Re: [Caml-list] Dimensional Analysis question

[Thomas Gazagnaire <thomas@gazagnaire.org>]

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Thomas

On 16 Oct 2014, at 17:37, Shayne Fletcher <shayne.fletcher.50@gmail.com> wrote:

> Dear OCamlers,
> 
> In 1994, Barton and Nackman in their book 'Scientific Engineering in
> C++' [1] demonstrated how one could encode the rules of Dimensional
> Analysis [2] into the C++ type system enabling compile-time checking
> (no runtime-cost) of the plausibility (at least up to the dimensional
> correctness) of computations.
> 
> In 2004, Abrahams & Gurtovy in 'C++ Template Metaprogramming' [3]
> showed the Barton Nackman technique to be elegantly implementable
> using compile time type sequences encoding integer constants. At the
> end of this post, I provide a complete listing of their example
> program [4].
> 
> The key properties of the system (as I see it) are:
>   - Encoding of integers as types; 
>   - Compile time manipulation of sequences of these integer encodings
>     to deduce/produce new derived types.
> 
> Now, it is not immediately obvious to me how to approach this problem
> in OCaml. It irks me some that I can't immediately produce a yet more
> elegant OCaml program for this problem and leaves me feeling like C++
> has "got something over on us" here ;)
> 
> My question therefore is: Does anyone have suggestions/pointers
> on how to approach automatic dimensional analysis via the OCaml type
> system? 
> 
> Best,
> 
> -- 
> Shayne Fletcher
> 
> [1] John J. Barton and Lee R. Nackman. Scientific and Engineering C++:
>     an Introduction with Advanced Techniques and Examples. Reading,
>     MA: Addison Wesley. ISBN 0-201-53393-6. 1994.
> 
> [2] Wikipedia http://en.wikipedia.org/wiki/Dimensional_analysis
> 
> [3] David Abrahams and Aleksey Gurtovy C++ Template Metaprogramming:
>     Concepts, Tools, and Techniques from Boost and Beyond (C++ in
>     Depth Series), Addison-Wesley Professional. ISBN:0321227255. 2004.
> 
> [4] Code listing:
> 
>     //"c:/program files (x86)/Microsoft Visual Studio 10.0/vc/vcvarsall.bat" x64
>     //cl /Fedimension.exe /EHsc /I d:/boost_1_55_0 dimension.cpp
>     
>     #include <boost/mpl/vector_c.hpp>
>     #include <boost/mpl/transform.hpp>
>     #include <boost/mpl/placeholders.hpp>
>     #include <boost/mpl/equal.hpp>
>     #include <boost/mpl/plus.hpp>
>     #include <boost/mpl/minus.hpp>
>     #include <boost/static_assert.hpp>
>     
>     typedef boost::mpl::vector_c<int,1,0,0,0,0,0,0> mass;
>     typedef boost::mpl::vector_c<int,0,1,0,0,0,0,0> length;
>     typedef boost::mpl::vector_c<int,0,0,1,0,0,0,0> time;
>     typedef boost::mpl::vector_c<int,0,0,0,1,0,0,0> charge;
>     typedef boost::mpl::vector_c<int,0,0,0,0,1,0,0> temperature;
>     typedef boost::mpl::vector_c<int,0,0,0,0,0,1,0> intensity;
>     typedef boost::mpl::vector_c<int,0,0,0,0,0,0,1> angle;
>     typedef boost::mpl::vector_c<int,0,1,-1,0,0,0,0> velocity;     // l/t
>     typedef boost::mpl::vector_c<int,0,1,-2,0,0,0,0> acceleration; // l/(t2)
>     typedef boost::mpl::vector_c<int,1,1,-1,0,0,0,0> momentum;     // ml/t
>     typedef boost::mpl::vector_c<int,1,1,-2,0,0,0,0> force;        // ml/(t2)
>     typedef boost::mpl::vector_c<int,0,0,0,0,0,0,0> scalar;
>     
>     template <class T, class Dimensions>
>     class quantity
>     {
>     public:
>       explicit quantity (T val) 
>         : val (val)
>       {}
>       template <class OtherDimensions>
>       quantity (quantity<T, OtherDimensions> const& other)
>         : val (other.value ()) {
>         BOOST_MPL_ASSERT( (boost::mpl::equal<Dimensions, OtherDimensions>));
>       }
>       T value () const { return val; }
>     private:
>       T val;
>     };
>     
>     template <class T, class D>
>     quantity<T, D>
>     operator + (quantity<T, D> x, quantity<T, D> y )
>     {
>       return quantity<T, D>(x.value () + y.value ());
>     }
>     
>     template <class T, class D>
>     quantity<T, D>
>     operator - (quantity<T, D> x, quantity<T, D> y )
>     {
>       return quantity<T, D>(x.value () - y.value ());
>     }
>     
>     template <class T, class D1, class D2>
>     quantity <
>       T
>     , typename boost::mpl::transform<
>         D1, D2, boost::mpl::plus<
>                   boost::mpl::placeholders::_1
>                 , boost::mpl::placeholders::_2> >::type 
>     >
>     operator* (quantity<T, D1> x, quantity <T, D2> y)
>     {
>       typedef typename boost::mpl::transform<
>         D1, D2, boost::mpl::plus<
>                   boost::mpl::placeholders::_1
>                   , boost::mpl::placeholders::_2> >::type D;
>     
>       return quantity<T, D> (x.value () * y.value ());
>     }
>     
>     template <class T, class D1, class D2>
>     quantity <
>       T
>     , typename boost::mpl::transform<
>         D1, D2, boost::mpl::minus<
>                   boost::mpl::placeholders::_1
>                 , boost::mpl::placeholders::_2> >::type 
>     >
>     operator/ (quantity<T, D1> x, quantity <T, D2> y)
>     {
>       typedef typename boost::mpl::transform<
>         D1, D2, boost::mpl::minus<
>                   boost::mpl::placeholders::_1
>                   , boost::mpl::placeholders::_2> >::type D;
>     
>       return quantity<T, D> (x.value () / y.value ());
>     }
>     
>     // -- test
>     
>     #include <iostream>
>     #include <limits>
>     #include <cassert>
>     
>     int main ()
>     {
>       quantity<float, mass> m (5.0f);
>       quantity<float, acceleration> a(9.8f);
>       quantity<float, force> f = m * a;
>       quantity<float, mass> m2 = f / a;
>     
>       assert ((std::abs ((m2 - m).value ())) <= std::numeric_limits<double>::epsilon ());
>     
>       return 0;
>     }
> 


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