# Special forms that provide function references (not expressions)

## Function definition (fcndef)¶

Functions may be defined and given names in the "fcns" top-level field and they may be defined without names within the argument list of some library functions and special forms. Technically, a function definition is not an expression because it does not return an Avro-typed value. A function cannot be defined and assigned to a variable, but it can be defined and passed to a generic algorithm that takes a callback.

The structure of a function definition is

 1 2 3 {"params": [{ARG1: TYPE1}, {ARG2: TYPE2}, ...], "ret": RETURN-TYPE, "do": EXPRESSION-OR-EXPRESSIONS} 

The "params" can have any number of parameters, including zero. Each ARG is a string defining a variable that can be used in the "do" expressions. The RETURN-TYPE must be an Avro type, though "null" can be used if the function doesn’t return anything useful. EXPRESSION-OR-EXPRESSIONS may be a single expression or a JSON array of them.

### Example¶

The following computes an absolute difference:

 1 2 3 {"params": [{"x": "double"}, {"y": "double"}], "ret": "double", "do": {"m.abs": {"-": ["x", "y"]}}} 
which could be passed as an argument to the a.zipmap function, for instance.

When used to create anonymous functions, those functions can access but not modify variables in the containing scope (captured by value).

## Function reference (fcnref)¶

Named user-defined functions and library functions can be referenced in the argument list of some library functions and special forms. Technically, a function reference is not an expression because it does not return an Avro-typed value. A function cannot be assigned to a variable, but it can be passed to a generic algorithm that takes a callback.

The structure of a function reference is

{"fcn": FUNCTION-NAME}

where FUNCTION-NAME is a string naming the function. User-defined functions always start with "u." (even though they are declared in the "fcns" section without the "u.").

Library functions can only be referenced if they have exactly one signature and no wildcards. For instance, s.len can be referenced because its only signature takes one "string" argument, but a.len cannot because its signature takes an array of any A (array of strings, array of integers, array of records, etc.). A function reference must resolve the function’s signature to a fixed sequence of Avro types.

### Example¶

The following references "s.len", which returns the length of a string.

{"fcn": "s.len"}

Below is an example of wrapping "a.len" with a user-defined function so that it returns the length of an array of numbers.

 1 2 3 {"params": ["x": {"type": "array", "items": "double"}] "ret": "int", "do": {"a.len": "x"}} 

The wrapped form can be used anywhere that a direct function reference can be used.

## Function reference with partial application (fcnref-fill)¶

Function references can also reduce the number of arguments in the function by partially applying some of the arguments.

The structure of a partially applied function reference is

{"fcn": FUNCTION-NAME, "fill": {ARG1: EXPR1, ARG2: EXPR2, ...}}

where FUNCTION-NAME is a string naming the function and the ARG keys are a subset of the function's parameter names. The expressions EXPR provide values.

### Example¶

To turn the two-argument m.special.nChooseK function into a one-argument function reference that computes 100 choose k, we can reference it like this:

{"fcn": "m.special.nChooseK", "fill": {"n": 100}}