Proof checking

Recursor

The elimination rule used to define functions or proofs by cases on an inductive value.

Definition

Recursor

A recursor describes how to consume every constructor of an inductive type.

For natural numbers, a recursor takes a zero case and a successor step. Induction is the dependent form in which the result type may vary with the number.

01

Example

Addition can recurse on its second natural-number argument with a zero case and a successor case.

02

Important distinction

A recursor must follow the rules generated for its specific inductive declaration.

After reading this article, you should be able to

  • Define Recursor in the sense used on this site.
  • Match each constructor of an inductive type to the case required by its recursor.