I think the author and Armstrong have significantly different ideas of what a "type" is. That's not a huge surprise—depending on background, you'll often get several definitions from different people.<p>One way to see types are things with fundamentally different access pattern: individual entities, sequentially retrieved ones (e.g. lists), fixed-length ordered lists whose elements are accessed positionally (e.g. tuples/vectors, fixed-length maps whose keys are known at compile-time/records/objects can also be viewed this way), unordered collections of distinct entities (sets), etc. I'd argue Armstrong's view is similar to this based on what he put in Erlang.<p>I can't tell what the author's view is, aside from "a class is a data type". This suggests that he equates a type with the set of functions that can be called on something and not have the compiler or runtime blow up (or perhaps, the set of functions that the programmer, by putting them in the same file, has explicitly said won't blow-up, whether or not that set is correct or complete). This throws fundamentally different things like lists, tuples, sets onto the same level as Person, Account, and PayrollRecord—which are often just short-hand names for tuples with different arities or names for their elements' positions.<p>If one has the later view, confusion over the point 3 is understandable: creating a new type for time is easy, just do class Time and define a bunch of properties and methods. In Armstrong's example, time is just a 6-tuple (or 3-tuple if all you want is hms). If you wanted to store it or send it over the wire, anything that could handle a tuple of integers would already know how to use it. If one function calls the last member "sec" and another "second", they're local names, so it doesn't matter as long as they're both accessing the same member.<p>One can object that it's easy to write serializers or that a compiler or library could figure it out, or that having different names for the same data elements indicates inconsistency in code that should be caught earlier. De gustibus non est disputandum. But, don't throw up your hands and say "this makes no sense!" without considering another perspective first.