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1 Basic Laws of Object Modeling Rohit Gheyi Tiago Massoni Paulo Borba Software Productivity Group http://www.cin.ufpe.br/spg Informatics Center – UFPE http://www.cin.ufpe.br/spg

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2 Introduction Semantics-preserving model transformations are usually proposed in an ad hoc way Simple mistakes may lead to incorrect transformations introduce inconsistencies

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3 Introduction Modeling Laws each law defines two transformations have not been sufficiently studied yet might bring similar benefits of programming laws Reliability Productivity Identify, formalize and study modeling laws Focus: modeling laws for Alloy earlier stages of the software development process

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4 Alloy sig Bank { accounts: set Account } sig Account {} sig ChAcc extends Account {} sig SavAcc extends Account {} fact AccPartition { Account = ChAcc + SavAcc }

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5 Basic Laws We propose basic laws defining properties about: signatures facts relations Predicate calculus and relational operator properties are used here

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6 Example: Introduce Relation =,v

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7 Introduce Relation Law (Law 2) () if r belongs to then v contains the rexp item; () The family of S in ps does not declare r; () r does not appear in ps and forms. ps sig S { rs } fact F { forms } ps sig S { rs, r : set T } fact F { forms r = exp } =,v

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8 Equivalence Notion =,v = {Bank, accounts, Account} v = {(accounts col.elems)} Alphabet View

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9 Example: Pull Up Relation (Law 3) no (Account-ChAcc).chOwner =,v

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10 Introduce Formula Law (Law 4) provided () The formula f can be deduced from the formulas in ps and forms. ps fact F { forms } ps fact F { forms f } =,v

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11 Bank System Atomization Law 2 ()Law 4 ()Law 3 () Law 4 () Law 2 ()

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12 Components: Specification Matching public class DBHandler { private static OleDbConnection connection; public static OleDbConnection Connection { get { if (connection == null) { string dataSource = "BancoCS.mdb"; string strConexao = "Provider= Microsoft.Jet.OLEDB.4.0; " + "Data Source=" + dataSource; connection = new OleDbConnection(strConexao); } return connection; } public static void StartTransaction() { Connection.Open(); transaction = Connection.BeginTransaction(); } public class DBHandler { private static OleDbConnection connection; public static void StartTransaction() { transaction = Connection.BeginTransaction(); } public static void main(String []args) { System.out.rintln(); connection = new OleDbConnection(strConexao); } public static OleDbConnection Connection { get { if (connection == null) { string dataSource = "BancoCS.mdb"; "Data Source=" + dataSource; } return connection; } M1 =,v... M2Mn Component Syntactic conditions

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13 Conclusions Axiomatic semantics Optimize analysis Substitute Components Derive refactorings

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14 Future Work Propose more basic laws and refactorings Show that our set of laws are complete propose a normal form for Alloy PVS (Prototype Verification System) Model Refactoring X Code Refactoring

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15 Basic Laws of Object Modeling Rohit Gheyi Tiago Massoni Paulo Borba Software Productivity Group http://www.cin.ufpe.br/spg Informatics Center – UFPE http://www.cin.ufpe.br/spg

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16 Introduce Empty Signature Law provided () ps does not declare any paragraph named S; S is not in; () S does not appear in ps; if S is in then v contains an item for S. ps sig S {} Set of paragraphs =,v

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17 Pull Up Relation Law ps sig T { rs } sig S extends T { rs, r : set U } fact F { forms } ps sig T { rs, r : set U } sig S extends T { rs } fact F { forms all t: T-S | no t.r } =,v

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18 Move Formula Law ps fact F { forms f } fact G { forms } ps fact F { forms } fact G { forms f } =,v

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19 Split Relation Law ps sig S { rs, r : set T } fact F { forms } ps sig S { rs, r : set T, u : set U } fact F { forms && r = u.t } sig U { t : set T } () if r belongs to then v contains the ru.t item;... () ps does not declare any paragraph named U; the family of S does not declare any relation named u in ps; () U, t and u do not appear in ps, rs and forms. =,v

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20 Introduce a Generalization Law ps sig S { rs } sig T { rs } fact F { forms } ps sig U {} sig S extends U { rs } sig T extends U { rs } fact F { forms U=S+T } () if U belongs to then v contains the U(S+T) item; () ps does not declare any paragraph named U and the family of S and T does not declare any relation with the same name in ps () U, S and T do not appear in ps, rs, rs and forms. =,v

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21 Change Relation Qualifier Type: from set to one Law ps sig S { rs, r : set T } fact F { forms all s: S | one s.r } ps sig S { rs, r : one T } fact F { forms } =,v

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22 Example: Split Relation accounts = col.elements =,v = {Bank, accounts, Account} v = {(accounts col.elements)}

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23 Example: Introduce a Generalization = {ChAcc, SavAcc} v = {(Account ChAcc+SavAcc )}

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24 Introduce a Generalization Refactoring Architects x Designers All basic laws are very simple to apply since their pre-conditions are simple syntactic conditions

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25 Extract Interface Refactoring () if C belongs to then v contains the CB item; () ps does not declare any paragraph named C; () C does not appear in ps, rs, rs and forms.

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26 Inserting a Collection Refactoring =,v

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27 Moving a Relation Refactoring =,v

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28 Extending a Signature Constraint S in T Formula deduced (S in T) => (#S <= #T) #S = 5 && #T = 3 =,v

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29 Inserting a Relation Constraint all s: S | one s.r Formula deduced (#S != 0) => (#T > 0) #S != 0 && #T = 0 =,v

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30 Inserting a Relation in a Subsignature Suppose s be an element that does not belong to T and relates with an element u of U in r After including t=r, we have (((s->u) in r) && (t = r)) => ((s->u) in t) some s:S | s !in Tt=r =,v

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