Type Inference for Variant Object Types

Existing type systems for object calculi are based on invariant subtyping. Subtyping invariance is required for soundness of static typing in the presence of method overrides, but it is often in the way of the expressive power of the type system. Flexibility of static typing can be recovered in different ways: in first-order systems, by the adoption of object types with variance annotations, in second-order systems by resorting to Self types. Type inference is known to be P-complete for first-order systems of finite and recursive object types, and NP-complete for a restricted version of Self types. The complexity of type inference for systems with variance annotations is yet unknown. This paper presents a new object type system based on the notion of Split types, a form of object types where every method is assigned two types, namely, an update type and a select type. The subtyping relation that arises for Split types is variant and, as a result, subtyping can be performed both in width and in depth. The new type system generalizes all the existing first-order type systems for objects, including systems based on variance annotations. Interestingly, the additional expressive power does not affect the complexity of the type inference problem, as we show by presenting an O(n^3) inference algorithm.

An Examination of a Church-Based Recovery Program on the Quality of Physical and Spiritual Life of Mentally Ill Persons in Korea

This study explores the effectiveness of a Church-based recovery program for the mentally ill in Korea where many Christian communities view mental illness as evidence of sin. Building on theological and psychological literature, an empirical study was conducted with participants in the alternative program of the Han-ma-um community. Data analysis revealed that this program, which views mental disorders as illness rather than sin, helps participants build self-respect and enables families to provide support as they move toward recovery. Based on this empirical examination, recommendations for refinement and expansion of the program and avenues for future research are proposed.