introduction to function notation like re-use formulas. The convention for using function notation is that you write the name of the rule, the variable that represents the value on which the rule acts, and then the rule that defines the function. Figure 3 unpacks the terms and conventions having to do with function notation. V Nam e (u Input ) Aug 19, 2004 · In Church’s notation, this means that predicative functions are all of the first level, with types of the form \((\ldots)/1\). As a result, predicative functions will be of order one more than the highest order of any of their arguments. Dec 12, 2012 · The syntax of basic \(\lambda\)-calculus is quite sparse, making it an elegant, focused notation for representing functions. Functions and arguments are on a par with one another. The result is a non-extensional theory of functions as rules of computation, contrasting with an extensional theory of functions as sets of ordered pairs.