Type System - Types of Types

Types of Types

A type of types is a kind. Kinds appear explicitly in typeful programming, such as a type constructor in the Haskell language.

Types fall into several broad categories:

• Primitive types – the simplest kind of type; e.g., integer and floating-point number
  • Boolean
  • Integral types – types of whole numbers; e.g., integers and natural numbers
  • Floating point types – types of numbers in floating-point representation
• Reference types
• Option types
  • Nullable types
• Composite types – types composed of basic types; e.g., arrays or records.

  Abstract data types

• Algebraic types
• Subtype
• Derived type
• Object types; e.g., type variable
• Partial type
• Recursive type
• Function types; e.g., binary functions
• universally quantified types, such as parameterized types
• existentially quantified types, such as modules
• Refinement types – types that identify subsets of other types
• Dependent types – types that depend on terms (values)
• Ownership types – types that describe or constrain the structure of object-oriented systems
• Pre-defined types provided for convenience in real-world applications, such as date, time and money.