The paradigm of type-based termination is explored for functional programming with recursive data types. The article introduces , a lambda-calculus with recursion, inductive types, subtyping and bounded quanti cation. Decorated type variables representing approximations of inductive types are used to track the size of function arguments and return values. The system is shown to be type safe and strongly normalizing. The main novelty is a bidirectional type checking algorithm whose soundness is established formally.

We introduce a polymorphic #-calculus that features inductive types and that enforces termination of recursive definitions through typing. Then, we define a sound and complete type inference algorithm that computes a set of constraints to be satisfied for terms to be typable.

. This paper presents a tool for proving safety properties of