diff --git a/.vscode/launch.json b/.vscode/launch.json
new file mode 100644
index 0000000..4f39eb2
--- /dev/null
+++ b/.vscode/launch.json
@@ -0,0 +1,21 @@
+{
+  // Use IntelliSense to learn about possible attributes.
+  // Hover to view descriptions of existing attributes.
+  // For more information, visit: https://go.microsoft.com/fwlink/?linkid=830387
+  "version": "0.2.0",
+  "configurations": [
+    {
+      "type": "node",
+      "request": "launch",
+      "name": "Debug tests",
+      "skipFiles": ["<node_internals>/**"],
+      "program": "${workspaceFolder}/node_modules/.bin/mocha",
+      "runtimeArgs": ["--require", "ts-node/register"],
+      "args": ["${relativeFile}"],
+      "outFiles": [
+        "${workspaceFolder}/src/**/*.js",
+        "${workspaceFolder}/test/**/*.js"
+      ]
+    }
+  ]
+}
diff --git a/package.json b/package.json
index 0fef426..a4d1765 100644
--- a/package.json
+++ b/package.json
@@ -31,6 +31,7 @@
     "eslint-plugin-jsx-a11y": "^6.7.1",
     "eslint-plugin-prettier": "^5.0.0",
     "eslint-plugin-react": "^7.33.2",
+    "fast-check": "^3.13.1",
     "husky": "^8.0.3",
     "mocha": "^10.2.0",
     "nyc": "^15.1.0",
diff --git a/src/index.ts b/src/index.ts
index d9ef4ca..f0fca43 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -6,6 +6,7 @@ import byString from "./sortables/byString";
 import byNumber from "./sortables/byNumber";
 import byBoolean from "./sortables/byBoolean";
 import sortAsync, { AsyncArray } from "./sortables/byAsyncValue";
+import lexicographically from "./sortables/lexicographically";
 
 export default {
   byAny,
@@ -17,6 +18,7 @@ export default {
   sortAsync,
   byBoolean,
   AsyncArray,
+  lexicographically,
 };
 
 export {
@@ -29,4 +31,5 @@ export {
   sortAsync,
   byBoolean,
   AsyncArray,
+  lexicographically,
 };
diff --git a/src/sortables/lexicographically.ts b/src/sortables/lexicographically.ts
new file mode 100644
index 0000000..ab65dad
--- /dev/null
+++ b/src/sortables/lexicographically.ts
@@ -0,0 +1,44 @@
+import { SortOption } from "src/interfaces/interfaces";
+import { sortable } from "../types/types";
+
+/**
+ * the sortable to sort **sequences** lexicographically
+ *
+ * The values `null` and `undefined` are treated as empty sequences.
+ *
+ * @param sortFn the sortable to be applied corresponding items in each sequence
+ * @param options the option to control whether the sort is descending
+ */
+function lexicographically<T>(
+  sortFn: sortable<T>,
+  options: Omit<SortOption, "nullable"> = {}
+): sortable<Iterable<T>> {
+  const { desc = false } = options;
+  const sign = desc ? -1 : 1;
+  return (
+    left: Iterable<T> | null | undefined,
+    right: Iterable<T> | null | undefined
+  ): number => {
+    const leftIter = (left || [])[Symbol.iterator]();
+    const rightIter = (right || [])[Symbol.iterator]();
+    for (;;) {
+      const { done: leftDone, value: leftValue } = leftIter.next();
+      const { done: rightDone, value: rightValue } = rightIter.next();
+      if (leftDone && rightDone) {
+        return 0;
+      }
+      if (leftDone) {
+        return -sign;
+      }
+      if (rightDone) {
+        return sign;
+      }
+      const v = sortFn(leftValue, rightValue);
+      if (v !== 0) {
+        return sign * v;
+      }
+    }
+  };
+}
+
+export default lexicographically;
diff --git a/test/lexicographically.spec.ts b/test/lexicographically.spec.ts
new file mode 100644
index 0000000..1c2a2e0
--- /dev/null
+++ b/test/lexicographically.spec.ts
@@ -0,0 +1,98 @@
+import "mocha";
+import fc from "fast-check";
+import { lexicographically } from "../src";
+import { sortable } from "../src/types/types";
+import { expect } from "chai";
+import { descToSign } from "./utils/sort";
+
+function comparators(): fc.Arbitrary<{
+  sign: number;
+  itemCmp: sortable<number>;
+  seqCmp: sortable<number[]>;
+}> {
+  return fc.tuple(fc.compareFunc(), fc.boolean()).chain(([itemCmp, desc]) => {
+    return fc.constant({
+      sign: descToSign(desc),
+      itemCmp,
+      seqCmp: lexicographically(itemCmp, { desc }),
+    });
+  });
+}
+
+describe("sorting lexiocgraphically", () => {
+  it("treats identical sequences as equal", () => {
+    fc.assert(
+      fc.property(comparators(), fc.array(fc.integer()), ({ seqCmp }, seq) => {
+        expect(seqCmp(seq, [...seq])).to.equal(0);
+      })
+    );
+  });
+
+  it("treats treats null or undefined as an empty sequence", () => {
+    fc.assert(
+      fc.property(
+        fc.oneof(fc.constantFrom(null, undefined, [])),
+        fc.oneof(fc.constantFrom(null, undefined, [])),
+        fc.array(fc.integer(), { minLength: 1 }),
+        comparators(),
+        (empty1, empty2, nonempty, { seqCmp, sign }) => {
+          expect(seqCmp(empty1, nonempty) * sign).to.be.below(0);
+          expect(seqCmp(nonempty, empty1) * sign).to.be.above(0);
+          expect(seqCmp(empty1, empty2)).to.equal(0);
+        }
+      )
+    );
+  });
+
+  it("sorts a shorter sequence before a longer sequence", () => {
+    fc.assert(
+      fc.property(
+        fc.array(fc.integer()),
+        fc.integer(),
+        comparators(),
+        (prefix, item, { seqCmp, sign }) => {
+          expect(seqCmp(prefix, [...prefix, item]) * sign).to.be.below(0);
+          expect(seqCmp([...prefix, item], prefix) * sign).to.be.above(0);
+        }
+      )
+    );
+  });
+
+  it("sorts sequences like their first differing element", () => {
+    fc.assert(
+      fc.property(
+        fc.array(fc.integer()),
+        fc.integer(),
+        fc.integer(),
+        fc.array(fc.integer()),
+        fc.array(fc.integer()),
+        comparators(),
+        (prefix, item1, item2, suffix1, suffix2, { seqCmp, itemCmp, sign }) => {
+          fc.pre(itemCmp(item1, item2) !== 0);
+          expect(
+            seqCmp(
+              [...prefix, item1, ...suffix1],
+              [...prefix, item2, ...suffix2]
+            ) * sign
+          ).to.equal(itemCmp(item1, item2));
+        }
+      )
+    );
+  });
+
+  it("sorts sequences with a common prefix like their tails", () => {
+    fc.assert(
+      fc.property(
+        fc.array(fc.integer()),
+        fc.array(fc.integer()),
+        fc.array(fc.integer()),
+        comparators(),
+        (prefix, tail1, tail2, { seqCmp }) => {
+          expect(
+            seqCmp([...prefix, ...tail1], [...prefix, ...tail2])
+          ).to.be.equal(seqCmp(tail1, tail2));
+        }
+      )
+    );
+  });
+});
diff --git a/test/utils/sort.ts b/test/utils/sort.ts
index 665099a..3aea0cc 100644
--- a/test/utils/sort.ts
+++ b/test/utils/sort.ts
@@ -5,4 +5,6 @@ const getFirstAndLast = <T>(array: T[]): [T, T] => {
 
 const reverse = <T>(array: T[]): T[] => array.concat().reverse();
 
-export {getFirstAndLast, reverse}
+const descToSign = (desc: boolean): number => desc ? -1 : 1;
+
+export {getFirstAndLast, reverse, descToSign}
diff --git a/yarn.lock b/yarn.lock
index b209cba..60e2b35 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -1859,6 +1859,13 @@ execa@^7.1.1:
     signal-exit "^3.0.7"
     strip-final-newline "^3.0.0"
 
+fast-check@^3.13.1:
+  version "3.13.1"
+  resolved "https://domoreexp.pkgs.visualstudio.com/_packaging/npm-mirror/npm/registry/fast-check/-/fast-check-3.13.1.tgz#32c7a78621098bd30d71e40c0e269a728a3188e2"
+  integrity sha1-MsenhiEJi9MNceQMDiaacooxiOI=
+  dependencies:
+    pure-rand "^6.0.0"
+
 fast-deep-equal@^3.1.1, fast-deep-equal@^3.1.3:
   version "3.1.3"
   resolved "https://registry.yarnpkg.com/fast-deep-equal/-/fast-deep-equal-3.1.3.tgz#3a7d56b559d6cbc3eb512325244e619a65c6c525"
@@ -3436,6 +3443,11 @@ punycode@^2.1.0:
   resolved "https://registry.yarnpkg.com/punycode/-/punycode-2.3.0.tgz#f67fa67c94da8f4d0cfff981aee4118064199b8f"
   integrity sha512-rRV+zQD8tVFys26lAGR9WUuS4iUAngJScM+ZRSKtvl5tKeZ2t5bvdNFdNHBW9FWR4guGHlgmsZ1G7BSm2wTbuA==
 
+pure-rand@^6.0.0:
+  version "6.0.4"
+  resolved "https://domoreexp.pkgs.visualstudio.com/_packaging/npm-mirror/npm/registry/pure-rand/-/pure-rand-6.0.4.tgz#50b737f6a925468679bff00ad20eade53f37d5c7"
+  integrity sha1-ULc39qklRoZ5v/AK0g6t5T831cc=
+
 queue-microtask@^1.2.2:
   version "1.2.3"
   resolved "https://registry.yarnpkg.com/queue-microtask/-/queue-microtask-1.2.3.tgz#4929228bbc724dfac43e0efb058caf7b6cfb6243"