Chapter 12 P olymorphism The term p olymorphic has Greek ro - PDF document

Chapter 12 P olymorphism The term p olymorphic has Greek ro ots and means roughly \man y forms." ( p oly = man y , morphos = form. Morphos is related to the Greek go d Morph us, who could app ear to sleeping individuals in an y form he wished and hence w as truly p olymorphic.) In biology , a p olymorphic sp ecies is one, suc h as Homo Sapiens , that is c haracterized b y the o ccurrence of di�eren t forms or color t yp es in individual organisms or among organisms. In c hemistry , a p olymorphic comp ound is one that can crystallize in at least t w o distinct forms, suc h as carb on, whic h can crystallize b oth as graphite and as diamond. 12.1 V arieties of P olymorphism In ob ject-orien ted languages, p olymorphism is a natural result of the is-a relationship and of the mec hanisms of message passing, inheritance, and the concept of substitutabilit y. One of the great strengths of the OOP approac h is that these devices can b e com bined in a v ariet y of w a ys, yielding a n um b er of tec hniques for co de sharing and reuse. Pur e p olymorphism o ccurs when a single function can b e applied to argumen ts of a v ariet y of t yp es. In pure p olymorphism, there is one function (co de b o dy) and a n um b er of in terpretations. The other extreme o ccurs when w e ha v e a n um b er of di�eren t functions (co de b o dies) all denoted b y the same name{a situation kno wn as overlo ading or sometimes 1 ad ho c p olymorphism . Bet w een these t w o extremes are overriding and deferr e d metho ds . 1 Note that there is little agreemen t regarding terminology in the programming language comm u- nit y . In [Horo witz 1984 ], [Marcott y 1987 ], [MacLennan 1987 ], and [Pinson 1988 ] for example, p olymor- phism is de�ned in a manner roughly equiv alen t to what w e are here calling overlo ading . In [Sethi 1989 ] and [Mey er 1988a ] and in the functional programming languages comm unit y (suc h as [Wikstr� om 1987 , Milner 1990 ]), the term is reserv ed for what w e are calling pur e p olymorphism . Other authors use the term for one, t w o, or all of the mec hanisms describ ed in this c hapter. Tw o complete, but tec hnically daun ting, analyses are [Cardelli 1985 ] and [Danforth 1988 ]. 207

208 CHAPTER 12. POL YMORPHISM 12.2 P olymorphic V ariables With the exception of o v erloading, p olymorphism in ob ject-orien ted languages is made p os- sible only b y the existence of and the idea of substitutabilit y . A p olymorphic variables p olymorphic v ariable is one with man y faces; that is, it can hold v alues of di�eren t t yp es. P olymorphic v ariables em b o dy the principle of substitutabilit y . In other w ords, while there is an exp ected t yp e for an y v ariable the actual t yp e can b e from an y v alue that is a subt yp e of the exp ected t yp e. In dynamically b ound languages (suc h as Smalltalk), all v ariables are p oten tially p olymorphic{ an y v ariable can hold v alues of an y t yp e. In these languages the desired t yp e is de�ned b y a set of exp ected b eha viors. F or example, an algorithm ma y mak e use of an arra y v alue, exp ecting the subscripting op erations to b e de�ned for a certain v ariable; an y t yp e that de�nes the appropriate b eha vior is suitable. Th us, the user could de�ne his or her o wn t yp e of arra y (for example, a sparse arra y) and, if the arra y op erations w ere implemen ted using the same names, use this new t yp e with an existing algorithm. In statically t yp ed languages, suc h as Ja v a, the situation is sligh tly more complex. P oly- morphism o ccurs in Ja v a through the di�erence b et w een the declared (static) class of a v ariable and the actual (dynamic) class of the v alue the v ariable con tains. A go o d example of a p olymorphic v ariable is the arra y allPiles in the Solitare game presen ted in Chapter 9. The arra y w as declared as main taining a v alue of t yp e Ca rdPile , but in fact it main tains v alues from eac h of the di�eren t sub classes of the paren t class. A message presen ted to a v alue from this arra y , suc h as in the example co de sho wn displa y b elo w, executes the metho d asso ciated with the dynamic t yp e of the v ariable and not that of the static class. public class Solitaire extends Applet f ... static CardPile allPiles [ ]; ... f public void paint(Graphics g) for (int i = 0; i < 13; i++) allPiles[i].disp lay (g ); g ... g 12.3 Ov erloading W e sa y a function name is if there are t w o or more function b o dies asso ciated overlo ade d with it. Note that o v erloading is a necessary part of o v erriding, whic h w e and will describ e

12.3. O VERLO ADING 209 in the next section, but the t w o terms are not iden tical and o v erloading can o ccur without o v erriding. In o v erloading, it is the function name that is p olymorphic{it has man y forms. Another w a y to think of o v erloading and p olymorphism is that there is a single abstract function that tak es v arious t yp es of argumen ts; the actual co de executed dep ends on the argumen ts giv en. The fact that the compiler can often determine the correct function at compile time (in a strongly t yp ed language), and can therefore generate only a single co de sequence are simply optimizations. 12.3.1 Ov erloading Messages in Real Life In Chapter 1 w e sa w an example in whic h o v erloading o ccurred without o v erriding, when I w an ted to surprise m y friend with �o w ers for her birthda y . One p ossible solution w as to send the message sendFlo w ersT o to m y lo cal �orist; another w as to giv e the same message to m y wife. Both m y �orist and m y wife (an instance of class Sp ouse ) w ould ha v e understo o d the message, and b oth w ould ha v e acted on it to pro duce a similar result. In a certain sense, I could ha v e though t of sendFlo w ersT o as b eing one function understo o d b y b oth m y wife and m y �orist, but eac h w ould ha v e used a di�eren t algorithm to resp ond to m y request. Note, in particular, that there w as no inheritance in v olv ed in this example. The �rst common sup erclass for m y wife and m y �orist w as the category Human . But certainly the b eha vior sendFlo w ersT o w as not asso ciated with all h umans. My den tist, for example, who is also a h uman, w ould not ha v e understo o d the message at all. 12.3.2 Ov erloading and Co ercion As an example more closely tied to programming languages, supp ose a programmer is dev el- oping a library of classes represen ting common data structures. A n um b er of data structures can b e used to main tain a collection of elemen ts (sets, bags, dictionaries, arra ys, and priorit y queues, for example), and these migh t all de�ne a metho d, add , to insert a new elemen t in to the collection. This situation{in whic h t w o totally separate functions are used to pro vide seman tically similar actions for di�eren t data t yp es{o ccurs frequen tly in all programming languages, not simply in ob ject-orien ted languages. P erhaps the most common example is the o v erloading of the addition op erator, +. The co de generated b y a compiler for an in teger addition is often radically di�eren t from the co de generated for a �oating-p oin t addition, y et programmers tend to think of the op erations as a single en tit y , the \addition" function. In this example it is imp ortan t to p oin t out that o v erloading ma y not b e the only activit y taking place. A seman tically separate op eration, cion , is also usually asso ciated with c o er arithmetic op erations. It o ccurs when a v alue of one t yp e is con v erted in to one of a di�eren t t yp e. If mixed-t yp e arithmetic is p ermitted, the addition of t w o v alues ma y b e in terpreted in a n um b er of di�eren t w a ys: