Re: Looking for Ada Technique Name and References

["Diana Webster" <dkweb@arlut.utexas.edu>]

This technique is called "composition" in mathematics, i.e., the composition
of two functions,
i.e, sum (average (xnum)).  Most programming languages support this.

John Halleck <nahaj@u.cc.utah.edu> wrote in message
news:88kh6q$j4j$1@coward.ks.cc.utah.edu...
> > John Halleck (nahaj@u.cc.utah.edu) wrote:
> > : I would appreciate it if someone could give me the name and a
> > : print reference for the following technique.
>
> > Someone Replied:
>
> >  It is called overloading.
>
>   It uses overloading, but that was not the technique I was trying
>   to get accross.
>
>   The technique in question is turning the what is normally written
>   as two function calls  (More or less:)
>       "*" (Transpose (A), B)
>   into a type mark and a single function call to a special function
>   that can handle it all more effeciently.
>
> >
> > : Background:
> >
> > :    Many matrix methods are written in the form  A := Transpose(B)*C
> > :    But, actually forming the transpose is expensive, and you are
better
> > :    off just writing a second matrix multiply routine that takes the
> > :    two matrices and treats the one as a transpose without actually
> > :    doing the transpose.
> >
> > :    Below is a technique that allows one to write it as one normally
> > :    sees it written, but lets the Ada compiler do the selection of
> > :    an appropriate routine.
> >
> > : Is there a name for this technique?   Does it appear already
documented
> > : somewhere?
> >
> >
: --------------------------------------------------------------------------
----
> >
> > : --  ...
> >
> > : type Matrix is array (positive range <>, positive range <>) of Float;
> > : type Transpose is new Matrix;
> >
> > : --  ...
> >
> > : -- This is just a matrix multiply routine.
> > : function "*" (Left : Matrix; Right : Matrix) return Matrix;
> >
> > : -- This routine multiplies the transpose of Left by Right.
> > : function "*" (Left : Transpose; Right : Matrix) return Matrix;
> >
> > : ----------
> >
> > : --  Examples:
> > : A, B, C, D, E: Matrix;
> >
> > : --  ...
> >
> > : A := B * C;              --  Matrix multiply.
> > : D := Transpose (E) * F;  --  D gets the result of multiplying E'F
> > :                          --  (By selecting the appropriate routine.
> >
> > : ---------------------------------------------------------------------