diff --git a/CHANGELOG.md b/CHANGELOG.md
index 69c048bcf7..728f2a313c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -33,7 +33,9 @@ Items that are related, such as breaking changes, new features, or changes to ex
 
 - [@siteimprove/alfa-json](packages/alfa-json): `JSON.parse()` and `JSON.stringify()` are now available.
 
-- [@siteimprove/alfa-trampoline](packages-alfa-trampoline): `Trampoline#tee()` and `Trampoline.empty()` are now available.
+- [@siteimprove/alfa-trampoline](packages/alfa-trampoline): `Trampoline#tee()` and `Trampoline.empty()` are now available.
+
+- [@siteimprove/alfa-either](packages/alfa-either): `Either<L, R>` now provides an implementation of `Hashable`.
 
 ### Fixed
 
diff --git a/packages/alfa-either/package.json b/packages/alfa-either/package.json
index f31eeb69e7..e3f6d9f12a 100644
--- a/packages/alfa-either/package.json
+++ b/packages/alfa-either/package.json
@@ -21,6 +21,7 @@
     "@siteimprove/alfa-equatable": "^0.10.0",
     "@siteimprove/alfa-foldable": "^0.10.0",
     "@siteimprove/alfa-functor": "^0.10.0",
+    "@siteimprove/alfa-hash": "^0.10.0",
     "@siteimprove/alfa-json": "^0.10.0",
     "@siteimprove/alfa-mapper": "^0.10.0",
     "@siteimprove/alfa-monad": "^0.10.0",
diff --git a/packages/alfa-either/src/either.ts b/packages/alfa-either/src/either.ts
index 3629890336..0f2b291084 100644
--- a/packages/alfa-either/src/either.ts
+++ b/packages/alfa-either/src/either.ts
@@ -1,6 +1,7 @@
 import { Equatable } from "@siteimprove/alfa-equatable";
 import { Foldable } from "@siteimprove/alfa-foldable";
 import { Functor } from "@siteimprove/alfa-functor";
+import { Hashable } from "@siteimprove/alfa-hash";
 import { Serializable } from "@siteimprove/alfa-json";
 import { Mapper } from "@siteimprove/alfa-mapper";
 import { Monad } from "@siteimprove/alfa-monad";
@@ -16,6 +17,7 @@ export interface Either<L, R = L>
     Foldable<L | R>,
     Iterable<L | R>,
     Equatable,
+    Hashable,
     Serializable<Either.JSON<L, R>> {
   isLeft(): this is Left<L>;
   isRight(): this is Right<R>;
@@ -40,11 +42,11 @@ export namespace Either {
     return Left.isLeft(value) || Right.isRight(value);
   }
 
-  export function left<L>(value: L): Either<L, never> {
+  export function left<L, R = never>(value: L): Either<L, R> {
     return Left.of(value);
   }
 
-  export function right<R>(value: R): Either<never, R> {
+  export function right<R, L = never>(value: R): Either<L, R> {
     return Right.of(value);
   }
 }
diff --git a/packages/alfa-either/src/left.ts b/packages/alfa-either/src/left.ts
index 919f43ccfe..b58849d1fa 100644
--- a/packages/alfa-either/src/left.ts
+++ b/packages/alfa-either/src/left.ts
@@ -1,4 +1,5 @@
 import { Equatable } from "@siteimprove/alfa-equatable";
+import { Hash, Hashable } from "@siteimprove/alfa-hash";
 import { Serializable } from "@siteimprove/alfa-json";
 import { Mapper } from "@siteimprove/alfa-mapper";
 import { None, Option } from "@siteimprove/alfa-option";
@@ -56,10 +57,19 @@ export class Left<L> implements Either<L, never> {
     return reducer(accumulator, this._value);
   }
 
-  public equals(value: unknown): value is this {
+  public equals<L>(value: Left<L>): boolean;
+
+  public equals(value: unknown): value is this;
+
+  public equals(value: unknown): boolean {
     return value instanceof Left && Equatable.equals(value._value, this._value);
   }
 
+  public hash(hash: Hash): void {
+    Hash.writeBoolean(hash, false);
+    Hashable.hash(hash, this._value);
+  }
+
   public *[Symbol.iterator](): Iterator<L> {
     yield this._value;
   }
diff --git a/packages/alfa-either/src/right.ts b/packages/alfa-either/src/right.ts
index 3158ad65c6..7a599c4233 100644
--- a/packages/alfa-either/src/right.ts
+++ b/packages/alfa-either/src/right.ts
@@ -1,4 +1,5 @@
 import { Equatable } from "@siteimprove/alfa-equatable";
+import { Hash, Hashable } from "@siteimprove/alfa-hash";
 import { Serializable } from "@siteimprove/alfa-json";
 import { Mapper } from "@siteimprove/alfa-mapper";
 import { None, Option } from "@siteimprove/alfa-option";
@@ -56,12 +57,21 @@ export class Right<R> implements Either<never, R> {
     return reducer(accumulator, this._value);
   }
 
-  public equals(value: unknown): value is this {
+  public equals<R>(value: Right<R>): boolean;
+
+  public equals(value: unknown): value is this;
+
+  public equals(value: unknown): boolean {
     return (
       value instanceof Right && Equatable.equals(value._value, this._value)
     );
   }
 
+  public hash(hash: Hash): void {
+    Hash.writeBoolean(hash, true);
+    Hashable.hash(hash, this._value);
+  }
+
   public *[Symbol.iterator](): Iterator<R> {
     yield this._value;
   }
diff --git a/packages/alfa-either/tsconfig.json b/packages/alfa-either/tsconfig.json
index 01a2ee637e..3bc864162e 100644
--- a/packages/alfa-either/tsconfig.json
+++ b/packages/alfa-either/tsconfig.json
@@ -12,6 +12,9 @@
     {
       "path": "../alfa-functor"
     },
+    {
+      "path": "../alfa-hash"
+    },
     {
       "path": "../alfa-json"
     },
diff --git a/packages/alfa-selective/package.json b/packages/alfa-selective/package.json
new file mode 100644
index 0000000000..f43b9f6fcf
--- /dev/null
+++ b/packages/alfa-selective/package.json
@@ -0,0 +1,37 @@
+{
+  "$schema": "http://json.schemastore.org/package",
+  "name": "@siteimprove/alfa-selective",
+  "homepage": "https://siteimprove.com",
+  "version": "0.10.0",
+  "license": "MIT",
+  "description": "An implementation of a selective functor for modelling conditional function application",
+  "repository": {
+    "type": "git",
+    "url": "https://github.com/siteimprove/alfa.git",
+    "directory": "packages/alfa-selective"
+  },
+  "bugs": "https://github.com/siteimprove/alfa/issues",
+  "main": "src/index.js",
+  "types": "src/index.d.ts",
+  "files": [
+    "src/**/*.js",
+    "src/**/*.d.ts"
+  ],
+  "dependencies": {
+    "@siteimprove/alfa-either": "^0.10.0",
+    "@siteimprove/alfa-equatable": "^0.10.0",
+    "@siteimprove/alfa-functor": "^0.10.0",
+    "@siteimprove/alfa-hash": "^0.10.0",
+    "@siteimprove/alfa-json": "^0.10.0",
+    "@siteimprove/alfa-mapper": "^0.10.0",
+    "@siteimprove/alfa-predicate": "^0.10.0",
+    "@siteimprove/alfa-refinement": "^0.10.0"
+  },
+  "devDependencies": {
+    "@siteimprove/alfa-test": "^0.10.0"
+  },
+  "publishConfig": {
+    "access": "public",
+    "registry": "https://npm.pkg.github.com/"
+  }
+}
diff --git a/packages/alfa-selective/src/index.ts b/packages/alfa-selective/src/index.ts
new file mode 100644
index 0000000000..0d92aa5c85
--- /dev/null
+++ b/packages/alfa-selective/src/index.ts
@@ -0,0 +1 @@
+export * from "./selective";
diff --git a/packages/alfa-selective/src/selective.ts b/packages/alfa-selective/src/selective.ts
new file mode 100644
index 0000000000..5e1fc60f63
--- /dev/null
+++ b/packages/alfa-selective/src/selective.ts
@@ -0,0 +1,103 @@
+import { Either, Left, Right } from "@siteimprove/alfa-either";
+import { Equatable } from "@siteimprove/alfa-equatable";
+import { Functor } from "@siteimprove/alfa-functor";
+import { Hash, Hashable } from "@siteimprove/alfa-hash";
+import { Serializable } from "@siteimprove/alfa-json";
+import { Mapper } from "@siteimprove/alfa-mapper";
+import { Predicate } from "@siteimprove/alfa-predicate";
+import { Refinement } from "@siteimprove/alfa-refinement";
+
+export class Selective<S, T = never>
+  implements
+    Functor<T>,
+    Iterable<S | T>,
+    Equatable,
+    Hashable,
+    Serializable<Selective.JSON<S, T>> {
+  public static of<T>(value: T): Selective<T> {
+    return new Selective(Left.of(value));
+  }
+
+  private readonly _value: Either<S, T>;
+
+  private constructor(value: Either<S, T>) {
+    this._value = value;
+  }
+
+  public map<U>(mapper: Mapper<T, U>): Selective<S, U> {
+    return new Selective(
+      this._value.either(
+        (value) => Left.of(value) as Either<S, U>,
+        (value) => Right.of(mapper(value))
+      )
+    );
+  }
+
+  public if<P extends S, U>(
+    refinement: Refinement<S, P>,
+    mapper: Mapper<P, U>
+  ): Selective<Exclude<S, P>, T | U>;
+
+  public if<U>(
+    predicate: Predicate<S>,
+    mapper: Mapper<S, U>
+  ): Selective<S, T | U>;
+
+  public if<U>(
+    predicate: Predicate<S>,
+    mapper: Mapper<S, U>
+  ): Selective<S, T | U> {
+    return this._value.either(
+      (value) =>
+        predicate(value) ? new Selective(Right.of(mapper(value))) : this,
+      () => this
+    );
+  }
+
+  public else<U>(mapper: Mapper<S, U>): Selective<never, T | U> {
+    return new Selective<never, T | U>(
+      Right.of(
+        this._value.either<T | U>(
+          (value) => mapper(value),
+          (value) => value
+        )
+      )
+    );
+  }
+
+  public get(): S | T {
+    return this._value.get();
+  }
+
+  public equals<S, T>(value: Selective<S, T>): boolean;
+
+  public equals(value: unknown): value is this;
+
+  public equals(value: unknown): boolean {
+    return value instanceof Selective && value._value.equals(this._value);
+  }
+
+  public hash(hash: Hash): void {
+    this._value.hash(hash);
+  }
+
+  public *iterator(): Iterator<S | T> {
+    yield this._value.get();
+  }
+
+  public [Symbol.iterator](): Iterator<S | T> {
+    return this.iterator();
+  }
+
+  public toJSON(): Selective.JSON<S, T> {
+    return this._value.toJSON();
+  }
+
+  public toString(): string {
+    return `Selective { ${this._value} }`;
+  }
+}
+
+export namespace Selective {
+  export type JSON<S, T = never> = Either.JSON<S, T>;
+}
diff --git a/packages/alfa-selective/test/selective.spec.ts b/packages/alfa-selective/test/selective.spec.ts
new file mode 100644
index 0000000000..dedd7cdc02
--- /dev/null
+++ b/packages/alfa-selective/test/selective.spec.ts
@@ -0,0 +1,58 @@
+import { test } from "@siteimprove/alfa-test";
+
+import { Refinement } from "@siteimprove/alfa-refinement";
+
+import { Selective } from "../src/selective";
+
+const isFoo: Refinement<string, "foo"> = (string): string is "foo" =>
+  string === "foo";
+
+const isBar: Refinement<string, "bar"> = (string): string is "bar" =>
+  string === "bar";
+
+test("#if() conditionally applies a function to a selective value", (t) => {
+  Selective.of("foo")
+    .if(isFoo, (value) => {
+      t.equal(value, "foo");
+    })
+    .if(isBar, () => {
+      t.fail();
+    });
+});
+
+test(`#else() applies a function to a selective value that matched no other
+      conditions`, (t) => {
+  Selective.of("bar")
+    .if(isFoo, () => {
+      t.fail();
+    })
+    .else((value) => {
+      t.equal(value, "bar");
+    });
+});
+
+test("#get() returns the value of a selective", (t) => {
+  t.equal(
+    Selective.of("foo")
+      .if(isFoo, () => "was foo")
+      .get(),
+    "was foo"
+  );
+
+  t.equal(
+    Selective.of("bar")
+      .if(isFoo, () => "was foo")
+      .get(),
+    "bar"
+  );
+});
+
+test(`#map() applies a function to a matched selective value`, (t) => {
+  t.equal(
+    Selective.of("foo")
+      .if(isFoo, () => "was foo")
+      .map((string) => string.toUpperCase())
+      .get(),
+    "WAS FOO"
+  );
+});
diff --git a/packages/alfa-selective/tsconfig.json b/packages/alfa-selective/tsconfig.json
new file mode 100644
index 0000000000..5ca01b7524
--- /dev/null
+++ b/packages/alfa-selective/tsconfig.json
@@ -0,0 +1,34 @@
+{
+  "$schema": "http://json.schemastore.org/tsconfig",
+  "extends": "../tsconfig.json",
+  "files": ["src/index.ts", "src/selective.ts", "test/selective.spec.ts"],
+  "references": [
+    {
+      "path": "../alfa-either"
+    },
+    {
+      "path": "../alfa-equatable"
+    },
+    {
+      "path": "../alfa-functor"
+    },
+    {
+      "path": "../alfa-hash"
+    },
+    {
+      "path": "../alfa-json"
+    },
+    {
+      "path": "../alfa-mapper"
+    },
+    {
+      "path": "../alfa-predicate"
+    },
+    {
+      "path": "../alfa-refinement"
+    },
+    {
+      "path": "../alfa-test"
+    }
+  ]
+}
diff --git a/packages/tsconfig.json b/packages/tsconfig.json
index fdceb3f010..7876d2500a 100644
--- a/packages/tsconfig.json
+++ b/packages/tsconfig.json
@@ -80,6 +80,7 @@
     { "path": "alfa-rules" },
     { "path": "alfa-scraper" },
     { "path": "alfa-sarif" },
+    { "path": "alfa-selective" },
     { "path": "alfa-selector" },
     { "path": "alfa-sequence" },
     { "path": "alfa-set" },
diff --git a/yarn.lock b/yarn.lock
index 26eeb27f56..e396658fef 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -9084,9 +9084,9 @@ typedarray@^0.0.6:
   integrity sha1-hnrHTjhkGHsdPUfZlqeOxciDB3c=
 
 typescript@^4.0.2:
-  version "4.1.3"
-  resolved "https://registry.yarnpkg.com/typescript/-/typescript-4.1.3.tgz#519d582bd94cba0cf8934c7d8e8467e473f53bb7"
-  integrity sha512-B3ZIOf1IKeH2ixgHhj6la6xdwR9QrLC5d1VKeCSY4tvkqhF2eqd9O7txNlS0PO3GrBAFIdr3L1ndNwteUbZLYg==
+  version "4.1.4"
+  resolved "https://registry.yarnpkg.com/typescript/-/typescript-4.1.4.tgz#f058636e2f4f83f94ddaae07b20fd5e14598432f"
+  integrity sha512-+Uru0t8qIRgjuCpiSPpfGuhHecMllk5Zsazj5LZvVsEStEjmIRRBZe+jHjGQvsgS7M1wONy2PQXd67EMyV6acg==
 
 ua-parser-js@^0.7.21:
   version "0.7.21"