Lambda calculus with algebraic simplification for reduction parallelisation: Extended study

Parallel reduction is a major component of parallel programming and widely used for summarisation and aggregation. It is not well understood, however, what sorts of non-trivial summarisations can be implemented as parallel reductions. This paper develops a calculus named λAS, a simply typed lambda c...

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Veröffentlicht in:Journal of functional programming Jg. 31
1. Verfasser: MORIHATA, AKIMASA
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cambridge, UK Cambridge University Press 2021
Schlagworte:
Algebra
Associativity
Calculus
Commutativity
ICFP 2019
Mathematical analysis
Parallel programming
Reduction
Simplification
ISSN:0956-7968, 1469-7653
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Zusammenfassung:Parallel reduction is a major component of parallel programming and widely used for summarisation and aggregation. It is not well understood, however, what sorts of non-trivial summarisations can be implemented as parallel reductions. This paper develops a calculus named λAS, a simply typed lambda calculus with algebraic simplification. This calculus provides a foundation for studying a parallelisation of complex reductions by equational reasoning. Its key feature is δ abstraction. A δ abstraction is observationally equivalent to the standard λ abstraction, but its body is simplified before the arrival of its arguments using algebraic properties such as associativity and commutativity. In addition, the type system of λAS guarantees that simplifications due to δ abstractions do not lead to serious overheads. The usefulness of λAS is demonstrated on examples of developing complex parallel reductions, including those containing more than one reduction operator, loops with conditional jumps, prefix sum patterns and even tree manipulations.
Bibliographie:ObjectType-Article-1
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ISSN:0956-7968
1469-7653
DOI:10.1017/S0956796821000058