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About: Inductive type     Goto   Sponge   NotDistinct   Permalink

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In type theory, a system has inductive types if it has facilities for creating a new type from constants and functions that create terms of that type. The feature serves a role similar to data structures in a programming language and allows a type theory to add concepts like numbers, relations, and trees. As the name suggests, inductive types can be self-referential, but usually only in a way that permits structural recursion. The standard example is encoding the natural numbers using Peano's encoding. Inductive nat : Type := | 0 : nat | S : nat -> nat.