Distributions are defined in modules/Distributions.hs.

For a distribution, you need to add a function that constructs a ProbDensity object.

Here `densities`

returns a list of terms which yield the density when multiplied together.

For example, the Normal distribution is defined as:

```
builtin normal_density 3 "normal_density" "Distribution"
builtin normal_quantile 3 "normal_quantile" "Distribution"
builtin builtin_sample_normal 2 "sample_normal" "Distribution"
sample_normal m s = Random (IOAction2 builtin_sample_normal m s)
normal m s = ProbDensity (\x -> [normal_density m s x]) (normal_quantile m s) (sample_normal m s) realLine
```

A density function takes an extra argument after the distribution parameters. For example, the normal density takes 3 arguments, so that `(normal_density m s)`

is a function of the third argument.

A density function should return type `log_double_t`

.

A quantile function takes an extra argument after the distribution parameters. For example, the normal quantile takes 3 arguments, so that `(normal_quantile m s)`

is a function of the third argument. The extra argument should have type `double`

, and ranges from 0 to 1.

If the function is not univariate, or does not have a quantile functon, set the quantile function to `(no_quantile "distribution name")`

. This will later change to use polymorphism, where only 1-dimensional functions will have a quantile attribute.

To construct a random sample from a C++ procedure, access the `n`

th parameter via `Args.evaluate_(n)`

(with an underscore) instead of `Args.evaluate(n)`

. For example:

```
extern "C" closure builtin_function_sample_normal(OperationArgs& Args)
{
double a1 = Args.evaluate_(0).as_double();
double a2 = Args.evaluate_(1).as_double();
return { gaussian(a1, a2) };
}
```

Then use one of the following patterns, depending on how many arguments your sampling routine takes:

```
sample_dist arg1 = Random (IOAction1 builtin_sample_dist arg1)
sample_dist arg1 arg2 = Random (IOAction2 builtin_sample_dist arg1 arg2)
sample_dist arg1 arg2 arg3 = Random (IOAction3 builtin_sample_dist arg1 arg2 arg3)
```

For example:

```
builtin builtin_sample_normal 2 "sample_normal" "Distribution"
sample_normal m s = Random (IOAction2 builtin_sample_normal m s)
```

The `(dist_sample parameters)`

function returns an object in the Random monad, where executing a distribution has the semantics of sampling from the distribution. The sampling procedure can also call other actions in the Random monad. For example, here we sample from the distribution `(dist2 args)`

and transform the result.

Ranges for real numbers are:

- above x
- below x
- between x y
- realLine

Ranges for Integers are:

- integer_above i
- integer_below i
- integer_between i j

In each case, the range includes the bounds. For example, `(integer_above 0)`

includes `0`

, and `(integer_between 0 1)`

includes `0`

and `1`

.

Ranges for Booleans are:

- TrueFalseRange

Ranges for simplices are

- Simplex n sum

where `n`

is the number of dimensions, and `sum`

is the sum of the values (usually `1.0`

).