Algebraic data types

Table of Contents

A deeper look at Sum and Product types
- Values of algebraic types
Examples
Project Structure
Further reading

Algebraic data types (ADTs) were introduced in Hope, a small functional programming language developed in the 1970s at the University of Edinburgh.

Algebraic refers to the property that an ADT is created by algebraic operations. The algebra here, is sums, products and patterns:

sum: alternation (for three values A, B, C → A or B or C but not any combination or other subset).
product: combination (for three values A, B, C → A and B and C, possible to hold empty for one or more).

Algebraic data types are also known as composite types - a type formed by combining other types.

Algebraic data types (ADTs) can be identified and analyzed using Pattern Matching.

A deeper look at Sum and Product types

Let us look at the two common types: sum types and product types.

Values of algebraic types

Table 1. Deeper look at the algebraic data types

	Sum Types	Product Types
Use	Define variants	Hold Values
Logic	Logical OR operation (only one of the variants is possible)	Logical AND operation (combination of several values)
Content	Each variant can have its own constructor with specified number of arguments	Contains several values of possibly different types themselves
Examples	`Enums` (additional data cannot be associated with an enum, once created)	`Class`
	`Optional`	Tuple (developer created/third party libraries)
	`Sealed` types	`Records` (Java 14,15) Java 16
		`Visitor`

Examples

Sum types

Table 2. Examples of Sum Types

Example	Description
Example1Enum	Enums in Java
Example2Optional	Using Optional in Java
Example3Sealed	Sealed Types in Java

Product Types

Table 3. Examples of Product Types

Example	Description
Example1Class	A Class in Java
Example2Tuple	Tuples in Java
Example3Record	Records in Java

Table 4. Examples of patterns used in Algebraic Java

Example	Description
Example1Variance	Covariance and Contravariance
Example2VisitorPattern	A walk-through of the visitor pattern

Project Structure

|____LICENSE
|____README.adoc       <----- This file
|____assets            <----- Images linked above
|____src
| |____none
| | |____cgutils
| | | |____algebraic
| | | | |____sum       <----- Examples of Sum types
| | | | |____product   <----- Examples of Product types
| | | | |____other     <----- Examples of patterns

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A walkthrough of algebraic data types in Java

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