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    ^f(x) ::= x f(x)

    0   - f(x)
    1   - x f(x)
    2   - x x f(x)
    3   - x x x f(x)
    ...

    ^g(x) ::= x x

    g(f(x))

    0   - g(f(x))
    1   - f(x) f(x)
    2   - x f(x) x f(x)
    3   - x x f(x) x x f(x)
    ...

    my $x = 3;
    my $y = 3;
...
    if (3 == $y) {                  # substitutability fails
        print "$x equals $y.\n";
    }

    my $x = 3;      # start frame of reference for variable $x
                    # start frame of reference for value $x==3
...
                    # end frame of reference for variable $x
                    # end frame of reference for value $y==3
                    # end frame of reference for variable $y

    p1  ::= 'the morning star' equals 'the planet venus'
    p2  ::= 'the evening star' equals 'the planet venus'
...
            the same thing, equal each other'

    =>  ::= an operator which means 'this rule produces this result'

    p1 (+) p2 => p3
    p1 (+) p3 => p2
    p2 (+) p3 => p1

    j1  ::= john knows 'the morning star' equals 'the planet venus'
    j2  ::= john knows 'the evening star' equals 'the planet venus'
    j3  ::= john knows 'the morning star' equals 'the evening star'

    j1 (+) p2 => j3
    p1 (+) j2 => j3
...
    p1 (+) j3 => j2
    j2 (+) p3 => j1
    p2 (+) j3 => j1

    sub outer_1 {
        local ($x) = 1;
...
        my $y = shift;
        return ($x + $y);
    }

    sub equals {
        my ($str, $num) = @_;
...
            return 0;
        }
    }

    my $inc  = sub { return ($_[0] + 1) };
    my $dec  = sub { return ($_[0] - 1) };
...
    ----
    
    output == '0 1 2 3 2 3 2 1 2 0 1 2 3'

    sub apply {
        my ($val, $func, @etc) = @_;
...
            return ($func->($val));
        }
    }

    my @x = ($inc, $inc, $inc);
    my @y = ($inc, $inc, $inc);
...
           printf "%d equals %d.\n", counter (@x), counter (@y);
        }
    }