# Functions¶

Functions encapsulate calculations.

## Type¶

The type of a function with a parameter type D returning a value type C is written

D -> C


## Definition by Expression¶

A function can be defined by an expression:

fun square (x:int) : int => x * x;


or without the return type:

fun square (x:int) => x * x;


in which case it is deduced.

## Definition by Statements¶

More complex functions can be defined by statements.

fun addUp(xs:int^4) : int = {
var sum = 0;
for x in xs do
sum = sum + x;
done
return sum;
}


The return type can be elided:

fun addUp(xs:int^4) = {
var sum = 0;
for x in xs do
sum = sum + x;
done
return sum;
}


## No side effects¶

The effect of a function must be entirely captured in its returned value; that is, it may not have any side effects. This asumption is currently not checked, so you could write code like this:

var mutMe = 0;

fun addUp(xs:int^4) : int = {
var sum = 0;
for x in xs do
sum = sum + x;
done
return sum;
}


However, this kind of usage may be useful from time to time, for example for debugging.

The lack of side effects in a function are used in optimizations, and the optimizations may have an effect on program behavior. For example, the following toy program takes the second projection (. 1) on a tuple involving three function calls. Since functions are assumed to have no side effects, the other function calls (f and h) are erased as their return values are never used.

fun f(x:int) = {
println "hi from f!";
return 2*x;
}
fun g(x:int) = {
println "hi from g!";
return 3*x;
}
fun h(x:int) = {
println "hi from h!";
return 4*x;
}

val res =  (f 5, g 5, h 5) . 1;
println res;


The output of the program is just:

hi from g!
15


## Purity¶

Functions can further be annotated to be pure or impure, but at the moment, the semantics of these are not defined and are not checked:

pure fun addUp(xs:int^4) : int = {
// ...
}

// or

impure fun addUp(xs:int^4) : int = {
// ...
}