Thoughts about "Compile-time types" talk

[Alex]

On Friday, 17 May 2019 at 18:09:16 UTC, Ola Fosheim Grøstad wrote:
> On Friday, 17 May 2019 at 16:35:16 UTC, Alex wrote:
>>
>> We must have different concepts of abstraction.
>
> Well, if you are talking about abstraction mechanisms that 
> languages provide then I kinda get you.
>
> But in general abstraction starts with modelling. One does this 
> best with pencil and paper, no need for a fixed theoretical 
> framework. What one can benefit from is experience with various 
> modelling techniques, or just experience. The most important 
> aspect of this, in the beginning is to build intuition, which 
> is modelling, albeit a fuzzy and "emotional" model.
>
>> What abstraction does is allow for symbolic representation of 
>> complex processes.
>
> Simplified representation, usually. So, it is a view or an 
> interpretation of reality, but not actually a true 
> representation of reality.
>
>> A oop hierarchy is an abstraction as is a struct.
>
> Not quite.  You start with object oriented modelling, then you 
> pick a set of tools that lets you implement the model, and 
> possibly evolve it over time. That is the real purpose of OOP, 
> to enable the implementation of a model and to make it 
> maintainable. Keep in mind that Nygaard and Dahl created Simula 
> for doing simulations. It provided a set of mechanism to enable 
> that such as coroutines, block prefixing, class main program 
> with an inner injection point (IIRC) and class inheritance with 
> virtual functions.
>
> So, the abstraction (of reality) is the model. The OOP 
> mechanisms are mechanisms for implementing the model.
>
>> You cannot abstract in masm because masm does not have 
>> language capabilities to abstract.
>
> I don't know about masm, but there is no problem implementing 
> an OO model in machine language or C.
>
>> everything is logic. Even a baby playing is an abstraction of 
>> logic because neurons that fire in the baby's brain are just
>
> No, you are modelling a baby using logic, that model is the 
> abstraction, the baby is reality.
>
>> The point is that we humans see the world in abstraction. 
>> There are no lines in the world. A cup of water IS an 
>> abstraction.
>
> Yes, we create models of reality in our heads and classify 
> parts of reality that we have segmented into objects. Our 
> visual system has that in part hardcoded.
>
> So yes, everything that isn't the signal of a sensing cell is 
> an interpretation that is turned into a model.
>
>> But I've only went in one direction. All that stuff was built 
>> up from the most concrete to the most abstract in reality by 
>> humans. Humans NEVER build from the abstract to the concrete, 
>> it doesn't even make sense to do so(we can specialize 
>> abstractions but but all abstractions start out as less 
>> abstract things).
>
> That's not quite true. Say, an artist can start by drawing a 
> circle, then put two more circles within that circle and then 
> gradually refine it into a face. You can do the same with 
> programming.
>
> Also, in genetic programming there isn't necessarily 
> programming level abstraction in play, except for the fitness 
> function (measuring degree of success). It could be viewed as a
>  randomized  search within a technical architecture (that 
> implements a low level model, that model is an abstraction of 
> what happens in the hardware). But it might not be fruitful to 
> view the mechanisms as abstractions, since they are not 
> approached as such. Thus abstraction is something that is in 
> our heads, in our model, something entirely subjective. 
> Although some might argue that programmers have an 
> inter-subjective model of the programming field.
>
> But it is not like all programmers view or use the same 
> constructs for the same purposes.
>
> So a programming construct has the potential to be used to 
> implement a model (an abstraction), but the meaning of how the 
> construct was used depends on the individual programmer.
>
>> OOP allowed one to write far more complex programs SOLELY 
>> because it allowed one to abstract the bits and pieces and the 
>> abstraction allows the human mind to understand it.
>
> Mostly by making programs more maintainable and easier to 
> evolve. Of course, the availability of OO mechanisms in 
> languages created a market for OO modelling techniques. So yes, 
> more people started modelling differently because of the 
> availability. However, the modelling should happen before you 
> program...
>
>> abstraction is in everything. Mathematics is all about 
>> abstraction.
>
> Well, that is one interpretation.
>
> Another one is that it just is a space of possible symbolic 
> models that one (try to) prove to be internally consistent. 
> Then you can try to do abstractions over the interpretation of 
> the symbolic models and come up with concepts like rings, 
> groups etc. The school math is one particular version, but 
> there are infinitely many others available... perhaps not 
> useful or interesting, but they are available, you just have to 
> define them. No real abstraction in that. It could be viewed as 
> uninterpreted symbolic machinery. Doesn't have to represent 
> anything in particular. That is of course unusual, but that 
> doesn't mean that you cannot do it.
>
>> We start with the integers and get the rationals, the 
>> rationals were abstracted to the reals, the reals to the 
>> complex, and then one gets more such as padics, quaternions, 
>> and then vectors come out of and then tensors out of vectors...
>
> Yes, but those are interpretations or rather, the model that 
> you map over to the symbolic machinery. So you have a mapping 
> from your model to something more concrete.
>
>> OOP is simply the ability to abstract. Inheritance is 
>> abstraction. When one inherits from a class they are 
>> generalizing or abstracting that class. It's very powerful 
>> when you had no ability to do this before(C).
>
> No. OO-modelling is a tool for abstraction. Inheritance is a 
> relationship that is in the model. When you inherit you 
> specialize the more abstract super class. The superclass is 
> more abstract because it lacks more information about the 
> phenomon (reality) being modelled than the subclass. So the 
> subclass contains more details, and closer reflects the 
> properties of reality than the superclass.
>
> However, the language constructs are just tools that provide 
> machinery for implementing the model. Just like the symbolic 
> machinery of logic is a tool for implementing integers and 
> operations over integers in math. You can have many different 
> symbolic implementations of integers. Right? Unfortunately, in 
> math people might say that a specific symbolic representation 
> is a model of integer. Whereas in computer-terminology 
> "integer" would be the model and the representation would be 
> the implementation.
>
>> Ultimately it has nothing to do with specific languages except 
>> that they provide examples of where we are at in the process 
>> of all this.
>
> Well, the whole is greater than the sum of the individual 
> parts, so what really does make a difference is how everything 
> work together. That includes the IDE and different tools for 
> interactive code analysis.
>
>> If you understand all that then what I'm saying is that 
>> category theory IS the theory of abstraction
>
> There is no doubt that it is A theory of abstraction...
>
>> Of course, if one abstracts too much one arrives a singular 
>> point! Which turns out to be quite powerful! ;)
>
> The problem with abstraction is that one deliberately (or 
> mistakenly) ignores information, that is true.

You keep saying that something is not an abstraction then use 
that abstraction. E.g., oop is a tool used to abstract...

Do you realize that a tool itself is an abstraction?

Until we can agree on a precise definition of abstraction we will 
just go in circles.

If you agree that your brain takes sensory data and presents it 
to you as abstractions. E.g., some cells fire on your finger tips 
and eventually through the magic of life your brain tells you 
that you just chopped off the tip of your finger is a process of 
abstraction(your brain builds up a model about reality and what 
happened given the sensory data and presents it to you as the 
reality(but it is still a model))... then, in fact, everything 
you know is an abstraction... because all your information came 
through you by sensory data which was abstracted.

You don't think about pumping your heart, your body does it for 
you... but your perception of what is going on is really an 
abstraction.

The problem we have is you seem to think abstractions are not 
real. That is the typical way to view them... But abstractions 
are not like a unicorn... abstracts are very real. Without them 
we couldn't even have this conversation, literally.

I'm presenting you with my extended definition of what 
abstraction is, you can keep using use or choose to use mine and 
see something new. My definition includes yours, where do you 
think I got mine from? (and that itself was an abstracting 
process)

Stop thinking of abstraction as what you learned from Stroustrup 
and think of it in modern terms. Concepts grow and evolve for a 
reason.

In mathematics, one of the most basic principles is the concept 
of a point/element... something that is so abstracted as to 
include everything and nothing at the same time. That singular 
concept IS what as allowed mathematics to do very real things. 
Abstractions are not imaginary. A baby is very much an 
abstraction. What a baby really is far more complex than anything 
our brains understand. Most people have no clue what a baby is 
but some simple abstraction of something that whines, shits, and 
giggles.