Syntax and Semantics of Type Assignment Systems

Abstract

This paper gives a survey on syntax and semantics for type assignment systems, with a special attention to semantic completeness of the systems. Starting with the most basic system with function types only, it introduces polymorphic types, intersection types, union types, and existential type quantifier in a step-by-step manner. It also provides several sequent-style formulations of type assignment systems. With the sequent calculi, it shows the properties of type assignment systems concerning the completeness and the conservativity of various systems.