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:
“It is not enough for theory to describe and analyse, it must itself be an event in the universe it describes. In order to do this theory must partake of and become the acceleration of this logic. It must tear itself from all referents and take pride only in the future. Theory must operate on time at the cost of a deliberate distortion of present reality.”
—Jean Baudrillard (b. 1929)
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—Anna Quindlen (20th century)
“There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
—Albert Einstein (1879–1955)