Norman D. Thomson Raymond P. Polivka. APL2 in Depth. Springer-Verlag. New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest

Transcription

1 APL2 in Depth

2 Norman D. Thomson Raymond P. Polivka APL2 in Depth Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest

3 Nonnan D. Thomson Finnock House Cliff Terrace Road Wemyss Bay Scotland PA18 6AP Raymond P. Polivka 60 Timberline Drive Poughkeepsie, NY USA Library of Congress Cataloging-in-Publication Data Thomson. Nonnan (Nonnan D.) APL2 in depth / Nonnan Thomson, Ray Polivka. p. cm. Includes bibliographical references and index. ISBN-13: e-isbn-13: DOl: / l. APL2 (Computer program language) I. Polivka. Raymond P. (Raymond Peter), II. Title. QA76.73.A655T '3-dc20 Printed on acid-free paper Springer-Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written pennission of the publisher (Springer-Verlag New York. Inc., 175 Fifth Avenue, New York, NY 10010, USA). except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any fonn of infonnation storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc.. in this publication, even if the fonner are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Laura Carlson; manufacturing supervised by Jeffrey Taub. Camera-ready copy prepared by the authors

4 Preface This book is designed for people with a working knowledge of APL who would like to increase their fluency in the wide range of extra facilities offered by second-generation APL products. Although the primary product in view is IBM's APL2 as implemented on mainframe, PC and RS/6000, the language features covered share considerable common ground with APL *PLUS II and Oyalog APL. This is a book about skills rather than knowledge, and an acquaintance with some variety of APL on the reader's part is assumed from the start. It is designed to be read as a continuous text, interspersed with exercises designed to give progressively deeper insight into what the authors conceive as the features which have the greatest impact on programming techniques. It would also be suitable as a text-book for a second course in APL2, although experience suggests that most programming language learning is now by selfstudy, so that this volume is more likely to provide follow-up reading to more elementary texts such as "APL2 at a Glance" by Brown, Pakin and Polivka. Material is discussed more informally than in a language manual - in this book textual bulk is in proportion to difficulty and importance rather than to the extent of technical details. Indeed, some APL2 extensions are not covered at all where the technicalities pose no great problems in understanding and can be readily assimilated from the language manuals. Second-generation APL is dominated by two ideas - nested arrays and operator extension. Nested arrays are in principle so simple a concept that only a few minutes are needed for an experienced APL user to read and absorb their technical specifications, and also those of the closely associated functions enclose, disclose and depth, and the operator each. Nevertheless the increase in expressiveness and potential complexity which these few simple ideas add is truly astonishing. The first chapter discusses APL2 arrays and functions, grouping the latter into broad areas such as structuring, selection and inquiry. Chapter 2 considers operators, both primitive and user-defined. Chapter 3 contains demonstrations to show how nested arrays deal with simple data structures in a way which makes their behavior comprehensible and useful to people with very limited pro-

5 vi Preface gramming background and experience. Chapters 4-6 then retrace and develop the ideas of chapters 1-3. Chapter 4 develops the ideas of chapter 1, but focusing more on the way in which functions interact. Chapter 5 develops the Chapter 2 discussion of operators in a similar way, and Chapter 6 gives more sophisticated examples which use all the powerful features of APL2 which have been developed in the previous five chapters. Applications Using APL2 to its full capability is a skill whose acquisition takes time and patience which are an order of magnitude greater than the skills needed for a mastery of first-generation APLs. The reward, on the other hand, is the stimulus of a language whose exploration is a source of constant delight through its seemingly endless capacity for expressing ideas of indefinite complexity in unambiguous and succinct terms. Of the existing APL texts and primers, some were originally first-generation APL works upgraded to APL2 by the addition of new sections and appendices. Others assume that APL2 is the first language which the user encounters. This book is addressed to the thousands of people, some programmers and some not, who have achieved both enhancement to their professional skills and personal satisfaction in learning and using APL, and who would like to build on this foundation by acquiring a matching fluency in the skills associated with APL2. Extra weight is therefore given in the text to those APL2 language features which extend user versatility in describing data structures and communicating algorithms in ways which mirror current thinking in computing science and software engineering. The exercises are designed to give the reader practice in these processes. Frequently, subtler points of difference are best illustrated by exercises with long sequences of similar expressions to be evaluated. With many exercises, a few keystrokes on a terminal will deliver the answer, and whilst the reader is encouraged to use a computer as a check, the fullest value of most exercises is obtained by predicting the result before having the computer deliver it. All solutions are

6 APL2 IN DEPl'H vii given in an appendix so that it is possible to use the book as a study guide even without the availability of an APL2 system. The functions, operators, and much of the data in the text are available on a 3.5" disk. Either of the authors can supply particulars. APL2 has its roots in Ken Iverson's original concepts of a symbolic notation for use with computers. Through the efforts over the years of Jim Brown and his team at IBM's Santa Teresa Laboratory these have matured into a language which can be consistently used through the whole range of software development, that is specification, design, coding, and testing. We have attempted to penetrate beyond the mere description of the syntax and semantics of the language and provide a study in greater depth of the interaction between nested arrays and the various functions and operators. We hope that the present work, "APL2 in Depth" will encourage greater use of APL2. We should like to acknowledge the thorough and thoughtful review by Curtis Jones, without which this text would have been greatly poorer, and also helpful comments and suggestions from Garth Foster, Helmut Engelke, Bert Rosencrantz, Phil Benkard, and Ron Wilks. We are also greatly indebted to Jon McGrew for his invaluable help in the typographical preparation of the text. Ray Polivka 60 Timberline Drive Poughkeepsie, New York USA Norman Thomson Finnock House Cliff Terrace Rd. Wemyss Bay Scotland PA18 6AP

7 Conventions Used for Arrays, Functions, Operators and Indentities Names of Arrays A general principle is that "small" arrays, that is those which require fewer than 15 non-blank characters to construct them by direct keyboard entry, are given either meaningful names, or one-character names, usually s for scalar, V for vector, M for matrix, A for array. Larger objects are given either descriptive names or a name such as V23 which denotes the third vector defined in Chapter 2. Objects so named are stored on the disk which is available to accompany the book. Functions and Operators When a word like "pick" is used in its specific role as an APL function or operator, it is printed in a heavy font thus: pick. The following conventions are used in writing defined functions and operators: F a function z result of a function or derived function L, R left and right arguments of a function P, Q left and right operands of an operator T, U, V local variables Operations which behave identically, or nearly so, but contain different code are distinguished by using different combinations of upper and lower case letters in their names. A subsidiary operation is indicated by the prefix 6.

8 x APL2 IN DEPTH Labels and Comments Labels are named L 1. L2. L3.... and so on. The general format for a line in an operation (i.e. a function or operator) is: [line-number] Lnl expression FI comment There are several distinguishable uses for comments, in particular they may describe (a) constraints on arguments and operands prior to execution; (b) description of a result following execution; (c) effects on global variables in the workspace; (d) clarification in words of a single APL line; (e) description of current execution status of data and/or a program. Comments are permitted on the header line in many APL2 implementations. Where type (a) comments can be expressed sufficiently briefly this usage is adopted, otherwise they are given in separate lines at the head of the function. Most of the functions in this book are very short, and the emphasis is on transforming ideas into APL2 program fragments rather than on the development of programming systems where type (e) comments are more likely to be found. Where these occur in production APL2 code they frequently indicate the possibility of breaking down a function into subfunctions. Labels may be floating, that is a function line may consist of a label and its colon only, possibly with a comment. Judicious use of the floating label and comment combination can add considerably to legibility, adaptability and maintenance of functions. Floating labels used in this way are another frequent indication of suitable points for subdividing a function into subfunctions. Identities The symbol ++ is used to denote "is identically equal to."

9 Contents Preface Conventions used for Arrays, Functions, Operators and Identities Names of Arrays Functions and Operators Labels and Comments Identities.V.ix.ix.ix x x 1 Functions and Arrays in APL2 1.1 Nested Arrays and Depth Complex Numbers 1.2 Construction of Arrays Vector Notation Exercises 1 a Enlist Ravel with Axis Default Display of Arrays Enclose and Disclose Exercises 1 b Partial Enclose and Disclose Relationship between Partial Enclosure and Axis Qualifiers Exercises 1 c Partition 1.3 Selection Pick and Path First Indexing Scatter Indexing Indexing with Axes Index of Exercises 1 d Without 1.4 Replacement Vector Assignment Selective Assignment 1.5 Restructuring Formatting Default rules for mixed data type Sorting 1.6 Comparison and Inquiry

10 xli APL2 IN DEPTH Depth Match Find. Exercises 1 e Summary of Functions used in Chapter Operators The Each Operator Pervasiveness Scalar Extension. Exercises 2a Each with non-pervasive Functions Exercises 2b Index with Each Extensions to the Slash Operator Replicate Dyadic Reduction.... Exercises 2c..... Summary of Functions used in Chapter Elementary Data Structuring 3.1 Example 1. Product Stocks Exercises 3a Example 2. Optimizing Rental Charges. Exercises 3b..... Summary of Functions used in Chapter Using Functions and Arrays. 4.1 Cross-sections, Picking and Indexing Each and Scalar Functions Some lliustrations using Nested Arrays Exercises 4a Further lliustrations using Nested Arrays Exercises 4b Distinctions between Similar Primitives First and Take/Drop First and Pick Type and Prototype Pick and Disclose First and Disclose Summary of Relationship between above Functions Exercises 4c Empty Arrays and Fill Functions Identity Items and Identity Functions Identity Items III

11 Contents xiii Identity and Inverse Functions Exercises 4d. Summary of Functions used in Chapter Using Operators 5.1 The Role of Operators in APL User-defined Operators 5.2 Binding Exercises Sa 5.3 Matching Function Arguments Function Composition Ambi-valency 5.4 Recursion with Functions and Operators Exercises 5b 5.5 Extensions to First-generation APL Operators Reduction Reduction with Rank Greater than one Scan Reversing scans Expand Outer Product Inner Product Exercises 5c Further Topics on Inner and Outer Products Inner Product and Scan Decode/Encode and Inner/Outer Products Exercises 5d 5.6 Applications of User-Defmed Operators Control Structures ONLY UNLESS UPTO UNTIL Conditional and Alternative Function Execution Exercises 5e LEVEL LEVEL with Monadic P LEVEL with Dyadic P : Exercises Sf Summary of Functions used in Chapter 5 Summary of U ser-defmed Operators in Chapter Advanced Modelling and Data Structures 6.1 Trees Without Keys 6.2 Trees with Keys Finding Ancestors Subtrees Eliminating and Swapping Subtrees...,

12 xlv APL2 IN DEPTH 6.3 Binary Trees Trees with non-simple Scalar Nodes Searching Binary Trees Selective Enlist with Binary Trees Data-equivalent Binary Trees Alternative Comparisons.... Exercises 6a Networks The Vector of Paths through a network Parallel computation along paths Assignment of Flows Minimum Spanning Tree Precedence and Reachability Exercises 6b.... Summary of Operations used in Chapter Appendix A. Solutions to Exercises.... Solutions la.... Solutions lb.... Solutions 1 c Solutions ld Solutions Ie Solutions 2a.... Solutions 2b.... Solutions 2c Solutions 3a.... Solutions 3b.... Solutions and Notes 4a.... Solutions 4b.... Solutions 4c Solutions 4d Solutions Sa.... Solutions Sb.... Solutions and Notes Sc.... Solutions 5d.... Solutions 5e.... Solutions Sf.... Solutions 6a.... Solutions 6b Appendix B. Some Key Rules and Identities Appendix C. Ust of Dlustrations Index