A type assignment for lambda-calculus complete both for FPTIME and strong normalization

One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of computer science. One of the more promising approaches to this aim is based on the use of lambda-calculus as paradigmatic programming language and the design of type assignment systems for lambda-terms, where types guarantee both the functional correctness and the complexity bound. Here we propose a system of stratified types, inspired by intersection types, where intersection is a non-associative operator. The system, called STR, is correct and complete for polynomial time computations; moreover, all the strongly normalizing terms are typed in it, thus increasing the typing power with respect to the previous proposals. Moreover, STR enjoys a stronger expressivity with respect to the previous system STA, since it allows to type a restricted version of iteration.