Language constructs for non-well-founded computation

Authors:
Jean-Baptiste Jeannin;Dexter Kozen;Alexandra Silva
Affiliations:
Cornell University, Ithaca, NY;Cornell University, Ithaca, NY;Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands
Venue:
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
Year:
2013

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Abstract

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.