Church Encoding

In mathematics, Church encoding is a means of embedding data and operators into the lambda calculus, the most familiar form being the Church numerals, a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this way.

Terms that are usually considered primitive in other notations (such as integers, booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding; the Church-Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding.

Many students of mathematics are familiar with Gödel numbering members of a set; Church encoding is an equivalent operation defined on lambda abstractions instead of natural numbers.