Void Functions
Stan does not technically support functions that do not return values. It does support two types of statements, one printing and one for rejecting outputs.
Although print and reject appear to have the syntax of functions, they are actually special kinds of statements with slightly different form and behavior than other functions. First, they are the constructs that allow a variable number of arguments. Second, they are the the only constructs to accept string literals (e.g., "hello world") as arguments. Third, they have no effect on the log density function and operate solely through side effects.
The special keyword void is used for their return type because they behave like variadic functions with void return type, even though they are special kinds of statements.
Print statement
Printing has no effect on the model’s log probability function. Its sole purpose is the side effect (i.e., an effect not represented in a return value) of arguments being printed to whatever the standard output stream is connected to (e.g., the terminal in command-line Stan or the R console in RStan).
void print(T1 x1,..., TN xN)
Print the values denoted by the arguments x1 through xN on the output message stream. There are no spaces between items in the print, but a line feed (LF; Unicode U+000A; C++ literal '\n') is inserted at the end of the printed line. The types T1 through TN can be any of Stan’s built-in numerical types or double quoted strings of characters (bytes).
Reject statement
The reject statement has the same syntax as the print statement, accepting an arbitrary number of arguments of any type (including string literals). The effect of executing a reject statement is to throw an exception internally that terminates the current iteration with a rejection (the behavior of which will depend on the algorithmic context in which it occurs).
void reject(T1 x1,..., TN xN)
Reject the current iteration and print the values denoted by the arguments x1 through xN on the output message stream. There are no spaces between items in the print, but a line feed (LF; Unicode U+000A; C++ literal '\n') is inserted at the end of the printed line. The types T1 through TN can be any of Stan’s built-in numerical types or double quoted strings of characters (bytes).