Programming Flix

Associated Effects

We have seen how associated types increase the flexibility of traits by allowing each instance to specify concrete types for the associated types. Associated effects work in the same manner, but concern effects.

We motivate the need for associated effects with a simple example.

We can define a trait for types that can be divded:

trait Dividable[t] {
    pub def div(x: t, y: t): t
}

and we can implement the trait for e.g. Float32 and Int32:

instance Dividable[Float32] {
    pub def div(x: Float32, y: Float32): Float32 = x / y
}

instance Dividable[Int32] {
    pub def div(x: Int32, y: Int32): Int32 = x / y
}

But what about division-by-zero? Assume we want to raise an exception and have it tracked by the type and effect system. We would like to write:

pub eff DivByZero {
    pub def throw(): Void
}

instance Dividable[Int32] {
    pub def div(x: Int32, y: Int32): Int32 \ DivByZero = 
        if (y == 0) DivByZero.throw() else x / y
}

But unfortunately this does not quite work:

❌ -- Type Error --------------------------------------------------

>> Mismatched signature 'div' required by 'Dividable'.

14 |     pub def div(x: Int32, y: Int32): Int32 \ DivByZero = 
                 ^^^
...

The problem, as the compiler explains, is that the definition of div in the trait Dividable is declared as pure. Hence we are not allowed to raise an exception. We could change the signature of Dividable.div, but that would be problematic for the Float32 instance, because division-by-zero returns NaN and does not raise an exception.

The solution is to use an associated effect: then the instance for Int32 can specify that a DivByZero exception may be raised whereas the instance for Float32 can be pure. We add an associated effect Aef to Dividable:

trait Dividable[t] {
    type Aef: Eff
    pub def div(x: t, y: t): t \ Dividable.Aef[t]
}

and we re-implement the instances for Float32 and Int32:

instance Dividable[Float32] {
    type Aef = { Pure } // No exception, div-by-zero yields NaN.
    pub def div(x: Float32, y: Float32): Float32 = x / y
}

instance Dividable[Int32] {
    type Aef = { DivByZero }
    pub def div(x: Int32, y: Int32): Int32 \ DivByZero = 
        if (y == 0) DivByZero.throw() else x / y
}

Associated Effects and Regions

We often want to use associated effects in combination with regions.

Assume we have the ForEach trait from the before:

trait ForEach[t] {
    type Elm
    pub def forEach(f: ForEach.Elm[t] -> Unit \ ef, x: t): Unit \ ef
}

As we have seen, we can implement it for e.g. List[t] but also Map[k, v]. But what if we wanted to implement it for e.g. MutList[t, r] or MutSet[t, r]. We can try:

instance ForEach[MutList[t, r]] {
    type Elm = t
    pub def forEach(f: t -> Unit \ ef, x: MutList[t, r]): Unit \ ef = 
        MutList.forEach(f, x)
}

But Flix reports:

❌ -- Type Error -------------------------------------------------- 

>> Unable to unify the effect formulas: 'ef' and 'ef + r'.

9 |         MutList.forEach(f, x)
            ^^^^^^^^^^^^^^^^^^^^^
            mismatched effect formulas.

The problem is that MutList.forEach has an effect in the region r, but the signature of forEach in the trait only permits the ef effect from the function f.

We can solve the problem by extending the ForEach trait with an associated effect:

trait ForEach[t] {
    type Elm
    type Aef: Eff
    pub def forEach(f: ForEach.Elm[t] -> Unit \ ef, x: t): Unit \ ef + ForEach.Aef[t]
}

We must specify that Aef is an effect with the kind annotation Aef: Eff. If we don't specify the kind then it defaults to Type which is not what we want here.

With the updated ForEach trait, we can implement it for both List[t] and MutList[t]:

instance ForEach[List[t]] {
    type Elm = t
    type Aef = { Pure }
    pub def forEach(f: t -> Unit \ ef, x: List[t]): Unit \ ef = List.forEach(f, x)
}

and

instance ForEach[MutList[t, r]] {
    type Elm = t
    type Aef = { r }
    pub def forEach(f: t -> Unit \ ef, x: MutList[t, r]): Unit \ ef + r = 
        MutList.forEach(f, x)
}

Notice how the implementation for List[t] specifies that the associated effect is pure, whereas the implementation for MutList[t, r] specifies that there is a heap effect in region r.