Relational Calculus

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RELATIONAL CALCULUS • Relational Algebra is a PROCEDURAL LANGUAGE => we must explicitly provide a sequence of operations to generate a desired output result • Relational Calculus is a DECLARATIVE LANGUAGE => we specify what to retrieve, not how to retrieve it Declarative ~ Non-Procedural • TUPLE Relational Calculus Two variants of Domain Relational Calculus relational calculus st Both based on 1 order predicate calculus RELATIONAL CALCULUS If a retrieval can be specified in the relational calculus, it can be specified in the relational algebra, and vise versa →expressive power of the languages is identical A query language L is Relationally complete if L can express any query that can be expressed in the relational calculus OPERATIONS in Tuple Relational Calculus ∧ - AND General power of ∨ - OR 1st order predicate calculus – allow ¬ - NOT more flexible ∃x – there exists x expression formats ∀x – for all x TUPLE RELATIONAL CALCULUS A query Predicate in the → { t| P(t) } T.R.C Set of all tuples such that P(t) is true for t Example: (∧) t.salary Employee.salary > 5000 {t | t ∈ Employee and t[SALARY] > 5000 Operator or single Boolean test that tuple Arrtibute of t tuple only t is a member of the employee realtion Standard conditional operation =>similar in function to SELECT(σ) T ← σ salary> 5000 (EMPLOYEE) condition relation TUPLE RELATIONAL CALCULUS Handling Projections (Π) Projection {t| э e € EMPLOYEE (t[LNAME] = e[LNAME]^e[SALARY] >5000 There exists Select condition (equiv to : ΠLNAME ( σ SALARY> 5000 (EMPLOYEE)) The new relation t is only defined for the attributes it is explicitly assigned (eg LNAME) JOINS IN THE TUPLE RELATIONAL CALCULUS projection {t | э d € DEPARTMENT (t[DNAME] = d[DNAME] projection ^ э e € EMPLOYEE (t[LNAME] = e[LNAME] ^ d[MGRSSN] = e[SSN] )) Join condition ~ Π DNAME,LNAME (DEPARTMENT MGRSSN=SSN (DNO=DNUMBER)EMPLOYEE Another join option GENERAL FORMAT OF THE TUPLE RELATIONAL CALCULUS { t | э d € DEPARTMENT (t[DNAME] = d[DNAME] Project and rename Result relation t ^t[DNO] = d[DNUMBER] (only has attributes : explicitly defined) Selection (σ) on ^d[DNUMBER] <3 DEPARTMENT : ^э e € EMPLOYEE( t[LNAME] = e[LNAME] Project and rename ^t[FNAME] = e[FNAME] ^ : ^ e[SEX] = M Selection (σ) conditions on ^ e[SALARY] <50000 EMPLOYEE : ^ d[MGRSSN] = e[SSN] )) } Join condition GENERAL FORMAT OF THE TUPLE RELATIONAL CALCULUS { t | э d € DEPARTMENT ( Existentialize Relations э e € EMPLOYEE ( d[DNUMBER] <3 Selection (σ) on ^ e[SEX] = M DEPARTMENT ^ e[SALARY] <50000 And EMPLOYEE ^ d[MGRSSN] = e[SSN] Join Condition(s) ^ t[DNO] = d[DNUMBER] ^ t[DNAME] = d[DNAME] ^ t[LNAME] = e[LNAME] Projection ^t[FNAME] = e[FNAME] )) } DOMAIN RELATIONAL CALCULUS Can represent/constraint domain/attribute values more directly TRC:{t | t € EMPLOYEE ^t[SALARY] >50000} DRC :{<f,l,s> | < f,l,s,b,a> € EMPLOYEE ^ S>50000} The “domain” Attributes listed An attribute of values satisfying explicitly <…> the following conditions DRC : { <l> | <f,l,s,b,a> € EMPLOYEE ^ S>50000} Projecting domain value for last name .

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Tuple Relational Calculus Formula Defines Relation
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