Re: Scalars & atomic values & variables

Dawn M. Wolthuis <dwolt_at_tincat-group.com> schrieb:
> Scalar value (mathematics): An object in a space for which there is no
> operation in that space that takes a single operand and maps that object to
> two or more other objects (decomposes the object), which can then be rebuilt
> into the original object with another operation in the space.

I don't understand what it means for a function to return two values in any other way then via some non-atomic type like a tuple, so I'm going to interpret your definition to read: given some set of agreed-upon non-atomic values, a value is non-atomic if there is an isomorphism between it and some subset of that set.

In that case, even integers are not scalars since they are isomorphic to the assumed-non-atomic set of ordered pairs <x, x> where x is an integer.

The definition I proposed elsewhere (for types the values of which are atomic), is that subtypes are non-atomic. What constitutes a subtype depends on the type system, I guess. Using the "set of values and associated functions" definition, my original guess is that A is a subtype of B if its values and functions are supersets of those of B.

So talking about lists, for example, these are all non-atomic except for the empty list. Which makes sense. On the other hand, you could also say by my definition that all types are non-atomic except for the type with only the value _|_, but then maybe this isn't a proper type at all.

Of course I haven't actually studied any formal type theories yet so I'm just talking out of my ass. Received on Sat Jan 03 2004 - 15:09:01 CST