Measuring Cohesion of Packages in Ada95

Transcription

1 Measurng Coheson of Packages n Ada95 Baowen Xu Zhenqang Chen Departent of Coputer Scence & Departent of Coputer Scence & Engneerng, Southeast Unversty Engneerng, Southeast Unversty Nanjng, Chna, Nanjng, Chna, bwxu@seu.edu.cn chenzq@seu.edu.cn Janjun Zhao Departent of Coputer Scence & Engneerng, Fukuoka Insttute of Technology, Japan zhao@cs.ft.ac.jp ABSTRACT Ada95 s an object-orented prograng language. Pack-ages are basc progra unts n Ada 95 to support OO prograng, whch allow the specfcaton of groups of logcally related enttes. Thus, the coheson of a package s anly about how tghtly the enttes are encapsulated n the package. Ths paper dscusses the relatonshps aong these enttes based on dependence analyss and presents the propertes to obtan these dependences. Based on these, the paper proposes an approach to easure the package coheson, whch satsfes the propertes that a good easure should have. Categores and Subject Descrptors D.2.8 [Software Engneerng]: Metrcs perforance easures. General Ters Measureent. Keywords Measureent, Coheson, Object-Orented.. INTRODUCTION Coheson s one of the ost portant software features durng ts developent. It tells us the tghtness aong the coponents of a software odule. The hgher the coheson of a odule, the ore understandable, odfable and antanable the odule s. A software syste should have hgh coheson and low couplng. Researchers have developed several gudelnes to easure coheson of a odule [, 3, 4]. Snce ore and ore applcatons are object-orented, the approaches to easure coheson of objectorented (OO) progras have becoe an portant research feld. Generally, each object-orented prograng language provdes facltes to support OO features, such as data abstracton, encapsulaton and nhertance. Each object conssts of a set of attrbutes to represent the states of objects and a set of operatons on attrbutes. Thus, n OO envronent, the coheson s anly about how tghtly the attrbutes and operatons are encapsulated. Persson to ake dgtal or hard copes of all or part of ths work for personal or classroo use s granted wthout fee provded that copes are not ade or dstrbuted for proft or coercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc persson and/or a fee. SIGAda 03, Deceber 7, 2003, San Dego, Calforna, USA. Copyrght 2003 ACM /03/002 $5.00. There are several approaches proposed n lterature to easure OO progra coheson [2, 5, 6, 7,, 2]. Most approaches are based on the nteracton between operatons and attrbutes. The coheson s easured as the nuber of the nteractons. Generally only the references fro operatons to attrbutes are consdered. And few care about the nteractons of attrbutes to attrbutes and operatons to operatons at the sae te. Ths ght lead to bas when easurng the coheson of a class. For exaple, when desgnng the trgonoetrc functon lb class, we ght set a global varable to record the teporal result. The varable s referred n all the operatons of the class. Accordng to ethods based on the nteracton between operatons and attrbutes [6, 7], the coheson s the axu. In fact, there are no relatons aong the operatons f the calls are not taken nto account. In ths vew, ts coheson s 0. The dfference s caused by consderng only the references fro operatons to attrbutes, whle not consderng the nter-operaton relatons. In our prevous work, we have done soe research n easurng OO progra coheson [0, 3, 4]. Our approach overcoes the ltatons of prevous class coheson easures, whch consder only one or two of the three facets. Snce the OO echanss n dfferent prograng languages are dfferent fro each other, ths paper apples our easure to Ada packages. The reanng sectons are organzed as follows. Secton 2 ntroduces the package n Ada 95. Secton 3 dscusses the basc defntons and propertes for our easure. Based on the defntons and propertes, Secton 4 proposes approaches to easure package coheson. Concluson rearks are gven n the last secton. 2. PACKAGES IN ADA 95 In Ada 95[ISO95], packages and tagged types are basc progra unts to support OO prograng. A package allows the specfcaton of groups of logcally related enttes. Typcally, a package contans the declaraton of a type along wth the declaratons of prtve subprogras of the type, whch can be called fro outsde the package, whle ts nner workngs rean hdden fro outsde users. In ths paper, we dstngush packages nto four groups. PG: Packages that contan any knd of enttes except tagged types. PG2: Packages that only contan the declaraton of one tagged type along wth those prtve subprogras of the type. There are two subgroups n PG2: - PG2-: The type s an orgnal tagged type. - PG2-2: The type s a derved type. 62

2 PG3: Cobnaton of PG and PG2. PG4: Generc packages. After a generc package s nstantated, t belongs to one of the forer three groups. Thus, only coheson easure of PG, PG2 and PG3 s dscussed n the paper. 3. DEFINITIONS 3. Basc Defntons In ths secton, we wll present our defntons n the for of PG. The coheson of a package fro PG s anly about how tghtly the objects and subprogras are encapsulated n the package. In ths paper, the relatonshps aong objects and subprogras are defned as three dependences: nter-object, nter-subprogra and subprogra-object dependence. Defnton In the package body or a subprogra of the package, f the defnton (odfcaton) of object A uses (refer, but not odfy) object B drectly or ndrectly, or whether A can been defned s deterned by the state of B, then A depends on B, denoted by A B. Generally, f B s used n the condton part of a control stateent (such as f and whle), and the defnton of A s n the nner stateent of the control stateent, the defnton of A depends on B s state. Defnton 2 If object A s referred n subprogra P, P depends on A, denoted by P A. Defnton 3 There are two types of dependences between subprogras: call dependence and potental dependence. If P s called n M, then M call depends on P, denoted by M P. If the object A used n M s defned n P, the A used n M depends on the A defned n P, denoted by M A, A P, where (A, A) s naed as a tag. For each call edge, add a tag (*, *) for unfcaton..e. f P Q, P *,* Q. To obtan these dependences, we ntroduce four sets for each subprogra M: IN(M) s an object set, each eleent of whch s an object referred before odfyng ts value n M; OUT(M) s an object set, each eleent of whch s an object odfed n M. DEP_A (M) s a dependence set whch represents the dependences fro the objects referred n M to the objects defned outsde M. Each eleent has the for <A, B>, where A and B are objects of the package. DEP_A_OUT(M) s a dependence set whch records the dependences fro the objects referred n M to the objects defned outsde M when extng M. In general, the nteredate results are nvsble outsde, and an object ght be odfed any tes n a subprogra. We ntroduce DEP_A_OUT to prove the precson. Obvously, DEP_A_OUT(M) DEP_A (M). Property A IN(M), A OUT(P) M A, A P. Property 2 <A, B> DEP_A(M), B OUT(P) M B A, P. Property 3 M A, B P, <B, C>(<B, C> DEP_A_OUT(P), C OUT(Q)) M A, C Q. In our prevous work [8, 9], we have proposed ethods to analyze dependences aong stateents for Ada progras. And these dependences can be easly transfored to the dependences proposed n ths paper. Due to the space ltaton, we do not dscuss the n detal here. To present our coheson easure n a unted odel, we ntroduce package dependence graph to descrbe all types of dependences. Defnton 4 The package dependence graph (PGDG) of a package PG s a drected graph, PGDG <N, E, T>, where N s the node set and E s the edge set, T s the tag set. N N O N P, N O s the object node set, each of whch represents a unque object; N P s the subprogra node set, each of whch represents a unque subprogra. PGDG conssts of three sub-graphs: Inter-Object Dependence Graph (OOG), OOG <N O, E O >, where N O s the object node set (the nae of a node s the nae of the object t represents); E O s the edge set, f A B, then edge <A, B> E O. Inter-Subprogra Dependence Graph (P, PPG <N P, E P, T>, where N P s the subprogra node set; E P s the edge set whch represents the dependences between subprogras; T (V V) s the tag set, where V s the unon of objects and {*}. Subprogra-Object Dependence Graph (POG), POG <N, E PO >, where N s the node set whch represents objects and subprogras; E PO s the edge set representng dependences between subprogras and objects. If P A, <P, A> E PO. Exaple shows the package Tr, whch contans three objects: tep, tep and tep2, and four subprogras: sn, cos, tg and ctg. Fgure shows the PGDG of the package Tr n Exaple (all the Tags on PPG are (*, *), because there are only call dependences n ths exaple. We ot the Tags for convenence). Exaple: package Tr. package Tr s tep, tep, tep2: real; functon sn (x: real) return real; functon cos (x: real) return real; functon tg (x: real) return real; functon ctg (x: real) return real; end Tr; package body Tr s functon sn (x: real) return real s begn tep: ; return tep; end sn; 63

3 functon tg (x: real) return real s begn tep:sn(x);tep2:cos(x); tep:tep/tep2; return tep; end tg; end Tr; tep (a) OOG tep2 tep 3.2 Extended Defntons Snce there s no object n the package of PG2, the defntons of Secton 3 can not be appled to these packages drectly. Therefore, ths secton wll extend the defntons of Secton 3. to a ore general odel by the followng steps: For PG, f there s an ebedded package, the package s taken as an object. For PG2, take the coponents of the type as objects of the package. Let A, B be object of a type T, M, P prtve subprogras, and Co and Co2 are coponents of T. Then A, B (A.Co B.Co2) Co Co2. A, P (P A.Co) P Co. A. Co, B. Co2 A, B, M, P (M P) Co, Co2 M P. For PG3, take the types as objects of the package. To present our easure n a unfed odel, we add powers for dfferent objects. PW(O) sn cos (c) PPG tep tep tep2 sn cos tg ctg (b) POG Fgure.. PGDG of class Tr tg ctg Coheson( O) Coheson( PG( O)) O s a package object O s a type object others where Coheson (O) s the coheson of O, PG (O) returns the package contanng O. 4. MEASURING PACKAGE COHESION Accordng to the PGDG, ths secton wll propose our ethod to easure the package coheson. In the followng dscussons, we assue package PG contans n objects and subprogras, where, n Measurng Inter-Object Coheson Inter-object coheson s about the tghtness aong objects n a package. To easure ths coheson, for each object A, ntroduce a set A_DEP to record the objects on whch A depends,.e. Let O_DEP(A) {B A B, A B}. PW _ DEP( A) PW ( B). B O _ DEP( A) Then, we defne the nter-object coheson as: Coheson ( O _ O, n n 0 PW ( A) PW _ DEP( A ) n n 0 n n > PW _ DEP( A) where represents the degree on whch A n depends on other objects. If n0, there s no object n the package, we set t to 0. If n, there s one and only one object n the package, the coheson s ts power. 4.2 Measurng Subprogra-Object Coheson Subprogra-object coheson s the ost portant feld n easurng coheson. Untl now, there have been several approaches proposed n lterature, such as Chae s ethods [6, 7]. But ost approaches are based on the POG. As we have entoned above, all these ethods descrbe the object reference n a sple way and subprogras are connected by the objects referred. Whether there are related aong these subprogras are not descrbed exactly. Thus, these approaches should be proved to descrbe these relatons. For copleteness, we use Co(Prev) to represent a prevous coheson easure, whch satsfes Brand s four propertes. For each subprogra P, we ntroduce another two sets: P_O and P_O_OUT. Where P_O(P) records all the objects referred n P. 64

4 Let P_O_OUT(P) records the objects referred n P, but these objects relate to objects referred by other subprogra,.e., P_O_OUT(P){A B, M (P ρ( P ) A P _ O _ A P _ O( P) M OUT ( P) B, A M A, P) A,B * }. B Then, we defne the subprogra-object coheson as: Coheson( P _ O, A P _ O( P) 0 Co( Prev) ρ( P ) 0 n 0 Others If P_O(P) Φ,.e. no objects are referred n P, we set ρ (P) 0. If the objects referred n P are not related to other subprogras, these objects can work as local varables. It decreases the coheson to take a local varable for a subprogra as an object for all subprogras. If there s no object or subprogra n the package, no subprogra wll depend on others. Thus, Coheson ( P _ O, Measurng Inter-Subprogra Coheson In the PGDG, although subprogras can be connected by objects, ths s not necessary sure that these subprogras are related. To easure the nter-subprogra coheson, we ntroduce another set P_DEP(P) {M P M} for each P. The nter-subprogra coheson Coheson(P_P, s defned as followng: Coheson( P _ P, 0 P _ DEP( P ) 0 > P _ DEP( P) where represents the tghtness between P and other subprogras n the package. If each subprogra depends on all other subprogras, Coheson(P_P,. If all subprogras have no relatons wth any other subprogra, Coheson(P_P, Measurng Package Coheson After easurng the three facets ndependently, we have a dscrete vew of the coheson of a package. We have two ways to easure the package coheson: ) Each easureent works as a feld, the package coheson s 3-tuple, Coheson( < Coheson(O_O,, Coheson(P_O,, Coheson(P_P, >. 2) Integrate the three facets as a whole Coheson( 0 k * Coheson( P _ P, 3 k Coheson ( where k ( 0,] ; k, k 2, k 3 >0, and k + k 2 + k 3. 0 n 0, 0 Others Coheson ( Coheson(O_O, Coheson 2 ( Coheson(P_P, Coheson 3 ( Coheson(P_O, If n0, 0, the package coheson descrbes only the tghtness of the call relatons, thus we ntroduce a paraeter k to constran t. For the exaple shown n Fgure, the coheson of Tr descrbes as follows: Coheson(O_O, Tr) /3 Coheson(P_O, Tr)0 Coheson(P_P, Tr)/3 Let k k 2 k 3 /3, Co(Prev), then Coheson(Tr) 2/9. Brand et al. [3, 4] have stated that a good coheson easure should be () Non-negatve and standardzaton. (2) Mnu and axu. (3) Monotony. (4) Coheson does not ncrease when cobnng two odules. These propertes gve a gudelne to develop a good coheson easure. Accordng to the defntons, t s easy to prove our easure satsfes these propertes. 4.5 Coheson for PG2-2 In the herarches of types, the derved type nherts the coponents and prtve subprogras of the super types. Generally, nhertance wll ncrease the couplng and decrease the 65

5 coheson. For the package fro PG2-2, we wll dscuss ts coheson n four cases: Case : Take the package ndependently. Case 2: Take all the prtve subprogras and coponents (contans those fro super type) nto consderaton. Case 3: If the prtve subprogras of the derved type ght access the coponents (or subprogra) of the super type, take these coponents (or subprogra) as those of the derved type. Case 4: Take the super type as an object of the derved type. The shortcong of Case s that: It only easures the coheson of the addtonal coponents and prtve subprogras of the derved type, not the coplete type. The prtve subprogras n the super type can not access the coponents of the derved type except dspatched subprogras. Consequently, n Case 2 or 3, the deeper the herarchy of types s, the saller the coheson. And t s hard to desgn a package whch coheson s bg enough. Although we present four cases n ths secton, none s good enough to descrbe the coheson for a package fro PG2-2. To easure the coheson of a derved type, uch ore aspects should be consdered. 5. RELATED WORKS There have several ethods proposed n lteratures to easure class coheson. Ths secton gves a bref revew of these ethods. ( ) () Chdaber s LCOM [0, ], t easures the 2 coheson by slar ethods and non-slar ethods. It s a reverse coheson easure. The bgger the easure, the lower the coheson. (2) The PPG n Htz s LCOM2 s represented by an undrected graph. LCOM2 s the nuber of sub-graphs connected. When there s one and only one sub-graph, he ntroduces connectvty to dstngush the. (3) Brand s RCI s the rato of the nuber of edges on POG to the ax nteracton between subprogras and objects. (4) Henderson s LCOM3 can be descrbed as follows. n µ ( A j ) n j LCOM 3( C) where µ(a) {M A P_O(M)}, A s attrbute and M s ethod. (5) Chae s CO [6] ntroduces glue ethods, and Xu-Zhou s CO [3] ntroduces cut set (glue edges) to analyze the nteract pattern. These two easures are ore ratonal than other easures. Fro the ntroductons above, we can see that All these ethods consder the attrbute reference n a sple way. Whether the ethods are related or not are not descrbed exactly. LCOM, LCOM2 and LCOM3 are non-standard, because ther up-bounds are related to the nuber of ethods n the class. LCOM s non-onotonous. The easurng results ght be nconsstent wth ntuton n soe cases RCI has the basc four propertes proposed by Brand. But t does not consder the patterns of the nteractons aong ts ebers, nether LCOM and LCOM2 nor LCOM3. Chae s CO overcoes ost ltatons of prevous easures. But t s non-onotonous [3]. Xu-Zhou s CO proves Chae s coheson easure, and akes ts result ore consstent wth ntuton. The chef dsadvantage of both easures s that they can be appled to connected POG; otherwse the result wll always be 0. LCOM and LCOM2 easure the coheson aong ethods n a class. We can prove the slar functon usng the dependences aong ethods proposed n ths paper. LCOM3, Chae and Xu-Zhou s CO easure the coheson aong ethods and attrbutes n a class. In ths paper we prove the by ntroducng ρ (M ) for each ethod M. 6. CONCLUSION Ths paper proposes an approach to easure the coheson of a package based on dependence analyss. In ths ethod, we dscussed the tghtness of a package fro the three facets: nterobject, subprogra-object and nter-subprogra. These three facets can be used to easure the package coheson ndependently and can also be ntegrated as a whole. Our approach overcoes the ltatons of prevous class coheson easures, whch consder only one or two of the three facets. Thus, our easure s ore consstent wth the ntuton. In the future work, we wll verfy and prove our easure by experent analyss When easurng package coheson, the followng should be pad attentons. () In the herarches of types, the prtve subprogras of super type ght access the objects of the derved type by dspatchng. Therefore, when easurng the coheson of PG2, t s hard to deterne whether the accesson of derved typed s consdered or not. (2) We can deterne polyorphc calls n an applcaton syste. However t s possble for a package, whch can be reused n any systes. (3) How to deal wth soe specal subprogras, such as access subprogras, snce such subprogras can access soe specal objects n the package. (4) How to apply the doan knowledge to coheson easure. In all, f a package can be appled to any applcatons, the coheson s anly about tself wthout consderng the applcaton envronents. Otherwse, t s the coheson n the specal envronents. 66

6 7. ACKNOWLEDGMENTS Ths work was supported n part by the Natonal Natural Scence Foundaton of Chna (NSFC) ( ), Natonal Grand Fundaental Research 973 Progra of Chna (G ), and Natonal Research Foundaton for the Doctoral Progra of Hgher Educaton of Chna ( ). 8. REFERENCES [] Allen, E.B., Khoshgoftaar, T.M. Measurng Couplng and Coheson: An Inforaton-Theory Approach. n Proceedngs of the Sxth Internatonal Software Metrcs Syposu. Florda USA, IEEE CS Press, 999, [2] Bansya, J.L., et al. A Class Coheson Metrc for Objectorented Desgns. Journal of Object-orented Prograng, 999, (8): [3] Brand, L.C., Morasca, S., Basl, V.R. Property-Based Software Engneerng Measureent. IEEE Trans. Software Engneerng, Jan. 996, 22(): [4] Brand, L.C., Daly, J., Wuest, J. A Unfed Fraework for Coheson Measureent n Object-Orented Systes. Eprcal Software Engneerng, 998, 3(): [5] Brand, L.C., Morasca, S., Basl, V.R. Defnng and Valdatng Measures for Object-Based Hgh-Level Desgn. IEEE Trans. Software Engneerng, 999, 25(5): [6] Chae, H.S., Kwon, Y.R., Bae, D.H. A Coheson Measure for Object-Orented Classes. Software Practce & Experence, 2000, 30(2): [7] Chae, H.S., Kwon, Y.R. A Coheson Measure for Classes n Object-Orented Systes. n Proceedngs of the Ffth Internatonal Software Metrcs Syposu. Bethesda, MD USA, 998, IEEE CS Press, [8] Chen, Z., Xu, B., Yang, H. Slcng Tagged Objects n Ada 95. n Proceedngs of AdaEurope 200, LNCS 2043: [9] Chen, Z., Xu, B., Yang, H., Zhao, J. Statc Dependency Analyss for Concurrent Ada 95 Progras. n Proceedngs of AdaEurope 2002, LNCS 236, [0] Chen, Z., Xu, B. Zhou, Y., Zhao, J., Yang, H. A Novel Approach to Measurng Class Coheson Based on Dependence Analyss. n Proceedngs of ICSM 2002, IEEE CS Press, [] Chdaber, S.R., Keerer, C.F. A Metrcs Sute for Object- Orented Desgn. IEEE Trans. Software Engneerng, 994, 20(6): [2] Htz, M., Montazer, B. Measurng Couplng and Coheson n Object-Orented Systes. n Proceedngs of Internatonal Syposu on Appled Corporate Coputng, Monterrey, Mexco, October 995: [3] Xu, B., Zhou, Y. Coents on A coheson easure for object-orented classes. Software Practce & Experence, 200, 3(4): [4] Zhou, Y., Guan, Y., Xu, B. On Revsng Chae s Coheson Measure for Classes. J. Software. 200, 2(Suppl.): (n Chnese) 67