Program Synthesis of Parallel Scans

We consider the problem of synthesis of data parallel and task parallel implementations of the scan also known as prefix sum. The user provides an example scan network as an input along with a partial program with missing array index expressions. We then manually extract the constraints for index expressions from the partial program such that the given example network is satisfied. Finally, the generated constraints are solved using linear programming solver. We found that our method is general enough to synthesize data parallel implementations of previously described parallel scan networks.