Behavior Trees (BTs) have found a widespread adoption in robotics due to appealing features, their ease of use as a conceptual model of control policies and the availability of software tooling for BT-based design of control software. However, BTs don't have formal execution semantics and, furthermore, subtle differences among implementations can make the same model behave differently depending on the underlying software. This paper aims at defining the execution semantics of behavior trees (BTs) as used in robotics applications. To this purpose, we present an abstract data type that formalizes the structure and execution of BTs. While our formalization is inspired by existing contributions in the scientific literature and state-of-the art implementations, we strive to provide an unambiguous treatment of most features that find incomplete or inconsistent treatment across other works.