Type Inference for Nested Self Types

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We address the issue of the decidability of the type inference problem for a type system of an object-oriented calculus with general selftypes. The fragment considered in the present paper is obtained by restricting the set of operators to method invocation only. The resulting system, despite its syntactical simplicity, is sufficiently complicated to merit the study of the intricate constraints emerging in the process of type reconstruction, and it can be considered as the core system with respect to typability for extensions with other operators. The main result of the paper is the decidability of type reconstruction, together with a certain form of a principal type property.