In re: #1 that's the kind of discussion I could have all day. (If you take the state of the machine including the filesystem, then almost all non-networked programs could be treated as pure functions, eh?)
#2 so how does that modify your original comment, if at all?
#3 What would you contrast our mainstream so-called "general purpose" languages with?
2. But yes, programs that act like functions definitely do exist. They even used to be in the majority.
3. ALGOL stands for ALGOrithmic Language. It's a DSL for the domain of algorithms. As are virtually all our mainstream so-called "general purpose" languages.