 260, 139–163 (2001)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • John G. Mersch
    • 1
  1. 1.Department of MathematicsNorthwestern State University of LouisianaNatchitochesUSA

Personalised recommendations