Editing Primitive recursive function (section)

=== Converting predicates to numeric functions ===

In some settings it is natural to consider primitive recursive functions that take as inputs tuples that mix numbers with [[truth value]]s (that is <math>t</math> for true and <math>f</math> for false),{{Citation needed|date=January 2025 |reason=Kleene never considers mixed domains - see p.226 where he lists the 4 types of functions he considers. Using N to represent the naturals, and T to represent the truth values: (a) N to N (b) N to T (c) T oto T (d) T to N}} or that produce truth values as outputs.{{sfn|Kleene|1952|pp=226–227}} This can be accomplished by identifying the truth values with numbers in any fixed manner.  For example, it is common to identify the truth value <math>t</math> with the number <math>1</math> and the truth value <math>f</math> with the number <math>0</math>.  Once this identification has been made, the [[indicator function|characteristic function]] of a set <math>A</math>, which always returns <math>1</math> or <math>0</math>, can be viewed as a predicate that tells whether a number is in the set <math>A</math>.  Such an identification of predicates with numeric functions will be assumed for the remainder of this article.