Proof checking

Inductive type

A type generated by a declared set of constructors.

Definition

Inductive type

An inductive type defines values by listing the constructors that can create them.

Natural numbers can be generated from zero and successor. The declaration also supports recursion and induction through a recursor.

01

Example

A Boolean inductive type has constructors false and true.

02

Important distinction

The kernel must check positivity and universe conditions before accepting an inductive declaration.

After reading this article, you should be able to

  • Define Inductive type in the sense used on this site.
  • List the constructors and structural cases for a small inductive type.