Jon Lang wrote:
Ruud H.G. van Tol wrote:
Did you consider "discrete"?
I think that "Discrete" could work quite well as the role that
encapsulates the ways in which Integer and Gauss are alike. It may
even be genralizable beyond that, although there might be some discord
between theory and practice. (In theory, Boolean is every bit as
discrete as Integer is; but in practice, it has no use for most if not
all of the methods in Integer that pertain to discreteness (factors,
remainders, primes, etc.)
I'm inclined to consider a "Discrete" to be broad enough to include Boolean, as
well as every single enum type in general; it would also include Order, say. So
I would also then add a more specific something, say "DiscreteNumeric".
I see some of the role relationships going like this:
- Numeric is a proper subset of the universal set
- Ordered is a proper subset of the universal set
- Discrete is a proper subset of the universal set
- Ordinal is a subset of [Ordered intersect Discrete]
- DiscreteNumeric is a subset of [Numeric intersect Discrete]
- Integral is a subset of [Ordinal intersect DiscreteNumeric]
- Real, Rational are subsets of [[Ordered intersect Numeric] minus Ordinal]
- Complex is a subset of [Numeric minus Ordered]
- Gaussian is a subset of DiscreteNumeric (or [Complex intersect Discrete])
- Boolean, Order are subsets of Discrete (or of Ordinal, take your preference)
- Stringy is subset of [Ordered minus Ordinal] (or [Ordered minus Discrete]?)
Or, sort of arranged visually (with some repeats):
universal-set
Numeric
Real, Rational
Complex
DiscreteNumeric
Integral (conceptually also Real, Rational)
Gaussian (conceptually also Complex)
Ordered
Ordinal
Integral
Boolean, Order
Real, Rational
Stringy
Discrete
Ordinal
Integral
Boolean, Order
Gaussian
A distinction between Ordered and Ordinal is that only Ordinal provides pred()
and succ() while both provide before(), after(), etc.
So, some thoughts.
-- Darren Duncan
