Subset pattern

A typed pattern can name more than one member. The arm box: Square | Rectangle => matches when the active member is either of the two, and box is then a smaller sum: still one of several types, but only the ones the arm let through.

That is useful when some members are handled the same way. A circle has no corners, while a square and a rectangle both have four — so counting corners needs two arms, not three. And when the shared members still need work of their own, the smaller sum can be handed on whole to a function that takes exactly those members.

The shapes

Each shape is a struct of its own, and Shape is the sum of all three:

struct Circle {
    radius: float64;
}

struct Square {
    side: float64;
}

struct Rectangle {
    width: float64;
    height: float64;
}

type Shape = Circle | Square | Rectangle;

Several members in one arm

Write the members after the colon, joined by | just as in the type itself:

func Corners(shape: Shape) -> int32 {
    return match shape {
        _: Circle => 0,
        _: Square | Rectangle => 4
    };
}

A subset needs no binding either: _: Square | Rectangle only asks the question. The match is still exhaustive — between them, the two arms cover all three members.

The binding is a smaller sum

With a name instead of _, the arm binds what it matched. Here box has the type Square | Rectangle:

func Describe(shape: Shape) {
    match shape {
        c: Circle => PrintLine("circle, radius {}, {} corners", c.radius, Corners(shape)),
        box: Square | Rectangle => PrintLine("box, area {}, {} corners", BoxArea(box),
            Corners(shape))
    }
}

box is not a square, and it is not a rectangle — it is whichever of the two shape held, and it remembers which. That is exactly what BoxArea takes, so box is passed on whole:

func BoxArea(box: Square | Rectangle) -> float64 {
    return match box {
        s: Square => s.side * s.side,
        r: Rectangle => r.width * r.height
    };
}

BoxArea only ever sees boxes, so it matches two members and no more. It never has to say what to do with a circle, because a circle cannot reach it.

flowchart LR
    s["shape: Shape"] --> d{"Describe"}
    d -- "c: Circle" --> c["radius, 0 corners"]
    d -- "box: Square | Rectangle" --> b{"BoxArea(box)"}
    b -- "s: Square" --> sq["side * side"]
    b -- "r: Rectangle" --> re["width * height"]

The first matching arm wins

Arms are tried from the top, and the first one whose types include the active member runs. Two subsets may share a member — with round: Circle | Square => above box: Square | Rectangle =>, a square goes to the first arm and a rectangle to the second.

What the compiler refuses is an arm that can never run. Once box: Square | Rectangle has taken every square, a later s: Square => would be dead code, and it is an error rather than a silent leftover.

The program

The whole lesson is one package in the Examples repository. Its comments explain every step.

// A typed pattern can name more than one member. The arm `box: Square | Rectangle =>` matches
// when the active member is either of the two, and `box` is then a *smaller sum*: it is still
// one of several types, but only the ones the arm let through.
//
// That is useful when some members are handled the same way. A circle has no corners and a
// square and a rectangle both have four, so the corner count needs two arms, not three. And when
// the shared members need their own work, the smaller sum can be handed on whole to a function
// that takes exactly those members, and matched again there.
//
// An arm after a subset may not repeat a member the subset already took. Add `s: Square =>`
// after the `box` arm in `Describe` and the compiler refuses the arm that can never run:
//     error: match arm is unreachable because earlier arms already match every value it matches
import Io::PrintLine;

struct Circle {
    radius: float64;
}

struct Square {
    side: float64;
}

struct Rectangle {
    width: float64;
    height: float64;
}

type Shape = Circle | Square | Rectangle;

// A subset needs no binding either: `_: Square | Rectangle` only asks the question.
func Corners(shape: Shape) -> int32 {
    return match shape {
        _: Circle => 0,
        _: Square | Rectangle => 4
    };
}

// This function only ever sees boxes, so it matches two members and no more.
func BoxArea(box: Square | Rectangle) -> float64 {
    return match box {
        s: Square => s.side * s.side,
        r: Rectangle => r.width * r.height
    };
}

func Describe(shape: Shape) {
    match shape {
        c: Circle => PrintLine("circle, radius {}, {} corners", c.radius, Corners(shape)),
        box: Square | Rectangle => PrintLine("box, area {}, {} corners", BoxArea(box),
            Corners(shape))
    }
}

func Main() -> int {
    let wheel: Shape = Circle { radius: 1.5 };
    let tile: Shape = Square { side: 2.0 };
    let door: Shape = Rectangle { width: 1.0, height: 2.5 };

    Describe(wheel);
    Describe(tile);
    Describe(door);
    return 0;
}

Run it

cd Examples/SumTypes/SubsetPattern
rux run

circle, radius 1.5, 0 corners
box, area 4.0, 4 corners
box, area 2.5, 4 corners

Common mistakes

Try it yourself

1. Add struct Triangle { base: float64; height: float64; } to Shape. Which matches does the compiler now reject, and what does each one need?
2. Write func IsRound(shape: Shape) -> bool with exactly two arms.
3. Move s: Square => above the box arm in Describe, so squares print differently from rectangles. Which members can still reach box now?

Learn more

• The is operator — ask which member a sum holds without unpacking it
• Sum widening — passing a smaller sum where a larger one is expected
• match in the Rux Reference