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## 9.5 Function bodies

The body of a function is between an open curly brace ({) and close curly brace (}). The body may contain local variable declarations at the top of the function body’s block and these scope the same way as local variables used in any other statement block.

The only restrictions on statements in function bodies are external, and determine whether the log probability accumulator or random number generators are available; see the rest of this section for details.

### Random number generating functions

Functions that call random number generating functions in their bodies must have a name that ends in _rng; attempts to use random-number generators in other functions lead to a compile-time error.

Like other random number generating functions, user-defined functions with names that end in _rng may be used only in the generated quantities block and transformed data block, or within the bodies of user-defined functions ending in _rng. An attempt to use such a function elsewhere results in a compile-time error.

### Log probability access in functions

Functions that include sampling statements or log probability increment statements must have a name that ends in _lp. Attempts to use sampling statements or increment log probability statements in other functions lead to a compile-time error.

Like the target log density increment statement and sampling statements, user-defined functions with names that end in _lp may only be used in blocks where the log probability accumulator is accessible, namely the transformed parameters and model blocks. An attempt to use such a function elsewhere results in a compile-time error.

### Defining probability functions for sampling statements

Functions whose names end in _lpdf and _lpmf (density and mass functions) can be used as probability functions in sampling statements. As with the built-in functions, the first argument will appear on the left of the sampling statement operator (~) in the sampling statement and the other arguments follow. For example, suppose a function returning the log of the density of y given parameter theta allows the use of the sampling statement is defined as follows.

real foo_lpdf(real y, vector theta) { ... }

Note that for function definitions, the comma is used rather than the vertical bar.

For every custom _lpdf and _lpmf defined there is a corresponding _lupdf and _lupmf defined automatically. The _lupdf and _lupmf versions of the functions cannot be defined directly (to do so will produce an error). The difference in the _lpdf and _lpmf and the corresponding _lupdf and _lupmf functions is that if any other unnormalized density functions are used inside the user-defined function, the _lpdf and _lpmf forms of the user-defined function will change these densities to be normalized. The _lupdf and _lupmf forms of the user-defined functions will instead allow other unnormalized density functions to drop additive constants.

The sampling shorthand

z ~ foo(phi);

will have the same effect as incrementing the target with the log of the unnormalized density:

target += foo_lupdf(z | phi);

Other _lupdf and _lupmf functions used in the definition of foo_lpdf will drop additive constants when foo_lupdf is called and will not drop additive constants when foo_lpdf is called.

If there are _lupdf and _lupmf functions used inside the following call to foo_lpdf, they will be forced to normalize (return the equivalent of their _lpdf and _lpmf forms):

target += foo_lpdf(z | phi);

If there are no _lupdf or _lupmf functions used in the definition of foo_lpdf, then there will be no difference between a foo_lpdf or foo_lupdf call.

The unnormalized _lupdf and _lupmf functions can only be used in the model block or in user-defined probability functions (those ending in _lpdf or _lpmf).

The same syntax and shorthand that works for _lpdf also works for log probability mass functions with suffixes _lpmf.

A function that is going to be accessed as distributions must return the log of the density or mass function it defines.