On Strictness and Totality

Abs t rac t . In this paper we present a revised and extended version of the strictness and totality type assignment system introduced by Solberg, Nielson and Nielson in the Static Analysis Symposium '9~. Our main result is that (w.r.t. the possibility of replacing safely a lazy application by a strict one) the strictness and totality information given by this system is equivalent to the information given by two separate systems: one for strictness, and one for totality. This result is interesting from both a theoretical (understanding of the relations between strictness and totality) and a practical (more efficient checking and inference algorithms) point of view. Moreover we prove that both the system for strictness and the system for totality have a sound and complete inclusion relation between types w.r.t, the semantics induced by the term model of a language including a convergence to weak head normal form test at higher types.