Commutation, transformation, and termination
Proc. of the 8th international conference on Automated deduction
FPCA '89 Proceedings of the fourth international conference on Functional programming languages and computer architecture
Autarkic Computations in Formal Proofs
Journal of Automated Reasoning
New equations for neutral terms: a sound and complete decision procedure, formalized
Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming
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Parametric inductive types can be seen as functions taking type parameters as arguments and returning the instantiated inductive types. Given functions between parameters one can construct a function between the instantiated inductive types representing the change of parameters along these functions. It is well known that it is not a functor w.r.t. intensional equality based on standard reductions. We investigate a simple type system with inductive types and iteration and show by modular rewriting techniques that new reductions can be safely added to make this construction a functor, while the decidability of the internal conversion relation based on the strong normalization and confluence properties is preserved. Possible applications: new categorical and computational structures on λ-calculus, certified computation.