ean 128 generator excel Semantics of Relations in Software

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Semantics of Relations
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We will in the view model always merge F Ds having the same ruling part, so that only one relation will be needed to describe all simple facts about an entity We applied this rule already when constructing tuples out of dependencies in Fig 7-4 The only time when we will have more than one relation with the same apparent ruling part A1 , A2 , , Aj occurs when the domains D(Ai ) di er in some sense
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Relations with di ering ruling part domains
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Consider the two relations Employee: RELATION employee number : jobtitle, date of birth, ; Managers: RELATION employee number
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: jobtitle, date of birth, , stock options;
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In the Managers relation the domain for employee number is restricted, but such restrictions are awkward to express in terms of domain rules A better way of expressing the restrictions is to state that jobtitle = "Manager" To keep our examples clear we will always use identical attribute names Ai to imply identical domains, so that D(Ai ) = D(Ry Ai ) = D(Rz Ai ) The notation D(Rx Ai ) to determine some Dd is based on Eq 7-2 Decomposition Dependent parts can be split, so that one relation can be transformed to several relations having the same ruling part If then and F D(A1 , A2 , , Aj ) = B1 , B2 , , Bk F D(A1 , A2 , , Aj ) = B1 , B2 , , Bi F D(A1 , A2 , , Aj ) = Bi+1 , Bi+2 , , Bk
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The selection of a dependent attribute Bd to become a member of the rst, the second, or both relations is of course arbitrary View models are decomposed mainly to form building blocks for new relations We also decompose relations to separate M VDs and F Ds Some secondary axioms can be derived from these by straightforward processes The union axiom (Eq 7-11) is in fact derived using Eqs 7-9 and 7-10 by augmenting both F Ds, one with the A s and the other with the B s and applying the transitivity axiom to the results The decomposition axiom (Eq 7-12) is derived by selecting a subset of the B s, recognizing the F D of this subset due to re exivity (Eq 7-8) and applying transitivity (Eq 7-10) to this F D and the original F D(A) = B These axioms can be used to rearrange the view models and to create the database model from the view models They are su cient to obtain a complete set of functional dependencies F D+ This set is obtained by initializing F D+ with the known set of F Ds, and applying the three Armstrong axioms (Eqs 7-8, 7-9, 7-10) in turn to F D+ to create more entries into F D+ for the next phase The process of obtaining all FD s may be costly, since the set F D+ becomes rapidly large, but could be useful to understand a view model
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A nonredundant model in terms of functional dependencies can be obtained from a set of relation-schemas by 1 Decomposing all dependent parts to single attributes in order to create binary relation-schemas 2 Ordering the simpli ed relation-schemas by their ruling part 3 Removing all redundant F Ds in this list by retaining only one, and only the simplest ruling part for any dependent attribute 4 Composing new relations where ruling parts match We frequently use these axioms when trying to arrive at a semantically clear and e ective model The transformations required for this purpose are typically easy to prove correct using these axioms, and if they cannot be shown correct are likely to have an error Functional dependencies continue to exist among relations that have been decomposed during normalization, and may also be de ned among relations that have been established separately Multivalued dependencies will always be between distinct relations in a structural model 7-2-6 Value and Reference Attributes When we analyze the attributes for a model, we nd two types of domains being used Figure 7-5 provides examples of both types Some attributes describe characteristic properties of an entity directly by assigning a value to the data element A permanent domain de nition, kept with the relation-schema, permits veri cation of values for new entries
Examples of value attributes are the height, weight, and age of the employee If the employee is dismissed and the employee s data tuple is deleted from the relation, the values will also disappear No instance of age = 34 may exist if Hare leaves the company
Other attributes describe characteristics of an entity indirectly by reference to another entity The domain used here is termed reference domain and the allowable values in the domain are de ned by the existence of tuples in another relation The domain de nition can be changed by an update to the referenced relation The referencing attribute and the referenced relation establish a reference connection in the model
The employee tuple, for example, has an attribute which contains the name of the employee s department The department will continue to exist when the employee leaves, and will even continue to exist, barring other action, even if all employees leave the department We will in our models nd distinct relations for the department, so that its existence is recorded in the database independently of assignments of employees
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