Type Theory and Language Constructs for Objects with States

In current class-based Object-Oriented Programming Languages (OOPLs), object types include only static features. How to add object dynamic behaviors modeled by Harel's statecharts into object types is a challenging task. We propose adding states and state transitions, which are largely unstated in object type theory, into object type definitions and typing rules. We argue that dynamic behaviors of objects should be part of object type definitions. We propose our type theory, the @t-calculus, which refines Abadi and Cardelli's @z-calculus, in modeling objects with their dynamic behaviors. In our proposed type theory, we also explain that a subtyping relation between object types should imply the inclusion of their dynamic behaviors. By adding states and state transitions into object types, we propose modifying programming language constructs for state tracking.