referential transparency

referential transparency
referentially transparent

   <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)