Head-Order Techniques and Other Pragmatics of Lambda Calculus Graph Reduction PDF Download
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Author: Nikos B. Troullinos
Publisher: Universal-Publishers
ISBN: 1612337570
Category : Computers
Languages : en
Pages : 250
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Book Description
Available in Paperback Available in eBook editions (PDF format) Institution: Syracuse University (Syracuse, NY, USA) Advisor(s): Prof. Klaus J. Berkling Degree: Ph.D. in Computer and Information Science Year: 1993 Book Information: 248 pages Publisher: Dissertation.com ISBN-10: 1612337570 ISBN-13: 9781612337579 View First 25 pages: (free download) Abstract The operational aspects of Lambda Calculus are studied as a fundamental basis for high-order functional computation. We consider systems having full reduction semantics, i.e., equivalence-preserving transformations of functions. The historic lineage from Eval-Apply to SECD to RTNF/RTLF culminates in the techniques of normal-order graph Head Order Reduction (HOR). By using a scalar mechanism to artificially bind relatively free variables, HOR makes it relatively effortless to reduce expressions beyond weak normal form and to allow expression-level results while exhibiting a well-behaved linear self-modifying code structure. Several variations of HOR are presented and compared to other efficient reducers, with and without sharing, including a conservative breadth-first one which mechanically takes advantage of the inherent, fine-grained parallelism of the head normal form. We include abstract machine and concrete implementations of all the reducers in pure functional code. Benchmarking comparisons are made through a combined time-space efficiency metric. The original results indicate that circa 2010 reduction rates of 10-100 million reductions per second can be achieved in software interpreters and a billion reductions per second can be achieved by a state-of-the art custom VLSI implementation.
Author: Nikos B. Troullinos
Publisher: Universal-Publishers
ISBN: 1612337570
Category : Computers
Languages : en
Pages : 250
Get Book Here
Book Description
Available in Paperback Available in eBook editions (PDF format) Institution: Syracuse University (Syracuse, NY, USA) Advisor(s): Prof. Klaus J. Berkling Degree: Ph.D. in Computer and Information Science Year: 1993 Book Information: 248 pages Publisher: Dissertation.com ISBN-10: 1612337570 ISBN-13: 9781612337579 View First 25 pages: (free download) Abstract The operational aspects of Lambda Calculus are studied as a fundamental basis for high-order functional computation. We consider systems having full reduction semantics, i.e., equivalence-preserving transformations of functions. The historic lineage from Eval-Apply to SECD to RTNF/RTLF culminates in the techniques of normal-order graph Head Order Reduction (HOR). By using a scalar mechanism to artificially bind relatively free variables, HOR makes it relatively effortless to reduce expressions beyond weak normal form and to allow expression-level results while exhibiting a well-behaved linear self-modifying code structure. Several variations of HOR are presented and compared to other efficient reducers, with and without sharing, including a conservative breadth-first one which mechanically takes advantage of the inherent, fine-grained parallelism of the head normal form. We include abstract machine and concrete implementations of all the reducers in pure functional code. Benchmarking comparisons are made through a combined time-space efficiency metric. The original results indicate that circa 2010 reduction rates of 10-100 million reductions per second can be achieved in software interpreters and a billion reductions per second can be achieved by a state-of-the art custom VLSI implementation.
Author: Anna Soós
Publisher: Springer
ISBN: 3540880593
Category : Computers
Languages : en
Pages : 309
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Book Description
This volume presents the revised lecture notes of selected talks given at the second Central European Functional Programming School, CEFP 2007, held June 23–30, 2007 at Babe ̧ s-Bolyai University, Cluj-Napoca, Romania. The summer school was organized in the spirit of the advanced progr- ming schools. CEFP focuses on involving an ever-growing number of students, researchers,andteachersfromcentral,andeasternEuropeancountries.We were glad to welcome the invited lecturers and the participants: 15 professors and 30 students from 9 di?erent universities. The intensive program o?ered a creative and inspiring environment and a great opportunity to present and exchange ideas in new topics of functional programming. The lectures covereda wide range of topics like interactive work ?ows for the Web, proving properties of lazy functional programs, lambda calculus and - stract lambda calculus machines, programming in ? mega, object-oriented fu- tional programming, and refactoring in Erlang. We are very grateful to the lecturers and researchers for the time and the e?ort they devoted to the talks and the revised lecture notes. The lecture notes were each carefully checked by reviewers selected from experts of functional programming. Afterwards the papers were revised once more by the lecturers. This revision process guaranteed that only high-quality papers are accepted in the volume of the lecture notes.
Author: Werner Kluge
Publisher: Springer Science & Business Media
ISBN: 354027359X
Category : Computers
Languages : en
Pages : 382
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Book Description
The book emphasizes the design of full-fledged, fully normalizing lambda calculus machinery, as opposed to the just weakly normalizing machines.
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 802
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Book Description
Author: Joseph H. Fasel
Publisher: Springer Science & Business Media
ISBN: 9783540184201
Category : Computers
Languages : en
Pages : 58
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Book Description
This volume describes recent research in graph reduction and related areas of functional and logic programming, as reported at a workshop in 1986. The papers are based on the presentations, and because the final versions were prepared after the workshop, they reflect some of the discussions as well. Some benefits of graph reduction can be found in these papers: - A mathematically elegant denotational semantics - Lazy evaluation, which avoids recomputation and makes programming with infinite data structures (such as streams) possible - A natural tasking model for fine-to-medium grain parallelism. The major topics covered are computational models for graph reduction, implementation of graph reduction on conventional architectures, specialized graph reduction architectures, resource control issues such as control of reduction order and garbage collection, performance modelling and simulation, treatment of arrays, and the relationship of graph reduction to logic programming.
Author:
Publisher:
ISBN:
Category : Dissertation abstracts
Languages : en
Pages : 704
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Book Description
Author: Henk Barendregt
Publisher: Cambridge University Press
ISBN: 1107276349
Category : Mathematics
Languages : en
Pages : 969
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Book Description
This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
Author: Philippe Flajolet
Publisher: Cambridge University Press
ISBN: 1139477161
Category : Mathematics
Languages : en
Pages : 825
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Book Description
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author: Franklyn Turbak
Publisher: MIT Press
ISBN: 0262303159
Category : Computers
Languages : en
Pages : 1347
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Book Description
Key ideas in programming language design and implementation explained using a simple and concise framework; a comprehensive introduction suitable for use as a textbook or a reference for researchers. Hundreds of programming languages are in use today—scripting languages for Internet commerce, user interface programming tools, spreadsheet macros, page format specification languages, and many others. Designing a programming language is a metaprogramming activity that bears certain similarities to programming in a regular language, with clarity and simplicity even more important than in ordinary programming. This comprehensive text uses a simple and concise framework to teach key ideas in programming language design and implementation. The book's unique approach is based on a family of syntactically simple pedagogical languages that allow students to explore programming language concepts systematically. It takes as premise and starting point the idea that when language behaviors become incredibly complex, the description of the behaviors must be incredibly simple. The book presents a set of tools (a mathematical metalanguage, abstract syntax, operational and denotational semantics) and uses it to explore a comprehensive set of programming language design dimensions, including dynamic semantics (naming, state, control, data), static semantics (types, type reconstruction, polymporphism, effects), and pragmatics (compilation, garbage collection). The many examples and exercises offer students opportunities to apply the foundational ideas explained in the text. Specialized topics and code that implements many of the algorithms and compilation methods in the book can be found on the book's Web site, along with such additional material as a section on concurrency and proofs of the theorems in the text. The book is suitable as a text for an introductory graduate or advanced undergraduate programming languages course; it can also serve as a reference for researchers and practitioners.
Author: Marek Cygan
Publisher: Springer
ISBN: 3319212753
Category : Computers
Languages : en
Pages : 618
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Book Description
This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.
