Language Constructs for Non-Well-Founded Computation

  • Jean-Baptiste Jeannin
  • Dexter Kozen
  • Alexandra Silva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7792)


Recursive functions defined on a coalgebraic datatype C may not converge if there are cycles in the input, that is, if the input object is not well-founded. Even so, there is often a useful solution. Unfortunately, current functional programming languages provide no support for specifying alternative solution methods. In this paper we give numerous examples in which it would be useful to do so: free variables, α-conversion, and substitution in infinitary λ-terms; halting probabilities and expected running times of probabilistic protocols; abstract interpretation; and constructions involving finite automata. In each case the function would diverge under the standard semantics of recursion. We propose programming language constructs that would allow the specification of alternative solutions and methods to compute them.


coalgebraic types functional programming recursion 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jean-Baptiste Jeannin
    • 1
  • Dexter Kozen
    • 1
  • Alexandra Silva
    • 2
  1. 1.Cornell UniversityIthacaUSA
  2. 2.Institute for Computing and Information SciencesRadboud University NijmegenNijmegenThe Netherlands

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