example, Truncated subtraction The limited subtraction function (also called "monus", and denoted "") is definable from the predecessor function. It satisfies the equations Since the recursion runs over the second argument, we begin with a primitive recursive definition of the reversed subtraction, . Its recursion then runs over the first argument, so its primitive recursive definition can be obtained, similar to addition, as . To get rid of the reversed argument order, then define . As a computation example, 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 values (that is t for true and f for false), or that produce truth values as outputs. 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 t with the number 1 and the truth value f with the number 0. Once this identification has been made, the characteristic function of a set A, which always returns 1 or 0, can be viewed as a predicate that tells whether a number is in the set A. Such an identification of predicates with numeric functions will be assumed for the remainder of this article. Predicate "Is zero" As an example for a primitive recursive predicate, the 1-ary function shall be defined such that if , and , otherwise. This can be achieved by defining . Then, and e.g. . Predicate "Less or equal" Using the property , the 2-ary function can be defined by . Then if , and , otherwise. As a computation example, Predicate "Greater or equal" Once a definition of is obtained, the converse predicate can be defined as . Then, is true (more precisely: has value 1) if, and only if, . If-then-else The 3-ary if-then-else operator known from programming languages can be defined by . Then, for arbitrary , and . That is, returns the then-part, , if the if-part, , is true, and the else-part, , otherwise. Junctors Based on the function, it is easy to define logical junctors. For example, defining , one obtains , that is, is true if, and only if, both and are true (logical conjunction of and ). Similarly, and lead to appropriate definitions of disjunction and negation: and . Equality predicate Using the above functions , and , the