Container Types: Sets in Programming

In this chapter, we will explore container types - a fundamental concept in functional programming that builds upon our understanding of sets.

Sets as Container Types

The sets we have been studying in mathematics are typically called container types in functional programming languages.

For example, a List is a container type that can hold multiple values:

// List of numbers
[1; 2; 3; 4; 5]

// List of strings
["apple"; "banana"; "cherry"]

// Nested lists (lists containing lists)
[[1; 2]; [3; 4]; [5; 6]]

The type declaration shows how Lists are generic containers:

The above is merely a conceptual illustration of container types, so please keep that in mind.

Come to think of it, types like Int and String are themselves sets - Int is a set of numbers like 1, 2, 3…, and String is a set of text strings. So even these basic types could be considered container types.

   // Sets are collections:
   type Numbers = int        // The set of all integers
   type Strings = string    // The set of all possible strings
   type Booleans = bool     // The set {true, false}

Everything is relative - a container type is nothing more than a “set of something”.

Since List type is the most intuitive image of a Set, for convenience, it’s good to start by understanding that List type is the representative example of container types.