Theory
In type theory, a recursive type has the general form μα.T where the type variable α may appear in the type T and stands for the entire type itself.
For example, the natural number (see Peano arithmetic) may be defined by the Haskell datatype:
data Nat = Zero | Succ NatIn type theory, we would say: where the two arms of the sum type represent the Zero and Succ data constructors. Zero takes no arguments (thus represented by the unit type) and Succ takes another Nat (thus another element of ).
There are two forms of recursive types: the so-called isorecursive types, and equirecursive types. The two forms differ in how terms of a recursive type are introduced and eliminated.
Read more about this topic: Recursive Data Type
Famous quotes containing the word theory:
“Won’t this whole instinct matter bear revision?
Won’t almost any theory bear revision?
To err is human, not to, animal.”
—Robert Frost (1874–1963)
“Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.”
—Willard Van Orman Quine (b. 1908)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)