Decorated interval operations: still a problem
Nate, Arnold
I recall this made me uneasy when we originally discussed Motion 8, but I didn't put my finger on the cause of my unease at the time:
> 2.4. An arithmetic operation on bare intervals is obtained by promoting the bare intervals to decorated intervals whose decorations are all-0 and then performing the operation with the resulting decorated intervals.
At an abstract level, this is false as stated, because the bare intervals are closed under arithmetic operations. If xx and yy are bare intervals, then xx+yy is a bare interval, not a decorated one as here asserted.
At a language level it would mean that xx, or yy, or "+", or an expression context, would need to know somehow that "decorated interval operation" was intended rather than "bare interval operation". I see various ways to specify and/or implement this, but none that are sensible.
The simplest solution IMO is to assume you meant
> 2.4. An arithmetic operation having some bare interval operands and some decorated interval or bare decoration operands is obtained by promoting the bare intervals to decorated intervals whose decorations are all-0 and then performing the operation with the resulting decorated intervals.
(Where "all-0" now becomes 4 for the bare empty set, 2 for all other bare intervals, according to Arnold's prescription.)
Is that correct?
John