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VOLUME 1, ISSUE 2, PAPER 1
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General recursion via coinductive types
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©Venanzio Capretta, University of Ottawa
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Abstract
We consider the problem of formalizing general recursive functions in intensional type theory. The proposed solution exploit coinductive types to model infinite computations. Every type A is associated to a type of partial elements Partial(A), coinductively generated by two constructors: the first, return(a) just returns an element a: A; the second, step(x), adds a computation step to a recursive element x: Partial(A). We show how this simple device is sufficient to formalize all recursive functions between two given types.
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Publication date: July 13, 2005
Full Text: PDF | PostScript
DOI: 10.2168/LMCS-1(2:1)2005
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