@MISC{Matthews99recursivefunction, author = {John Matthews}, title = {Recursive Function Definition over Coinductive Types}, year = {1999} }

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Abstract

Using the notions of unique xed point, converging equivalence relation, and contracting function, we generalize the technique of well-founded recursion. We are able to de ne functions in the Isabelle theorem prover that recursively call themselves an in nite number of times. In particular, we can easily de ne recursive functions that operate over coinductively-de ned types, such as in nite lists. Previously in Isabelle such functions could only be de ned corecursively, or had to operate over types containing \extra" bottom-elements. We conclude the paper by showing that the functions for ltering and attening in nite lists have simple recursive de nitions. 1 Well-founded recursion Rather than specify recursive functions by possibly inconsistent axioms, several higher order logic (HOL) theorem provers[3, 9, 12] provide well-founded recursive function de nition packages, where new functions can be de ned conservatively. Recursive functions are de ned by giving a series of...