diff --git a/src/index.ts b/src/index.ts
index 413625f..442ad4a 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -1 +1,5 @@
 export { getMatcher, getMatcherW } from "./primitive.ts";
+export {
+    getTaggedUnionMatcher,
+    getTaggedUnionMatcherW,
+} from "./tagged-union.ts";
diff --git a/src/tagged-union.test.ts b/src/tagged-union.test.ts
new file mode 100644
index 0000000..03b3cdf
--- /dev/null
+++ b/src/tagged-union.test.ts
@@ -0,0 +1,400 @@
+import { strict as assert } from "node:assert";
+import path from "node:path";
+import { test } from "node:test";
+
+import { expectTypeOf } from "expect-type";
+
+import {
+    type CompletionTarget,
+    LspSession,
+} from "#test-utils/lsp-completion.ts";
+
+import {
+    getTaggedUnionMatcher,
+    getTaggedUnionMatcherW,
+} from "./tagged-union.ts";
+
+interface Circle {
+    readonly kind: "circle";
+    readonly radius: number;
+}
+interface Square {
+    readonly kind: "square";
+    readonly side: number;
+}
+interface Triangle {
+    readonly kind: "triangle";
+    readonly base: number;
+    readonly height: number;
+}
+type Shape = Circle | Square | Triangle;
+
+// ============================================================================
+// API: getTaggedUnionMatcher — ✔️ Exhaustive / ✔️ ReturnsStrict
+// ============================================================================
+
+test("getTaggedUnionMatcher: exhaustive pattern infers one common return type", () => {
+    // Arrange
+    const factory = getTaggedUnionMatcher<Shape>()("kind");
+
+    // Act
+    const area = factory({
+        circle: (s) => {
+            // Each handler receives the member its tag selects, not the union.
+            expectTypeOf(s).toEqualTypeOf<Circle>();
+            assert.equal(s.kind, "circle");
+            return Math.PI * s.radius ** 2;
+        },
+        square: (s) => {
+            expectTypeOf(s).toEqualTypeOf<Square>();
+            assert.equal(s.kind, "square");
+            return s.side ** 2;
+        },
+        triangle: (s) => {
+            expectTypeOf(s).toEqualTypeOf<Triangle>();
+            assert.equal(s.kind, "triangle");
+            return (s.base * s.height) / 2;
+        },
+    });
+
+    // Assert
+    // ✔️ ReturnsStrict: R is the best common return type, not a widening union.
+    expectTypeOf(area).toEqualTypeOf<(shape: Shape) => number>();
+    assert.equal(area({ kind: "square", side: 2 }), 4);
+    assert.equal(area({ kind: "triangle", base: 2, height: 3 }), 3);
+});
+
+test("getTaggedUnionMatcher: dispatches on numeric tags", () => {
+    // Arrange
+    type Version =
+        | { readonly kind: 1; readonly a: number }
+        | {
+              readonly kind: 2;
+              readonly b: number;
+          };
+    const factory = getTaggedUnionMatcher<Version>()("kind");
+
+    // Act
+    const pick = factory({
+        1: (v) => {
+            expectTypeOf(v).toEqualTypeOf<{
+                readonly kind: 1;
+                readonly a: number;
+            }>();
+            assert.equal(v.kind, 1);
+            return v.a;
+        },
+        2: (v) => {
+            expectTypeOf(v).toEqualTypeOf<{
+                readonly kind: 2;
+                readonly b: number;
+            }>();
+            assert.equal(v.kind, 2);
+            return v.b;
+        },
+    });
+
+    // Assert
+    expectTypeOf(pick).toEqualTypeOf<(shape: Version) => number>();
+    assert.equal(pick({ kind: 1, a: 10 }), 10);
+    assert.equal(pick({ kind: 2, b: 20 }), 20);
+});
+
+// ============================================================================
+// API: getTaggedUnionMatcher — ❌ Exhaustive (fallback) / ✔️ ReturnsStrict
+// ============================================================================
+
+test("getTaggedUnionMatcher: a fallback receives the unhandled members", () => {
+    // Arrange
+    const factory = getTaggedUnionMatcher<Shape>()("kind");
+
+    // Act
+    const area = factory(
+        {
+            circle: (s) => {
+                expectTypeOf(s).toEqualTypeOf<Circle>();
+                assert.equal(s.kind, "circle");
+                return 1 as const;
+            },
+        },
+        (s) => {
+            // The fallback sees only the members `circle` did not handle.
+            expectTypeOf(s).toEqualTypeOf<Square | Triangle>();
+            assert.ok(s.kind === "square" || s.kind === "triangle");
+            return 2 as const;
+        },
+    );
+
+    // Assert
+    expectTypeOf(area).toEqualTypeOf<(shape: Shape) => 1 | 2>();
+    assert.equal(area({ kind: "circle", radius: 1 }), 1);
+    assert.equal(area({ kind: "square", side: 1 }), 2);
+    assert.equal(area({ kind: "triangle", base: 1, height: 1 }), 2);
+});
+
+test("getTaggedUnionMatcher: an open discriminant keeps the fallback open", () => {
+    // Arrange
+    interface Message {
+        readonly kind: string;
+        readonly text: string;
+    }
+    const factory = getTaggedUnionMatcher<Message>()("kind");
+
+    // Act
+    const matcher = factory({ info: () => 1 as const }, (s) => {
+        // The map's literal key does not close an open discriminant, so the
+        // remainder stays `Message` and the fallback is not redundant.
+        expectTypeOf(s).toEqualTypeOf<Message>();
+        assert.equal(typeof s.text, "string");
+        return 2 as const;
+    });
+
+    // Assert
+    expectTypeOf(matcher).toEqualTypeOf<(shape: Message) => 1 | 2>();
+    assert.equal(matcher({ kind: "info", text: "" }), 1);
+    assert.equal(matcher({ kind: "warn", text: "" }), 2);
+});
+
+// ============================================================================
+// API: getTaggedUnionMatcherW — ✔️ Exhaustive / ❌ ReturnsStrict
+// ============================================================================
+
+test("getTaggedUnionMatcherW: exhaustive pattern widens to the union of returns", () => {
+    // Arrange
+    const factory = getTaggedUnionMatcherW<Shape>()("kind");
+
+    // Act
+    const describe = factory({
+        circle: (s) => {
+            expectTypeOf(s).toEqualTypeOf<Circle>();
+            assert.equal(s.kind, "circle");
+            return "round" as const;
+        },
+        square: (s) => {
+            expectTypeOf(s).toEqualTypeOf<Square>();
+            assert.equal(s.kind, "square");
+            return 4 as const;
+        },
+        triangle: (s) => {
+            expectTypeOf(s).toEqualTypeOf<Triangle>();
+            assert.equal(s.kind, "triangle");
+            return true as const;
+        },
+    });
+
+    // Assert
+    // ❌ ReturnsStrict: mixed handler returns widen to their union.
+    expectTypeOf(describe).toEqualTypeOf<
+        (shape: Shape) => "round" | 4 | true
+    >();
+    assert.equal(describe({ kind: "circle", radius: 1 }), "round");
+    assert.equal(describe({ kind: "square", side: 1 }), 4);
+    assert.equal(describe({ kind: "triangle", base: 1, height: 1 }), true);
+});
+
+// ============================================================================
+// API: getTaggedUnionMatcherW — ❌ Exhaustive (fallback) / ❌ ReturnsStrict
+// ============================================================================
+
+test("getTaggedUnionMatcherW: a fallback widens gaps into the union", () => {
+    // Arrange
+    const factory = getTaggedUnionMatcherW<Shape>()("kind");
+
+    // Act
+    const matcher = factory({ circle: () => 1 as const }, (s) => {
+        expectTypeOf(s).toEqualTypeOf<Square | Triangle>();
+        // Returning the member verbatim lets the `Assert` block check the
+        // exact value dispatch passed.
+        return s;
+    });
+
+    // Assert
+    expectTypeOf(matcher).toEqualTypeOf<
+        (shape: Shape) => 1 | Square | Triangle
+    >();
+    assert.equal(matcher({ kind: "circle", radius: 1 }), 1);
+    assert.deepEqual(matcher({ kind: "square", side: 1 }), {
+        kind: "square",
+        side: 1,
+    });
+    assert.deepEqual(matcher({ kind: "triangle", base: 1, height: 1 }), {
+        kind: "triangle",
+        base: 1,
+        height: 1,
+    });
+});
+
+// ============================================================================
+// Factory contracts — calls that must not compile
+// ============================================================================
+
+test("getTaggedUnionMatcher factory rejects patterns outside its contract", () => {
+    // Arrange
+    const factory = getTaggedUnionMatcher<Shape>()("kind");
+
+    // Act / Assert — the calls below must not compile
+    factory({
+        circle: () => 1,
+        square: () => 2,
+        triangle: () => 3,
+        // @ts-expect-error `hexagon` is not a tag of Shape
+        hexagon: () => 4,
+    });
+    // @ts-expect-error a gap without a fallback is not exhaustive
+    factory({ circle: () => 1 });
+    // @ts-expect-error a `string` fallback does not fit the `number` handlers
+    factory({ circle: () => 1 }, () => "x");
+    // @ts-expect-error a fallback is redundant once the map covers the union
+    factory({ circle: () => 1, square: () => 2, triangle: () => 3 }, () => 0);
+});
+
+test("getTaggedUnionMatcher factory rejects a non-discriminant key", () => {
+    // Arrange
+    type Mixed =
+        | { readonly id: Date; readonly kind: "a" }
+        | { readonly id: Date; readonly kind: "b" };
+
+    // Act / Assert — the calls below must not compile
+    // @ts-expect-error `id` is a common key but its value is not a tag
+    getTaggedUnionMatcher<Mixed>()("id");
+    getTaggedUnionMatcher<Mixed>()("kind");
+});
+
+test("getTaggedUnionMatcherW factory rejects patterns outside its contract", () => {
+    // Arrange
+    const factory = getTaggedUnionMatcherW<Shape>()("kind");
+
+    // Act / Assert — the calls below must not compile
+    factory({
+        circle: () => 1 as const,
+        square: () => 2 as const,
+        triangle: () => 3 as const,
+        // @ts-expect-error `hexagon` is not a tag of Shape
+        hexagon: () => 4 as const,
+    });
+    // @ts-expect-error a gap without a fallback is not exhaustive
+    factory({ circle: () => 1 as const });
+    factory(
+        // @ts-expect-error a fallback is redundant once the map covers the union
+        {
+            circle: () => 1 as const,
+            square: () => 2 as const,
+            triangle: () => 3 as const,
+        },
+        () => 0,
+    );
+});
+
+// ============================================================================
+// Dispatch — runtime behavior
+// ============================================================================
+
+test("getTaggedUnionMatcher: an unhandled tag throws without a fallback", () => {
+    // Arrange — an open discriminant widens its handler map to an index
+    // signature, so the type system cannot prove the runtime map is exhaustive.
+    interface Message {
+        readonly kind: string;
+    }
+    const handlers: Record<string, (shape: Message) => number> = {
+        info: (shape) => {
+            // The full member reaches the handler, not its tag.
+            assert.equal(shape.kind, "info");
+            return 1;
+        },
+    };
+    const matcher = getTaggedUnionMatcher<Message>()("kind")(handlers);
+
+    // Act / Assert
+    assert.equal(matcher({ kind: "info" }), 1);
+    assert.throws(() => matcher({ kind: "warn" }), /Unhandled tag: warn/);
+});
+
+// ============================================================================
+// Autocomplete — the language server is the oracle, not the type system
+// ============================================================================
+
+const REPO_ROOT = path.resolve(import.meta.dirname, "..");
+const SHAPE_SOURCE = `type Shape = { kind: "a"; a: number } | { kind: "b"; b: number } | { kind: "c"; c: number };`;
+
+interface LabelsProbe {
+    readonly name: string;
+    readonly factory: "getTaggedUnionMatcher" | "getTaggedUnionMatcherW";
+    readonly body: string;
+    readonly tail?: string;
+}
+
+const labelsFor = ({
+    name,
+    factory,
+    body,
+    tail = "",
+}: LabelsProbe): Promise<readonly string[]> => {
+    const session = new LspSession(REPO_ROOT);
+    const target: CompletionTarget = {
+        file: `src/__autocomplete_${name}.ts`,
+        source: [
+            `import { ${factory} } from "./index.ts";`,
+            SHAPE_SOURCE,
+            `const m = ${factory}<Shape>()("kind")({`,
+            body,
+            `}${tail});`,
+            "",
+        ].join("\n"),
+    };
+    return session
+        .completionLabelsAt(target)
+        .then((result) => result.labels)
+        .finally(() => session.close());
+};
+
+test("autocomplete: a tagged-union pattern requires the tags", () => {
+    // Arrange
+    const name = "tagged_union_fresh";
+
+    // Act
+    const labels = labelsFor({
+        name,
+        factory: "getTaggedUnionMatcher",
+        body: "    /*COMPLETE*/",
+    });
+
+    // Assert
+    return labels.then((result) => {
+        assert.deepEqual([...result], ["a", "b", "c"]);
+    });
+});
+
+test("autocomplete: a handled tag drops out of the popup", () => {
+    // Arrange
+    const name = "tagged_union_after_key";
+
+    // Act
+    const labels = labelsFor({
+        name,
+        factory: "getTaggedUnionMatcher",
+        body: "    a: () => 1,\n    /*COMPLETE*/",
+    });
+
+    // Assert
+    return labels.then((result) => {
+        assert.deepEqual([...result], ["b", "c"]);
+    });
+});
+
+test("autocomplete: a fallback makes the remaining tags optional", () => {
+    // Arrange
+    const name = "tagged_union_with_fallback";
+
+    // Act
+    const labels = labelsFor({
+        name,
+        factory: "getTaggedUnionMatcher",
+        body: "    /*COMPLETE*/",
+        tail: ", () => 0",
+    });
+
+    // Assert
+    return labels.then((result) => {
+        assert.deepEqual([...result], ["a?", "b?", "c?"]);
+    });
+});
diff --git a/src/tagged-union.ts b/src/tagged-union.ts
new file mode 100644
index 0000000..978a588
--- /dev/null
+++ b/src/tagged-union.ts
@@ -0,0 +1,135 @@
+import type { Exact, ValueOf } from "type-fest";
+
+type UnaryFn<T, R> = (shape: T) => R;
+
+// A tagged union is discriminated by one property whose values are the tags.
+// Only `string` and `number` tags can key a handler map: `symbol` has no
+// literal syntax to write a handler under, and `bigint` is not a property key.
+type Tag = string | number;
+
+// The discriminant values of `T` under `K`. `Extract` keeps the finite literal
+// tags and leaves a widened `string`/`number` as itself, so an open universe
+// keeps an open fallback.
+type Tags<T extends object, K extends keyof T> = Extract<T[K], Tag>;
+
+// The keys of `T` that can act as a discriminant. `getTaggedUnionMatcher<T>()`
+// accepts only these, so the factory rejects a key whose values are not tags.
+type Discriminated<T extends object> = {
+    [K in keyof T]: T[K] extends Tag ? K : never;
+}[keyof T];
+
+// The member(s) of `T` tagged `V`. `Extract` distributes over the union, so a
+// duplicated tag maps to a union of members rather than silently dropping one.
+type MapTaggedUnion<T extends object, K extends keyof T> = {
+    [V in Tags<T, K>]: Extract<T, Record<K, V>>;
+};
+
+type Handlers<T extends object, K extends keyof T, R> = {
+    [V in Tags<T, K>]: UnaryFn<MapTaggedUnion<T, K>[V], R>;
+};
+
+// `Extract` drops optional handlers (`undefined`) so `PatternReturns` also works
+// when `P`'s constraint has optional keys.
+type PatternReturns<P> = ReturnType<
+    Extract<ValueOf<P>, (...args: never[]) => unknown>
+>;
+
+// The members `Handled` covers. Mapping over `Tags` keeps every index within
+// `MapTaggedUnion`'s keys, and the conditional drops a stray key outside `T` so
+// it cannot widen the remainder. The remainder is `Exclude<T, …>`, mirroring
+// the primitive matcher's `Exclude<T, PatternParam<keyof Handled>>`.
+type HandledMembers<T extends object, K extends keyof T, Handled> = {
+    [V in Tags<T, K>]: V extends keyof Handled
+        ? MapTaggedUnion<T, K>[V]
+        : never;
+}[Tags<T, K>];
+
+// The fallback is a *second argument*, not a property of the handler map, so
+// its parameter can be the remainder the map left open. See development/library.md.
+type Fallback<T extends object, K extends keyof T, Handled, R> = UnaryFn<
+    Exclude<T, HandledMembers<T, K, Handled>>,
+    R
+>;
+
+// A fallback is redundant once the handler map covers every tag of `T`. Folded
+// into `Handled`'s own (self-referential) constraint so it is checked *after*
+// inference; see the primitive matcher for why a conditional in the fallback's
+// parameter is evaluated too early.
+interface RedundantFallback {
+    readonly "every case is already handled, so the fallback is redundant": never;
+}
+type MustBePartial<T extends object, K extends keyof T, Handled> =
+    Tags<T, K> extends keyof Handled ? RedundantFallback : unknown;
+
+// TypeScript does not apply the excess-property check to a generic constraint,
+// so `Exact` restores it for the generic forms.
+
+// oxlint-disable typescript/unified-signatures
+// Strict returns: one common `R`. Overload order is load-bearing:
+//   #1 Handlers (first) -> the exhaustive form and the autocomplete popup
+//   #2 Fallback (last)  -> accepts a partial handler map plus a fallback
+interface TaggedUnionMatcherStrict<T extends object, K extends keyof T> {
+    <R>(handlers: Handlers<T, K, R>): UnaryFn<T, R>;
+    <
+        R,
+        Handled extends Exact<Partial<Handlers<T, K, R>>, Handled> &
+            MustBePartial<T, K, Handled>,
+    >(
+        handlers: Handled & Partial<Handlers<T, K, R>>,
+        fallback: Fallback<T, K, Handled, R>,
+    ): UnaryFn<T, R>;
+}
+// oxlint-enable typescript/unified-signatures
+
+// Widened returns: the union of every handler's return type. `P` is inferred
+// from the whole handler map, whose closed constraint supplies the
+// contextual/autocomplete type.
+// oxlint-disable typescript/unified-signatures
+interface TaggedUnionMatcherWidening<T extends object, K extends keyof T> {
+    <P extends Exact<Handlers<T, K, unknown>, P>>(
+        handlers: P,
+    ): UnaryFn<T, PatternReturns<P>>;
+    <
+        R,
+        Handled extends Exact<Partial<Handlers<T, K, unknown>>, Handled> &
+            MustBePartial<T, K, Handled>,
+    >(
+        handlers: Handled,
+        fallback: Fallback<T, K, Handled, R>,
+    ): UnaryFn<T, PatternReturns<Handled> | R>;
+}
+// oxlint-enable typescript/unified-signatures
+
+type HandlerMap = Record<string | number, UnaryFn<never, unknown> | undefined>;
+
+// `object` carries no index signature, so the read needs the assertion; the
+// factory admits only keys whose values are `string | number` tags, so the
+// result is narrowed to the map's key space.
+const tagAt = (shape: object, k: PropertyKey): string | number =>
+    // oxlint-disable-next-line typescript/no-unsafe-type-assertion
+    (shape as Record<PropertyKey, unknown>)[k] as string | number;
+
+const dispatch =
+    (k: PropertyKey) =>
+    (handlers: HandlerMap, fallback?: UnaryFn<never, unknown>) =>
+    (shape: object): unknown =>
+        (
+            handlers[tagAt(shape, k)] ??
+            fallback ??
+            (() => {
+                throw new Error(`Unhandled tag: ${String(tagAt(shape, k))}`);
+            })
+        )(
+            // oxlint-disable-next-line typescript/no-unsafe-type-assertion
+            shape as never,
+        );
+
+export const getTaggedUnionMatcher =
+    <T extends object>() =>
+    <K extends Discriminated<T>>(k: K): TaggedUnionMatcherStrict<T, K> =>
+        dispatch(k);
+
+export const getTaggedUnionMatcherW =
+    <T extends object>() =>
+    <K extends Discriminated<T>>(k: K): TaggedUnionMatcherWidening<T, K> =>
+        dispatch(k);