If anyone is interested in Type systems and what's a type, I highly recommend watching the first 20 mins of Sean Parent's presentation:
It will change the way you think about types after this.
It will change the way you think about types after this.
Maybe I missed something, or maybe I need to watch more. Can you explain why you recommend this segment in more detail?
CppCon 2015: Sean Parent "Better Code: Data Structures"
Goals for Better Code - Implement Complete TypesBoth talks are interesting. Both are from a very C++ perspective, particularly the one you suggest. That doesn't make them wrong, by any means. Much of it generalizes, although depending on your background it might take varying amounts of effort to understand the generalizations.
In the first talk in particular, I think he conflates (in a small way) type with representation in a way that's... not... ideal? But I don't think it does a lot of harm to the talk; he has very interesting things to say particularly about representation.
Some of the point of both talks overlaps with the common admonishment to "make illegal states unrepresentable", but I don't think any fully implies the other.
For a very different perspective on types, I highly recommend watching https://www.youtube.com/watch?v=3U3lV5VPmOU, although I don't highly recommend actually programming this way.
The entire talk is about memory layouts and how nothing has a meaning unless we ascribe a meaning to it.
I don't really know what this has to do with types, or type systems, which are an algebraic concern, as far as I'm concerned.