We present a constraint-based approach to computing winning strategies in two-player graph games over the state space of infinite-state programs. Such games have numerous applications in program verification and synthesis, including the synthesis of infinite-state reactive programs and branching-time verification of infinite-state programs. Our method handles games with winning conditions given by safety, reachability, and general Linear Temporal Logic (LTL) properties. For each property class, we give a deductive proof rule that --- provided a symbolic representation of the game players --- describes a winning strategy for a particular player. Our rules are sound and relatively complete. We show that these rules can be automated by using an off-the-shelf Horn constraint solver that supports existential quantification in clause heads. The practical promise of the rules is demonstrated through several case studies, including a challenging "Cinderella-Stepmother game" that allows infinite alternation of discrete and continuous choices by two players, as well as examples derived from prior work on program repair and synthesis.

A promising approach for type-safe generic codes in the objectoriented paradigm is variant parametric type, which allows covariant and contravariant subtyping on fields where appropriate. Previous approaches formalise variant type as a special case of the existential type system. In this paper, we present a new framework based on flow analysis and modular type checking to provide a simple but accurate model for capturing generic types. Our scheme stands to benefit from past (and future) advances in flow analysis and subtyping constraints. Furthermore, it fully supports casting for variant types with a special reflection mechanism, called cast capture, to handle objects with unknown types. We have built a constraint-based type checker and have proven its soundness. We have also successfully annotated a suite of Java libraries and client code with our flow-based variant type system.