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We describe pHPF, an research prototype HPF compiler for the IBM SP series parallel machines. The compiler accepts as input Fortran 90 and Fortran 77 programs, augmented with HPF directives; sequential loops are automatically parallelized. The compiler supports symbolic analysis of expressions. This allows parameters such as the number of processors to be unknown at compile-time without significantly affecting performance. Communication schedules and computation guards are generated in a parameterized form at compile-time. Several novel optimizations and improved versions of well-known optimizations have been implemented in pHPF to exploit parallelism and reduce communication costs. These optimizations include elimination of redundant communication using data-availability analysis; using collective communication; new techniques for mapping scalar variables; coarse-grain wavefronting; and communication reduction in multi-dimensional shift communications. We present experimental results for some well-known benchmark routines. The results show the effectiveness of the compiler in generating efficient code for HPF programs.