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We present a practical tool for defining and proving properties of recursive functions in the Coq proof assistant. The tool proceeds by generating from pseudo-code (Coq functions that need not be total nor terminating) the graph of the intended function as an inductive relation, and then proves that the relation actually represents a function, which is by construction the function that we are trying to define. Then, we generate induction and inversion principles , and a fixpoint equation for proving other properties of the function. Our tool builds upon state-of-the-art techniques for defining recursive functions, and can also be used to generate executable functions from inductive descriptions of their graph. We illustrate the benefits of our tool on two case studies.
Vlad Rusu
Vlad.Rusu@irisa.fr
@InProceedings{flop-barthe-forest-pichardie-rusu-06,
Author = {Barthe, G. and Forest, J. and Pichardie, D. and Rusu, V.},
Title = {Defining and reasoning about recursive functions: a practical tool for the Coq proof assistant},
BookTitle = {Functional and LOgic Programming Systems (FLOPS'06)},
Volume = {3945},
Pages = {114--129},
Series = {LNCS},
Address = {Fuji Susono, Japan},
Month = {April},
Year = {2006}
}
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