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How can I simply persist functions written in the current terminal session for later use?

Suppose I write a Bash function at the command line:

```
$ hello-world() { echo "Hello, world!"; }
```

and I revise (perhaps hitting up-arrow to retrieve it from command history and edit it) and test and debug it, and eventually have a working function that does what I want:

```
$ hello-world 
Hello, world!
```

Now I'd like to make this available in future sessions, so I... well, currently, the best I can come up with is `type hello-world | tail -n+2 >> ~/.bash_aliases` (using `tail` to remove the helpful `hello-world is a function` message).

Is there a built-in, or simpler way to do this? Ideally, something that would add every function I've written in the current shell?