Table Of Content

Functional C Pieter Hartel Henk Muller January 3, 1999 i Functional C Pieter Hartel Henk Muller University of Southampton University of Bristol Revision: 6.7 ii To Marijke Pieter To myfamily and othersources ofinspiration Henk Revision: 6.7 (cid:0)c1995,1996PieterHartel&HenkMuller,allrightsreserved. Preface The Computer Science Departments of many universities teach a functional language as the (cid:2)rst programming language. Using a functional language with its highlevelofabstractionhelpstoemphasizetheprinciples ofprogramming. Func- tional programming is only one of the paradigms with which a student should beacquainted. Imperative, Concurrent, Object-Oriented, and Logic programming arealso important. Depending on theproblem to besolved, one ofthe paradigms will bechosen as themost natural paradigmforthat problem. This book is the course material to teach a second paradigm: imperative programming, using C as the programming language. The book has been written so that it builds on the knowledge that the students have acquired during their (cid:2)rst course on functional programming, using SML. The prerequisite of this book is that the principles of programming are already understood; this book does not speci(cid:2)cally aim to teach‘problemsolving’ or‘programming’. This bookaims to: Familiarise the reader with imperative programming as another wayof imple- (cid:1) menting programs. The aim is to preserve the programming style, that is, the programmerthinks functionally while implementing an imperative program. (cid:1) Provide understanding of the differences between functionaland imperative programming. Functional programming is a high level activity. The ordering of computations and the allocation of storage are automatic. Imperative programming, particularly in C, is a low level activity where the programmer controlsboththeorderingofcomputationsandtheallocation ofstorage. This makes imperative programming more dif(cid:2)cult, but it offers the imperative programmeropportunitiesforoptimisations thatarenotavailabletothefunc- tional programmer. Familiarise the reader with the syntax and semantics of ISO-C, especially the (cid:1) power of the language (at the same time stressing that power can kill). We visit alldarkalleysofC,fromvoid *topointerarithmetic andassignments in expressions. On occasions, we use other languages (like C++ and Pascal) toillustrate conceptsofimperativelanguagesthatarenotpresentinC.Chas been chosen because it is a de facto standard for imperative programming, and becauseits low level naturenicely contrasts withSML. Thosewhowant to learn, forexample, Modula-2 or Ada-95 afterwardsshould not (cid:2)nd many dif(cid:2)culties. iii iv Preface (cid:1) Reinforce the principles of programming and problem solving. This is facilitated by the use of three different languages (mathematics, a functional language, and an imperative language). The fact that these widely differing languages havecommon aspectsmakestheidea thatprogrammingprinciples existand that theyareuseful quite natural. Reinforce the principle of abstraction. Throughout the book we encourage the (cid:1) student to look for more abstract solutions, for example, by viewing the sig- natureofa function asanabstraction ofits purpose, byusing procedural ab- stractions (in particular higher order functions) early on, and by using data abstraction. Guidethestudentfromspeci(cid:2)cationandmathematicstoimplementationand (cid:1) software engineering. In the (cid:2)rst chapters the emphasis is on writing correct functions and as we make progress the emphasis gradually shifts to trans- forming correct functions into ef(cid:2)cient and reusable functions. Clean inter- faces are of paramount importance, and are sacri(cid:2)ced for better ef(cid:2)ciency only asa last resort. Each problemin this bookis solved in threesteps: Aspeci(cid:2)cation ofthe problemis made. (cid:1) Anappropriate algorithm is found to deliver solutions that satisfy the speci- (cid:1) (cid:2)cation. Thealgorithmisimplementedasef(cid:2)cientlyaspossible. Throughoutthebook, (cid:1) theemphasis is on this third step. The language of mathematics is used to specify the problems. This includes the basics of set theory and logic. The student should have some familiarity with the calculi of sets, predicate logic, and propositional logic. This material is taught at most universities during a(cid:2)rst courseon discrete mathematics orformallogic. The appropriate algorithm is given in SML. SML is freelyavailable for a range ofplatforms(PC’s,UNIXworkstations, Apple),andisthereforepopularasateach- ing language. As many functional languages are not too different from SML, an appendixgivesabriefreviewofSMLforthosefamiliarwithanyoftheothermain streamfunctional languages,such as Miranda, Haskell, Clean, orScheme. As the target language to implement solutions in an imperative style we have chosen C. The choice to use C and not C++ was a dif(cid:2)cult one. Both languages aremainstreamlanguages,andwouldthereforebesuitable asthetargetlanguage. We havechosen C becauseit moreclearly exposes thelow level programming. To illustratethisconsiderthemechanismsthatthelanguagesprovideforcallbyrefer- ence. In C, arguments must be explicitly passed as a pointer. Thecaller must pass the address, the callee must dereference the pointer. This in contrast with the call by reference mechanism of C++ (and Pascal and Modula-2). This explicit call by ref- erenceis adidactical assetasit clearly exposesthemodel behindcall byreference, and its dangers(in theformofunwanted aliases). Revision: 6.8 Preface v Asthisbookisintended tobeusedina(cid:2)rstyearcourse,onlyfewassumptions were made about prior knowledge of the students. Reasoning about the correct- ness of programsrequires proof skills, which students might not have acquired at this stage. Therefore we have con(cid:2)ned all proofs to specially marked exercises. Todistinguish theprogrammingexercisesfromtheexercisesrequiringaproof,we have marked the latter with an asterisk. We are con(cid:2)dent that the book can be usedwithoutmakingasingleproof. Howeverwewouldrecommendthestudents to go through the proofs on a second reading. The answersto one third of the exercises areprovided inAppendix A. The student should have an understanding of the basic principles of comput- ing. This would include base 2 arithmetic and the principles of operation of the von Neumann machine. A computer appreciation course would be most appro- priatetocoverthis material. Thebookcontainsexamplesfromotherareasofcom- puter science, including data bases, computer graphics, the theory of programming languages, and computer architecture. These examples can be understood without prior knowledgeofthese areas. Acknowledgements ThehelpandcommentsofHughGlaser,AndyGravell,LauraLafave,DenisNicole, Peter Sestoft, and the anonymous referees have been important to us. The material ofthe bookhasundergoneits (cid:2)rsttest in Southamptonin 1995/1996. The(cid:2)rst year Computer Science students of 1995, and in particular Jason Datt and Alex Walkerhave givenus alot ofusefulfeedback. We have used a number of public domain software tools in the development of the book. The noweb literate programming tools of Norman Ramsey, the rail roaddiagrammingtoolsfromL.Rooijakkers,gpicbyBrianKernighan,TEX,LATEX, NewJerseySML, and theGnu C compiler wereparticularly useful. Revision: 6.8 vi Preface Revision: 6.8 (cid:0)c1995,1996PieterHartel&HenkMuller,allrightsreserved. Contents Preface iii 1 Introduction 1 1.1 Thefunctional andthe imperative paradigms . . . . . . . . . . . . . . 1 1.1.1 Theadvantageofstate . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Theadvantageofpurefunctions . . . . . . . . . . . . . . . . . 3 1.1.3 Idiomatic building blocks in C . . . . . . . . . . . . . . . . . . 3 1.2 Guide tothe book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Functionsand numbers 7 2.1 Amodel ofcomputation . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Acomputational model forSML programs . . . . . . . . . . . 8 2.1.2 Acomputational model forC programs . . . . . . . . . . . . . 9 2.1.3 Compiling and executingaC program . . . . . . . . . . . . . 10 2.2 Elementary functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 TheheaderofaC function, typesand identi(cid:2)ers . . . . . . . . 14 2.2.2 ThebodyofaC function and its behaviour . . . . . . . . . . . 15 2.2.3 Theexecutionof aC program . . . . . . . . . . . . . . . . . . . 17 2.2.4 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.5 Logical operators . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.6 De(cid:2)ningatypeforBooleans, typedefand enum . . . . . . . 20 2.3 Characters, patternmatching, partial functions . . . . . . . . . . . . . 21 2.3.1 Implementingpattern matching in C . . . . . . . . . . . . . . . 22 2.3.2 Partial functions . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.3 Differencesand similarities betweencharactersand integers . 27 2.4 Real numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.1 Coercions ofintegers and (cid:3)oating point numbers . . . . . . . 32 2.5 Functions asarguments . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5.1 Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5.2 Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5.3 Anextended exampleofhigherorder functions: bisection . . 39 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.7 Furtherexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 vii viii CONTENTS 3 Loops 51 3.1 Amodel ofthe store . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.2 Local variabledeclarations and assignments . . . . . . . . . . . . . . 53 3.3 While loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.3.1 Single argumenttail recursion . . . . . . . . . . . . . . . . . . 61 3.3.2 Multiple argumenttail recursion . . . . . . . . . . . . . . . . . 64 3.3.3 Non-tail recursion: factorial . . . . . . . . . . . . . . . . . . . . 68 3.3.4 Moreon assignments . . . . . . . . . . . . . . . . . . . . . . . . 73 3.3.5 Breakingout ofwhile-loops . . . . . . . . . . . . . . . . . . . . 75 3.4 Forloops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4.1 Factorial using afor-loop . . . . . . . . . . . . . . . . . . . . . 83 3.4.2 Folding fromthe right . . . . . . . . . . . . . . . . . . . . . . . 86 3.5 Generalizing loops andcontrol structures . . . . . . . . . . . . . . . . 88 3.5.1 Combining foldlwithmap: sum ofsquares . . . . . . . . . . 89 3.5.2 Combining foldlwithfilter: perfectnumbers . . . . . . . 91 3.5.3 Nested forstatements . . . . . . . . . . . . . . . . . . . . . . . 95 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.7 Furtherexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4 Structs and Unions 101 4.1 Structs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.2 Structs in structs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.3 Unions in structs: algebraic data types . . . . . . . . . . . . . . . . . . 105 4.3.1 Union types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.3.2 Patternmatching: theswitch statement . . . . . . . . . . . . . 108 4.3.3 Algebraictypesin otherimperative languages . . . . . . . . . 110 4.4 Pointers: referencesto values . . . . . . . . . . . . . . . . . . . . . . . 112 4.4.1 De(cid:2)ningpointers . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.4.2 Assignments throughpointers . . . . . . . . . . . . . . . . . . 114 4.4.3 Passing argumentsbyreference. . . . . . . . . . . . . . . . . . 116 4.4.4 Lifetime ofpointers and storage . . . . . . . . . . . . . . . . . 119 4.5 Void pointers: partial application . . . . . . . . . . . . . . . . . . . . . 120 4.5.1 Thedangerofexplicit typecasts . . . . . . . . . . . . . . . . . 125 4.5.2 Void pointers andparametric polymorphism . . . . . . . . . . 126 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.7 Furtherexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5 Arrays 133 5.1 Sequences asamodel oflinear data structures . . . . . . . . . . . . . 134 5.1.1 Thelengthofa sequence . . . . . . . . . . . . . . . . . . . . . . 134 5.1.2 Accessingan element ofasequence . . . . . . . . . . . . . . . 134 5.1.3 Updating anelement ofasequence . . . . . . . . . . . . . . . 135 5.1.4 Theconcatenation oftwo sequences . . . . . . . . . . . . . . . 135 5.1.5 Thesubsequence . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.2 Sequences asarraysinSML . . . . . . . . . . . . . . . . . . . . . . . . 136 5.2.1 Creatingan SML array . . . . . . . . . . . . . . . . . . . . . . . 136 Revision: 6.8 CONTENTS ix 5.2.2 Thelengthofan SML array . . . . . . . . . . . . . . . . . . . . 137 5.2.3 Accessingan element ofanSML array . . . . . . . . . . . . . . 137 5.2.4 Updating anelement ofanSML array . . . . . . . . . . . . . . 137 5.2.5 Destructiveupdates in SML . . . . . . . . . . . . . . . . . . . . 138 5.3 Sequences asarraysinC . . . . . . . . . . . . . . . . . . . . . . . . . . 138 5.3.1 DeclaringaC array . . . . . . . . . . . . . . . . . . . . . . . . . 138 5.3.2 Accessingan element ofaC array . . . . . . . . . . . . . . . . 139 5.4 Basic arrayoperations : Arithmetic mean . . . . . . . . . . . . . . . . 139 5.5 Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 5.5.1 Comparingstrings . . . . . . . . . . . . . . . . . . . . . . . . . 143 5.5.2 Returningstrings; morepropertiesof arrays . . . . . . . . . . 144 5.5.3 Anapplication ofarraysand strings: argcand argv . . . . . 146 5.6 Manipulating arraybounds, boundchecks . . . . . . . . . . . . . . . 147 5.7 Dynamicmemory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 5.7.1 Theallocation ofdynamic arrays . . . . . . . . . . . . . . . . . 153 5.7.2 Theextensionof dynamic arrays . . . . . . . . . . . . . . . . . 155 5.7.3 Thedeallocation of dynamic arrays . . . . . . . . . . . . . . . 159 5.7.4 Explicit versusimplicit memorymanagement . . . . . . . . . 161 5.7.5 Ef(cid:2)ciency aspectsof dynamic memory . . . . . . . . . . . . . 162 5.8 Slicing arrays: pointer arithmetic . . . . . . . . . . . . . . . . . . . . . 163 5.9 Combining arraysand structures . . . . . . . . . . . . . . . . . . . . . 168 5.10 Multi-dimensional arrayswith (cid:2)xedbounds . . . . . . . . . . . . . . 174 5.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 5.12 Furtherexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 6 Lists 181 6.1 Lists ofcharacters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 6.1.1 List access functions: head andtail . . . . . . . . . . . . . . . . 183 6.2 Thelength ofalist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 6.3 Accessing anarbitraryelementof alist . . . . . . . . . . . . . . . . . . 186 6.4 Append, (cid:2)lter and map: recursiveversions . . . . . . . . . . . . . . . 186 6.4.1 Appendingtwo lists . . . . . . . . . . . . . . . . . . . . . . . . 186 6.4.2 Filtering elements fromalist . . . . . . . . . . . . . . . . . . . 188 6.4.3 Mappinga function overalist . . . . . . . . . . . . . . . . . . 190 6.5 Open lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 6.5.1 Openlists byrememberingthelast cell . . . . . . . . . . . . . 193 6.5.2 Openlists byusingpointers to pointers . . . . . . . . . . . . . 195 6.5.3 Appendusing openlists . . . . . . . . . . . . . . . . . . . . . . 197 6.6 Lists versus arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 6.6.1 Converting anarrayto a list . . . . . . . . . . . . . . . . . . . . 199 6.6.2 Fromalist to anarray . . . . . . . . . . . . . . . . . . . . . . . 201 6.7 Variable numberofarguments . . . . . . . . . . . . . . . . . . . . . . 204 6.8 Store reuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 6.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 6.10 Furtherexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 Revision: 6.8