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

Abstract

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).

Anti-unification of Unordered Goals

“…The algorithms described in all of these works can be used to compute what we will call ⊑-common generalizations below in the present paper. Although none of these works develop a general (non-equational) taxonomy allowing to extend the results beyond that simple setting, nor discusses variable-or injectivity-based variants of antiunification operators, their usages do point out other interesting (and recent) applications of anti-unification when focused on unordered goals, namely detection of recursion schemes in functional programs (as explained in [2]) and techniques for learning bugfixes from software code repositories (an example being [27]).…”

A Framework for Approximate Generalization in Quantitative Theories

“…Anti-unification [12,14] is a logicbased method for computing generalizations. Being originally used for inductive and analogical reasoning, some recent applications include recursion scheme detection in functional programs [4], programming by examples in domainspecific languages [13], learning bug-fixing from software code repositories [3,15], automatic program repair [7], preventing bugs and misconfiguration in services [11], linguistic structure learning for chatbots [6], to name just a few.…”

One or Nothing: Anti-unification over the Simply-Typed Lambda Calculus

“…Anti-unification (generalization), first introduced in the 1970's by Plotkin and Reynolds [22,23], is a process that derives from a set of symbolic expressions a new symbolic expression possessing certain commonalities shared between its members. The concept has been apply to inductive theorem proving based on tree grammars [3], recursion scheme detection in functional programs [6], inductive synthesis of recursive functions [24], learning fixes from software code repositories [16,4], preventing bugs and misconfiguration [19], as well as uses within the fields of natural language processing and linguistics [17,2]. Applications, most related to our work are proof generalization [20] and higher-order term indexing [21], which use anti-unification over typed λ-terms and their extensions [5].…”