Table Of ContentUndergraduate Topics in Computer Science
Maribel Fernández
Programming
Languages
and Operational
Semantics
A Concise Overview
Undergraduate Topics in Computer Science
Undergraduate Topics in Computer Science (UTiCS) delivers high-quality instructional content for
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ousexamplesandproblems.Manyincludefullyworkedsolutions.
For furthervolumes:
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Maribel Fernández
Programming Languages
and Operational Semantics
A Concise Overview
123
Prof.Maribel Fernández
King’s CollegeLondon
London
UK
Series editor
IanMackie
Advisory Board
SamsonAbramsky, UniversityofOxford, Oxford, UK
KarinBreitman, Pontifical CatholicUniversityof Riode Janeiro, Rio deJaneiro, Brazil
ChrisHankin, ImperialCollege London, London,UK
DexterKozen, Cornell University, Ithaca, USA
Andrew Pitts, Universityof Cambridge,Cambridge,UK
HanneRiisNielson, Technical University ofDenmark, KongensLyngby, Denmark
StevenSkiena, Stony BrookUniversity, StonyBrook, USA
Iain Stewart,University ofDurham,Durham,UK
ISSN 1863-7310 ISSN 2197-1781 (electronic)
ISBN 978-1-4471-6367-1 ISBN 978-1-4471-6368-8 (eBook)
DOI 10.1007/978-1-4471-6368-8
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Preface
Aim
This book is addressed to undergraduate students as a complement to program-
ming courses. The general aim of the book is to present and compare alternative
programming language paradigms, and to provide the foundations and tools
needed to design new programming languages and understand the existing ones.
These are ambitious goals, and to achieve our aims, we have chosen to introduce
andexplaininaconcisewaythemostsignificantconstructsofmodernimperative,
functional and logic programming languages, and describe their operational
semantics first in an informal way, and then using transition systems.
About this Book
This book provides a concise introduction to the essential concepts in program-
minglanguages,usingoperationalsemanticstechniques.Thebookisforthemost
part self-contained, but we assume readers have some basic programming skills
and have used at least one programming language. Knowledge of more pro-
gramming languages will be helpful but is not necessary.
Each chapter includes exercises that provide an opportunity to apply the con-
cepts and techniques presented. Doing exercises is an important part of the
learningprocess:tounderstandhowaprogramminglanguageworksandbeableto
use it, it is not sufficient to read about it. Of course, the same can be said about
many other topics (learning to play a musical instrument or learning to ride a
bicycle are familiar examples). Since practice is unavoidable, we have included
not just exercises to be done on paper, but also some programming exercises that
require checking on a computer. Although some of the exercises are just intro-
ductory, most of the questions are designed with the goal of testing the under-
standing of the subject (for instance, by requiring students to adapt a given
technique to different contexts). Some challenging exercises for more advanced
students are also included; these are marked with . Answers to selected
ðyÞ
exercises are given in the final chapter of the book.
v
vi Preface
The book is organised as follows:
Part I provides an introduction to programming languages and operational
semantics in Chap. 1, followed by basic mathematical background for the rest of
the book in Chap. 2.
InPartIIwestudythemaincomponentsofimperativelanguages.Wefirstgive
aninformaldescriptioninChap.3,andthengiveaformalspecificationofthemain
constructs in imperative languages using transition systems in Chap. 4.
Part III is dedicated tofunctional languages and their type systems. InChap. 5
wegiveanoverviewoffunctionalprogramming(usingHaskellforourexamples),
and then give some examples of semantic descriptions offunctional languages in
Chap. 6.
Finally, in Part IV (Chaps. 7 and 8) we briefly study logic programming lan-
guages and describe the operational semantics of Prolog.
The last chapter of the book (Chap. 9) contains answers to a selection of
exercises.
We have not included chapters on object-oriented languages, but we do study
aspects of these languages in Chaps. 1 and 3.
Eachchapterincludesalistofrecommendedfurtherreading,alistofexercises,
and abibliographicalsection with references torelevant articles andbookswhere
the interested reader can find more information. In particular, for each program-
minglanguagethereisareferencetoitsdefinition,whichisindicatedthefirsttime
the language is mentioned.
Acknowledgments
The material presented in this book has been prepared using several different
sources, including the references mentioned above and lecture notes for my
coursesatKing’sCollegeLondonandinFrance.Iwouldliketothanktheeditors
of the UTiCS series for inviting me to write this book. I am very grateful to the
students in the Department of Informatics at King’s and the teaching assistants in
my courses (in particular, Asad Ali, Christophe Calvès, Jesús Domínguez, Elliot
Fairweather, Fabien Fleutot, François-Régis Sinot and Jeffrey Terrell) for their
comments on previous versions of the book. Special thanks to Elliot Fairweather
and Jeff Terrell for their careful reading and helpful suggestions. Last, but not
least, I thank my family for their continuous support.
London, January 2014 Maribel Fernández
Contents
Part I Preliminaries
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Programming Languages and Software Engineering. . . . . . . . . 4
1.2 Programming Paradigms. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Components of a Programming Language. . . . . . . . . . . . . . . . 5
1.3.1 Computer Architecture. . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.2 Language Implementation. . . . . . . . . . . . . . . . . . . . . . 7
1.3.3 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.4 Semantics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Mathematical Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1 Sets and Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Logic Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 Transition Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.6 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Part II Imperative Languages
3 General Features of Imperative Languages. . . . . . . . . . . . . . . . . . 45
3.1 Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Assignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 Control Statements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.1 Selection Statements . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.2 Iterative Statements (Loops) . . . . . . . . . . . . . . . . . . . . 53
vii
viii Contents
3.4 Branching Statements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5 Structuring the Program: Blocks and Subprograms. . . . . . . . . . 56
3.6 Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.7 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4 Operational Semantics of Imperative Languages. . . . . . . . . . . . . . 61
4.1 Abstract Syntax of SIMP . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 An Abstract Machine for SIMP. . . . . . . . . . . . . . . . . . . . . . . 65
4.3 Structural Operational Semantics for SIMP. . . . . . . . . . . . . . . 74
4.3.1 Reduction Semantics: Small-Step Semantics. . . . . . . . . 75
4.3.2 Evaluation Semantics: Big-Step Semantics . . . . . . . . . . 81
4.3.3 Equivalence between Small- and Big-Step Semantics. . . 83
4.4 Adding Blocks and Local Variables to SIMP . . . . . . . . . . . . . 85
4.5 Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.6 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Part III Functional Languages
5 General Features of Functional Languages. . . . . . . . . . . . . . . . . . 93
5.1 Defining Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2 Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3 Building Functional Programs. . . . . . . . . . . . . . . . . . . . . . . . 100
5.3.1 Local Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.4 Types: General Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5 Polymorphism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.6 Type Checking and Type Inference . . . . . . . . . . . . . . . . . . . . 107
5.7 Data Structures and Data Type Definitions. . . . . . . . . . . . . . . 110
5.8 Reasoning About Programs. . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.9 Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.10 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6 Operational Semantics of Functional Languages. . . . . . . . . . . . . . 121
6.1 Abstract Syntax of SFUN. . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2 A Type System for SFUN . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.3 Operational Semantics of SFUN . . . . . . . . . . . . . . . . . . . . . . 129
6.3.1 Call-by-Value Semantics of SFUN . . . . . . . . . . . . . . . 130
6.3.2 Properties of SFUN. . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.3.3 Call-by-Name Semantics of SFUN . . . . . . . . . . . . . . . 134
Contents ix
6.4 Extensions of SFUN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.4.1 Abstract Syntax of FUN. . . . . . . . . . . . . . . . . . . . . . . 137
6.4.2 A Type System for FUN . . . . . . . . . . . . . . . . . . . . . . 139
6.4.3 Operational Semantics of FUN . . . . . . . . . . . . . . . . . . 143
6.4.4 Properties of FUN. . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.5 Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.6 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Part IV Logic Languages
7 General Features of Logic Programming Languages. . . . . . . . . . . 155
7.1 The Herbrand Universe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.2 Logic Programs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.3 Finding Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.4 Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.5 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8 Operational Semantics of Prolog . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.1 Unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.2 The Principle of Resolution. . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.2.1 SLD-Resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.3 Prolog’s Search in the SLD-tree . . . . . . . . . . . . . . . . . . . . . . 173
8.4 Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
8.5 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9 Answers to Selected Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
