Sequential decision problems, dependently typed solutions

Abstract

We propose a dependently typed formalization for a simple class of sequential decision problems. For this class of problems, we im- plement a generic version of Bellman's backwards induction algorithm [2] and a machine checkable proof that the proposed implementation is correct. The formalization is generic. It is presented in Idris, but it can be easily translated to other dependently-typed programming languages. We conclude with an informal discussion of the problems we have faced in extending the formalization to generic monadic sequential decision problems.