m*x + b   // an expression


f(x) = m*x + b  // a function
m = 3
b = 5
f(4) = m*4 + b ===> 3*4 + 5 = 17


public static double m = 3.0;
public static double b = 5.0;
public static double f(double x)
{
   return m*x + b;  // m and b are non-local references
}


f(x,m,b) = m*x + b  // a different function (but same expression)

f(4,5,6) = 5*4 + 6


public static double f(double x, double m, double b)
{
   return m*x + b;  // no non-local variables
}


b = 4
f(m, x) = m*x + b  // a third function (still the same expression)


public static double b = 4.0
public static double f(double x, double m)
{
   return m*x + b;  // b is a non-local reference
}



x*y + z  // An expression. How many functions can we define using this expression?

y=4, z=6
f1(x) = x*y + z      // y,z are free variables

z=6
f2(x,y) = x*y + z    // z is a free variable

f3(x,y,z) = x*y + z  // no free variables

y=2
f4(x,z) = x*y + z    // y is free

y=2
f5(z,x) = x*y + z    // y is free

// f4 and f5 are not the same function even though they
// use the same expression with the same free variable
f4(2,3) ===> 2*2 + 3 = 7
f5(2,3) ===> 3*2 + 2 = 8



anonymous versions of f1, f2, f3, f4, f5

y=4, z=6
(x) => x*y + z       // y,z are free variables

z=6
(x,y) => x*y + z     // z is a free variable

(x,y,z) => x*y + z   // no free variables

y=2
(x,z) => x*y + z     // y is free
(z,x) => x*y + z     // y is free

((x,z) => x*y + z) (2,3) ===> 2*2 + 3 = 7
((z,x) => x*y + z) (2,3) ===> 3*2 + 2 = 8