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(1);y = y + z;return a + f(1);

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(1, y);y' = y+z;return (a + f(1, y'), y');

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.

(1997-03-25)