Product Type

In programming languages and type theory, a product of types is another, compounded, type in a structure. The "operands" of the product are types, and the structure of a product type is determined by the fixed order of the operands in the product. An instance of a product type retains the fixed order, but otherwise may contain all possible instances of its primitive data types. The expression of an instance of a product type will be a tuple, and is called a "tuple type" of expression. A product of types is a direct product of two or more types.

If there are only two component types, it can be called a "pair type". For example, if two component types A and B are the set of all possible values that type, the product type written A × B contains elements that are pairs (a,b), where "a" and "b" are instances of A and B respectively.

In many languages, product types take the form of a record type, for which the components of a tuple can be accessed by label. In languages that have algebraic data types, as in most functional programming languages, algebraic data types with one constructor are isomorphic to a product type.

In the Curry-Howard correspondence, product types are associated with logical conjunction (AND) in logic.

The notion directly extends to the product of an arbitrary finite number of types (a n-ary product type), and in this case, it characterizes the expressions which behave as tuples of expressions of the corresponding types. A degenerated form of product type is the unit type: it is the product of no types.

In call-by-value programming languages, a product type can be interpreted as a set of pairs whose first component is a value in the first type and whose second component is a value in the second type. In short, it is a cartesian product and it corresponds to a product in the category of types.

Most functional programming languages have a primitive notion of product type. For instance, the product of type1, ..., typen is written type1 * ... * typen in ML and (type1,...,typen) in Haskell. In both these languages, tuples are written (v1,...,vn) and the components of a tuple are extracted by pattern-matching. Additionally, many functional programming languages provide more general algebraic data types, which extend both product and sum types.

The brochure for the International System of Units starts out in section 1.1 saying "The value of a quantity is generally expressed as the product of a number and a unit", and also presents the unit product of a Newton and a meter with the product notation of mathematics: Newton meter (N m or N · m).

Data types
Uninterpreted
  • Bit
  • Byte
  • Trit
  • Tryte
  • Word
Numeric
  • Bignum
  • Complex
  • Decimal
  • Fixed-point
  • Floating-point
  • Integer
    • signedness
  • Interval
  • Rational
Text
  • Character
  • String
    • null-terminated
Pointer
  • Address
    • physical
    • virtual
  • Reference
Composite
  • Algebraic data type
    • generalized
  • Array
  • Associative array
  • Class
  • List
  • Object
    • metaobject
  • Option type
  • Product
  • Record
  • Set
  • Union
    • tagged
Other
  • Boolean
  • Bottom type
  • Collection
  • Enumerated type
  • Exception
  • Function type
  • Opaque data type
  • Recursive data type
  • Semaphore
  • Stream
  • Top type
  • Type class
  • Unit type
  • Void
Related topics
  • Abstract data type
  • Data structure
  • Generic
  • Kind
    • metaclass
  • Parametric polymorphism
  • Primitive data type
  • Protocol
    • interface
  • Subtyping
  • Type constructor
  • Type conversion
  • Type system


Famous quotes containing the words product and/or type:

    “These facts have always suggested to man the sublime creed that the world is not the product of manifold power, but of one will, of one mind; and that one mind is everywhere active, in each ray of the star, in each wavelet of the pool; and whatever opposes that will is everywhere balked and baffled, because things are made so, and not otherwise.”
    —Ralph Waldo Emerson (1803–1882)

    “But the mother’s yearning, that completest type of the life in another life which is the essence of real human love, feels the presence of the cherished child even in the debased, degraded man.”
    —George Eliot [Mary Ann (or Marian)