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Structured general corecursion and coinductive graphs [extended abstract]
Bove and Capretta's popular method for justifying function definitions by
general recursive equations is based on the observation that any structured
general recursion equation defines an inductive subset of the intended domain
(the "domain of definedness") for which the equation has a unique solution. To
accept the definition, it is hence enough to prove that this subset contains
the whole intended domain.
This approach works very well for "terminating" definitions. But it fails to
account for "productive" definitions, such as typical definitions of
stream-valued functions. We argue that such definitions can be treated in a
similar spirit, proceeding from a different unique solvability criterion. Any
structured recursive equation defines a coinductive relation between the
intended domain and intended codomain (the "coinductive graph"). This relation
in turn determines a subset of the intended domain and a quotient of the
intended codomain with the property that the equation is uniquely solved for
the subset and quotient. The equation is therefore guaranteed to have a unique
solution for the intended domain and intended codomain whenever the subset is
the full set and the quotient is by equality.Comment: In Proceedings FICS 2012, arXiv:1202.317