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Structural Induction and Coinduction in a Fibrational Setting
1998
Information and Computation
We present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coinductively de ned types. Our main results provide su cient criteria for the validity of such principles: in the presence of comprehension, the induction principle for initial algebras is admissible, and dually, in the presence of quotient types, the coinduction principle for terminal coalgebras is admissible. After giving an alternative formulation of induction in terms of
doi:10.1006/inco.1998.2725
fatcat:qwvx6yx3j5evdn7zrtdb6rox3i