On 3 Oct 2011, at 04:08, Aubrey Jaffer wrote:

> | > Shouldn't the predicates REAL? and COMPLEX? implement the
> | > mathematical semantics for which they are named?
> |
> | ...  There are two reasonable sets of semantics here, and by
> | providing two sets of procedures we can support both.  By adding an
> | "exact-complex" feature, a program that depends on exact complex
> | numbers can rely on being run only on an implementation that
> | supports them.
>
> The terms integer, rational, real, and complex are too few to
> adequately describe all the possible numeric Scheme types.  Rather
> than misuse basic mathematical terms, coin new names for the numeric
> types which don't match the mathematical types.

In math, there are two distinct copies of the integers in play: the ring of integers Z, and the copy of it embedded into the field Q of rational numbers. A similar thing happens with real and complex numbers.

One could think of having that model in a computer program.

Hans

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