DOCSLIB.ORG

Title: Region-Based Memory Management1 Authors: Mads Tofte and Jean-Pierre Talpin a Liation: Mads Tofte: Department of Computer

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Title: Region-Based Memory Management1 Authors: Mads Tofte and Jean-Pierre Talpin a Liation: Mads Tofte: Department of Computer Title RegionBased Memory Management Authors Mads Tofte and JeanPierre Talpin Aliation Mads Tofte Department of Computer Science Universityof Cop enhagen JeanPierre Talpin IRISA Campus de Beaulieu France An earlier version of this work was presented at the st ACM SIGPLANSIGACT Sym p osium on Principles of Programming Languages Portland Oregon January Abstract This pap er describ es a memory management disciplin e for programs that p erform dynamic memory allo cation and deallo cation At runtime all values are put into regions The store consists of a stack of regions All p oints of region allo cation and deallo cation are inferred automatically using a typ e and eect based program analysis The scheme do es not assume the presence of a garbage collector The scheme was rst presented byTofte and Talpin subse quently it has b een tested in The ML Kit with Regions a regionbased garbagecollection free implementation of the Standard ML Core language which includes recursive datatyp es higherorder functions and up datable references Birkedal et al Elsman and Hallenb erg This pap er denes a regionbased dynamic semantics for a skeletal pro gramming language extracted from Standard ML We present the inference system which sp ecies where regions can b e allo cated and deallo cated and a detailed pro of that the system is sound with resp ect to a standard se mantics We conclude by giving some advice on how to write programs that run well on a stack of regions based on practical exp erience with the ML Kit Intro duction Computers have nite memory Very often the total of memory allo cated by a program as it is run far exceeds the size of the memory Thus a practical discipline of programming must provide some form of memory recycling One of the key achievements of early work in programming languages is the invention of the notion of blo ck structure and the asso ciated implementation tech nology of stackbased memory management for recycling of memory In blo ck structured languages every p oint of allo cation is matched bya point of deallo ca tion and these p oints can easily b e identied in the source programNaur Dijkstra Prop erly used the stack discipline can result in very ecient use of memory the maximum memory usage b eing b ounded by the depth of the call stack rather than the numb er of memory allo cations The stack discipline has its limitations however as witnessed by restrictions in the typ e systems of blo ckstructured languages For example pro cedures are typically prevented from returning lists or pro cedures as results There are two main reasons for such restrictions First for the stackdiscipline to work the size of a value must b e known at the latest when space for that value is allo cated This allows for example arrays which are lo cal to a pro cedure and have their size determined by the arguments of the pro cedure by contrast it is not in general p ossible to determine howbig a list is going to b ecome when generation of the list b egins alues must com Second for the stackdiscipline to work the lifetime of v ply with the allo cation and deallo cation scheme asso ciated with blo ck structure When pro cedures are values there is a danger that a pro cedure value refers to values whichhave b een deallo cated For example consider the following program let x in fn y x y end This expression is an application of a function denoted by letendtothe number The function has formal parameter y and b o dy x y where stands for rst pro jection fn is pronounced in SML Thus the op erator expression is supp osed to evaluate to fn y x y where x is b ound to the pair so that the whole expression evaluates to the pair However if we regard the letend construct as a blo ck construct rather than just a lexical scop e we see why a stackbased implementation would not work we cannot deallo cate the space for x at the end since the rst comp onentof x is still needed by the function which is returned by the en tire let expression One way to ease the limitations of the stack discipline is to allow program mer controlled allo cation and deallo cation of memory as is done in C C has r r r r Figure The store is a stack of regions every region is uniquely identied bya region name eg r and is depicted bya box in the picture two op erations malloc and free for allo cation and deallo cation resp ectively Unfortunately it is in general very hard for a programmer to know when a blo ck of memory do es not contain any livevalues and may therefore b e freed conse quently this solution very easily leads to socalled spaceleaks ie to programs that use much more memory than exp ected Functional languages like Haskell and Standard ML and some ob jectoriented languages eg JAVA instead let a separate routine in the runtime system the garbage col lectortake care of deallo cation of memory Knuth Baker Lieb erman Allo cation is done by the program often at a very high rate In our example the three expressions fn y x y and x y each allo cate memoryeach time they are evaluated The part of memory used for holding suchvalues is called the heap the role of the garbage collector is to recycle those parts of the heap that hold only dead values ie values which are of no consequence to the rest of the computation Garbage collection can b e very fast provided the computer has enough mem ory Indeed there is a much quoted argument that the amortized cost of copying garbage collection tends to zero as memory tends to innity App el page It is not the case however that languages such as Standard ML frees the programmer completely from having to worry ab out memory management To write ecient SML programs one must understand the p otential dangers of for example accidental copying or survival of large data structures If a program is written without concern for space usage it maywell use much more memory than one would like even if the problem is lo cated using a space proler for example turning a spacewasting program into a spaceecient one may require ma jor changes to the co de The purp ose of the work rep orted in this pap er is to advo cate a compromise between the two extremes completely manual vs completely automatic memory management We prop ose a memory mo del which the user may use when pro gramming memory can b e thought of as a stack of regions see Figure Each region is like a stackofunb ounded size which grows upwards in the picture until the region in its entirety is p opp ed o the region stack For example a typical use of a region is to hold a list A program analysis automatically identies pro gram p oints where entire regions can b e allo cated and deallo cated and decides for eachvaluepro ducing expression into which region the value should b e put More sp ecicallywe translate every welltyp ed source language expression einto a target language expression e which is identical with e except for certain region annotations The evaluation of e corresp onds step for step to the evaluation of eTwo forms of annotations are e at letregion in e end The rst form is used whenever e is an expression which directly pro duces a value Constant expressions abstractions and tuple expressions fall into this category The is a region variable it indicates that the value of e is to b e put in the region b ound to The second form intro duces a region variable with lo cal scop e e At run time rst an unused region identied bya region name r is allo cated and b ound to Then e is evaluated probably using the region named r Finally the region is deallo cated The letregion expression is the only wayofintro ducing and eliminating regions Hence regions are allo cated and deallo cated in a stacklike manner The target program which corresp onds to the ab ove source program is e letregion in letregion in let x at at at in y x y at at end end at end We shall step through the evaluation of this expression in detail in Section Brieyevaluation starts in a region stack with three regions and and and evaluation then allo cates and deallo cates three more regions at the end and contain the nal result The scheme forms the basis of the ML Kit with Regions a compiler for the Standard ML Core language including higherorder functions references and recursive datatyp es The region inference rules we describ e in this pap er address life times only A solution to the other problem handling values of unknown size is addressed in Birkedal et al An imp ortant optimisation turns out to b e to distinguish b etween regions whose size can b e determined statically and those that cannot The former can b e allo cated on a usual stack Using C terminology region analysis infers where to insert calls to malloc and free but b eware that the analysis has only b een develop ed in the context of Standard ML and relies on the fact that SML is rather more strongly typ ed than C For a strongly typ ed imp erative language likeJAVA region inference mightbe useful for freeing memory unlikeCJAVA do es not have free For readers who are interested in co de generation App endix A shows the threeaddress program which the ML Kit pro duces from the ab ove program using b oth region inference and the additional optimisations describ ed in Birkedal et al However this pap er is primarily ab out the semantics of regions not their implementation Exp erience with the Kit is that prop erly used the region scheme is strong enough to execute demanding b enchmarks and to make considerable space sav ings compared to a garbagecollected system
Load more

Recommended publications
  • Four Lectures on Standard ML
    Mads Tofte March Lab oratory for Foundations of Computer Science Department of Computer Science Edinburgh University Four Lectures on Standard ML The following notes give an overview of Standard ML with emphasis placed on the Mo dules part of the language The notes are to the b est of my knowledge faithful to The Denition of Standard ML Version as regards syntax semantics and terminology They have b een written so as to b e indep endent of any particular implemen tation The exercises in the rst lectures can b e tackled without the use of a machine although having access to an implementation will no doubt b e b enecial The pro ject in Lecture presupp oses access to an implementation of the full language including mo dules At present the Edinburgh compiler do es not fall into this category the author used the New Jersey Standard ML compiler Lecture gives an introduction to ML aimed at the reader who is familiar with some programming language but do es not know ML Both the Core Language and the Mo dules are covered by way of example Lecture discusses the use of ML mo dules in the development of large programs A useful metho dology for programming with functors signatures and structures is presented Lecture gives a fairly detailed account of the static semantics of ML mo dules for those who really want to understand the crucial notions of sharing and signature matching Lecture presents a one day pro ject intended to give the student an opp ortunity of mo difying a nontrivial piece of software using functors signatures and structures
    [Show full text]
  • Understanding and Evolving the ML Module System
    Understanding and Evolving the ML Module System Derek Dreyer May 2005 CMU-CS-05-131 School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 Thesis Committee: Robert Harper (co-chair) Karl Crary (co-chair) Peter Lee David MacQueen (University of Chicago) Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Copyright c 2005 Derek Dreyer This research was sponsored in part by the National Science Foundation under grant CCR-0121633 and EIA- 9706572, and the US Air Force under grant F19628-95-C-0050 and a generous fellowship. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. Keywords: ML, module systems, type systems, functors, abstract data types, lambda calculus, recursive modules, singleton kinds Abstract The ML module system stands as a high-water mark of programming language support for data abstraction. Nevertheless, it is not in a fully evolved state. One prominent weakness is that module interdependencies in ML are restricted to be acyclic, which means that mutually recursive functions and data types must be written in the same module even if they belong conceptually in different modules. Existing efforts to remedy this limitation either involve drastic changes to the notion of what a module is, or fail to allow mutually recursive modules to hide type information from one another. Another issue is that there are several dialects of ML, and the module systems of these dialects differ in subtle yet semantically significant ways that have been difficult to account for in any rigorous way.
    [Show full text]
  • Lecture Notes in Computer Science 2566 Edited by G
    Lecture Notes in Computer Science 2566 Edited by G. Goos, J. Hartmanis, and J. van Leeuwen 3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo Torben Æ. Mogensen David A. Schmidt I. Hal Sudborough (Eds.) The Essence of Computation Complexity, Analysis, Transformation Essays Dedicated to Neil D. Jones 13 Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editors Torben Æ. Mogensen University of Copenhagen, DIKU Universitetsparken 1, 2100 Copenhagen, Denmark E-mail: [email protected] David A. Schmidt Kansas State University, Department of Computing and Information Sciences 234 Nichols Hall, Manhattan, KS 66506 USA E-mail: [email protected] I. Hal Sudborough University of Texas at Dallas, Department of Computer Science P.O. Box 830688, Richardson, TX 75083 USA E-mail: [email protected] The illustration appearing on the cover of this book is the work of Daniel Rozenberg (DADARA). Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress. Bibliographic information published by Die Deutsche Bibliothek. Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>. CR Subject Classification (1998): F.3, F.1, D.2 ISSN 0302-9743 ISBN 3-540-00326-6 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks.
    [Show full text]
  • A Simpli Ed Account of Polymorphic References 1 Introduction 2 a Language with Mutable Data Structures
    A Simpli ed AccountofPolymorphic References Rob ert Harp er Scho ol of Computer Science Carnegie Mellon University Pittsburgh, PA 15213-3891 Abstract A pro of of the soundness of Tofte's imp erativetyp e discipli ne with resp ect to a structured op erational semantics is given. The presentation is based on a semantic formalism that combines the b ene ts of the approaches considered byWright and Felleisen, and byTofte, leading to a particularly simple pro of of soundness of Tofte's typ e disciplin e. Keywords: formal semantics, functional programming, programming languages, typ e theory, refer- ences and assignment. 1 Intro duction The extension of Damas and Milner's p olymorphic typ e system for pure functional programs [2] to accomo- date mutable cells has proved to b e problematic. The nave extension of the pure language with op erations to allo cate a cell, and to retrieve and mo dify its contents is unsound [11]. The problem has received consid- erable attention, notably by Damas [3], Tofte [10,11], and LeroyandWeiss [7]. Tofte's solution is based on a greatest xed p oint construction to de ne the semantic typing relation [11] (see also [8]). This metho d has b een subsequently used by Leroy and Weiss [7]andTalpin and Jouvelot [9]. It was subsequently noted by Wright and Felleisen [13] that the pro of of soundness can b e substantially simpli ed if the argument is made by induction on the length of an execution sequence, rather than on the structure of the typing derivation. Using this metho d they establish the soundness of a restriction of the language to require that let-b ound expressions b e values.
    [Show full text]
  • The Definition of Standard ML, Revised
    The Definition of Standard ML The Definition of Standard ML (Revised) Robin Milner, Mads Tofte, Robert Harper and David MacQueen The MIT Press Cambridge, Massachusetts London, England c 1997 Robin Milner All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data The definition of standard ML: revised / Robin Milner ::: et al. p. cm. Includes bibliographical references and index. ISBN 0-262-63181-4 (alk. paper) 1. ML (Computer program language) I. Milner, R. (Robin), 1934- QA76.73.M6D44 1997 005:1303|dc21 97-59 CIP Contents 1 Introduction 1 2 Syntax of the Core 3 2.1 Reserved Words . 3 2.2 Special constants . 3 2.3 Comments . 4 2.4 Identifiers . 5 2.5 Lexical analysis . 6 2.6 Infixed operators . 6 2.7 Derived Forms . 7 2.8 Grammar . 7 2.9 Syntactic Restrictions . 9 3 Syntax of Modules 12 3.1 Reserved Words . 12 3.2 Identifiers . 12 3.3 Infixed operators . 12 3.4 Grammar for Modules . 13 3.5 Syntactic Restrictions . 13 4 Static Semantics for the Core 16 4.1 Simple Objects . 16 4.2 Compound Objects . 17 4.3 Projection, Injection and Modification . 17 4.4 Types and Type functions . 19 4.5 Type Schemes . 19 4.6 Scope of Explicit Type Variables . 20 4.7 Non-expansive Expressions . 21 4.8 Closure .
    [Show full text]
  • Implementation of the Typed Call-By-Value Λ-Calculus Using a Stack of Regions
    Implementation of the Typed Call-by-Value λ-calculus using a Stack of Regions Mads Tofte, University of Copenhagen∗ Jean-Pierre Talpin, European Computer-Industry Research Center † Abstract from the source program. Heap-based schemes are less eager to reuse memory. Generational garbage collec- We present a translation scheme for the polymorphi- tion collects young objects when the allocation space cally typed call-by-value λ-calculus. All runtime val- is used up. Hayes[11] discusses how to reclaim large, ues, including function closures, are put into regions. old objects. The store consists of a stack of regions. Region in- Garbage collection can be very fast. Indeed, there ference and effect inference are used to infer where is a much quoted argument that the amortized cost of regions can be allocated and de-allocated. Recursive copying garbage collection tends to zero, as memory functions are handled using a limited form of polymor- tends to infinity[2, page 206]. Novice functional pro- phic recursion. The translation is proved correct with grammers often report that on their machines, mem- respect to a store semantics, which models a region- ory is a constant, not a variable, and that this constant based run-time system. Experimental results suggest has to be uncomfortably large for their programs to that regions tend to be small, that region allocation is run well. The practical ambition of our work is to frequent and that overall memory demands are usually reduce the required size of this constant significantly. modest, even without garbage collection. We shall present measurements that indicate that our translation scheme holds some promise in this respect.
    [Show full text]
  • Tips for Computer Scientists Standard ML (Revised)
    Tips for Computer Scientists on Standard ML (Revised) Mads Tofte August 30, 2009 This document and all examples in it are available from http://www.itu.dk/people/tofte Preface Contents This note is inspired by a brilliant piece of writ- 1 Numbers 1 ing, entitled Tips for Danes on Punctuation in 2 Overloaded Arithmetic Operators 1 English, by John Dienhart, Department of En- 3 Strings 1 glish, Odense University (1980). In a mere 11 4 Lists 1 pages, Dienhart’s lucid writing gives the reader 5 Expressions 1 the impression that punctuation in English is 6 Declarations 1 pretty easy and that any Dane can get it right 7 Function Values 2 in an afternoon or so. 8 Constructed Values 3 In the same spirit, this note is written for col- 9 Patterns 4 leagues and mature students who would like to 10 Pattern Matching 5 get to know Standard ML without spending too 11 Function-value Bindings (revisited) 6 much time on it. It is intended to be a relaxed 12 Function Application 6 stroll through the structure of Standard ML, with 13 Type Expressions 7 plenty of small examples, without falling into 14 Type Abbreviations 7 the trap of being just a phrase book. 15 Datatype Declarations 7 I present enough of the grammar that the 16 Exceptions 8 reader can start programming in Standard ML, 17 References 9 should the urge arise. 18 Procedures 10 The full grammar and a formal definition of 19 Input and Output 10 the semantics can be found in the 1997 language 20 The top-level loop 11 definition[2].
    [Show full text]
  • A Retrospective on Region-Based Memory Management
    Higher-Order and Symbolic Computation, 17, 245–265, 2004 c 2004 Kluwer Academic Publishers. Manufactured in The Netherlands. A Retrospective on Region-Based Memory Management MADS TOFTE [email protected] LARS BIRKEDAL∗ [email protected] MARTIN ELSMAN [email protected] NIELS HALLENBERG [email protected] The IT University of Copenhagen, Denmark Abstract. We report on our experience with designing, implementing, proving correct, and evaluating a region- based memory management system. Keywords: dynamic storage management, regions, Standard ML 1. Introduction Originally, Region-based Memory Management was conceived as a purely theoretical idea intended to solve a practical problem in the context of Standard ML, namely inventing a dynamic memory management discipline that is less space demanding and more predictable than generic garbage collection techniques, such as generational garbage collection. Over the subsequent nine years, considerable effort has been devoted to refining the idea, proving it correct, and investigating whether it worked in practice. The practical experiments revealed weaknesses, which led to new program analyses, new theory, and yet more experimentation. In short, we have sought to work on memory management as an experimental science: the work should be scientific in the sense that it should rest on a solid mathematical foundation and it should be experimental in the sense that it should be tested against competing state-of-the-art implementation technology. The purpose of this paper is to step back and consider the process as a whole. We first describe the main technical developments, with an emphasis on what motivated the developments. We then summarise what we think has gone well and what has not gone so well.
    [Show full text]
  • A Region Inference Algorithm
    A Region Inference Algorithm MADS TOFTE University of Copenhagen and LARS BIRKEDAL Carnegie Mellon University Region Inference is a program analysis which infers lifetimes of values. It is targeted at a runtime model in which the store consists of a stack of regions and memory management predominantly consists of pushing and popping regions, rather than performing garbage collection. Region Infer- ence has previously been specified by a set of inference rules which formalize when regions may be allocated and deallocated. This article presents an algorithm which implements the specification. We prove that the algorithm is sound with respect to the region inference rules and that it always terminates even though the region inference rules permit polymorphic recursion in regions. The algorithm is the result of several years of experiments with region inference algorithms in the ML Kit, a compiler from Standard ML to assembly language. We report on practical experience with the algorithm and give hints on how to implement it. Categories and Subject Descriptors: D.3.3 [Programming Languages]: Language Constructs and Features—dynamic storage management; F.3.3 [Logics and Meanings of Programs]: Studies of Program Constructs—functional constructs; type structure General Terms: Algorithms, Reliability, Theory Additional Key Words and Phrases: Regions, Standard ML 1. INTRODUCTION Most programming languages have some mechanism for allocation and deallocation of dynamic data structures. In the Algol stack discipline [Dijkstra 1960; Naur 1963], every point of allocation is matched by a point of deallocation; these points are easily identified in the program text, which helps reasoning about memory usage. However, the pure stack discipline is rather restrictive.
    [Show full text]
  • Introduction to the Literature on Programming Language Design the Intended Audience
    Intro duction to the Literature On Programming Language Design Gary T Leavens TR c Jan revised Jan Feb and July Keywords programming languages semantics typ e systems p olymorphism typ e theory data abstrac tion functional programming ob jectoriented programming logic programming declarative programming parallel and distributed programming languages CR Categories D Programming Techniques ApplicativeFunctional Programming D Programming Techniques Concurrent Programming D Programming Techniques Ob jectoriented Pro gramming D Programming Techniques Logic Programming D Software Engineering To ols and Techniques Mo dules and interfaces D Software Engineering Program Verication D Software Engineering Program Verication D Programming Languages Formal Denitions and Theory D Programming Languages Language Classications D Programming Languages Language Constructs and F eatures F Logics and Meaning of Programs Sp ecifying and verifying and reasoning ab out pro grams F Logics and Meaning of Programs Semantics of Programming Languages F Logics and Meaning of Programs Studies of Program Constructs H Database Management LanguagesDatabase p ersistent programming languages I Articial Intel ligence Programming Languages and Software c Gary T Leavens Permission is granted for you to make copies for educational and scholarly purp oses but not for direct commercial advantage provided this notice app ears on all copies All other rights reserved Department of Computer Science Atanaso Hall Iowa State University Ames Iowa USA Intro duction
    [Show full text]
  • Paper in Order to Obtain a Similar Soundness and Completeness Result for Modular Type Classes
    Principal Type Schemes for Modular Programs Derek Dreyer and Matthias Blume Toyota Technological Institute at Chicago fdreyer,[email protected] Abstract. Two of the most prominent features of ML are its expres- sive module system and its support for Damas-Milner type inference. However, while the foundations of both these features have been studied extensively, their interaction has never received a proper type-theoretic treatment. One consequence is that both the official Definition and the alternative Harper-Stone semantics of Standard ML are difficult to imple- ment correctly. To bolster this claim, we offer a series of short example programs on which no existing SML typechecker follows the behavior prescribed by either formal definition. It is unclear how to amend the implementations to match the definitions or vice versa. Instead, we pro- pose a way of defining how type inference interacts with modules that is more liberal than any existing definition or implementation of SML and, moreover, admits a provably sound and complete typechecking algo- rithm via a straightforward generalization of Algorithm W. In addition to being conceptually simple, our solution exhibits a novel hybrid of the Definition and Harper-Stone semantics of SML, and demonstrates the broader relevance of some type-theoretic techniques developed recently in the study of recursive modules. 1 Introduction The standard way of defining the static semantics of languages with type in- ference is to give a set of declarative Curry-style typing rules that assign types to untyped terms. Since these rules are typically written in a nondeterministic fashion, it is not prima facie decidable whether a term can be assigned a type.
    [Show full text]
  • Typed Regions for Tag-Free Garbage Collection
    Typed Regions for Tag-Free Garbage Collection Martin Elsman⋆ IT University of Copenhagen. Glentevej 67, DK-2400 Copenhagen NV, Denmark. Email: [email protected] October, 2002 Abstract. This paper presents an extension to the Tofte-Talpin region type system, which makes it possible to combine region-based memory management with a partly tag-free garbage collection algorithm. The memory discipline is implemented for Standard ML in the ML Kit com- piler. Experiments show that, for a range of benchmark programs, the discipline improves performance, both with respect to memory usage and execution time. 1 Introduction In implementations of languages that support dynamic reference tracing garbage collection, such as most Java and ML implementations, tags are often used to distinguish between different types of values at runtime. The use of tags imposes a memory overhead, however, which for the most commonly used data structures, such as tuples, lists, and trees, can be as large as one third of the total memory usage. In this paper we present a memory discipline that integrates region-based memory management and reference tracing garbage collection in such a way that tagging of commonly used values such as tuples and lists is avoided. In the Tofte-Talpin region typing rules [18], two values are forced into the same region, only if their types are identical. This property suggests that, in systems based on the Tofte-Talpin region typing rules, tags to distinguish differ- ent types of values at runtime can be moved from individual values to the level of regions. We show that this “Big Bag of Pages” approach to avoid tagging improves memory usage and execution time for many programs.
    [Show full text]