Algebraic data types

Abstract

Algebraic data types are a concise representation of types permitted in some functional languages as StandardML and Haskell. They can also be defined in Scala, and although their definition is more cumbersome, they are useful. Formally, an algebraic data type defines a new type as a composition of other types or a set of possible constants. In the definition of the type, we can enumerate the set of alternatives, some of them can be recursive. For example, we can define a type for the four suits in playing cards (spades, hearts, diamonds, clubs), the days of the week, the values in Boolean or in Kleene’s trivalued logic. We can also consider the product of these types. For example, to form a deck we have e.g. 13 cards per suit (Ace, King, Queen, Jack, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), and two jokers. An advantage of algebraic definitions is that they permit to define functions by means of pattern matchin.