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+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)