The described technology is directed towards normalizing input received from various types of device types for providing the input to user interface (UI) elements in a unified way that reflects the invoke intent of the user. Input from different device types is classified as button input, pointer input or command input, and routed to a corresponding button provider, pointer provider or command provider. Each provider includes logic for communicating input data (e.g., events) to a UI element or elements. Based upon the input events, a UI element can execute a corresponding invoke handler to take an invoke action for that particular event.