Using Structural Recursion for Corecursion [article]

Yves Bertot, Ekaterina Komendantskaya (INRIA Sophia Antipolis)
2009 arXiv   pre-print
We propose a (limited) solution to the problem of constructing stream values defined by recursive equations that do not respect the guardedness condition. The guardedness condition is imposed on definitions of corecursive functions in Coq, AGDA, and other higher-order proof assistants. In this paper, we concentrate in particular on those non-guarded equations where recursive calls appear under functions. We use a correspondence between streams and functions over natural numbers to show that
more » ... classes of non-guarded definitions can be modelled through the encoding as structural recursive functions. In practice, this work extends the class of stream values that can be defined in a constructive type theory-based theorem prover with inductive and coinductive types, structural recursion and guarded corecursion
arXiv:0903.3850v1 fatcat:yadyrfmzd5hgxkux5izbesrnyy