Automatically deriving cost models for structured parallel processes using hylomorphisms

Abstract

Please cite this article as: D. Castro, et al., Automatically deriving cost models for structured parallel processes using hylomorphisms, Future Generation Computer Systems (2017), http://dx.doi.org/10.1016/j.future. 2017.04.035 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. An operational semantics of a queue language for streaming computations.  An operational semantics of algorithmic skeletons using this queue language.  Derive cost equations for algorithmic skeletons from the operational semantics.  Cost equations for algorithmic skeletons are combined with sized types. AbstractStructured parallelism using nested algorithmic skeletons can greatly ease the task of writing parallel software, since common, but hard-to-debug, problems such as race conditions are eliminated by design. However, choosing the best combination of algorithmic skeletons to yield good parallel speedups for a specific program on a specific parallel architecture is still a difficult problem. This paper uses the unifying notion of hylomorphisms, a general recursion pattern, to make it possible to reason about both the functional correctness properties and the extra-functional timing properties of structured parallel programs. We have previously used hylomorphisms to provide a denotational semantics for skeletons, and proved that a given parallel structure for a program satisfies functional correctness. This paper expands on this theme, providing a simple operational semantics for algorithmic skeletons and a cost semantics that can be automatically derived from that operational semantics. We prove that both semantics are sound with respect to our previously defined denotational semantics. This means that we can now automatically and statically choose a provably optimal parallel structure for a given program with respect to a cost model for a (class of) parallel architecture. By deriving an automatic amortised analysis from our cost model, we can also accurately predict parallel runtimes and speedups.

Lambda calculus with algebraic simplification for reduction parallelization by equational reasoning

“…Indeed, every example discussed in Section 2 requires a constant number of indeterminates. Such a subset might be obtained by considering structural recursions, as in the study of Castro et al [2016Castro et al [ , 2018, and restrict duplication of δ -abstracted functions. If such a subset is found, it might be worthwhile to consider nonlinear polynomials as well, because exponential blowups cannot occur.…”

“…In contrast, a δ abstraction in λ as requires subterm simplification that the standard evaluation strategy does not allow. Castro et al [2016Castro et al [ , 2018 proposed a type-based approach for introducing parallelism to purely functional programs. Their type system certifies not only the correctness but also the cost of an obtained parallel program.…”