# The neural network programming language

Here’s a JavaScript function that
returns a positive value if both `x`

and `y`

are positive:

```
function isNeg(x) {
return Math.max(0, -x);
}
function bothPos(x, y) {
return Math.max(0, 1-isNeg(x)-isNeg(y));
}
```

Surprise - the functions here are also neural networks! Neural networks are usually drawn as labelled, weighted graphs, but you can also view neural networks as a restricted programming language.

The above functions are in a subset of JavaScript that I call *NN*.
They approximate the one function below written in full JavaScript:

```
function bothPos(x, y) {
return x > 0 && y > 0;
}
```

This is perhaps how you might more naturally implement `bothPos`

.
So why would we ever use this more restrictive neural network language?
Compared to JavaScript, the language *NN* has two separate purposes.
Its first (philosophical) purpose is to model how real, physical neurons work.
Its second (much more specific) purpose is to allow for training:
you can take any function here,
compute its “loss” against a training set,
compute the *gradient* of that loss,
then adjust the constant numbers in the function
to (hopefully) improve the function.

This language is quite restrictive. Its only base data type is the floating-point number. Its only expressions are (non-recursive) function calls and the odd expression

```
expr ::=
"Math.max(0, " ")"
```

This can’t be done:

```
function max(x, y) {
// ???
}
```

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