I'm curious on supporting evidence for it being a basic mental model of how humans think? That sounds like a fairly strong claim.
However
What we do see is a bunch of mathematical disciplines that end up creating properties like: AND, OR, Universal, Existential, Implication, (and a few others). They end up in places like: set theory, type theory, category theory, various logics, lattice theory, etc.
Now, maybe they're only copying one another and this is more of a memetic phenomena. Or maybe they've hit upon something that's important for human comprehensibility.
That would be the 'evidence' of the positive effect of ADTs (scare quotes because it might just be math memes and not fundamental). But we can also think about what I feel is legit evidence for the negative effect of lacking ADTs.
Consider what happens if instead of having the standard boolean logic operators and, or, not, xor, we only have the universal not-and operator. Now a straightforward statement like: A && B || C becomes (((A !& B) !& (A !& B)) !& ((A !& B) !& (A !& B))) !& (B !& B) [I think...]. It's more complicated to tell what's actually supposed to be going on AND the '&&' simulation can get intertwined with the '||' simulation. The result being that requirements changes or defect fixes end up modifying the object level expression in a way where there is no longer any mapping back to standard boolean logic. Comprehensibility approaches zero.
And we've seen this happen with interfaces and inheritance being used to implement what would otherwise be a relatively simple OR property (with the added benefit that pattern matching ADTs often comes with totality checking; not something you can do with interfaces which can always have another instance even up to and including objects loaded at runtime).
Now, I should add that I did not mean my question to be a criticism of them! I'm genuinely curious on evidence that they are a basic building block. Feels save to say they are a good building block, and those aren't the same thing.
As an easy example for them not being basic building blocks, I can't remember ever seeing anything like them in any assembly instructions for things. Put together a batting net for the kids. Lots of instructions, but nothing algebraic, in this sense. Looking at recipes for food. Nothing algebraic, really? Maybe I can squint and see some, but it would be hard. Exercise plans? Music lessons? Playbooks for a sport?
Again, though, I /do not/ intend this as a criticism of them. Genuinely curious on any investigation into them.
There is the still the ongoing debate about how much human perception and human reason are shaped by cultural forces vs. universal forces (where the latter asserts humans reason in the same/similar ways).
There's evidence that certain optical illusions don't work across cultures for example (I seem to remember those in Western countries have a tendency to mentally group things in rectangular boxes). The exact balance between cultural and universal forces isn't known and I doubt we could say anything about sum types in that regard.
For two, addition is a wildly disparate thing everywhere we use it. We like to joke that computers made that hard, but literally half of intro chemistry is learning how to get thing to add together in a meaningful way, no? Balancing a chemical equation is a thing.
Logic doesn't really have a direction, it works backwards or forwards. Even if you're solving a system "backwards", whatever that means, you still have to satisfy all of the necessary AND and OR constraints for a solution to be valid, so you're effectively still building ADTs or records just using a different evaluation order.
You can /model/ it that way. But you are making a symbolic model to justify how a solution is reached.
Now, it can be frustrating to consider that this model could produce an agent that is better at the ball game than the players. But it is silly to think that means you have mirrored them.
You're attempting a sleight of hand here by saying "they're" not "doing trig". Clearly they are not doing anything like that consciously, but equally clearly some part of their brain is triangulating objects and predicting trajectories based on gradients, meaning that part is "doing trig and calculus" subconsciously. What else does it mean to "do something" if not "process X is isomorphic to process Y"?
> You can /model/ it that way. But you are making a symbolic model to justify how a solution is reached.
I really don't understand what you think people are doing when they're compiling a grocery list. They're clearly thinking, "I need x AND y OR I can substitute z".
Or if they're planning to paint their fence, they're thinking, "I need paint AND brushes AND I have to start before lunch OR I won't finish before dinner".
You seem to think I have to prove your model false to show others don't do that. But I am specifically not claiming your model is false. I'm saying folks don't think that way, necessarily. For example, many build lists for shopping that they were taught. Not that they reasoned.
Most people learn to build lists through mimicry. They literally mimic the lists they were taught they need to build to go to the store. With enough experience, many of us learn to build our own lists from other principals, but it almost all starts with mimicry and simulation. Is why "going shopping" is such a fun game for kids. They are learning.
None of which is to say that you can't make your thinking better with logic. You almost certainly can. But you are begging the question with your examples and explanations. Heavily.
Implication is one of the primitives in logic, and gives us several of the classic logical fallacies: affirming the consequent, denying the antecedent, fallacy of the converse, and fallacy of the inverse.
All of which are examples of trying to work logic as though it doesn't have a direction.