# function

CQL has a primitive function facility. A function filter has the following elements in order:- The keyword
`function`

- A variable name, the name of the function
- An
*argument list*, which is a sequence of variable names enclosed in parentheses. These variables are called the*formal parameters*of the function - A compound filter, called the
*body*of the function.

Examples of functions:

function mate_or_stalemate() { mate or stalemate }function PurePieces(z) { z&[RBNQrbnq] }

function double(x) { 2*x }

function sets_smaller(x y){ #x<#y }

## Function calling

A function is called by putting its *actual arguments* in parentheses after the name of the function. The number of arguments must equal the number of formal parameters of the function. The *i'th* formal parameter is said to *correspond* to the *i'th* actual argument (and vice versa).

For example, if the above functions are defined, then the following code matches a position that is mate or stalemate:

mate_or_stalemate()

The value of a function call is whatever the value of its body is when invoked with the arguments:

comment("The number of squares on a chessboard is: " double(#a-d1-8));

The code below matches a position in which there are more rooks than queens

sets_smaller ([Qq] [Rr])In the above call, the formal parameters of

`double`

are `x`

and `y`

. The corresponding actual arguments are `[Qq]`

and `[Rr]`

respectively.
Invocation of a function is performed as follows:

- For each actual argument
*z*of the function call:- If
*z*is a variable then the*corresponding variable*of*z*is*z* - Otherwise,
*z*is assigned to a new, unique variable*Z*which is called the*corresponding variable*for*z*.

- If
- The body of the function is modified as follows: each occurrence of a formal parameter
*w*in the body corresponding to an argument*z*of the function call is renamed to be the corresponding variable for*z* - The modified body of the function is evaluated in place of the function call

`sets_smaller([Qq] [Rr])`

, the modified body might look like this:
{CQL_var_1=[Qq] CQL_var_2=[Rr] {#CQL_var_1<#CQL_var_2}}

Note that as a consequence of these rules:

- If a formal parameter is assigned a value in the function body, and if the corresponding actual argument is a variable, then the value of the actual argument will be changed.
- If an actual argument is a piece variable, and if the current position in the function body is modified, the value of the corresponding formal parameter will reflect the value of the actual argument piece variable in that current position. However, if the actual argument is a set variable, the value of its corresponding formal parameter will not vary according to the current position.
- Direct or indirect function recursion is not allowed
- There is no time penalty associated with function invocation.

## Using transforms with functions

A transform operator, like`flipcolor`

, does not affect the function definition. However, it does modify the function *call*. That's because function calls textually replace the call with the function body, and that replacement can be transformed like any other CQL code.

# Examples

The`function`

filter is used in averagedistance.cql, idealmate.cql, modelmate.cql, parallelpaths.cql, and puremate.cql.