I upvoted you because I think this is an interesting line of reasoning, but I disagree that it's a very useful one. You seem to be implicitly defining "computa

I upvoted you because I think this is an interesting line of reasoning, but I disagree that it's a very useful one. You seem to be implicitly defining "computation" as that which a physical computer does (machines, biological brains...). Something that literally consumes physical resources. By that logic, a Turing machine is not a computer and lambda calculus is not about computation. As I said, you could spin the semantics that way but is it useful? Does that give us useful insights? Functions are not just syntactic notation. Functions are, by definition, mappings from set A to set B. They don't have anything to do with notation. "cos(x)" is merely a notation, yes, but not of a number but of a function. This is an important distinction. "cos(5)" evaluates to a certain number, yes, but it's not just syntactic sugar for that number. Not to mention that functions don't need to operate on sets of numbers.