See also "shift left"
> All the information _has_ to exist somewhere, and the only question is where.
Not entirely sure what you mean about this, but not all type information has to exist somewhere. Sometimes things get encoded into a type that might never be represented otherwise -- like whether an integer is a width or a height, or whether a string is a name or an address.
Then the code is written to make sure you never make the mistake of sending a width to a height, because that would be silly.
The type (width or height) is represented as logic in the code.
theoretically - if you have a type system that allows you to know something is a width or height you can often reduce logic to keep track of these things but my experience is that level of granularity in your typing reduces dynamism too much. I would rather keep track of that in code (as it probably will have to deal with it anyway) than make my type system deal with it.
But note that to make all of that work well you really need your language to provide a lot of syntactic sugar features which are missing in most older languages, so all the operations read seamlessly, instead of being full of ceremony. One could do all of this in, say, old Java 1.4 or something, but the amount of type annotation, along with the massive mounts of boilerplate to get all of the operationg working right, and checked at compile time would make it all Not-Worth-It(tm) But with enough language features, and a smart enough compiler, `val acc = mySpeed / someSeconds` will work, straight up, with the safety included.
I was thinking about this as I was reading your comment, and wondering: is it nonsense? If I have 5 seconds of time as well as 10 milliliters of water... I can consider them as being packaged together... which is addition. And I can subtract 3 milliliters and 6 seconds from them without running out of what I had. Nothing wrong with that, really. Five potatoes and a gallon of water is the same notion, just more familiar. Seems no more nonsensical than dividing length by time, right? Food for thought...
Which means, for example: (3 liters and (i.e. "+") 6 seconds) + (4 liters and 2 oranges) = (7 liters and 6 seconds and 2 oranges). Perfectly sensible addition, which you do all the time. There's no stipulation the output has to be a single number...
The point is, making a vector, that's not addition.
> because it's very much not
I don't expect to change the mind of someone who thinks that addition and defining a vector are the same thing. You've just redefined generally common terms and then started accusing people of being uneducated for not sharing your own eccentric definitions. Poor show.
I didn't intend that to be rude, I was pointing out this is something everyone learns in a standard curriculum i.e. that this is very much the opposite of esoteric. But you seemed determined to reply that way, so I'll stop here.
surely, you have an idea of what you're using that function for, while you're writing it.
The compiler is doing a check to see if the function makes some minimal logical sense (ala, a typecheck), but it cannot read your mind. But this implies the types are actually an actualization of the thoughts in your head, in a formal manner.
Is a pretty bad system because you say "won't even exist in your head" but I dont even know if I should pass it integers, floats a srtring. Or what it will return.
I'm skeptical that sophisticated type systems need to exist.
Perhaps I should dust off my copy and start reading SICP
For instance, the part about tagging objects with their type reshaped my thinking about static type systems in general. Static typing, for example in C, is essentially just moving the location of the type tag from existing at runtime within the struct, to the "analysis" phase of the compiler. It's a pretty simple idea, but it made the "degree of dynamism" tradeoff click in my head. All the information _has_ to exist somewhere, and the only question is where. And Scheme is just at an extreme where the _everything_ is stored dynamically.