referential transparency


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referential transparency

(programming)
An expression E is referentially transparent if any subexpression and its value (the result of evaluating it) can be interchanged without changing the value of E. This is not the case if the value of an expression depends on global state which can change value. The most common example of changing global state is assignment to a global variable. For example, if y is a global variable in:

f(x) { return x+y; }

g(z) a = f

function g has the "side-effect" that it alters the value of y. Since f's result depends on y, the two calls to f(1) will return different results even though the argument is the same. Thus f is not referentially transparent. Changing the order of evaluation of the statements in g will change its result.

Pure functional languages achieve referential transparency by forbidding assignment to global variables. Each expression is a constant or a function application whose evaluation has no side-effect, it only returns a value and that value depends only on the definition of the function and the values of its arguments.

We could make f above referentially transparent by passing in y as an argument:

f(x, y) = x+y

Similarly, g would need to take y as an argument and return its new value as part of the result:

g(z, y) a = f

Referentially transparent programs are more amenable to formal methods and easier to reason about because the meaning of an expression depends only on the meaning of its subexpressions and not on the order of evaluation or side-effects of other expressions.

We can stretch the concept of referential transparency to include input and output if we consider the whole program to be a function from its input to its output. The program as a whole is referentially transparent because it will always produce the same output when given the same input. This is stretching the concept because the program's input may include what the user types, the content of certain files or even the time of day. If we do not consider global state like the contents of files as input, then writing to a file and reading what was written behaves just like assignment to a global variable. However, if we must consider the state of the universe as an input rather than global state then any deterministic system would be referentially transparent!

See also extensional equality, observational equivalence.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)

functional programming

A programming language that is based primarily on writing algorithms (functions). The syntax of functional programming (FP) is mathematical, and the languages are used for applications such as artificial intelligence and distributed networks, not typically for business data processing.

Experienced FP programmers generally have strong opinions about what constitutes essential FP features, as well as which languages are more FP-like than others. However, ask any of the IT professionals you know for a definition of FP, and you will likely get a range of responses, including "huh?" The reason is that traditional programming, known as "imperative programming," also uses functions (subroutines). In fact, every C program ever written is wrapped in a "main" function that encapsulates all the other functions the programmer writes. However, FP adheres to certain principles, including the following. See function.

Referential Transparency and No Side Effects
Referential transparency means that the function will always return the same value given the same set of inputs. Also called "no side effects," pure functions do not use data defined outside of the function, although a few functions in most programs deal with external events such as reading and writing a disk. Pure functions help to avoid errors in parallel operations. For example, in multithreading, data being changed in one executing thread can cause problems in another.

Higher-Order Functions
Functions can be treated like data, and higher-order functions can take other functions as parameters, enabling the called function to perform the algorithm in the function being passed to it.

Pattern Matching and Recursion
Instead of a series of if-then-else statements, a pattern matching statement compares an argument with a list to find a match. Recursion is a function that can call itself to repeat the processing on the next set of data. These capabilities as well as others attributed to FP can also be found in both imperative and object-oriented languages. See recursion.

FP Languages
LISP was the first functional programming language, followed by Erlang, Scheme, Haskell, OCaml, Scala, Clojure, F# and others.
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