Types with physical dimension

Types with physical dimension

[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."

Re: Types with physical dimension

[Robert Dewar]

"What do Ada programmers do to guard against dimensional errors"

Probably not much, because in practice, at least in my experience, such
errors are rare, although they are an obvious target for theoretical
discussions.

Using private types is of course the appropriate way to do things in 
Ada 83. In Ada 9X, abstract operations can be used to eliminate unwanted
operations.

Re: Types with physical dimension

[R_Tim_Coslet]

>"What do Ada programmers do to guard against dimensional errors"
>
>Probably not much, because in practice, at least in my experience, such
>errors are rare, although they are an obvious target for theoretical
>discussions.

When is 0 multiplied by 0 equal to 4 million?

When a programmer dropped an equation from a data sheet directly
into the code, without thinking that the equation used units of volts
but the A/D converter supplying the numbers has some "arbitrary"
unit scaling and is offset binary instead of twos complement.

Example:

	0V = 2048 A/D converter units.

Therfore 0V * 0V = about 4 million.


Admitedly not directly related to the current subject, but does
illustrate a case of a problem with processing real world physical
data without thinking the units and scaling thru...

At least Ada reported constraint errors instead of just scrambling the
result and giving a totally inexplicable wrong answer like Certain
other languages would :-)

                                        R. Tim Coslet

Usenet: R_Tim_Coslet@cup.portal.com
        technology, n.  domesticated natural phenomena

Re: Types with physical dimension

[Stephen A. Leake]

In article <GRAHAM.94Sep27181841@canopus.clsi.COM> graham@clsi.COM
(Paul Graham) writes:

   ...

   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?

I run robots with Ada, so I deal with real dimensions all the time. Very early
on, I started to write a package that enforced dimensionality; I defined 
METERS, METERS_PER_SECOND, etc. I quickly discovered that even simple equations
need up to cubic dimensions, in all combinations of length, mass and time.
Defining all these types and the associated operators was far too
time-consuming to be worth it. So now I rely on code reviews and careful
testing.

The moral; strong typing is nice, but is no substitute for careful design
and thorough testing.

--
Stephen Leake, NASA Goddard Space Flight Center
email: Stephen.Leake@gsfc.nasa.gov

Re: Types with physical dimension

[Robert I. Eachus]

In article <SAL714.94Oct3133110@rs710.gsfc.nasa.gov> sal714@rs710.gsfc.nasa.gov (Stephen A. Leake) writes:

 > I run robots with Ada, so I deal with real dimensions all the time.
 > Very early on, I started to write a package that enforced
 > dimensionality; I defined METERS, METERS_PER_SECOND, etc. I quickly
 > discovered that even simple equations need up to cubic dimensions,
 > in all combinations of length, mass and time.  Defining all these
 > types and the associated operators was far too time-consuming to be
 > worth it. So now I rely on code reviews and careful testing.

 > The moral; strong typing is nice, but is no substitute for careful design
 > and thorough testing.

  Paul Hilfinger did a nice paper on using discriminants to check
dimensionality.   I don't have the paper in front of me but it works
something like this:

   type Measure(Length,Mass,Time: Integer) is record
     Value: Float;
   end record;

   subtype Meters is Measure(1,0,0);
   subtype Kilograms is Measure(0,1,0);
   subtype Time is Measure(0,0,1);
   ...etc.

   Now you can define all the standard arithmetic operations on type
Measure so that they keep the discriminants correct:

   function "*"(L,R: Measure) return Measure is
   begin
     return(L.Length+R.Length,L.Mass+R.Mass,L.Time+R.Time,L.Value*R.Value);
   end "*";

   function "+"(L,R: Measure) return Measure is
   begin
     if L.Length /= R.Length or L.Mass /= R.Mass or L.Time /= R.Time
     then raise Constraint_Error; end if;
     return L.Value+R.Value;
   end "+";

     In theory, if you use pragma INLINE, a good compiler should never
store the discriminants and eliminate all the discriminant related
code at compile time.  In practice, when I used this technique, I had
two versions of the specification of the types package, one with the
discriminants and one which said "type Measure is Float;" and kept all
the subtype declarations.  I used the full package during unit test,
and the streamlined package thereafter.

     The only problem I had was with square roots.  I thought about
changing the package to double all the dimensional values, so length
would be (2,0,0), but I never did.

--

					Robert I. Eachus

with Standard_Disclaimer;
use  Standard_Disclaimer;
function Message (Text: in Clever_Ideas) return Better_Ideas is...

Re: Types with physical dimension

[Mark A Biggar]

In article <EACHUS.94Oct4115107@spectre.mitre.org> eachus@spectre.mitre.org (Robert I. Eachus) writes:
>In article <SAL714.94Oct3133110@rs710.gsfc.nasa.gov> sal714@rs710.gsfc.nasa.gov (Stephen A. Leake) writes:
> > Very early on, I started to write a package that enforced
> > dimensionality; I defined METERS, METERS_PER_SECOND, etc. I quickly
> > discovered that even simple equations need up to cubic dimensions,
> > in all combinations of length, mass and time.  Defining all these
> > types and the associated operators was far too time-consuming to be
> > worth it. So now I rely on code reviews and careful testing.
> > The moral; strong typing is nice, but is no substitute for careful design
> > and thorough testing.
>  Paul Hilfinger did a nice paper on using discriminants to check
>dimensionality.   I don't have the paper in front of me but it works
>something like this:
>   type Measure(Length,Mass,Time: Integer) is record
>     Value: Float;
>   end record;
>   subtype Meters is Measure(1,0,0);
>   subtype Kilograms is Measure(0,1,0);
>   subtype Time is Measure(0,0,1);
>   ...etc.
>     The only problem I had was with square roots.  I thought about
>changing the package to double all the dimensional values, so length
>would be (2,0,0), but I never did.


Unless you are doing some really wierd physics, the square root of a base
dimension doesn't really make any sense.  So just raise CONSTRAINT_ERROR
whenever any of the dimensions is odd.

--
Mark Biggar
mab@wdl.loral.com

Re: Types with physical dimension

[gamache]

In article <CxBBx8.7L@irvine.com>, adam@irvine.com (Adam Beneschan) writes:
> mab@dst17.wdl.loral.com (Mark A Biggar) writes:
> 
>> >  Paul Hilfinger did a nice paper on using discriminants to check
>> >dimensionality.   I don't have the paper in front of me but it works
>> >something like this:
>> >   type Measure(Length,Mass,Time: Integer) is record
>> >     Value: Float;
>> >   end record;
>> >   subtype Meters is Measure(1,0,0);
>> >   subtype Kilograms is Measure(0,1,0);
>> >   subtype Time is Measure(0,0,1);
>> >   ...etc.
this part of the original post was snipped:
>Now you can define all the standard arithmetic operations on type
>Measure so that they keep the discriminant correct:
>
>function "+" (L,R : Measure) return Measure is
>begin
>   if L.Length /= R.Length or L.Mass /= R.Mass or L.Time /= R.Time
>   then raise Constraint_Error; end if;
>   return L.Value + R.Value;
>end "+";

I *really* liked this for a while after I saw it.  For some scary reason, I
guess I kept thinking about it in the back of my mind and now I'm not so sure.
Couldn't I declare:

	Not_Kg : Measure(1,1,1);
	Not_Time : Measure(1,1,1);

and then bypass all the protection this schema offers?  Maybe use of membership
tests in the if statement would help?  But then again, I guess I never
understood the *big deal* with units here anyway.  Skipping to the chase scene:
its my contention that most unit-related problems are systemic from engineers
not wishing to declare the same units twice (or more).  It's like, well we're
building a couple 100K lines of code and I'm really gonna save by only
defining Kilograms (or worse PI) once!  My thinking is that if inside a given
unit one is implementing D=R*T (distance = rate * time) then define all typesb
as subtypes of a parent type that can be combined:

	subtype Feet is Float_32 range a..b;
	subtype Feet_per_Sec is Float_32 range c..d;
	subtype Sec is Float_32 range e..f;

(assume float_32 is a 32-bit redefinition of a predefined type).  Now variables
can easily be combined in the necessary fashion WHILE AT LEAST INSURING VALID
RANGE CONSTRAINTS ON THE INPUT DATA.  In the example above one could envision
either negative values (removable via a range constraint) or fractional values
that may be nonesensical for certain inputs.

Later in the application, some other object may need a type for seconds as
well.  In my experience often times these two objects never meet.  So I say -
define another type!  In those interfacing situations between objects where
there is commonality (in say the Seconds type) then I like the approach of a
Time Package which provides needed operations (including conversion to
float_32).  Given the ability to build larger objects from small, isn't this
the intent anyway?

Just my 0.01 (two cents adjusted for inflation).

------------------------------------------------
with all_necessary_disclaimers;
use 'em_2;
-------------------------------------------------

Re: Types with physical dimension

[Matt Kennel]

Robert I. Eachus (eachus@spectre.mitre.org) wrote:

: In article <SAL714.94Oct3133110@rs710.gsfc.nasa.gov> sal714@rs710.gsfc.nasa.gov (Stephen A. Leake) writes:

:  > I run robots with Ada, so I deal with real dimensions all the time.
:  > Very early on, I started to write a package that enforced
:  > dimensionality; I defined METERS, METERS_PER_SECOND, etc. I quickly
:  > discovered that even simple equations need up to cubic dimensions,
:  > in all combinations of length, mass and time.  Defining all these
:  > types and the associated operators was far too time-consuming to be
:  > worth it. So now I rely on code reviews and careful testing.

:  > The moral; strong typing is nice, but is no substitute for careful design
:  > and thorough testing.

:   Paul Hilfinger did a nice paper on using discriminants to check
: dimensionality.   I don't have the paper in front of me but it works
: something like this:

:    type Measure(Length,Mass,Time: Integer) is record
:      Value: Float;
:    end record;

:    subtype Meters is Measure(1,0,0);
:    subtype Kilograms is Measure(0,1,0);
:    subtype Time is Measure(0,0,1);
:    ...etc.

At one point I thought this was a good idea.  Now my feeling is that you
should have already non-dimensionalized your equations into systems of units
specific for the problem.

That way you get more understanding and "less number".  Paradoxically,
once you DON'T have physical units on your variables, it's easier to
say whether something is "big" or "small".

--
-Matt Kennel  		mbk@inls1.ucsd.edu
-Institute for Nonlinear Science, University of California, San Diego
-*** AD: Archive for nonlinear dynamics papers & programs: FTP to
-***     lyapunov.ucsd.edu, username "anonymous".

Re: Types with physical dimension

[Robert Dewar]

strong typing is like anything else, fine in moderation, but dangerous to
health if overdoses are encountered.

there is a common tendency in Ada programming to assume that since strong
typing is a GOOD THING, it must make sense to use it as much as possible.
This leads to programs which thousands of different integer types and
conversions all over the place. For my taste that actually decreases
reliability, since 

(a) it makes the code less readable

(b) once you get in the habit of freely breaking type barriers by writing
conversions, then the value of the type barriers is diminished.

I much prefer a style in which different integer types are used only when
it is very rare that the need for conversions will arise, or when the
necessary conversions can be nicely abstracted.

Similarly, if setting up an abstraction requires writing a huge amount of
code, which might itself have errors, then the mere fact that you can use
the abstraction neatly when you are done may not leave you ahead (this is
an instance of the common behavior of spending your time building tools
to increase your productivity, spending all your time on this is NOT
a good idea :-)

Obviously everyone knows that strong typing is helpful (says he after
spending a frstrating half hour finding a bug in an idiotic little C
program -- left the & off in a call to sscanf, resulting in unimaginable
and hard to debug chaos). But that doesn't mean "the more strong typing
tne better".

Good software engineering is the art of choosing the right abstractions,
and structures, and it is not the case that it is always preferable to
raise the level of abstraction as far as possible -- it needs to be at
just the right level. 

The units case is an interesting one. Sure there are are programming
situations where providing some automatically type checked units checking
makes sense, but there are also situations where the attempt to provide
such checking is precisely abstraction overkill. It's a nice example that
way, because it lies somewhere near the borderline, and you need the skill
to make the right cut on this border.

Re: Types with physical dimension

[Bob Gilbert]

In article km7@gnat.cs.nyu.edu, dewar@cs.nyu.edu (Robert Dewar) writes:
->strong typing is like anything else, fine in moderation, but dangerous to
->health if overdoses are encountered.
->
->there is a common tendency in Ada programming to assume that since strong
->typing is a GOOD THING, it must make sense to use it as much as possible.
->This leads to programs which thousands of different integer types and
->conversions all over the place. For my taste that actually decreases
->reliability, since 

{good stuff deleted}

I can't agree more with this.  

I my work, I deal with mostly embedded processors with lots of
interfaces to hardware. I have found that a very common mistake
is to over-type, especially on input data from less than reliable
sources.

As an example, we had an interface with an IRIG time code generator
which was supposed to generate a BCD format of the time.  One of
our programmers quickly set out to generate a BCD type to accomodate
the input.  Unfortunately, hardward does not always behave itself,
and on occasion the time code generator would lock up and produce
an output of all one's.  Well needless to say we got constraint
exceptions like crazy, and being a real-time system we could not
tolerate the indeterminate nature of exceptions (besides software
always has the burden of proving the hardware went south, and we
needed to know what the illegal values being sent to us were in
order to provide the necessary evidence). The solution was to just
accept the BCD time value as an array of bytes, and then perform 
explicit conversion of this array to either a string value for 
output to a terminal, or a numeric value for use in internal 
computations. The explicit routines to perform the conversions
would handle the case where illegal inputs were received without
the use of exception handling. Anyway, I have found it very 
useful to never place constaints on input data from outside 
sources, and explicitly check the data for correctness.

Now output data is a different matter. If I am generating something
like gimbal commands where hardware could possibly be damaged if
I output invalid or out of range values, then I definitely use
strong typing to guarantee my output. Here getting the rare exception
is usually much preferred, people get very upset when we software
types break hardware.  And of course the exception is rare since I
(sould) have control of the data.

I'm also usually very leery when constraint limits are placed on 
floats.  I've seen too many instances where a programmer generated
something like a float to represent a value from say 0..360 degrees
on a circle and found that some intermediate result would take the
value outside the range, or possibly rounding effects gave a value
of 360.00000001, or the like. Many times it is easier to track down
the error if you have the incorrect result rather than just an
exception at the point where the value went out of the type range.

-Bob

Re: Types with physical dimension

[Jean-Pierre Rosen]

In article <SAL714.94Oct3133110@rs710.gsfc.nasa.gov>, sal714@rs710.gsfc.nasa.gov (Stephen A. Leake) writes:
> I run robots with Ada, so I deal with real dimensions all the time. Very early
> on, I started to write a package that enforced dimensionality; I defined 
> METERS, METERS_PER_SECOND, etc. I quickly discovered that even simple equations
> need up to cubic dimensions, in all combinations of length, mass and time.
> Defining all these types and the associated operators was far too
> time-consuming to be worth it. So now I rely on code reviews and careful
> testing.
> 
> The moral; strong typing is nice, but is no substitute for careful design
> and thorough testing.
> 
There is another solution: run-time checking of dimensionality. You define a
type like:
   type Physical is
      record
         Length : Dimension;
         Time   : Dimension;
         Mass   : Dimension;
         Charge : Dimension;
         Value  : Float;
      end record;
 (Dimension being some Integer type).
You redefine operators so that "+" and "-" operate only if the dimensions are
the same (and raise Dimension_error otherwise), and "*" and "/" add 
(or subtract) dimensions.
Note that if you are concerned about efficiency, you use this type for 
debugging, and then change it to:
   type Physical is new Float;
for the working version (assuming a Value_of function to access the value).

Alternatively, you can make the dimensions discriminants; this will improve
safety and allow you to define nice subtypes like:
   subtype Meters is Physical(1, 0, 0, 0);
but will make moving to plane Floats more difficult.

Acknowledgements:
  I saw this idea in a paper long ago. As far as I recall, it was by
  N. Cohen. Norm, are you listening?

Re: Types with physical dimension

[Stephen J Bevan]

In article <36tole$j5e@cyclope.enst.fr> rosen@enst.fr (Jean-Pierre Rosen) writes:
     ... I saw this idea in a paper long ago. As far as I recall, it was by
     N. Cohen. Norm, are you listening?

This sounds like the method discussed in [Hilfinger:acm:toplas:1988],
I don't remember if Hilfinger referenced/acknowledged Norman though.
For interested parties, I've also included some references to other
work on adding dimensions to programming languages :-


@article
{ Biedl:acm:sigplan:1977
, author=   "Albrecht Biedl"
, title=    "An Extension of Programming Languages for Clerical
Computation in Science and Engineering With Special Reference to
PASCAL"
, journal=  acm:sigplan
, volume=   12
, number=   4
, pages=    "31--33"
, month=    apr
, year=	    1977
, checked=  19940516
, keywords= "Pascal, dimensional types"
, sjb=      "Proposes an extension to Pascal that allows dimensional
information to be added to declarations."
}


@article
{ Karr:Lovemann:cacm:1978
, author=   "Michael Kaar and Lovemann, III, David B."
, title=    "Incorporation of units into programming languages"
, journal=  cacm
, volume=   21
, number=   5
, pages=    "385--391"
, month=    may
, year=     1978
, keywords= "dimensional types"
, reffrom=  Horning:pc:1978c
, reffrom=  Hilfinger:acm:toplas:1988
}


@article
{ House:bcscj:1983
, author=   "R. T. House"
, title=    "A proposal for an extended form of type checking of expressions"
, journal=  bcscj
, volume=   26
, number=   4
, pages=    "366--374"
, month=    nov
, year=	    1983
, cr=       "8610-0116 (uncomplementary)"
, cr=       "8704-0276 (rebuttal+response)"
, cr=       "8705-0377 by Luca Cardelli - complementary"
, keywords= "dimensional types"
, sjb=      "describes adding physical ``dimensions'' and ``units''
in a strongly typed language (Pascal in used)."
, reffrom=  Hilfinger:acm:toplas:1988
}


@article
{ Gehani:spe:1985
, author=   "N. H. Gehani"
, title=    "Ada's Derived Types and Units of Measure"
, journal=  spe
, volume=   15
, year=     1985
, pages=    "555--569"
, keywords= "Ada, dimensional types"
, reffrom=  Dreiheller:Moerschbacher:Mohr:acm:sigplan:1986
, reffrom=  Hilfinger:acm:toplas:1988
}


@article
{ Manner:acm:sigplan:1986
, author=   "R. M{\"a}nner"
, title=    "Strong Typing and Physical Units"
, journal=  acm:sigplan
, volume=   21
, number=   3
, pages=    "11--20"
, month=    mar
, year=	    1986
, keywords= "dimensional types"
, reffrom=  Dreiheller:Moerschbacher:Mohr:acm:sigplan:1986
}


@article
{ Dreiheller:Moerschbacher:Mohr:acm:sigplan:1986
, author=   "A. Dreiheller and M. Moerschbacher and B. Mohr"
, title=    "Programming Pascal with Physical Units"
, journal=  acm:sigplan
, volume=   21
, number=   12
, pages=    "114--123"
, month=    dec
, year=	    1986
, refs=     7
, checked=  19940617
, source=   "Dept. Library"
, keywords= "Pascal, dimensional types"
, abstract= "In~\cite{Manner:acm:sigplan:1986} (SIGPLAN Notices
3/1986) M\"anner proposes an extension of Pascal permitting the use of
physical units in programs.  We discuss his issues in this paper and
describe our own somewhat different approach.  Our language extension
PHYSCAL of Pascal not merely satisfies the requirements suggested
by~\cite{Manner:acm:sigplan:1986}, but also supports predfined units
(International Standard), thorough realisation of the concept of scale
factors, input/output facilities for number with units.  The new
concepts are motivated, and the language description is given formally
and by examples.  Finally we discuss some details of the realised
language implementation by a PHYSCAL-to-Pascal preprocessor in an UNIX
environment."
}


@article
{ Jones:ddj:pp:1987
, author=   "Do-While Jones"
, title=    "Dimensional Data Types"
, journal=  ddj:pp
, volume=   12
, number=   127
, pages=    "50--54"
, month=    may
, year=     1987
, refs=     3
, checked=  19940513
, keywords= "Ada, dimensional types"
, abstract= "Using dimensional units as data types can facilitate the
writing of clearer, more easily maintained code.  Do-While presents
example programs in Ada."
, xref=     Ludquist:ddj:pp:1987
}


@article
{ Hilfinger:acm:toplas:1988
, author=   "Paul N. Hilfinger"
, title=    "An Ada Package for Dimensional Analysis"
, journal=  acm:toplas
, volume=   10
, number=   2
, pages=    "189--203"
, month=    apr
, year=     1987
, refs=     8
, checked=  19940623
, source=   "Dept. Library"
, keywords= "dimensional analysis, language design, units, dimentional types"
, abstract= "This paper illustrates the use of Ada's abstraction
facilities -- notably, operator overloading and type parameterization
-- to define an oft-requested feature: a way to attribute units of
measure to variables and values.  The definition given allows the
programmer to specify units of measure for variables, constants, and
parameters; checks uses of these entities for dimensional consistency;
allows arithmetic between them, where legal; and provides scale
conversions between commensurate units.  It is not constrained to a
particular system of measurement (such as the metric or English
systems).  Although the definition is in standard Ada and requires
nothing special of the compiler, certain reasonable design choices in
the compiler, discussed here at some length, can make its
implementation particularly efficient."
, sjb=      "Proposes the use of a UNITS package which exports a QUANT
type which encodes the various dimensions and which can be checked at
runtime.  Logically each variable/constant becomes a record with 5
integers representing the dimensions and a single float representing
the scalar value.  It is noted that With a naive compiler, this is
very inefficient!"
}

Re: Types with physical dimension

[Jean-Pierre Rosen]

In article <BEVAN.94Oct5113509@lemur.cs.man.ac.uk>, bevan@cs.man.ac.uk (Stephen J Bevan) writes:
> In article <36tole$j5e@cyclope.enst.fr> rosen@enst.fr (Jean-Pierre Rosen) writes:
>      ... I saw this idea in a paper long ago. As far as I recall, it was by
>      N. Cohen. Norm, are you listening?
> 
> This sounds like the method discussed in [Hilfinger:acm:toplas:1988],
> I don't remember if Hilfinger referenced/acknowledged Norman though.
> For interested parties, I've also included some references to other
> work on adding dimensions to programming languages :-
My mistake - apologies to Paul Hilfinger

Re: Types with physical dimension

[Norman H. Cohen]

In article <36tole$j5e@cyclope.enst.fr>, rosen@enst.fr (Jean-Pierre Rosen)
writes: 

|> Alternatively, you can make the dimensions discriminants; this will improve
|> safety and allow you to define nice subtypes like: 
|>    subtype Meters is Physical(1, 0, 0, 0);
|> but will make moving to plane Floats more difficult.
|>
|> Acknowledgements: 
|>   I saw this idea in a paper long ago. As far as I recall, it was by
|>   N. Cohen. Norm, are you listening?

Yes, I'm listening.

I wrote the paper under the pseudonym "Paul Hilfinger".   :-)

Here is the reference: 

   Paul N. Hilfinger.  An Ada package for dimensional analysis.
   ACM Transactions of Programming Languages and Systems 10, No. 2
   (April 1988), 189-203

But seriously, folks, I disagree with Paul's approach.  In the absence of
heroic measures on the part of the compiler, besides imposing an added
run-time overhead, it defers until run time the detection of errors that
can be caught by static analysis.  I've long felt that the best way to
address this problem is at compile time, with a tool that takes a tabular
specification of a system of units and generates a series of declarations
declaring distinct types for distinct units, along with trivial
subprogram bodies for overloaded versions of "*", "/", and "**".

One complication in this approach is the need to define types for
intermediate results that do not correspond to natural physical units.
For example, the number of ergs spent in applying, over a distance of D
centimeters, the amount of force required to accelerate a mass of M grams
A centimeters per second per second is M*D*A.  The intermediate result
M*D is measured in gram centimeters, a physically meaningless unit.  Had
we written M*(D*A) instead, the intermediate result D*A would be measured
in terms of centimeters squared over seconds squared, also physically
meaningless.  The tool must generate types for a reasonable number of
such intermediate units of measure.  There are an infinite number of
possibilities--for example computing a mass by dividing mass to the fifth
power by mass to the fourth power--that are not likely to arise in real
expressions, but some rather strange-looking units like time to the power
-2 ARE likely to arise.  The trick is knowing where to draw the line so
that a user of the automatically generated package will not be surprised
by the illegality of a given expression.

Another complication is scaling, when converting between different
systems for measuring the same kind of quantity, such as the cm-g-sec
(CGS) system and the m-kg-sec (MKS) system, or mixing units from
different systems.  One solution is to provide conversions only for a
given kind of physical quantity--between kilograms and grams, or between
meters and centimeters, for example, and to provide combining operators
only within a given system.  Thus you can't multiply kilograms times
centimeters per second squared to obtain a force.  You have to convert
kilograms to grams and apply the CGS operators to obtain a result in
dynes, or convert centimeters to meters and apply the MKS operators to
obtain a result in newtons.  If all these types are implemented as real
types rather than private types, so that real literals can be used in
expressions, then a conversion between, say, Dyne_Type and Newton_Type is
automatically defined as a basic operation, but it does not have the
right semantics.  (It does not scale upon converting.) It is easy to
write conversion functions that do the right thing, but there is no way
to hide the automatically defined type conversions, which a programmer
could easily be seduced into using by mistake.  (The "is abstract" trick
cannot be applied to type conversions.)

--
Norman H. Cohen    ncohen@watson.ibm.com

Re: Types with physical dimension

[Simtel20 Transfer]

Paul Grham writes:
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.

The now renamed ABET (Ada Based Environment for Test) IEEE
standard has an Ada package that defines _many_ physical
types.  If you need pointers let me know.
p.s. It just occurred to e that maybe the SEI sghould
consider putting references to it on their home
page under programming languages.
p.p.s. Its a shame they can't put the entire standard
on-line but it is copyrighted by the IEEE (one of my
favorite gripes is that such standards are not on-line).
Now the IEEE may have changedd  their policy.  If so
will someone please correct me.
hope this helps.
sam harbaugh HARBAUGH@ROO.FIT.EDU

Re: Types with physical dimension

[Mark A Biggar]

Another possibility is to use a discriminated type to keep track of dimensions
like so:

generic
	type Base is digits <>;
package Units is

type Unit(Length_DIM: Integer; Mass_DIM: Integer; Time_DIM: Integer) is
	private;

function "*"(Left, Right: Unit) return Unit;
function "*"(Left: Unit; Right: Base) return Unit;
function "+"(Left, Right: Unit) return Unit;
function "-"(X: Unit) return Unit;

-- etc;

subtype Length is Unit(1,0,0);
subtype Area is Unit(2,0,0);
subtype Mass is Unit(0,1,0);
subtype Time is Unit(0,0,1);
suntype Frequency is Unit(0,0,-1);
subtype Energy is Unit(2,1,-2);

-- etc;

private

type Unit(Length_DIM: Integer; Mass_DIM: Integer; Time_DIM: Integer) is
	record
		Value: Base;
	end record;
end Units;

package body Units is

procedure Check_DIM(Left, Right: Unit) is
begin
	if Left.Length_DIM \= Right.Length_DIM or else
	   Left.Mass_DIM \= Right.Mass_DIM or else
	   Left.Time_DIM \= Right.Time_DIM then
		raise CONSTRAINT_ERROR;
end Check_DIM;

function "*"(Left, Right: Unit) return Unit is
begin
	return Unit'(Left.Length_DIM+Right.Length_DIM,
		     Left.Mass_DIM+Right.Mass DIM,
		     Left.Time_DIM+Right.Time_DIM,
		     Left.Value * Right.Value);
end "*";

	

function "+"(Left, RIght: Unit) return Unit is
begin
	Check_DIM(Keft, Right);
	return UniL'(Left.Length_DIM,
		     Left.Mass_DIM,
		     Left.Time_DIM,
		     Left.Value + Right.Value);
end "+";

function "-"(X: Unit) is
begin
        return Unit'(X.Length_DIM,
                     X.Mass_DIM,
                     X.Time_DIM,
                     -X.Value);
end "-";

-- etc;

end Units;

Yes I know that this requires runtime dimension checking, but you only
have to use it until you are through debugging your code then
you can replace the body with one that turns off all the checking.

--
Mark Biggar
mab@wdl.loral.com

Re: Types with physical dimension

[lmiller]

Stephe Leake at NASA GSFC (NBSSAL@stdvax.gsfc.nasa.gov) worked on something
like this some years ago.  I never worked with the packages produced but was
told by Stephe that the huge number of types generated made for long compile
times on good compilers and vast ugly deaths on poor ones.  His final analysis: 
neat, but not quite worth the effort.  For cartesian and other multi
dimensional stuff I found creating types which reflected reality quite useful
in pointing out errors at compile time.  Overloading the operators then made
for very readable expressions in code.  

type CART_AXES is (X, Y, Z);
type POLAR_AXES is (Lat, Long, Radius);
-- continue for all helpful coordinate systems...

type CART_VECTORS is array (CART_AXES) of Float;
type POLAR_VECTORS is array (POLAR_AXES) of Float;


Then the compiler will always kick you in the shin if you try to add
cart_vectors and Polar_Vectors without defining the proper operators.  One can
just imagine all of the opportunities C provides to make multitudes of mistakes
related to this situation.  

Re: Types with physical dimension

[William Brennan]

In article <GRAHAM.94Sep27181841@canopus.clsi.com>,
Paul Graham <graham@clsi.COM> wrote:
>
>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?
>

Ummm... I did it by using private types and writing a lot of operators.

Yes, it's a bit unwieldy.  But once it's done, it's done. Well, not really.  
If you want to create subtypes to have automatic constraint checking performed, 
you have to modify the package to add subtype definitions which I don't like 
too much.  It would be best if the package remained totally stable, and
subtypes could be added without surgery.  Ada 9X may fix this with child units, 
but it doesn't do much for us living with Ada 83.

If anyone wants to see an example of what I've got so far, please send me 
e-mail.  These packages are still a work in progress, being done in my spare 
time.  
-- 
----------------------------------------------------------------------------
                                                     === Team-Ada member ===
Bill Brennan                                  brennan@panther.warm.inmet.com

Re: Types with physical dimension

[Tucker Taft]

In article <GRAHAM.94Sep27181841@canopus.clsi.com>,
Paul Graham <graham@clsi.COM> wrote:

>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).  
> ...

>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?

In Ada 9X, there is a new option.  You can override the
predefined operators of a numeric type with an abstract
function.  This flags any attempt to use the operation.

For example, here we define 3 types and override their predefined
multiplying and exponentiating operators with abstract versions:

    type Cm is digits 6;
    type Seconds is digits 6;
    type Cm_Per_Sec is digits 6;

    function "*"(Left, Right : Cm) return Cm is abstract;
    function "/"(Left, Right : Cm) return Cm is abstract;
    function "**"(Left : Cm; Right : Integer) return Cm is abstract;

    function "*"(Left, Right : Seconds) return Seconds is abstract;
    function "/"(Left, Right : Seconds) return Seconds is abstract;
    function "**"(Left : Seconds; Right : Integer) return Seconds is abstract;

    function "*"(Left, Right : Cm_Per_Sec) return Cm_Per_Sec is abstract;
    function "/"(Left, Right : Cm_Per_Sec) return Cm_Per_Sec is abstract;
    function "**"(Left : Cm_Per_Sec; Right : Integer) 
      return Cm_Per_Sec is abstract;

Then you can define the appropriate combinations:

    function "/"(Left : Cm; Right : Sec) return Cm_Per_Sec;
    function "*"(Left : Cm_Per_Sec; Right : Sec) return Cm;
    function "*"(Left : Sec; Right : Cm_Per_Sec) return Cm;

You would probably want to put pragma Inline on these.
You could actually define a generic to simplify this,
so you wouldn't have to write the trivial bodies repeatedly:

   generic
      type Left_Type is digits <>;
      type Right_Type is digits <>;
      type Result_Type is digits <>;
   function Mul(Left : Left_Type; Right : Right_Type) return Result_Type;
   pragma Inline("*");  -- This means to inline calls on any instantiation

   function Mul(Left : Left_Type; Right : Right_Type) 
     return Result_Type is
   begin
       return Result_Type(Left) * Result_Type(Right);
	  -- Note that predefined operators "reemerge" in generics
	  -- This is probably one of the few times where that is useful!
   end Mul;

... Ditto for a generic Div.

Now you can just write:

    function "/" is new Div(Cm, Sec, Cm_Per_Sec);
    function "*" is new Mul(Cm_Per_Sec, Sec, Cm);
    function "*" is new Mul(Sec, Cm_Per_Sec, Cm);

... which is relatively painless.

Of course it would be nice to have more direct support for
units (given infinite resources, that is ;-), but at least 
with "abstract" and "generics" you can build your own consistency
checks.

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

S. Tucker Taft
Ada 9X Mapping/Revision Team
Intermetrics, Inc.
Cambridge, MA  02138

P.S. "abstract" subprograms weren't invented for this purpose,
but they seem to do the job fairly nicely.
Note that any untagged type may have an "abstract" primitive
subprogram.  But if a tagged type has an "abstract" primitive,
then it must itself be "abstract."
-T

Re: Types with physical dimension

[Robert Dewar]

"Of course it would be nice to have more direct support for units"

In the "of course" here likes a rather fundamental assumption which I
question, namely that it is always desirable to have features at hand
that do exactly what you want in the most convenient way. While that
may seem locally optimal, I am afraid that following this inclination
repeatedly leads to too much complexity in language design. Remember
that a reader must be able to read the code, that means that a reader
has to be able to pretty much understand the whole language since there
is no restriction on what the writer can write. A big language is not
so bad from the writer's point of view, since you only learn what you
need, but from the reader's point of view, the complexity is much
harder to handle.

To me, the units case crosses the line. I think you can build this well enough
in Ada, esp in Ada 9X with the abstract feature, and I think that (even
given infinite resources :-) it would be a mistake to add an additional
(inevitably somewhat complex) feature that would handle this more
directly.

Re: Types with physical dimension

[Peter Hermann]

Robert Dewar (dewar@cs.nyu.edu) wrote:
: "Of course it would be nice to have more direct support for units"

: In the "of course" here likes a rather fundamental assumption which I
: question, namely that it is always desirable to have features at hand
: that do exactly what you want in the most convenient way. While that
: may seem locally optimal, I am afraid that following this inclination
: repeatedly leads to too much complexity in language design. Remember
: that a reader must be able to read the code, that means that a reader
: has to be able to pretty much understand the whole language since there
: is no restriction on what the writer can write. A big language is not

agreed. The reader would be "overloaded".
but (see below)

: so bad from the writer's point of view, since you only learn what you
: need, but from the reader's point of view, the complexity is much
: harder to handle.

: To me, the units case crosses the line. I think you can build this well enough

Because you are involved in compiler construction?  ;-) :-)

: in Ada, esp in Ada 9X with the abstract feature, and I think that (even
: given infinite resources :-) it would be a mistake to add an additional
: (inevitably somewhat complex) feature that would handle this more
: directly.

I don't see it necessarily as an add-on feature like another "rucksack".
Ada has done a good job to prevent semantic errors.
I think however, that for Ada2000+ there are still reserves
which are not digged out in the abstraction process.
I am feeling that there must be better methods
which fit smoothly into a language concept.
A good solution would bring another major step 
in the abstraction process.

Today, we are able to prevent an expression like
meter times meter giving meter.   (you may substitute inch for meter :-)
We may allow meter times meter giving an_area_type.
The tools are here but certainly only rarely used.

Did I tease your phantasy?

The problem is with any language. We need some words to 
communicate but the optimal set is seldom reached.

--
Peter Hermann  Tel:+49-711-685-3611 Fax:3758 ph@csv.ica.uni-stuttgart.de
Pfaffenwaldring 27, 70569 Stuttgart Uni Computeranwendungen
Team Ada: "C'mon people let the world begin" (Paul McCartney)

Re: Types with physical dimension

[Dr John Stockton]

In article <36e7sf$19ql@info2.rus.uni-stuttgart.de> ucaa2385@iris3.csv.ica.uni-stuttgart.de (Peter Hermann) writes:
>Robert Dewar (dewar@cs.nyu.edu) wrote:
>: "Of course it would be nice to have more direct support for units"
>Today, we are able to prevent an expression like
>meter times meter giving meter.   (you may substitute inch for meter :-)
>We may allow meter times meter giving an_area_type.

I missed the beginning of this.  FYI, there was an article in European Journal 
of Physics earlier this decade AFAIR about a language, AMPERE?, which had 
types including physical dimensions for compile-time checking, and run-time 
limit (upper- & lower- bound) arithmetic.

As a metrologist, I would find both very desirable, though I'd need 
"statistical" rather than "worst-case" arithmetic - and have implemented this 
to some extent in Borland Pascal.
-- 
Regards, John Stockton.       
	JRS@newton.npl.co.uk from off-site, or header address should now work.
	National Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK
	Direct Phone +44 181-943 6087, Nearby Fax +44 181-943 7138    

Re: Types with physical dimension

[Robert Dewar]

Peter, your meters * meters not being allowed to give meters can be
done in a perfectly straightforward manner using abstract subprograms
in Ada 9X, why isn't that solution good enough for you?

Re: Types with physical dimension

[Tucker Taft]

In article <36deok$dce@gnat.cs.nyu.edu>, Robert Dewar <dewar@cs.nyu.edu> wrote:

>"Of course it would be nice to have more direct support for units"

That's cheating a bit (you must have a politician in the family) -- 
you left off my parenthetical comment and smiley "(given infinite 
resources, that is ;-)"

>In the "of course" here likes a rather fundamental assumption which I
>question, namely that it is always desirable to have features at hand
>that do exactly what you want in the most convenient way. While that
>may seem locally optimal, I am afraid that following this inclination
>repeatedly leads to too much complexity in language design. 
> ...

I completely agree with the above, and that is one reason why Ada 9X
does *not* have direct support for units.  You always have to weigh 
complexity versus benefits (some people's scales are sturdier than
others ;-).  I guess I should have "expanded" on my smiley a bit more...

-Tucker Taft

Re: Types with physical dimension

[Robert Dewar]

Tuck takes me to task for not including the "given infinite resources :-) 
from his original message.

But of course the point is that infinite resources for implementation are
totally besides the point, I have no concern for implementors in this
discussion, only for readers, and unless infinite resources also gives
readers infinite brain power, it won't help :-)

Re: Types with physical dimension

[Paul Pukite]

Paul Graham  <graham@clsi.COM> wrote:
>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?

You don't necessarily need to invoke private types in Ada. By creating a 
derived type like:

   type Dollars is new INTEGER;  -- Also can put in range constraints

you cannot multiply two dollar objects in another package unless you
specifically state that you want the "*" operator used. (Ada 9X reduces 
the extra code required to "use" the "*".)

This guards against some of the dimensional errors as do the range 
constraints, but I agree that VHDL physical types are rather neat.

--
Paul Pukite (pukite@daina.com)       
DAINA Engineering 612/781-7600       
4111 Central AVE NE, Suite 212       
Minneapolis, MN  55421-2953