Strictness, totality, and non-standard type inference

In this paper we present two non-standard-type inference systems for conjunctive strictness and totality analyses of higher-order-typed functional programs and prove completeness results for both the strictness and the totality-type entailment relations. We also study the interactions between strictness and totality analyses, showing that the information obtainable by a system that combines the two analyses, even though more refined than the information given by the two separate systems, cannot be effectively used. A main feature of our approach is that all the results are proved by relying directly on the operational semantics of the programming language considered. This leads to a rather direct presentation which involves relatively little mathematical overhead.