We apply Mints’ technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.

We study perpetuality in calculi with explicit substitutions having full composition. A simple perpetual strategy is used to define strongly normalising terms inductively. This gives a simple argument to show preservation of β-strong normalisation as well as strong normalisation for typed terms. Particularly, the strong normalisation proof is based on implicit substitution rather than explicit ...

We give several new algorithms for dense polynomial multiplication based on the Kronecker substitution method. For moderately sized input polynomials, the new algorithms improve on the performance of the standard Kronecker substitution by a sizeable constant, both in theory and in empirical tests.