Nope. No program can be composed 100% of pure code because every program must do I/O work, which is inherently stateful. Most programs also need to carry around some amount of internal state, to one degree or another. The goal of functional programming, then, is to maximize the proportion of pure code to impure code in your program.
What does it mean for data and code to be pure? The short answer is that pure things are immutable, but this is not quite accurate: all pure things are immutable, but not all immutable things are pure. Pure things are not only unmodifiable but also definitional.
