Programs written using a deterministic-by-construction model of parallel computation are guaranteed to always produce the same observable results, offering programmers freedom from subtle, hard-to-reproduce nondeterministic bugs that are the scourge of parallel software. We present LVars, a new model for deterministicby-construction parallel programming that generalizes existing single-assignment models to allow multiple assignments that are monotonically increasing with respect to a user-specified lattice. LVars ensure determinism by allowing only monotonic writes and "threshold" reads that block until a lower bound is reached. We give a proof of determinism and a prototype implementation for a language with LVars and describe how to extend the LVars model to support a limited form of nondeterminism that admits failures but never wrong answers.
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