referentially transparent ⇝
referential transparency
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+ySimilarly, 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.
Last updated: 1997-03-25
Nearby terms:
referentially transparent ♦ referential transparency ♦ referer ♦ referrer
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