Discriminated union pattern matching by function call

Question

My question is inspired by this one: link

Here is a code:

    type A = 
        | X of int * int
        | Y of string

    let f (A.X(a, b)) = a + b 

It works, but with a warning:

Makes sense; I have no match for Y.

But if I add a line

    let f (A.Y(s)) = 10

Then I get an error:

Is there a nice way to fix it and still use pattern matching in function parameters? If not, then why did they create such strange syntax, which always leads to a warning?

Answer 1

Some pattern matches can be complete and might be useful in function parameters, e.g. this definition of fst is pattern matching a tuple and is complete for all 2 tuples.

let fst (a,_) = a

Some other examples:

type Container = Container of string
let unwrap (Container(v)) = v

type Person = { Name:string; Age:int }
let getName {Name=name} = name

Answer 2

As other answers say, the best way seems to be using pattern matching with function or match keywords.
However, native pattern matching of F# is pretty much powerful thing by itself. Consider the code below, however I'm not advocating to use it in a real-world project. I would rather use it as an exercise for better understanding of the language.

let f ((A.X(a, b), _ ) | (A.Y(_), (a, b))) = a + b

// usage
let x1 = f(A.X(10, 42), (100, 1)) // x1 = 52
let x2 = f(A.Y("foo"),  (100, 1)) // x2 = 101

What's going on here?

• The body of the function computes a sum of two values in a tuple;
• A tuple is either extracted from A.X or provided as a separate argument;
• The function takes an extra argument which can be considered a fallback value. Namely, when the first argument is A.Y(string), we still need to sum something.
• The fallback value is ignored if the first argument has some meaning value of A.X(int, int).

Yet again, don't use it blindly in real-world projects since it doesn't seem to be readable.

Further reading: A similar approach for list processing.

Answer 3

You need to pattern match on the argument:

let f = function
| X(a, b) -> a + b
| Y(_) -> 10

When you define

let f (A.X(a, b)) = a + b 

f has type A -> int, not A.X -> int. It is not defined for values which are instances of A.Y, so you get the incomplete match warning.

Your second definition of f also has type A -> int and so is a duplicate definition of the first, hence the error. If you want to write a total function over some union type you should use pattern matching with function or match.

EDIT: In response to the comment, if you have multiple arguments you want to match at the same time, you can use match e.g.:

let f a1 a2 =
    match (a1, a2) with
    | (X(a, b), X(a', b')) -> a + b
    | (X(a, b), Y(s)) -> a + 10
    | (Y(s), X(a, b)) -> 10
    | (Y(s), Y(s')) -> 20