Higher-Order Model Checking by Abstraction of Type Derivation Rewriting

Model checking of recursion schemes, known as higher-order model checking, has actively been studied recently and is becoming a basis for verification of higher-order programs. Some practical model checking algorithms have been developed based on the reduction from model checking to intersection type inference, but they are not completely satisfactory. We propose a novel approach to developing model checking algorithms, based on abstract interpretation of a rewriting system on (incomplete) derivations in a “rigid” intersection type system. The derivation rewriting can be regarded as a simple type inference process that is sound and complete in a certain sense. However it is not practical since the state space (i.e. the set of all incomplete derivations) is too large. We construct an abstraction of the rewriting system, and develop an algorithm based on the abstract model. We have implemented the algorithm and confirmed that it outperforms previous model checkers in certain cases.