Programs written using a deterministic-by-construction model of parallel computation always produce the same observable results, offering programmers the promise of freedom from subtle, hard-to-reproduce nondeterministic bugs. A common thread that emerges in the study of deterministic-by-construction systems, from venerable models like Kahn process networks to modern ones like Intel’s Concurrent Collections system, is that the determinism of the model hinges on some notion of monotonicity. Taking monotonicity as a guiding principle, then, I’ll present a new model for deterministic parallel programming that generalizes existing single-assignment models to allow multiple assignments that are monotonically increasing with respect to a user-specified lattice. As I’ll show in my talk, this model achieves determinism by using a shared data structure with an API that allows only monotonically increasing writes and restricted reads. The resulting model also provides a theoretical grouunding for exploring a limited form of nondeterminism that admits failures but never wrong answers.