Transfinite step-indexing for termination

Transfinite Step-Indexing: Decoupling Concrete and Logical Steps

Step-indexing has proven to be a powerful technique for defining logical relations for languages with advanced type systems and models of expressive program logics. In both cases, the model is stratified using natural numbers to solve a recursive equation that has no naive solutions. As a result of this stratification, current models require that each unfolding of the recursive equation – each ...

Transfinite Equations in Transfinite Strings

A Step-Indexing Approach to Partial Functions

We describe an ACL2 package for defining partial recursive functions that also supports efficient execution. While packages for defining partial recursive functions already exist for other theorem provers, they often require inductive definitions or recursion operators which are not available in ACL2 and they provide little, if any, support for executing the resulting definitions. We use stepin...

Transfinite Diameter

The transfinite diameter is a way of quantifying the size of compact sets in Euclidean space. This quantity is related to the Hausdorff dimension and the Lebesgue measure, but gives a slightly different perspective on the set than either of those do. In this paper, we introduce the transfinite diameter, and outline some attempts to calculate this quantity for three sets in R. For z1, z2, . . . ...

Epsilon substitution for transfinite induction

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.