Using Structural Recursion for Corecursion

Details Using Structural Recursion for Corecursion Using Structural Recursion for Corecursion

2009-03-23

arxiv.org/abs/0903.3850v1

Types 2008 5497 (2008) 220-236

Computer Science

Logic in Computer Science

Scientific paper

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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