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An Algebraic Framework for Parallelizing Recurrence in Functional Programming [chapter]

Rodrigo C. O. Rocha, Luís F. W. Góes, Fernando M. Q. Pereira
2016 Lecture Notes in Computer Science  
In this paper, we propose an algebraic framework for parallelizing -automatically -two special classes of recursive functions.  ...  The main challenge faced by automatic parallelization tools in functional languages is the fact that parallelism is often hidden under the syntax of complex recursive functions.  ...  To achieve this objective, we propose an algebraic framework for parallelizing two special classes of recursive functions. These functions need to have two core properties.  ... 
doi:10.1007/978-3-319-45279-1_10 fatcat:mcjm4c5y7zc55hso7dnhns3f54

A cost-aware logical framework [article]

Yue Niu
2021 arXiv   pre-print
We present calf, a cost-aware logical framework for studying quantitative aspects of functional programs.  ...  We evaluate calf as a general framework for cost analysis by implementing two fundamental techniques for algorithm analysis: the method of recurrence relations and physicist's method for amortized analysis  ...  ACKNOWLEDGMENTS We are grateful to Carlo Angiuli and Alex Kavvos for productive discussions on the topic of this research, and to Tristan Nguyen at AFOSR for his support.  ... 
arXiv:2107.04663v2 fatcat:3bit6tz77ff65drvkyiid5zgne

Parallelizing CAD

Bryan Catanzaro, Kurt Keutzer, Bor-Yiing Su
2008 Proceedings of the 45th annual conference on Design automation - DAC '08  
We believe that frameworks for these patterns will enable CAD to successfully capitalize on increased processor performance through parallelism.  ...  We believe that an ad hoc approach to parallelizing CAD applications will not lead to satisfactory results: neither in terms of return on engineering investment nor in terms of the computational efficiency  ...  A PARALLEL FRAMEWORK FOR LOGIC OPTIMIZATION In this section we work through a high-level architecture for a parallel logic-optimization framework.  ... 
doi:10.1145/1391469.1391475 dblp:conf/dac/CatanzaroKS08 fatcat:gyirvtvsf5bh3l5l7fevugj4mm

An Algebraic Framework for Compositional Program Analysis [article]

Azadeh Farzan, Zachary Kincaid
2013 arXiv   pre-print
A program analysis in our framework defined by an algebraic structure equipped with sequencing, choice, and iteration operations.  ...  This paper presents algebraic framework for designing, implementing, and proving the correctness of compositional program analyses.  ...  Table 8 Conclusion and Related work In this paper, we presented an algebraic framework for compositional program analysis.  ... 
arXiv:1310.3481v1 fatcat:42sj26xl5jbe5iasdgczyi4vpe

DLVM: A modern compiler infrastructure for deep learning systems [article]

Richard Wei, Lane Schwartz, Vikram Adve
2018 arXiv   pre-print
However, many of the existing deep learning frameworks are software libraries that act as an unsafe DSL in Python and a computation graph interpreter.  ...  With our prototypical staged DSL embedded in Swift, we argue that the DLVM system enables a form of modular, safe and performant frameworks for deep learning.  ...  The function @foo_grad in Figure 3 is an example of such a function.  ... 
arXiv:1711.03016v5 fatcat:6rh2hyxr6zh4bikxpqf4ar6vee

Automatic Parallelization Using the Value Evolution Graph [chapter]

Silvius Rus, Dongmin Zhang, Lawrence Rauchwerger
2005 Lecture Notes in Computer Science  
This results in the automatic parallelization of loops that contain arrays indexed by induction variables without closed forms. We implemented this framework in the Polaris research compiler.  ...  We introduce a framework for the analysis of memory reference sets addressed by induction variables without closed forms.  ...  Preliminary results show that, with minor improvement, we could solve more complex problems such as the parallelization of loop INTERF do1000 in code MDG from the PERFECT suite.  ... 
doi:10.1007/11532378_27 fatcat:3ay57pbe3rc5hj2vzoizmf4n7e

Automatic Feynman diagram calculation with xloops--a short overview [article]

Lars Brucher
2000 arXiv   pre-print
In this paper it is shown which problems to be solved by computer algebra arise during such calculations, and how this problems are handled in the framework of xloops.  ...  xloops is a program package that calculates Feynman diagrams by using computer algebra systems.  ...  A fast technique: recurrence relations with R-functions In the case of the one-loop two-point function the resulting R-functions gained by integration fulfill the following recurrence relation: (b 1 +  ... 
arXiv:hep-ph/0002028v1 fatcat:r5s7hxtogngqxjlc3hapsjghi4

Book announcements

1993 Discrete Applied Mathematics  
PART 4: NONLINEAR PROGRAMMING. Chapter 12: Nonlinear Programming. An Initial Algebra Framework for Unifying the Structured Models. Introduction. Algebras. Initial algebras. Yourdon structure charts.  ...  Defining unstructuredness (An entry in the middle of a selection or parallel connection. An exit in the middle of a selection or parallel connection.  ...  Example on an application  ... 
doi:10.1016/0166-218x(93)90117-7 fatcat:mo4kjmd2czdg5hejcof7fmm6u4

Page 9565 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
(UZ-SAM; Samarkand) Recurrence functions and numerical characteristics of graphs. (English summary) Computer algebra in scientific computing (Konstanz, 2001), 187-194, Springer, Berlin, 2001.  ...  Many examples are given of the problematic treatment of equality in var- ious computer algebra systems, and of data structure equality in programming languages.  ... 

Automatic parallelization via matrix multiplication

Shigeyuki Sato, Hideya Iwasaki
2011 Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation - PLDI '11  
We have also implemented our framework and techniques as a parallelizer in a compiler.  ...  One enhances its capability for parallelization by extracting max-operators automatically, and the other improves the performance of parallelized programs by eliminating redundancy.  ...  Acknowledgments We would like to thank Masato Takeichi and Zhenjiang Hu for encouraging our research.  ... 
doi:10.1145/1993498.1993554 dblp:conf/pldi/SatoI11 fatcat:wp5zxl2lyranxmi2kb2hpxk3zu

GPU Parallelization of Algebraic Dynamic Programming [chapter]

Peter Steffen, Robert Giegerich, Mathieu Giraud
2010 Lecture Notes in Computer Science  
The ADP compiler translates such ADP programs into C. As all the ADP problems have similar data dependencies in the dynamic programming tables, a generic parallelization is possible.  ...  Algebraic Dynamic Programming (ADP) is a framework to encode a broad range of optimization problems, including common bioinformatics problems like RNA folding or pairwise sequence alignment.  ...  Steffen's stay in Université Lille 1. This research was carried through the "NVIDIA Professor Partnership" program.  ... 
doi:10.1007/978-3-642-14403-5_31 fatcat:dnrrorltljgmddh37md5vj3no4

Symbolic Analysis of Imperative Programming Languages [chapter]

Bernd Burgstaller, Bernhard Scholz, Johann Blieberger
2006 Lecture Notes in Computer Science  
This novel representation of program semantics closes the gap between program analysis and computer algebra systems, which makes supercontexts an ideal intermediate representation for all domainspecific  ...  We present a generic symbolic analysis framework for imperative programming languages. Our framework is capable of computing all valid variable bindings of a program at given program points.  ...  In [17] a symbolic representation for contexts is introduced. Closure contexts are an extension of this algebraic structure.  ... 
doi:10.1007/11860990_12 fatcat:xox4gsnob5efxacafendgbjz4y

Page 4654 of Mathematical Reviews Vol. , Issue 89H [page]

1989 Mathematical Reviews  
The paper then extends the approach used as the basis for the performance compiler so that the theoretical framework includes functional programs that make use of recursion and complex data  ...  It generates a system of recurrence equations derived from a given program whose efficiency one wishes to analyze.  ... 

Page 4620 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
Summary: “Tabular functions were invented to form a formal framework for normal and inverted function tables used in docu- menting complex software systems.  ...  The reader is invited to use Maple (or any other computer algebra system) to follow most algebraic developments; a pencil and paper 68 COMPUTER SCIENCE 4620 approach could result in an absurd number of  ... 

Page 6233 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
Shafarenko, RETRAN: a recurrent paradigm for data-parallel computing (169-186); Thomas J.  ...  considerations for object-oriented programming on distributed memory paral- lel computers (295-313); Thierry Cornu and Stéphane Vialle, A framework for implementing highly parallel applications on dis  ... 
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