Unifying structured recursion schemes

HinzeRalf,; Wu, Nicolas; GibbonsJeremy,

doi:10.1145/2544174.2500578

Cited by 14 publications

(23 citation statements)

References 24 publications

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“…In summary, recursion schemes fall into three categories: catamorphisms ('folding'), anamorphisms ('unfolding') and hylomorphisms ('refolding'). A menagerie of roughly 20 (not by any means exhaustive) variants on these basic patterns have been identified, including zygomorphisms, futumorphisms, chronomorphisms, and Elgot (co)algebras [12]. Some of these variants offer the potential for induced recursive functions which are 'efficient by construction'.…”

Section: Other Recursion Schemesmentioning

confidence: 99%

Stochastic synthesis of recursive functions made easy with bananas, lenses, envelopes and barbed wire

Swan

Krawiec

Kocsis

2019

Genet Program Evolvable Mach

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Stochastic synthesis of recursive functions has historically proved difficult, not least due to issues of non-termination and the often ad hoc methods for addressing this. This article presents a general method of implicit recursion which operates via an automatically-derivable decomposition of datatype structure by cases, thereby ensuring well-foundedness. The method is applied to recursive functions of longstanding interest and the results outperform recent work which combines two leading approaches and employs 'human in the loop' to define the recursion structure. We show that stochastic synthesis with the proposed method on benchmark functions is effective even with random search, motivating a need for more difficult recursive benchmarks in future.

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Section: Other Recursion Schemesmentioning

confidence: 99%

Stochastic synthesis of recursive functions made easy with bananas, lenses, envelopes and barbed wire

Swan

Krawiec

Kocsis

2019

Genet Program Evolvable Mach

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“…For the proof of this fact we refer to [7]. Now, if a is in, the action of the initial algebra, the homomorphism h is uniquely defined, and hence f , as well.…”

Section: Recursion Schemes From Comonadsmentioning

confidence: 99%

“…That paper also provides an implementation of various recursion schemes in Haskell although it does not make use of type class synonyms, since it predates that work. The correspondence between histomorphisms and recursion schemes from comonads is a direct application of the work in [7], which further explores the relationship between recursion schemes from comonads and the adjoint folds that were developed in [5].…”

Section: Related Workmentioning

confidence: 99%

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Histo- and dynamorphisms revisited

Hinze

2013

Proceedings of the 9th ACM SIGPLAN Workshop on Generic Programming

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Dynamic programming algorithms embody a widely used programming technique that optimizes recursively defined equations that have repeating subproblems. The standard solution uses arrays to share common results between successive steps, and while effective, this fails to exploit the structural properties present in these problems. Histomorphisms and dynamorphisms have been introduced to expresses such algorithms in terms of structured recursion schemes that leverage this structure. In this paper, we revisit and relate these schemes and show how they can be expressed in terms of recursion schemes from comonads, as well as from recursive coalgebras. Our constructions rely on properties of bialgebras and dicoalgebras, and we are careful to consider optimizations and efficiency concerns. Throughout the paper we illustrate these techniques through several worked-out examples discussed in a tutorial style, and show how a recursive specification can be expressed both as an array-based algorithm as well as one that uses recursion schemes.

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“…By rewriting safe as a composition of an unfold and an (implicit) foldr, our prototype can detect the foldr over the tree generated by the unfold. safe may alternatively be considered an instance of a zygomorphism[28], it may therefore be worth investigating this pattern as part of our future work. Another function, pargen, enumerates the different possible locations of the queens on the board.1 This is because in the original definition of safe, d is updated between recursive calls meaning a standard foldr is not equivalent (Def.…”

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confidence: 99%

Finding parallel functional pearls: Automatic parallel recursion scheme detection in Haskell functions via anti-unification

Barwell

Brown

Hammond

2018

Future Generation Computer Systems

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Please cite this article as: A.D. Barwell, C. Brown, K. Hammond, Finding parallel functional pearls: Automatic parallel recursion scheme detection in Haskell functions via anti-unification, Future Generation Computer Systems (2017), http://dx. AbstractThis paper describes a new technique for identifying potentially parallelisable code structures in functional programs. Higher-order functions enable simple and easily understood abstractions that can be used to implement a variety of common recursion schemes, such as maps and folds over traversable data structures. Many of these recursion schemes have natural parallel implementations in the form of algorithmic skeletons. This paper presents a technique that detects instances of potentially parallelisable recursion schemes in Haskell 98 functions. Unusually, we exploit anti-unification to expose these recursion schemes from source-level definitions whose structures match a recursion scheme, but which are not necessarily written directly in terms of maps, folds, etc. This allows us to automatically introduce parallelism, without requiring the programmer to structure their code a priori in terms of specific higher-order functions. We have implemented our approach in the Haskell refactoring tool, HaRe, and demonstrated its use on a range of common benchmarking examples. Using our technique, we show that recursion schemes can be easily detected, that parallel implementations can be easily introduced, and that we can achieve real parallel speedups (up to 23.79× the sequential performance on 28 physical cores, or 32.93× the sequential performance with hyper-threading enabled).

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Unifying structured recursion schemes

Cited by 14 publications

References 24 publications

Stochastic synthesis of recursive functions made easy with bananas, lenses, envelopes and barbed wire

Stochastic synthesis of recursive functions made easy with bananas, lenses, envelopes and barbed wire

Histo- and dynamorphisms revisited

Finding parallel functional pearls: Automatic parallel recursion scheme detection in Haskell functions via anti-unification

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