Imperative programming languages such as C and Java involve mutable state that changes throughout execution. Commands specify how to compute by destructively changing that state. Procedures (or methods) can have side effects that update state in addition to producing a return value.

The fantasy of mutability is that it's easy to reason about: the machine does this, then this, etc.

The reality of mutability is that whereas machines are good at complicated manipulation of state, humans are not good at understanding it. The essence of why that's true is that mutability breaks referential transparency: the ability to replace an expression with its value without affecting the result of a computation. In math, if f(x)=yf(x)=y, then you can substitute yy anywhere you see f(x)f(x). In imperative languages, you cannot: ff might have side effects, so computing f(x)f(x) at time tt might result in a different value than at time tt'.

It's tempting to believe that there's a single state that the machine manipulates, and that the machine does one thing at a time. Computer systems go to great lengths in attempting to provide that illusion. But it's just that: an illusion. In reality, there are many states, spread across threads, cores, processors, and networked computers. And the machine does many things concurrently. Mutability makes reasoning about distributed state and concurrent execution immensely difficult.

Immutability, however, frees the programmer from these concerns. It provides powerful ways to build correct and concurrent programs. OCaml is primarily an immutable language, like most functional languages. It does support imperative programming with mutable state, but we won't use those features until about two months into the course—in part because we simply won't need them, and in part to get you to quit "cold turkey" from a dependence you might not have known that you had. This freedom from mutability is one of the biggest changes in perspective that 3110 can give you.

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