Formal verification of programs and their transformations

Formal verification is an act of using formal methods to check the correctness of intended programs. The verification is done by providing a formal proof on an abstract mathematical model of the program, with respect to a certain formal specification or property. We present three case studies on using formal methods to verify programs and their transformations: (1) we use term rewriting and theorem proving to construct and validate a compiler from logic specifications to ARM assembly code; the equivalence of a source specification and the generated assembly code is proven mechanically with respect to the formal semantics; (2) we model, in an \executable" declarative language TLA+, the Message Passing Interface (MPI) 2.0 library as well as C programs using MPI calls for parallel computations; and use explicit model checking to check the specifications and programs; and (3) we model CUDA kernel programs as symbolic logical formulas, and use constraint solving to automatically reason about these Graphics Processing Unit (GPU) kernels.