Sum Type¶

A sum type is a type whose value is exactly one of a fixed set of cases, where each case may carry a different payload. It is the OR half of algebraic data types, as distinct from product types which represent AND.

In Haskell: data Shape = Circle Double | Rectangle Double Double. In Rust: enum Shape { Circle(f64), Rectangle(f64, f64) }. In each language the case name acts as a tag, and the type system tracks which case is active, enabling exhaustive, type-safe dispatch.

PHP union types, such as int|string, share the OR semantics but are not true sum types: they carry no tag, they do not associate different payloads with different arms, and match cannot decompose them structurally. PHP enums without backing are the closest PHP equivalent for pure tag-only sum types, but they cannot attach variant-specific associated data.

The standard PHP workaround is a sealed class hierarchy: an abstract base class with one concrete subclass per variant, each holding its own fields. instanceof checks and match on class strings approximate discriminated dispatch, but the compiler does not enforce exhaustiveness.

PHP does not suport sum types.

<?php

    // PHP workaround: sealed class hierarchy as a sum type approximation
    abstract class Shape {}

    final class Circle extends Shape {
        public function __construct(public readonly float $radius) {}
    }

    final class Rectangle extends Shape {
        public function __construct(
            public readonly float $width,
            public readonly float $height,
        ) {}
    }

    function area(Shape $shape): float {
        return match (true) {
            $shape instanceof Circle    => M_PI * $shape->radius ** 2,
            $shape instanceof Rectangle => $shape->width * $shape->height,
            // PHP will not warn if a new subclass is added and not handled here
        };
    }

?>

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Sum Type¶

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