Semantics-based parallel cost models and their use in provably efficient implementations

Understanding the performance issues of modern programming language execution can be di cult. These languages have abstract features, such as higher-order functions, laziness, and objects, that ease programming, but which make their mapping to the underlying machine more di cult. Understanding parallel languages is further complicated by the need to describe what computations are performed in parallel and how they are a ected by communication and latency in the machine. This lack of understanding can obscure even the asymptotic performance of a program and can also hide performance bugs in the language implementation. The dissertation introduces a framework of provably e cient implementations in which performance issues of a language can be de ned and analyzed. We de ne several language models, each consisting of an operational semantics augmented with the costs of execution. In particular, the dissertation examines three functional languages based on fork-and-join parallelism, speculative parallelism, and data-parallelism, and it examines their time and space costs. We then de ne implementations of each language model onto several common machine models, prove these implementations correct, and derive their costs. Each of these implementations uses an intermediate model based on an abstract machine to stage the overall implementation. The abstract machine executes a series of steps transforming a stack of active states and store into new states and store. The dissertation proves the e ciency of the implementation by relating the steps to the parallel traversal of a computation graph de ned in the augmented operational semantics. Provably e cient implementations are useful for programmers, language implementors, and language designers. For example, they provide a formal de nition of language and implementation costs for program analysis, compiler speci cation, and language comparisons. The dissertation describes performance problems in existing implementations of Id and NESL and gives provably more e cient alternatives for each. It also compares the example language models, rst using several speci c algorithms, and also in more generality, for example, quantifying the speedup obtainable in the data-parallel language relative to the fork-and-join language.