Relational Algebra And Calculus

Summary

• Closed Algebra
• Operators
• Selection Example
• Relational Calculus

Closed Algebra

Closed Algebra := A set of operations where the input operands and output operands are of the same type.

Operators

https://cs.brown.edu/courses/csci1270/website_2020/static/files/cs127_cheatsheet.pdf

$R \cup S$ is a union.

$R \cap S$ is an intersection.

$R \setminus S$ is the set difference.

$R \times S$ is the Cartesian Product.

$\pi A_1, A_2, \dots, A_n (R)$ is the projection (eliminating columns).

$\sigma _\text{expression} (R)$ is the selection (eliminating rows).

$R * S$ or $R \bowtie S$ is the natural join.

$R \div S$ is divide by (universal quantification).

$\rho [A_1 B_1, \dots, A_N B_N]$ is the rename operator.

Selection Example

$\sigma _\text{expression} (R) =>$ select all records from set $R$ that match $expression$.

$\sigma CurrentCity = HomeTown \lor HomeTown = \text{'Atlanta'} (RegularUser)$

Relational Calculus

${t | P(t)}$ := Set of tuples t that satisfy predicate $P(t)$

Predicates are built from atoms

Range Expression: $t \in R \text{ or } R(t)$ denote that t is a tuple of relation R.

Attribute Value: $t.A \text{ denotes the value of } t \text{ on attribute } A$.

Constants are defined by c

Comparison operators: $\theta =, \neq \leq, \geq, <, >$

Atoms := $t \in R, r.A \theta s.B, r.A \theta c$