Algebraic Data Types in

About Algebraic Data Types

An Algebraic Data Type (ADT) represents a fixed number of named cases. Each value of an ADT corresponds to exactly one of the named cases.

An ADT is defined using the data keyword, with cases separated by pipe (|) characters. If none of the cases have data associated with them the ADT is similar to what other languages usually refer to as an enumeration (or enum).

data Season
  = Spring
  | Summer
  | Autumn
  | Winter

Each case of an ADT can optionally have data associated with it, and different cases can have different types of data. When the case has data associated, a constructor is required.

data Number
  = NInt Int      --'NInt' is the constructor for an Int Number.
  | NFloat Float  --'NFloat' is the constructor for an Float Number.
  | Invalid       --'Invalid' does not have data associated to it.

Creating a value for a specific case can be done by referring to its name (e.g, NInt 22). As case names are just constructor functions, associated data can be passed as a regular function argument.

ADTs have structural equality, which means that two values for the same case and with the same (optional) data are equivalent.

While one can use if/else expressions to work with ADTs, the recommended way to work with them is through pattern matching using case statement:

add1 :: Number -> String
add1 number =
    case number of
      NInt    i -> show (i + 1)
      NFloat  f -> show (f + 1.0)
      Invalid   -> error "Invalid input"