Functional Dependencies and Relational Schemas Library

This library provides tools for working with functional dependencies and relational schemas in database theory. It supports common operations such as determining closures, decomposing functional dependencies, and checking for normalization forms like 3NF and BCNF.

Installation

npm  install  relational-schema-normalization

Usage

Functional Dependency Class

The FunctionalDependency class represents a functional dependency in a relational database.

Example:

import { FunctionalDependency } from 'relational-schema-normalization';

const determinant = new Set(['A']);
const dependent = new Set(['B', 'C']);

const fd = new FunctionalDependency(determinant, dependent);

console.log(fd.determinant); // Set { 'A' }
console.log(fd.dependent);   // Set { 'B', 'C' }

Methods

• equals(fd: FunctionalDependency): boolean: Compares two functional dependencies for equality.
• decompose(): FunctionalDependency[]: Decomposes a functional dependency with multiple dependents into multiple functional dependencies, each with one dependent.

Functional Dependency Set Class

The FunctionalDependencySet class is a collection of FunctionalDependency objects with operations for union, comparison, and manipulation.

Example

import { FunctionalDependency, FunctionalDependencySet } from 'relational-schema-normalization';

const fd1 = new FunctionalDependency(new Set(['A']), new Set(['B']));
const fd2 = new FunctionalDependency(new Set(['B']), new Set(['C']));
const fdSet = new FunctionalDependencySet([fd1, fd2]);

console.log(fdSet.size());  // 2
console.log(fdSet.contains(fd1));  // true` 

Methods

• add(fd: FunctionalDependency): boolean: Adds a functional dependency to the set.
• union(otherFds: FunctionalDependencySet): FunctionalDependencySet: Returns the union of two functional dependency sets.
• remove(fd: FunctionalDependency): FunctionalDependencySet: Removes a functional dependency from the set.
• isSubsetOf(otherFds: FunctionalDependencySet): boolean: Checks if the set is a subset of another functional dependency set.

Relational Schema Class

The RelationalSchema class represents a relational schema, which is a set of attributes.

Example

import { RelationalSchema } from 'relational-schema-normalization';

const relationalSchema = new RelationalSchema(['A', 'B', 'C']);
console.log(relationalSchema.attributes);  // Set { 'A', 'B', 'C' }` 

Methods

• equals(rs: RelationalSchema): boolean: Compares two relational schemas for equality.

Utils Class

The Utils class provides various utility methods for computing closures, decomposing relations, and testing normalization forms.

Public Methods

1. closureOfSetOfFunctionalDependenciesUsingAttributesClosure(relationalSchemaParam: RelationalSchema, fdsParam: FunctionalDependencySet): FunctionalDependencySet

   • Description: Computes the closure of a set of functional dependencies using attributes closure for a given relational schema and functional dependencies.

2. closureOfSetOfFunctionalDependencies(relationalSchemaParam: RelationalSchema, fdsParam: FunctionalDependencySet): FunctionalDependencySet

   • Description: Computes the closure of a set of functional dependencies for a given relational schema and set of functional dependencies (slower method).

3. closureOfSetOfAttributes(alpha: Set<string>, fds: FunctionalDependencySet): Set<string>

   • Description: Computes the closure of a set of attributes for a given set of functional dependencies.

4. computeMinimalCover(fdsParam: FunctionalDependencySet): FunctionalDependencySet

   • Description: Computes the minimal cover of a set of functional dependencies.

5. computeCandidateKeys(relationalSchemaParam: RelationalSchema, fdsParam: FunctionalDependencySet): Set<string>[]

   • Description: Computes the candidate keys for a given relational schema and set of functional dependencies.

6. syntesisAlgorithmFor3NF(relationalSchemaParam: RelationalSchema, fdsParam: FunctionalDependencySet): RelationalSchema[]

   • Description: Decomposes a relational schema into into 3NF (Third Normal Form).

7. bcnfDecomposition(relationalSchemaParam: RelationalSchema, fdsParam: FunctionalDependencySet): RelationalSchema[]

   • Description: Decomposes a relational schema into BCNF (Boyce-Codd Normal Form).

8. removeRedundantRelationalSchemas(relationalSchemasParam: RelationalSchema[]): RelationalSchema[]

   • Description: Removes redundant relational schemas from the decomposition result.

9. extractFunctionalDependenciesForSchema(relationalSchemaParam: RelationalSchema, fdsParam: FunctionalDependencySet): FunctionalDependencySet

   • Description: Extracts the functional dependencies for a given relational schema.

10. isSchemaIn3NF(relationalSchemaParam: RelationalSchema, fdsParam: FunctionalDependencySet): boolean

    • Description: Checks whether a relational schema is in 3NF (Third Normal Form).

11. isSchemaInBNCF(relationalSchemaParam: RelationalSchema, fdsParam: FunctionalDependencySet): boolean

    • Description: Checks whether a relational schema is in BCNF (Boyce-Codd Normal Form).

12. removeExtraneousAttributes(fdParam: FunctionalDependency, fdsParam: FunctionalDependencySet): FunctionalDependencySet

    • Description: Removes extraneous attributes from a functional dependency.

13. decomposeFunctionalDependencies(fds: FunctionalDependencySet): FunctionalDependencySet

    • Description: Decomposes each functional dependency that has multiple attributes on the right-hand side into single-attribute dependencies.

14. areSetOfAttributesEqual(s1: Set<string>, s2: Set<string>): boolean

    • Description: Compares two sets of attributes for equality.

15. areSetsOfAttributesEqual(s1: Set<string>[], s2: Set<string>[]): boolean

    • Description: Compares two array of sets of attributes for equality.

Example: BCNF Decomposition

import { Utils, RelationalSchema, FunctionalDependencySet } from 'relational-schema-normalization';

const relationalSchema = new RelationalSchema(['A', 'B', 'C', 'D']);
const fds = new FunctionalDependencySet([
  new FunctionalDependency(new Set(['A']), new Set(['B'])),
  new FunctionalDependency(new Set(['B']), new Set(['C'])),
]);

const bcnf = Utils.bcnfDecomposition(relationalSchema, fds);
console.log(bcnf);  // Array of RelationalSchema objects after BCNF decomposition` 

License

MIT