Tbe Database Language GEM Carlo Zaniolo Bell Laboratories Holmdel, New Jersey 07733
ABSTRACT
GEM (bn acronym for General Entity Manipulator) is a general-purpose query and update language for the DSIS data model, which is a semantic data model of the Entity-Relationship type. GEM is designed as -an easy-to-use extension of the relational language QUEL. providing supporr for. the notions of entities with surrogates, aggregation, generalization, null values, and set-valued attributes.
1. INTRODUCTION generalization. The possibility of extending the relational model to capture more meaning - as A main thrust of computer technology is towards opposed to introducing a new model - was simplicity and ease of use. Database management investigated in [CoddZl, where, surrogates and null systems have come a long way in this respect, values were found necessaryfor the task. particularly after the introduction of the relational approach [Ullml, which provides users with a simple ,-‘Most previous work with semantic data models has tabular view of data and powerful and convenient concentrated on the problem of modeling reality and query languages for interrogating and manipulating on schema design; also the problem of integrating the database. These features were shown to be the the database into a programming environment key to reducing the cost of database-intensive supporting abstract data types has received application programming Ecddll and to providing considerable attention [Brad, KMCI. However, the a sound environment for back-end support and problem of providing easy to use queries and distributed databases. friendly user-interfaces for semantic data models has received comparatively little attention’. Thus the The main limitation of the relational model is its question not yet answered is whether semantic data semantic scantiness, that often prevents relational models can retain the advantages of the relational , schemas from modeling completely and expressively model with respect to ease of use, friendly query the’ natural relationships and mutual constraints languages and user interfaces, back-end support and between entities. This shortcoming, acknowledged distributed databases. by most supporters of the relational approach [CoddZl, has motivated. the introduction of new This work continues the DSIS effort [DSISI to semantic data models, such as that described in enhance the UNIX* environment with a DBMS [Chenl where reality is modeled in terms of entjties combiiing the advantages of the relational approach and relationships among entities, and that presented with those of semantic data models. Thus, we begin in [SmSml where relationships are characterized by extending the relational model to a rich semantic along the orthogonal coordinates of aggregation and model su&rting the notions of entities with surrogates, generalization and aggregation, null values and set-valued attributes. Then we show that simple extensions to the relational language QUEL Permission to copy without kc all QC.part of this material is gmual provided that the topics arc not msde or distributed for dimct are sufficient to provide an easy-to-use and ,general- commercial advantage, tha ACk cbpyright notice and the titk of the purpose user interface for the specification of both pubiiition and its date l ppcac, and notice is given that copying is by queries and updates on this semantic model. permission of the Association for Computing Machinery. To copy otbcrwisc. or to republish. tequiru a fee and/or spccif~ permission.
1. To the extent that the functional data m6del [SiKel can be viewed as a semantic data model,~DAPLEX Bhipl stipplier a remarkable exception to this trend. @1983 ACM -O-89791-104-O/83/005/0207 $00.75 * UNIX is a trademark of Bell Laboratories.
207 ITEMS Name: c, Type: c, Colors: {c)> key(Name); DEPT (Dname: c, Floor: i2) key(Dname) ; SUPPLIER (Company: c, Address: c) key(Company); SALES ( Dept: DEPT, Item: ITEM, Vol: i2) key(Dept, Item) ; SUPPLY (Camp: SUPPLIER, Dept: DEPT, Item: ITEM, Vol: i2) ; EMP (Name: c, Spv: EXMPT nuU aIlowed, Dept: DEPT, [EXMPT(Sal: i4), NEXMPTtHrlwg: i4, Ovrt: i4)1,
[EMARRIED (Spoused: i4), otkd key (Name), key @OUSC#) ;
Figure 1. A GEM schema describing the following database: ITEM.. for each item. its name, its type, and a set of colors DEPT: for each department its name and the floor where it ts located. SUPPLIER.. the names and addressesof supplier companies. SALES: for each department and item the volume of sales. SUPPLY. what compan supplies what item to what department in what wlume 6f current st 0ck.f EMP: the name, the supervisor, and the deportment of each employee; EXMPT: employees can either be exempt 611 supervisors arc) or NEXMPT: non-exempt; the former earn a monthly salary while the latter have an hourly wage with an overtime rate. EMARRIED: Employees can either be married or not; the spouse’s social security number is of interest for the married ones.
2. ‘!-HE DATA MODEL member of that set is of type c (character string). _ Figure 1 gives a GEM schema for an example Name and Spouse# are the two keys for this family, adapted from that used in [LaPi]. The attributes However, since the uniqueness constraint is waived Dept and Item in SALES illustrate how an for keys that are partially or totally null Spouse##is aggregation is specified by declaring these two to be in effect a key for the s&entity EMARRIED only. of type DEPT and ITEM, respectively. Therefore, We will next define GEM’s Data Definition Dept and Item have occurrences of the entities Language, using the same me¬ation as in DEPT and ITEM as their respective values. The [IDMI to define its syntax. Thus (...I denote a set entity EMP supplies an example of generalization of zero or more occurrences, while [:..I denotes one hierarchy consisting of EMP and two generalization or zero occurrences. Symbols ‘enclosedin semiquotes sublists shown in brackets. The attributes Name, denote themselves. Spv and Dept are common to EMP and its subentities in brackets. The first generalization A GEM schema consists of a set of uniquely named sublist captures the employment status of an entities. smployee and consists of the two mutually exclusive 1.
208 3.
209 I Dname I Floor I
SALES Dent: DEPT 1 Item: ITEM 1 Vol
SUPPLY Comp: SUPPLIER 1 Dept: DEPT 1 Item: ITEM 1 Vol
EMP [ EXMPT NEXMPT 1 1 EMARRIED I ., Name 1 Spv:EXMPT I Dept:DEPT I Sal Hrlwg I Gvrt I SpOUSd#
Figure 2. A graphical representation of the GEM schema of Figure 1.
Query results of GEM are also presented in output particularly the simple ones; nor does any loss of as row-column tables derived from these tables. generality occur since range declarations can always be included when needed. 4. THE QUERY LANCUACE The query of Example 2 is therefore interpreted by GEM is designed to be a generalization of QUEL GEM as if it were as follows: IINGRI; both QUEL and IDM’s IDL are upward- range of DEPT Is DEPT compatible with GEM. Whenever the underlying retrieve (DEPT.Dname) schema is strictly relational (i.e., entities only have where DEPT.Floor-3 data attributes): Example 3. Same as examples 1 and 2.
210 range of S is SALES single-valued non-redundant functions; multivalued retrieve 6) and inverse functions and other involved constructs are not part of GEM, which is based on the bedrock. Example 4. A syntactically incorrect query. of the relational theory and largely retains the is incorrect in GEM (as it would be in QUEL). “Spartan simplicity” of the relational model. Therefore, these statements are also incorrect: Joins implicitly specified through the’use of the dot range of S is SAL& notation will be called functional joins. An retrieve (S.Dept) alternative way to specify joins k9 by using sexpltcit entity joins, where entity occurrences are directly Example 5. An incorrect query. compared, to verify that they are the same, using and the identity test opera&* is3. For ‘instance the ,. previous query can also beexpressed as fol10ws:~ retrieve (SALESItem) -< 3 range of S is SALES ,Example 6. A second jncorrect query. range of I Is ITEM Thus, reference attributes cannot be printed. rmgeofDisDEPT, However both single-valued and set-valued attributes retrieve (D.Floor) can be obtained by using QUEL’s usual dot- wIrereD Is S.Dept arrd S.Item Is I .’ notation; thus and I.T~~~P”SPORT” rdrieve (SALESVol) Example 9. Same query as in example& : Example 7. Find the volumes of all SALES. Comparison operators such as -, !=, >, >-, ‘<, and < - are not applicable to entity”o%urrences: : will get us the volumes of all SALES. Moreover, since SALFSDept denotes an entity of type DEPT. The names of entities and their’subentities - all in we can obtain the value of Floor by simply applying the top row of our templates - are unique and can the notation. “Floor” to it. Thus, be used in two basic ways.” Their first use is in defining range, variables. Thus, to request the name retrieve (SALES.Dept.Floor) and the salary of each married employee one can where SALES.Item.Name-“SPORT” write: Example 8. Floors where departments selling range of e is EMARRlbD items of type SPORT are located. retrieve (e.Name, e.Sal) will print all the floors where departments that sell Example 10. Find the name and salary of each s sport items are located. The importance of this married employee. natural extension of the ‘dot notation cannot be overemphasized, as illustrated by the sixty-six or simply, queries in Appendix IIIof IZani31, it supplies a very retrieve (EMARRIED.:Name, EMARRIED.SalJ convenient and natural construct that eliminates the need for :complex join statements in most queries. Example Il. Same as in example IO. For. instance, the previous query implicitly specifies Thus all attributes within an entity can be applied two joins: one of SALES with ,DEPT, the other of to any of its subtypes kithout ambiguity since their SALES with ITEM. To express the same query, names are unique within the family). QUEL would require three range variables and two join conditions in the where clause. A comparison to functional query languages may be useful here. Reference attributes can be viewed as 3. The operator isnot is used to test that two objects are not functions from an entity to ‘another, and GEM’s identical. 4. ,que&s in Examples 8 and 9 are u&&t only under’ the dot-notation can be interpreted as the usual dot- assumntion that the Dent attribute in SALES cannot be null. notation of functional composition. Thus GEM has a If so& SALES occur&c& havi? a null Dcpt link, then the functional flavor; in particular it shares with results of the two queries are ndt the same, as dkusscd in languages such as DAPLEX [Ship] the convenience detail in the section on null values. of providing a functional composition notation to relieve users of the burden of explicitly specifying joins. Yet the functions used by GEM are strictly
211 Subentity names can also be used in the retrieve (EXMPT.alll qualification conditions of a where clause. For where EXMPT.Sal > EXMPT.Spv.Sal instance, an equivalent restatement of the last query is Example 17. Use of all with subentities. retrieve (EMP.Name, EMP.Sal) returns only the salaries of those employees. where EMP Is EMARRIED The following query gives another example of the Example. 12. Same as example 1I. use of entity joins and the use of subentity names as default range variables ( EMP and EMARRIED (Retrieve the name and salary of each employee are the two variables of our query). who ’ is an employee-married.) For all those employees who are married but ’ non-exempt this’ retrieve (EMARRIED.Name) where EMP.Name-“J.Black” query returns their names and a null salary. Thus, and EMPDept is EMARRIED.Dept it is different from 4. Example 18. ‘Find all married employees iir the retrieve (EXMPT.Name, EXMPTSal) where EXMPT is EMARRIED same department as J.Black. Example 13. Find all exempt employees that 6. NULLVAIAJES are vuuried. A important advantage of GEM over other DBMSs that excludes all non-exempt employees at once. is that it provides for a complete and consistent The query, treatment of null values. The theory underlying our approach was developed in fZani1, Zani21; where a retrieve (EMP.Name) wbare rigorous justification is given for the practical E&fP Is EXMPT or EMP Is EMARRIED conclusions summarized next. Example 14. Find ,a11 employees that are GEM conveniently provides several representations exempt or married. of null values in storage and in output tables; at the will retrieve the names ‘of all employees that are logical level, however, all occurrences of nulls are exempt or married. treated according to the no4nformation interpretation discussed in [Zanill. In conformity to QUEL, GEM also allows the use of the keyword aII in the role of a target attribute. A three-valued logic is required to handle Thus to print the whole table ITEM one need only qualification expressions involving negation. Thus, a specify, condition such as, retrieve OTEM.~I~ ITEM.Type- “SPORT” Example 15. Use of all. evaluates to DUBfor an ITEM occurrence where the Type attribute is null. Boolean expressions of such In the presence of ‘generalization and aggregation terms are evaluated according to the three-valued the aII construct can be extended as .follows. Say logic tables of Figure 3. Qualified tuples are only that t ranges over an entity or a subentity E. Then those that yield a TRUE value; tuples that yield “t.aii” specifies all sitiple and set-Galtied attributes FALSE or the logical UUII are discarded. in b and ‘its subentities. Thus, It was suggested in [&id21 that a IIUB version of a retrieve (EMP.~~ query should also be p&dad to retrieve those tuples where EMP.Sal > EMP.Spv.Sal where the qualification, although not yielding Example 16. Extended use of all. TRUE, does not yield FALSE either. By contrast it was, ,hown in [Zani21 that the TRUE version’. returns the name, the salary, the hourly wage and suffices once ‘the expression “t.A is null” and its overtime rate, and the spouse’s social security negation 4.B ‘isnot rmII” are allowed in the number of every employee earning more than his or qualification expression. Therefore, ‘we have included her supervisor (the values of some of these attributes these clauses in GEM. %nts,‘rather than requesting being null, of course); while a null version answer for the query in Example 2, a user will instead enter this query: *
212 OR T F nuII AND 1 T 1 F ) nuII
nuil null F null
Figure 3. Three-valued logic: tables.
range of dep Is DEPT retrieve (S.B, S.Ref1.A) retrieve (dep.Name) Example 21. Implicit join without nulls. where dep.Floor is nutI produces the following table. (For clarity we show Example 19. Find the departments whose jloors the reference columns although they are never are unspecified. included in the output presented to a user.) Indeed, this query returns the names of those departments that neither, meet nor fail the qualification of Example 2 (depEloor -3). pj?Jj In (Zani21 it is shown that a query language featuring the three-valued logic with the extension Figure 5. The result of example 21. described above is complete - relational calculus and relational algebra are equivalent in power, as However, the query query languages. GEM, which is also complete, retrieve (S.B, S.Ref2.A) consists of a mixture of relational calculus and algebra, just like QUEL. In particular, both Example 22. Implicit join with nulls. languages draw from the relational algebra generates the table, inasmuch as they use set-theoretic notions to eliminate the need for. universal quantifiers in queries, The treatment of set and aggregate operations in the presence of null values will be ppJg discussed in the next section. Figure 6. Result of example 22. We can compare these queries with the explicit-join queries: retrieve (S.B, R.A) where S.Refl Is R Example 23. Explicit join without nulls.
S T and # B Refl:R ‘Ref2:R retrieve (S.B, R.A) where S.Ref2 is R 6 bl 1 2 7 b2 2 nuIi Example 24. Explicit join with null. Figure 4: A database. Since two entities are identical if and only if their surrogate values are equal, these queries are Null values make possible a precise definition of equivalent (in a system that, unlike GEM, allows the notion of implicit join defined by ‘the dot- direct accessto surrogate values) to: notation. For concreteness consider the database of Figure 4. On this database, the query
213 retrieve (S.B, R.A) where S.Refl-R.# Thus inclusion of set-valued attributes is desirable also in view of the set and aggregate functions Example 25. Implementing Example 23 by already provided by QUEL. In QUEL, and joining on surrogates. therefore in GEM, the set-valued primitives are and, provided through the (grouped) by construct. For example, a query such as, “for each item print its retrieve (S.B, R.A) where S.Ref2-R.# name, its type and the number of colors in which it Example 26. Implementing Example 24 by comes” can be formulated as follows: joining on surrogates. range of I is NewITEM Applying the three-valued logic described above, one retrieve (I.Name, I.Type, concludes that the queries of Examples 21 and 25 Tot-count( I.Color by I.Name, I.Type)) return the same result; however, the query of Example 27. Use of by. Example 22 produces the. table of Figure 6, while that of Example 26 produces the same table but (Since Type is functionally dependent on Name, without the last row. I.Type can actually be excluded from the by variables without changing the result of the query It can be proved that an implicit functional join, above.) such as the one of Figure 6, corresponds to a semi- j union join [Zanill, alias a semi-outer join [Codd21, Using the set-valued Colors in ITEM, the same which is in turn defined as the union of S with the query can be formulated as follows: entity join, S w R. Therefore, implicit functional range of I is ITEM joins are equivalent to explicit entity joins whenever retrieve (I.Name, I.Type, Tot-count
214 expressions that are more efficient to support. Then append to DEPT (Dname-“SHOES”, Floor- 2) we plan to exploit the fact that set-valued attributes Example 31. Add the shoe department, 2nd floor. can only be used in this capacity, so that substantial improvements in performance can be achieved by adds the shoe department to the database. specialixed storage organizations. Performance To insert a soap-dish that comes in brass and improvements obtained by declaring set-valued bronze finishes, one can write: attributes may alone justify their addition to th3 relational interface. append to ITEM (Name-“Soapdis”, Type=“Bath”, Colors-(brass, bronze}) , In the more germane domain of user convenience, set-valued attributes entail a more succinct and Example 32. Inserting a new item. _ expressive formulation .,of powerful queries. For . Attributes that do not appear in the target list are instance, the query “Find all items for which there set to qwII if single-valuad, if set-valued, they are exist items of the same type with a better selection assigned the empty set. of colors,” can be expressedas follows: . The statement, ruge of 11 for ITEM rarrge of 12 for ITEM append to ITEM (Name- “towel-bar”, retrieve (Il.aIB where Type- ITEM.Type, Colors- ITEM.Colors~ Il.Typc - 12.Type md 11Colors < 12.Colors where ITEM.Name - “Soap-dish” Exampli 29. Items offering an inadequate Example 33. Completing our bathroom set. selection of colors for their allows us to add a towel-bar of the same type and types). colors as our soap-dish. ( Accordiig to the syntax of Thus, set-valued attributes can only be operands of the append to statement, the first occurrence of set-valued ‘operators and aggregate functions. The “ITEM” is interpreted ‘as an entity name, while the latter, however, can also apply to sets of values from others are interpreted as range variables declared by single-valued ‘attributes and reference attributes. default.) Thus, to find all the items supplied to all Hiring T. Green, a new single employee in the, shoe departments one can use the following query: department under J. Black, with hourly wage of S &eve (SUPPLY.Item.Name) where 5.40 and overtime multiple of 2.2, can be specified (SUPPLYDept by SUPPLY.Item) >- (DEPT) by the statement, Example 30. Items supplied to all departments. append to EMP (Name-“T.Green”, Spv- EXMPT, Dept. - DEPT, Hrlwg-5.&,Ovrt-2.2) Observe that sets are denoted by enclosing them in where EXMPT.Name=“J.Black” braces. Also, GEM enforces the basic integrity tests and DEPTDname- “SHOE” on set and aggregate functions (sets must consist of elements of compatible type). Example 34. Adding a new single non-exempt employee. In the presenceof null values, the set operators must be properly extended. A comprehensive solution of In thii statement, we can replace EMP by this complex problem is presented in [Zanil I; for the NEXMPT without any change in meaning since the specific case at hand (sets of values rather than sets fact that Hrlwg and o;f’ are not null already of tuples), that reduces to the following simple rule: implies that the employee is non-exempt. Moreover, Null values are excluded from the computation of since no attribute of EMARRIED is mentioned in all aggregate functions or expressions; moreover, the target list, the system will set the new EMP to they must also be disregarded in the computation of others, rather than EMARRIED. (If no attribute of the subset relationship. either EXMPT or NEXMPT were in the target lit an error message would result, since others is not 8. UPDAm allowed for this generalization sublist.) GEM supports tQUEL*s standard style of updates, If after a .while T. Green becomes an exempt via the three commands iiuert, delete and replace. employee eth a salary of $12000 and a supervisor Thus, yet to be assigned, the following update statement can be used:
215 replace EMP (Spv -null, Sal- 12000 1 A request such as, where EMP.Name - “T.Green” delete EXMPT Example 35. Tom Green becomes exempt and where EXMPT.Name=“T.Green” loses his supervisor. Example 39. T. Green goes too. Note that the identifier following a replace is a range variable, unlike the identifier following a is evaluated as the following: qpend to. The fact that salary is assigned a new delete EMP value forces an ‘automatic change of type from where EMP.Name=“T.Green” NEXMPT to EXMPT. Finally, note the assignment and EMP is EXMPT of nuII to a reference attribute. Example 40. Same as above. GEM also allows explicit reassignment of entity subtypes. Thus the previous query could, more Thus, since T. Green. is exempt, his record is eliminated, otherwise it would not be. explicitly, be formulated as follows: I replace NEXMPT 9. CONCLUSION wltb EXMPT &v-mdI, Sal- 12000) A main conclusion of this work is that’ relational where NEXMPT.Name- “T.Green” query languages and interfaces are very robust. We Example 36. Same as Example 35. have shown that with suitable extensions the relational model provides a degree of modeling Say now that after being married for some time, power that matches or surpassesthose of the various T. Green divorces; then the following update can be conceptual and semantic models proposed in the used: literature. Furthermore, with simple extensions, the @ace EMARRIED with EMP relational language QUEL supplies a congenial ., where EMP.Name- “T.Green” query language for such a model. The result is a,:. friendly and powerful semantic user interface that Example 37. T. Green leaves wedlock. retains, and in many ways surpasses,the ease of use This example illustrates the rule that, when an and power of a strictly relational one. Because of entity el is replaced with an ancestor entity e2, all these qualities, GEM provides an attractive interface the entities leading from el to e2 are set to others. for end-users; moreover, as shown in [A&J, it Thus the EMP T. Green will be set to others than supplies a good basis on which to ‘build database EMARRIED. interfaces for programming languages. The deletion of an entity occurrence will set to nuU The approach of extending the relational model is all references pointing to.it. Thus the resignation of preferable to adopting a new semantic model for T. Green’s supervisor, many reasons. These include compatibility and graceful evolution, since users that do not want the, delete EMP.Spv extra semantic features need not learn nor use them; where EMP.Name - “T.Green” for these users GEM reduces to QUEL. Other Example 38. T. Green’s supervisor quits. advantages concern definition and ease of implementation. As indicated in this ‘paper and causes the Spv field in T. Green’s record, and in the shown in [Tsur, TsZal, all GEM queries can be records of those under the same supervisor, to be set mapped into equivalent QUEL expressions., In this to xmR ( if null were not allowed for Spv, then the way a precise semantic definition and also a notion update would abort and an error message be of query completeness for GEM can be derived generated), and then the supervisor record is from those of QUEL, which in turn maps into the deleted’. relational calculus [Ullml. This is a noticeable improvement with respect to many semantic data 5. Of course. according to standard management practices T. models that lack formal, precise definitions. Finally, Green’s people may instead be reassigned to another the mapping of GEM into standard QUEL supplies supcrvkor. e.g. Green’s hose; this policy can be implemented by preceding the deletion of Green’s record with an update an expeditious and, ‘for most queries,’ efficient means reassigning hi people. of implementation; such an implementation, planned for the commercial database machine IDM 500, is described in [Tsur, TsZal.
216 Acknowlcdgmcnta [INGRI Stonebraker, M., E. Wong, P. Kreps and G. Held. “The The author is grateful to J. Andrade and S. Tsur for Design and Implementation of INGRES”, ACM helpful discussions and recommendations on the Trans on Database Syst. 1:3, pp. 189- design of GEM. Thanks are due to D. Fishman, M. S. Hecht, E. Y. Lien, E. Wolman and the referees 222,1976. for their comments and suggestedimprovements. [LaPil Lacroix, M. and A. Pirotte, “Example queries in relational languages,” MBLE RtBf- Tech. note 107, 1976 (MBLE, Rue Des Deux Gares 80, 1070 Brussels). [Andrl Andrade J. M. “Genus: a programming language for the design of database [QUELI Woodfill, J. et al., “INGRES Version 6.2 applications,” Internal Memorandum, Reference Manual,” Electronic Research Bell Laboratories, 1982. Laboratory, Memo UCB/ERL-M78/43, 1979. [Brodl Brodie, M.L., “On Modelling Behavioural Semantics of Databases,” [Ship] Shipman, D.W., “The Functional Model 7th Znt. Conf. Very Large Data Bases, and the Lata Language DAPLEX,” pp. 32-42, 1981. ACM Trans. Data Base Syst., 6,1, pp. 140-173, 1982. [Coddll Codd, E.F., “Relational Database: A Practical Foundation for Productivity” ISiKe Sibley, E.H. and L. Kershberg, “Data Comm. ACM, 25,2, pp. 109-118, 1982. Architecture and Data Model Considerations,” AFZPS Nat. Computer [CoddZl Codd, E.F., “Extending Database Con& pp. 85-96,1977. Relations to Capture More Meaning, ACM Trans. Data Base Syst., 4,4, pp. [SmSml Smith, J.M: and C.P. Smith, “Database 391-434, 1979. Abstractions: Aggregation and Generalization,” ACM Trans. Database [Chenl Chen, P.P., “The Entity-Relationship syst., 2, 2, pp. 105-133, 1977. Model - Toward an Unified View of Data,” ACM Trans. Database Syst., 1, [Tsurl TSUT,S., “Mapping of GEM into IDL,” 1, ‘pp. 9-36, 1976. internal memorandum, Bell Laboratories, 1982. [DSISl Lien, Y.E., J.E. Shopiro and S. Tsur. “DSIS - A Database System with [TsZaI Tsur, S. and C. Zaniolo, “The Interrelational Semantics,” 7th Znt. Co& Implementation of GEM - Supporting Very Large Data Bases, pp. 465-411, a Semantic Data Model on a Relational 1981. Backend”, submitted for publication. [HeSWl Held, G.D, M.R. Stonebraker and E. HJllml Ullman, J., “Principles of Database Wong, “INGRES: a Relational Data Systems;” Computer Science Press, 1980. Base System,” AFZPS Nat. Computer [Zanill Zaniolo, C., “Database Relations with Conf., Vol. 44, pp. 409-416, 1975. Null Values,” ACM SZGACT-SZGMOD [KiMcl King, R. and D. McLeod, “The Event Symposium on Principles Of Database Database Specification Model,” 2nd Znt. Systems, Los Angeles, California, March Co& Databases - Improving Usability 1982. and Responsiveness, Jerusalem, June 1Zani21 Zaniolo, C., “A Formal Treatment of 22.24, 1982. Nonexistent Values in Database [IDMI IDM 500 Software Reference Manual. Relations,” Internal Memorandum, Bell Ver. 1.3,’ Sept 1981. Britton-Lee Inc., Laboratories, 1983. 90 Albright Way, Los Gatos, CA, 1Zani31 Zaniolo, C., “The Database language 95030. GEM,” Internal Memorandum, Bell Laboratories, 1982.
217 _. .- .
AppdiXkCRMSYNTAX This syntax fs an extensfm of. and we the same m¬ation as, that of bDhf1. Thus (...) denotea set of zero or man! occurrences,while L.J denotesone or zero occumnns. Symbols encltmd in m&potu denote themselves. retrim [ dqw I(
qged t to1
218