My key takeaway was that mathematical properties like associativity, commutativity, idempotency, and having an identity value are good tools for communicating w

My key takeaway was that mathematical properties like associativity, commutativity, idempotency, and having an identity value are good tools for communicating with compilers. An associative binary operator plus an identity is enough to automatically turn your + into a Σ, with the compiler being able to choose a parallel or sequential implementation. Guy's example code uses a language that looks like mathematical notation, but I think that if you could tell the compiler what's associative and what the identity value is, you could get there with procedural code provided you use for-each instead of classic for. There's also probably a better way to phrase the first line than "var x = operator.identity;" so that more natural code ends up parallelizable, but I don't know what it is.