Programming Flix

Monadic For-Yield

Flix supports a monadic forM-yield construct similar to Scala's for-comprehensions and Haskell's do notation. The forM construct is syntactic sugar for uses of point and flatMap (which are provided by the Monad trait). The forM construct also supports a guard-expression that uses empty (which is provided by the MonadZero trait).

For example, the monadic forM expression:

let l1 = 1 :: 2 :: Nil;
let l2 = 1 :: 2 :: Nil;
forM (x <- l1; y <- l2)
    yield (x, y)

evaluates to the list:

(1, 1) :: (1, 2) :: (2, 1) :: (2, 2) :: Nil

Using Guard Expressions

We can use guard expressions in forM expressions. For example, the program:

let l1 = 1 :: 2 :: Nil;
let l2 = 1 :: 2 :: Nil;
forM (x <- l1; y <- l2; if x < y)
    yield (x, y)

evaluates to the list:

(1, 2) :: Nil

Working with Options and Results

We can also use forM to work with the Option data type. For example:

def divide(x: Int32, y: Int32): Option[Int32] = 
    if (y == 0) None else Some(x / y)

def f(): Option[Int32] = 
    forM (
        x <- divide(5, 2);
        y <- divide(x, 8);
        z <- divide(9, y)
    ) yield x + y + z

Here the function f returns None since x = 5 / 2 = 2 and 2 / 8 = 0 hence the last division fails.

Similarly, we can use forM to work with the Result[e, t] data type. For example:

def main(): Result[String, Unit] \ IO = 
    println("Please enter your first name, last name, and age:");
    forM (
        fstName <- Console.readLine();
        lstName <- Console.readLine();
        ageLine <- Console.readLine();
        ageNum  <- Int32.parse(10, ageLine)
    ) yield {
        println("Hello ${lstName}, ${fstName}.");
        println("You are ${ageNum} years old!")
    }

Here main prompts the user to enter their first name, last name, and age. Each call to Console.readLine returns a Result[String, String] value which is either an error or the input string. Thus the local variables fstName, lstName, and ageLine are Strings. We parse ageLine into an Int32 using Int32.parse, which returns a Result[String, Int32] value. If every operation is successful then we print a greeting and return Ok(()) (i.e., Ok of Unit). Otherwise, we return an Err(msg) value.

Working with Other Monads

We can use forM with other types of Monads, including Chain and Nels (non-empty lists). For example, we can write:

let l1 = Nel(1, 2 :: Nil);
let l2 = Nel(1, 2 :: Nil);
forM (x <- l1; y <- l2)
    yield (x, y)

which evaluates to the non-empty list:

Nel((1, 1), (1, 2) :: (2, 1) :: (2, 2) :: Nil)

Note: We cannot use an if-guard with non-empty lists because such an if-guard requires an instance of the MonadZero trait which is not implemented by non-empty list (since such a list cannot be empty).

Desugaring

The forM expression is syntactic sugar for uses of Monad.flatMap, Applicative.point, and MonadZero.empty.

For example, the expression:

let l1 = 1 :: 2 :: Nil;
let l2 = 1 :: 2 :: Nil;
forM (x <- l1; y <- l2; if x < y)
    yield (x, y)

is de-sugared to:

Monad.flatMap(x -> 
    Monad.flatMap(y -> 
        if (x < y)
            Applicative.point((x, y))
        else 
            MonadZero.empty(), 
    l2), 
l1);