Types with physical dimension

[graham@clsi.COM (Paul Graham)]

While Ada's strong typing mechanism can catch errors like this:

    d : dollars;
    f : francs;
...
    d := d + f;		-- error

it does allow such nonsensical constructs as

    d := d * d;		-- what does it mean to multiply dollars by dollars?
    d := d ** 10;	-- ??

VHDL provides physical types to model values with physical dimensions.  A
VHDL physical type lacks certain predefined multiplication operations, lacks
exponentiation, and its division operation returns a universal_integer (or
root_integer in Ada 9x terminolgy).  An example of physical types:

    type length is range integer'low to integer'high
        units inches;
            feet = 12 inches;
            yards = 3 feet;
        end units;

    type area is range integer'low to integer'high
        units inches_2;
            feet_2 = 144 inches_2;
            yards_2 = 9 feet_2;
        end units;

    function "*"(x, y : length) return area is
    begin
        return length'pos(x) * length'pos(y) * inches_2;
    end;

    function "/"(x : area; y : length) return length is
    begin
        return area'pos(x) / length'pos(y) * inches;
    end;

...
    variable L : length;
    variable A : area;
...
    L := L * 2;			-- legal
    L := L * L;			-- illegal
    A := L * L;			-- legal
    
    A := 2 inches * 2 inches;	-- legal (= 4 inches_2)

    L := 4 feet_2 / 2 inches;	-- legal (= 288 inches)

(Please excuse any typos; I haven't simulated this.)

One can model physical types in Ada by using private types, but this
involves writing a lot of operators.  What do Ada programmers do to guard
against dimensional errors?

Paul
--
Paul Graham 	graham@compass-da.com	Compass Design Automation, Inc.
(speaking only for myself)	"Cekoslovakyalilastiramadiklarimizdanmissiniz."