We propose a framework for the evaluation of implicitly parallel functional programs on message passing multiprocessors with special emphasis on the issue of load bounding. The model is based on a new encoding of the lambda-calculus in Milner's pi-calculus and combines lazy evaluation and eager (parallel) evaluation in the same framework. The pi-calculus encoding serves as the specification of a more concrete compilation scheme mapping a simple functional language into a message passing, parallel program. We show how and under which conditions we can guarantee successful load bounding based on this compilation scheme. Finally we discuss the architectural requirements for a machine to support our model efficiently and we present a simple RISC-style processor architecture which meets those criteria.