Using Structural Recursion for Corecursion

Yves Bertot 1 Ekaterina Komendantskaya 1
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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 some 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
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Submitted on : Monday, March 23, 2009 - 1:21:02 PM
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  • HAL Id : inria-00322331, version 4
  • ARXIV : 0903.3850



Yves Bertot, Ekaterina Komendantskaya. Using Structural Recursion for Corecursion. Types 2008, 2008, Torino, Italy. pp.220-236. ⟨inria-00322331v4⟩



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