On Wed, Nov 15, 2017 at 1:41 PM, Koos Zevenhoven <k7hoven@gmail.com> wrote:

[..] 

What do we call such a "type"? Maybe we have both "concrete" and "strictly concrete" types. Perhaps we also have both "abstract" and "strictly abstract" types. An ABC with some concrete default implementations might then be both a concrete type and an abstract type.

Note that in the above bullet point "definition" of concrete type, I intentionally left out the requirement that the type can be instantiated.

The other two bullet points are:

* strictly concrete type: a concrete type that is not abstract––it concretely implements everything that it represents / describes. This is almost always a normal class, so it might be also known as "class".

* strictly abstract type: an abstract type that is not concrete––it does not implement any functionality or storage.

There might be a way to improve terminology from this, but I feel that what I sketched here is usable but still not very ambiguous.

​Let me rephrase that last sentence: I think this terminology is more clear.

And here's some additional clarification:

I expect that the possibility of a type being both concrete and abstract may sound strange. In some ways it is indeed strange, but this overlap of concepts definitely exists already, we just need to categorize and define the concepts clearly, but without introducing too many concepts whose relations to each other are messy.

This might also seem strange if you are not used to how "strict" is often used in mathematics and related sciences. Essentially, it's synonymous to "proper"​. For example,  "strict subset" and "proper subset" of a set both refer to a subset that is not the set itself. Any set is both a superset and subset of itself (in non-strict terms).  Also "pure" might sometimes refer to something similar.

So in some sense it means excluding the "gray area". Often that "gray area" is kept part of the non-strict/improper concept for convenience. 

​

––Koos

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+ Koos Zevenhoven + http://twitter.com/k7hoven +