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Cours 4 : Langage SQL & Algèbre relationnelle

Cours 4 : Langage SQL & Algèbre relationnelle. Nguyen TuanLoc. Rappel sur l’algèbre relationnel. Normalisation Forme conjonctive (p11 ν p12 v … v p1n) Λ (pm1 ν pm2 v … v pmn) Forme disjonctive (p11 Λ p12 Λ … Λ p1n) v (pm1 Λ pm2 Λ … Λ pmn) (souvent disjonctive).

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Cours 4 : Langage SQL & Algèbre relationnelle

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  1. Cours 4 : Langage SQL & Algèbre relationnelle Nguyen TuanLoc

  2. Rappel sur l’algèbre relationnel • Normalisation • Forme conjonctive (p11 ν p12 v…v p1n) Λ (pm1 ν pm2 v…v pmn) • Forme disjonctive (p11 Λ p12Λ…Λp1n) v (pm1 Λ pm2Λ…Λ pmn) (souvent disjonctive)

  3. Exemple: schéma de la base de données pour les étudiants de la MIAGE Paris 12

  4. Conjonctive SELECT ENSEIGNANTS.nom, ENSEIGNANTS.prenom, MATIERES.nommat FROM MATIERES INNER JOIN (ENSEIGNANTS INNER JOIN ENSEIGN_MAT ON ENSEIGNANTS.codens = ENSEIGN_MAT.codens) ON MATIERES.codemat = ENSEIGN_MAT.codemat WHERE (((ENSEIGNANTS.nom)="NGUYEN") AND ((MATIERES.nommat)="ACCESS" Or (MATIERES.nommat)="BASE DE DONNEES"));

  5. Disjonctive SELECT ENSEIGNANTS.nom, ENSEIGNANTS.prenom, MATIERES.nommat FROM MATIERES INNER JOIN (ENSEIGNANTS INNER JOIN ENSEIGN_MAT ON ENSEIGNANTS.codens = ENSEIGN_MAT.codens) ON MATIERES.codemat = ENSEIGN_MAT.codemat WHERE ( ( (ENSEIGNANTS.nom)="NGUYEN" AND (MATIERES.nommat)="BASE DE DONNEES") OR ( (MATIERES.nommat)="ACCESS" AND (MATIERES.nommat)="BASE DE DONNEES"));

  6. Normalisation de requête • p1 Λ p2 < => p2 Λ p1 • p1 v p2 < => p2 v p1 (commutativité) • p1Λ(p2 Λ p3) < => p1Λp2Λp3 • p1v(p2 v p3) < => p1vp2vp3 (associativité) • p1Λ(p2vp3) < =>(p1Λp2)v(p1Λp3) • p1v(p2Λp3) < =>(p1vp2) Λ(p1vp3) • !(p1 Λ p2) < =>!p1 v !p2 • !!(p) < => p

  7. Exercice SELECT Title FROM Emp WHERE (Not (Title=’’linux’’) AND (Title=’’linux’’ OR Title=’’windows’’) AND Not (Title = ’’unix’’)) OR Ename = ’’Toward Linus’’; On suppose: p1 = Title=’’linux’’ p2 = Title=’’windows’’ p3 = Ename = ’’Toward Linus’’

  8. Forme normale (!p1 Λ (p1 v p2) Λ !p2) v p3 • Disjonctive: [(!p1 Λ p1) v (!p1 Λp2)] Λ !p2) v p3< => (!p2 Λ [(!p1 Λ p1) v (!p1 Λp2)]) v p3< => (!p2Λ(!p1 Λ p1))v(!p2Λ(!p1Λp2)) v p3 < =>(!p2Λ!p1Λp1)v(!p2Λ!p1Λp2) v p3 < =>(!p2 Λfalse) v (!p1 Λ false) v p3 < => false v false v p3 < => p3

  9. Requête finale SELECT Title From Emp WHERE Ename =’’Toward Linus’’;

  10. Règle de transformation • Commutativité: R x S Ξ S x R R |x| S Ξ S |x| R R U S Ξ S U R • Associativité ( R x S ) x T = R x ( S x T) ( R |x| S ) |x| T = R |x| ( S |x| T) • Idempotence ΠA’ (ΠA’’(R) ) = ΠA’(R) (avec A’’ dans A’) …

  11. Analyse • Mise de la requête en forme normale • Analyse lexical et syntaxique • Type incorrect ou inexistant (schéma de la relation)

  12. Simplification • p Λ p < => p • p v p < => p • p Λ true < =>p • p v false < => p • p Λ false < => false • p v true < => true • p Λ !p < => false • p v !p < => true • p1 Λ (p1 v p2) < => p1 • P1 v (p1 Λ p2) < => p1

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