infratypes of surtypes, phyla of taxa

8.13: adda/oop/rethinking terminology:
. I have terminology for biop (binary operations) oop
arranged as supertypes existing as
one of fixed number of subtypes;
eg, Number is a supertype because it manages the
binary interactions between the following types
which are therefore called subtypes of number:
integer, real, decimal, rational, irrational, complex .
. classic oop hasn't played well with biop's:
being objected-oriented has meant that
(obj+x) had to be expressed as (obj.+(x))
and then obj's type, say int, needed to have
(+)-operations for each possible numeric type
(int, real, rational, irrational, complex);
what we needed was multi-dispatching:
where (obj+ x) gets sent to the supertype,
which finds the right subtype to handle it .

. the notion of subtype
can also include range limits .
. there are naturally limits imposed by
the numeric types that machines provide,
such as what can fit in multiple of bytes;
eg, int8, int16, int32, float32 .
. within my theory of oop,
these might be called infratypes,
for reminding of the term infrastructure .
[10.5:
. infratype is a relative term:
regardless of whether it's a cpu type,
or a type you reused from a library,
an infratype of T.type is any type that has been
reused for implementing T .
10.7:
. I'm realizing that infratypes
should be supported by the type.tag
(simply because we should support
space-efficient numerics,
and we do that, then we need to know
which infratype we're using in
(8, 16, 32, extendible);
therefore,
what I've been calling subtypes
(in the biop oop context)
can instead be called ideal infratypes
(in contrast to optimized infratypes);
likewise,
what I've been calling the supertype
can instead be the opposite of infratype:
that seems to be the word: surtype .
-- also some extra checking just now
shows that the idea I'm trying to convey,
is the same as that found in the words:
{surname, surface} -- the outermost part .]

[10.5: 10.7:
. in contrast to the ideal infratypes
that are designed by mathematicians,
the optimized infratypes are chosen by the
intersection of what types the platform provides
and what is of use by the
constrained versions of the ideal infratypes .

. there is a relationship between
subtypes and infratypes:
. within a polymorphic type,
infratypes are the type's possible forms (morphs);
whereas an value whose type is a subtype of T,
can be used anywhere a T-typed obj is permitted;
but the reverse is not true:
if you have a variable obj whose type is a subtype of T,
it cannot be used anywhere a T-typed obj is permitted;
rather the replacing obj must be able to handle
every value and every operation
that could be handled by the obj' it's replacing .

. a surtype has a finite set of ideal infratypes,
ie, types distinguished by having differences in
either the allowed set of operations,
or the data format of the current state .
. within each ideal infratype,
we then have a possibly infinite number of
additional subtypes
according to constraints on
value attributes, eg, on the value's range,
or the scientific format's number of digits,
or on the number of fraction digits .]