A short cut to parallelization theorems

Akimasa Morihata

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)


The third list-homomorphism theorem states that if a function is both foldr and foldl, it has a divide-and-conquer parallel implementation as well. In this paper, we develop a theory for obtaining such parallelization theorems. The key is a new proof of the third list-homomorphism theorem based on shortcut deforestation. The proof implies that there exists a divide-and-conquer parallel program of the form of h (x 'merge' y) = h1 × ⊙ h 2 y, where h is the subject of parallelization, merge is the operation of integrating independent substructures, h1 and h 2 are computations applied to substructures, possibly in parallel, and ⊙ merges the results calculated for substructures, if (i) h can be specified by two certain forms of iterative programs, and (ii) merge can be implemented by a function of a certain polymorphic type. Therefore, when requirement (ii) is fulfilled, h has a divide-and-conquer implementation if h has two certain forms of implementations. We show that our approach is applicable to structure-consuming operations by catamorphisms (folds), structure-generating operations by anamorphisms (unfolds), and their generalizations called hylomorphisms.

Original languageEnglish
Title of host publicationICFP 2013 - Proceedings of the 2013 ACM SIGPLAN International Conference on Functional Programming
Number of pages12
Publication statusPublished - 2013 Nov 12
Event2013 18th ACM SIGPLAN International Conference on Functional Programming, ICFP 2013 - Boston, MA, United States
Duration: 2013 Sep 252013 Sep 27

Publication series

NameProceedings of the ACM SIGPLAN International Conference on Functional Programming, ICFP


Other2013 18th ACM SIGPLAN International Conference on Functional Programming, ICFP 2013
Country/TerritoryUnited States
CityBoston, MA


  • Divide-and-conquer parallelism
  • Shortcut deforestation
  • Third list-homomorphism theorem

ASJC Scopus subject areas

  • Software


Dive into the research topics of 'A short cut to parallelization theorems'. Together they form a unique fingerprint.

Cite this