1. A method of terminating an accelerator application program in a hybrid computing environment, the hybrid computing environment comprising a host computer having a host computer architecture and an accelerator having an accelerator architecture, the accelerator architecture optimized, with respect to the host computer architecture, for speed of execution of a particular class of computing functions, the host computer and the accelerator adapted to one another for data communications by a system level message passing module (‘SLMPM’), wherein the accelerator is configured to execute one or more accelerator application programs, the method comprising: receiving, by the SLMPM from a host application executing on the host computer, a request to terminate an accelerator application program executing on the accelerator, wherein the request to terminate the accelerator application comprises an accelerator identifier uniquely identifying the accelerator, and a process identifier uniquely identifying the accelerator application; terminating, by the SLMPM, execution of the accelerator application program; returning, by the SLMPM to the host application, a signal indicating that execution of the accelerator application program was terminated; and performing, by the SLMPM, a cleanup of the execution environment associated with the terminated accelerator application program by causing undelivered messages associated with the terminated accelerator application program to indicate an error.