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In computer science, purely functional programming usually designates a programming paradigm—a style of building the structure and elements of computer programs—that treats all computation as the evaluation of mathematical functions.

Program state and mutable objects are usually modeled with temporal logic, as explicit variables that represent the program state at each step of a program execution: a variable state is passed as an input parameter of a state-transforming function, which returns the updated state as part of its return value. This style handles state changes without losing the referential transparency of the program expressions.

Purely functional programming consists of ensuring that functions, inside the functional paradigm, will only depend on their arguments, regardless of any global or local state. A pure functional subroutine only has visibility of changes of state represented by state variables included in its scope.