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Concept
Purely functional programming
Summary
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.
The exact difference between pure and impure functional programming is a matter of controversy. Sabry's proposed definition of purity is that all common evaluation strategies (call-by-name, call-by-value, and call-by-need) produce the same result, ignoring strategies that error or diverge.
A program is usually said to be functional when it uses some concepts of functional programming, such as first-class functions and higher-order functions. However, a first-class function need not be purely functional, as it may use techniques from the imperative paradigm, such as arrays or input/output methods that use mutable cells, which update their state as side effects. In fact, the earliest programming languages cited as being functional, IPL and Lisp, are both "impure" functional languages by Sabry's definition.
Persistent data structure
Purely functional data structures are persistent. Persistency is required for functional programming; without it, the same computation could return different results. Functional programming may use persistent non-purely functional data structures, while those data structures may not be used in purely functional programs.
Official source
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