fn0n

fn0n is a hypothetical term used in computer science education to denote an operator that composes a finite list of unary functions into a single function. It is not a widely recognized programming construct and is mainly used in thought experiments, textbooks, and online glossaries to illustrate composition concepts.

The name combines fn as an abbreviation for function, 0 to indicate a base case in a sequence, and n to mark the length of the composition. The construct is typically introduced to explore how higher-order functions build complex behavior from simple steps.

Definition. Given unary functions f1, f2, ..., fn, the expression fn0n denotes the function x -> f1(f2(...(fn(x))...)). In some presentations the order of application is reversed (fn0n can be defined as f_n composed with ... composed with f_1). The choice of convention is used in classrooms to illustrate the effect of argument order on results.

In pedagogy, fn0n helps show function composition, currying, and the idea that many simple steps can be chained to produce a complex function. It also serves as a concrete example when discussing evaluation strategies and associativity.

Status. Because fn0n is informal, there is no standard syntax, type system, or semantics. It appears mainly in lecture notes, tutorials, and informal discussions as a didactic device rather than a real programming feature.

See also: function composition, higher-order function, lambda calculus.