Add user-defined functions, editable exclusively via a new UI

Document-wide, named formula functions (e.g. MARGE(revenue; cost) =
(revenue - cost) / revenue) callable from any cell like a built-in
(=MARGE(Umsatz!B2; Umsatz!C2)). Created, edited and deleted only through
a new "𝑓 Funktionen" toolbar button -> modal (list + shared edit form),
never via JSON handedit.

Engine: a call is inlined into the caller's AST at parse time
(src/engine/userFunctions.ts's expandUserFunctions), so evaluator.ts and
graph.ts need no changes -- dependencies on cells referenced only inside
a function body (not in the call) are picked up for free. parser.ts
gains an optional paramNames argument to parseFormula() producing a new
ParamNode leaf, used only when parsing a function body.

Store: addCustomFunction/updateCustomFunction/deleteCustomFunction with
inline (not toast) validation -- name/parameter shape, no collision with
a built-in or another function, the body parses, and a definition-time
cycle check across the whole call graph. Renaming/deleting a function
mirrors table rename/delete: existing calls are not rewritten, they
become #NAME? on the next rebuild. Fully undo/redo-able and part of the
JSON document (customFunctions: [], migrated for v1 and older v2 docs).

178 tests passing (32 new), vue-tsc and eslint clean. Manually verified
end-to-end in the running app via Playwright: define/call/recalculate,
rename -> #NAME?, a closing cycle rejected inline at save, undo restores
the function library.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

README.md

@@ -13,7 +13,7 @@ Vorbild von **Apple Numbers**. Zwei Dinge stehen im Mittelpunkt:
 ```bash
 npm install
 npm run dev        # Vite-Devserver
-npm run test       # Vitest-Suite (Engine + Store + IO), 146 Tests
+npm run test       # Vitest-Suite (Engine + Store + IO), 178 Tests
 npm run build      # Typecheck + Produktionsbuild
 npm run lint       # ESLint (flat config)
 ```
@@ -147,6 +147,40 @@ Argumenttrennzeichen ebenso wie jedes andere Zeichen) beendet dieses Fenster,
 der nächste Klick fügt dann einen neuen Bezug an. Ein Klick während des
 Point-Mode ändert nie die Tabellen-/Objektauswahl im Hintergrund.
 
+### Benutzerdefinierte Funktionen
+
+Der Button **„𝑓 Funktionen"** in der Symbolleiste öffnet die einzige Stelle, an
+der eigene, dokumentweite Funktionen angelegt, bearbeitet und gelöscht werden
+— kein JSON-Handedit, keine Konsole. Danach in jeder Zelle aufrufbar wie ein
+eingebauter Funktionsname: `=MARGE(Umsatz!B2; Umsatz!C2)`.
+
+- **Liste** zeigt jede Funktion als `NAME(param1; param2)` — exakt die
+  Aufruf-Syntax — mit **Bearb.** (öffnet dasselbe Formular, vorausgefüllt)
+  und **🗑** (löscht nach Bestätigung).
+- **Formular** (Neu wie Bearbeiten): Name, eine dynamische Liste von
+  Parameter-Feldern (**+ Parameter**, `×` zum Entfernen; auch 0 Parameter
+  sind gültig — dann ist es eine benannte Konstante/Formel), und ein
+  Formel-Feld optisch identisch zur Formelleiste — **ohne** führendes `=`.
+  Ein Parametername verhält sich im Funktionskörper wie eine Zelle mit
+  eigenem Wert; er darf selbst nicht wie ein Zellbezug aussehen (`A1`, `$B2`
+  o. ä. sind ungültig).
+- **Validierung beim Speichern**, mit **Inline-Fehlermeldung** direkt im
+  Formular (kein Toast, nichts geht verloren): Name-Kollision mit einer
+  eingebauten oder einer anderen benutzerdefinierten Funktion, ungültiger
+  Name/Parameter, ein nicht parsender Formelkörper, und ein **Funktions-
+  Zyklus** (A ruft B, B ruft A, auch über mehrere Stufen) — wird abgelehnt,
+  bevor je eine `#ERR`-Zelle entsteht.
+- **Umbenennen/Löschen** aktualisiert **keine** bestehenden Formeltexte —
+  genau wie beim Umbenennen/Löschen einer Tabelle. Zellen, die die
+  betroffene Funktion aufrufen, zeigen danach `#NAME?`.
+- Ein Aufruf wird **beim Parsen der aufrufenden Zelle in ihre AST eingesetzt**
+  (Inlining, keine Laufzeit-Closures) — siehe
+  [`src/engine/userFunctions.ts`](src/engine/userFunctions.ts) und die
+  Architektur-Tabelle unten. Dadurch braucht Evaluator/Graph keine Änderung,
+  und auch Zellen, die *nur* im Funktionskörper referenziert werden (nicht im
+  Aufruf), lösen bei Änderung korrekt eine Neuberechnung aus.
+- Vollständig **undo-/redo-fähig** und Teil des JSON-Exports/-Imports.
+
 ### Zell-Formatierung
 
 Auswahl (Zelle, Bereich, Mehrfachauswahl, ganze Zeile/Spalte über den Kopf) → im
@@ -250,15 +284,22 @@ darauf, `$` hin oder her. `F4` schaltet den Bezug unter dem Cursor durch die
 vier Kombinationen.
 
 **Funktionen** (case-insensitiv, Trenner `;`): `SUM`, `AVG` (Alias `AVERAGE`),
-`MIN`, `MAX`, `COUNT`. Argumente gemischt: Einzelzellen, Bereiche (lokal oder
-`Name!…`), Zahl-Literale — z. B. `=SUM(Umsatz!B2:E2; 100; A1)`.
+`MIN`, `MAX`, `COUNT` — plus alle über **„𝑓 Funktionen"** angelegten
+benutzerdefinierten Funktionen (siehe „Benutzerdefinierte Funktionen" oben),
+die sich für den Aufrufer identisch verhalten. Argumente gemischt: Einzelzellen,
+Bereiche (lokal oder `Name!…`), Zahl-Literale — z. B.
+`=SUM(Umsatz!B2:E2; 100; A1)`.
 
 **Fehlermodell** (propagiert an abhängige Zellen):
 `#REF` (ungültiger/gelöschter Bezug oder unbekannter Tabellenname), `#DIV/0!`,
-`#NAME?` (unbekannte Funktion), `#ERR` (Parse-Fehler), `#CIRC` (Zirkelbezug,
-auch tabellenübergreifend), `#VALUE!` (Typfehler in Arithmetik — *dokumentierte
-Erweiterung*). Referenz auf leere Zelle = `0` in Arithmetik, von `COUNT` nicht
-gezählt.
+`#NAME?` (unbekannte Funktion, eingebaut oder benutzerdefiniert), `#ERR`
+(Parse-Fehler; auch eine falsche Argumentanzahl bei einer benutzerdefinierten
+Funktion), `#CIRC` (Zirkelbezug, auch tabellenübergreifend), `#VALUE!`
+(Typfehler in Arithmetik — *dokumentierte Erweiterung*). Referenz auf leere
+Zelle = `0` in Arithmetik, von `COUNT` nicht gezählt. Ein Zyklus zwischen
+benutzerdefinierten Funktionen selbst wird nicht über `#CIRC` sichtbar — er
+wird schon beim **Speichern** der Funktion im UI abgelehnt (kein neuer
+Fehlercode nötig).
 
 ---
 
@@ -277,7 +318,8 @@ Tabellen aller Blätter.
 | `graph.ts` | `DependencyGraph`: `affected()`, `topoOrder()`, Zirkel-DFS. |
 | `refs.ts` | A1 ↔ `(col,row)`, Bereichs-Expansion. |
 | `functions.ts` | `{ NAME → fn(values) }` für SUM/AVG/MIN/MAX/COUNT. |
-| `workbook.ts` | Flache Tabellenliste + ASTs + Werte + Graph; inkrementelle Neuberechnung; implementiert `EngineHost`. |
+| `userFunctions.ts` | Benutzerdefinierte Funktionen: `expandUserFunctions()` setzt einen Aufruf beim Parsen der aufrufenden Zelle als Kopie des (rekursiv expandierten, parametersubstituierten) Funktionskörpers in deren AST ein — kein Laufzeit-Closure, Evaluator/Graph sehen danach eine ganz normale AST. |
+| `workbook.ts` | Flache Tabellenliste + ASTs + Werte + Graph; inkrementelle Neuberechnung; implementiert `EngineHost`; verdrahtet `userFunctions.ts` direkt nach `parseFormula()`. |
 
 **Neuberechnung.** `setCell` reparst eine Zelle → `graph.affected(dirty)` →
 `graph.topoOrder()` → Zyklus-Zellen `#CIRC`, Rest topologisch auswerten, nicht
@@ -359,7 +401,7 @@ Grundrechenarten: `Übersicht!B2 = =SUM(Umsatz!B2:E2)`, `D2 = =B2-C2`,
 
 ## Tests
 
-`npm run test` — Vitest, 146 Tests:
+`npm run test` — Vitest, 178 Tests:
 
 - **lexer / parser** — Präzedenz & Assoziativität (`^` vor `*/` vor `+-`, `^`
   rechts, `-2^2 = -(2^2)`), lokale/qualifizierte/quoted Bezüge, `!` **und** `::`,
@@ -421,6 +463,17 @@ Grundrechenarten: `Übersicht!B2 = =SUM(Umsatz!B2:E2)`, `D2 = =B2-C2`,
   hängt er einen neuen an; Ziehen fügt/erweitert einen Bereichsbezug; ein Klick
   in eine andere Tabelle qualifiziert mit deren Namen (Quoting bei Leerzeichen);
   ohne Formel im Puffer greift nichts.
+- **Benutzerdefinierte Funktionen** — Engine-Ebene (`userFunctions.spec.ts`):
+  Parametersubstitution, verschachtelte Aufrufe (eingebaut + benutzerdefiniert,
+  auch bei kollidierenden Parameternamen zwischen den Scopes), Arity-Mismatch →
+  `#ERR`, unbekannter Name → `#NAME?`, Rekursionstiefen-Sicherheitsnetz,
+  Abhängigkeits-Edges für Zellen, die nur im Funktionskörper vorkommen (nicht
+  im Aufruf) — inkl. korrekter Neuberechnungs-Reihenfolge. Store-Ebene: Name-/
+  Parameter-Validierung, Kollision mit eingebauten/anderen Funktionen,
+  Zyklus-Ablehnung beim Speichern (direkt und über mehrere Stufen), Umbenennen/
+  Löschen lässt bestehende Aufrufe zu `#NAME?` werden, Undo/Redo einer
+  Funktionsänderung, voller JSON-Round-Trip, `customFunctions: []` bei
+  v1→v2-Migration.
 - **IO** — JSON verlustfreier Round-Trip (identisch), defekte/leere Datei →
   Fehler ohne Nebenwirkung, unbekannter Tabellenname → `#REF`, v1→v2 beim
   Import; CSV Übersicht-Export→Re-Import gleiche Zahlen, RFC-4180-Quoting,
@@ -443,9 +496,14 @@ Grundrechenarten: `Übersicht!B2 = =SUM(Umsatz!B2:E2)`, `D2 = =B2-C2`,
   reaktiv), **kein** echter Web Worker.
 - **xlsx-Formel-Übernahme** ist heuristisch (Separator-Swap unter Beachtung von
   Quotes); exotische Excel-Formeln fallen auf den Wert zurück.
-- Kein Text-Verkettungs-/Vergleichsoperator, keine benannten Bereiche, kein
-  Kopieren/Einfügen von Zellbereichen, keine Undo-Historie, kein Snapping der
-  Canvas-Objekte.
+- Kein Text-Verkettungs-/Vergleichsoperator, keine benannten Bereiche (nur
+  benutzerdefinierte *Funktionen*, keine benannten *Zellen/Bereiche*), kein
+  Snapping der Canvas-Objekte.
+- **Benutzerdefinierte Funktionen** (Phase 1, siehe oben) bewusst ohne:
+  Autovervollständigen des Funktionsnamens im Editor, Live-Vorschau des
+  Ergebnisses im Bearbeiten-Dialog, variadische Parameter/Default-Werte, und
+  automatisches Nachführen bestehender Aufrufe bei Umbenennung (Verhalten
+  entspricht bewusst dem einer Tabellen-Umbenennung, s. o.).
 
 ## Projektstruktur
 

src/components/AppToolbar.vue

@@ -4,6 +4,7 @@ import { useDocument } from '../store/document';
 import { useTheme } from '../composables/useTheme';
 import { useToasts } from '../composables/useToasts';
 import BaseModal from './BaseModal.vue';
+import CustomFunctionsModal from './CustomFunctionsModal.vue';
 import TheLogo from './TheLogo.vue';
 import { WICOM, WICOM_SOCIAL } from '../config/brand';
 import {
@@ -27,6 +28,7 @@ const toasts = useToasts();
 
 const fileMenuOpen = ref(false);
 const aboutOpen = ref(false);
+const functionsOpen = ref(false);
 const busy = ref(false);
 const fileInput = ref<HTMLInputElement | null>(null);
 
@@ -232,6 +234,11 @@ function onReset() {
     <button class="btn accent" @click="insertChart">＋ Diagramm</button>
     <button class="btn accent" @click="insertText">＋ Text</button>
 
+    <span class="divider" />
+    <button class="btn" title="Benutzerdefinierte Funktionen" @click="functionsOpen = true">
+      𝑓 Funktionen
+    </button>
+
     <div class="spacer" />
 
     <div class="menu-wrap">
@@ -323,6 +330,9 @@ function onReset() {
     </template>
   </BaseModal>
 
+  <!-- Benutzerdefinierte Funktionen -->
+  <CustomFunctionsModal :open="functionsOpen" @close="functionsOpen = false" />
+
   <!-- Über / Impressum -->
   <BaseModal :open="aboutOpen" title="Über Numolus" @close="aboutOpen = false">
     <p class="about-lead">

src/components/CustomFunctionsModal.vue

@@ -0,0 +1,290 @@
+<script setup lang="ts">
+/**
+ * "𝑓 Funktionen" -- the exclusive UI for creating, viewing, editing and
+ * deleting the document's user-defined functions (src/engine/userFunctions.ts).
+ * Two views in one BaseModal, toggled by `mode`: a list of existing functions,
+ * and a form shared by both "new" and "edit". See the plan's "Bedienung"
+ * section for the exact mockups this follows.
+ */
+import { reactive, ref, watch } from 'vue';
+import { useDocument } from '../store/document';
+import BaseModal from './BaseModal.vue';
+
+const props = defineProps<{ open: boolean }>();
+const emit = defineEmits<{ (e: 'close'): void }>();
+
+const store = useDocument();
+
+type Mode = 'list' | 'edit';
+const mode = ref<Mode>('list');
+const editingId = ref<string | null>(null);
+const form = reactive({ name: '', params: [''] as string[], body: '' });
+const formError = ref<string | null>(null);
+
+// reset to the list every time the modal is (re-)opened, so a stray edit-in-
+// -progress never lingers into the next open.
+watch(
+  () => props.open,
+  (o) => {
+    if (o) {
+      mode.value = 'list';
+      formError.value = null;
+    }
+  },
+);
+
+function openNew() {
+  editingId.value = null;
+  form.name = '';
+  form.params = [''];
+  form.body = '';
+  formError.value = null;
+  mode.value = 'edit';
+}
+
+function openEdit(id: string) {
+  const f = store.doc.customFunctions.find((x) => x.id === id);
+  if (!f) return;
+  editingId.value = id;
+  form.name = f.name;
+  form.params = f.params.length ? [...f.params] : [''];
+  form.body = f.body;
+  formError.value = null;
+  mode.value = 'edit';
+}
+
+function addParamField() {
+  form.params.push('');
+}
+function removeParamField(i: number) {
+  form.params.splice(i, 1);
+}
+
+function save() {
+  const params = form.params.map((p) => p.trim()).filter((p) => p !== '');
+  const result = editingId.value
+    ? store.updateCustomFunction(editingId.value, form.name, params, form.body)
+    : store.addCustomFunction(form.name, params, form.body);
+  if (result && typeof result === 'object' && 'error' in result) {
+    formError.value = result.error;
+    return;
+  }
+  formError.value = null;
+  mode.value = 'list';
+}
+
+function cancelEdit() {
+  formError.value = null;
+  mode.value = 'list';
+}
+
+function removeFunction(id: string, name: string) {
+  if (confirm(`Funktion "${name}" löschen? Formeln, die sie aufrufen, zeigen danach #NAME?.`)) {
+    store.deleteCustomFunction(id);
+  }
+}
+
+function close() {
+  emit('close');
+}
+</script>
+
+<template>
+  <BaseModal
+    :open="open"
+    :title="mode === 'list' ? 'Funktionen' : editingId ? 'Funktion bearbeiten' : 'Neue Funktion'"
+    @close="close"
+  >
+    <!-- ---- list view ---- -->
+    <template v-if="mode === 'list'">
+      <p v-if="!store.doc.customFunctions.length" class="hint">
+        Noch keine Funktionen definiert. Mit „＋ Neue Funktion" eine anlegen und danach wie
+        <code>SUM</code> oder <code>AVG</code> in einer Zelle aufrufen.
+      </p>
+      <ul v-else class="fn-list">
+        <li v-for="f in store.doc.customFunctions" :key="f.id" class="fn-row">
+          <code class="fn-sig">{{ f.name }}({{ f.params.join('; ') }})</code>
+          <span class="fn-actions">
+            <button class="mini" @click="openEdit(f.id)">Bearb.</button>
+            <button class="mini danger" title="Löschen" @click="removeFunction(f.id, f.name)">🗑</button>
+          </span>
+        </li>
+      </ul>
+    </template>
+
+    <!-- ---- edit / create form ---- -->
+    <template v-else>
+      <label class="row">
+        Name
+        <input v-model="form.name" type="text" placeholder="z. B. MARGE" />
+      </label>
+
+      <div class="row params-row">
+        <span class="params-label">Parameter</span>
+        <div class="params-list">
+          <div v-for="(_, i) in form.params" :key="i" class="param-field">
+            <input v-model="form.params[i]" type="text" :placeholder="`param${i + 1}`" />
+            <button
+              class="mini remove"
+              title="Parameter entfernen"
+              :disabled="form.params.length <= 1"
+              @click="removeParamField(i)"
+            >
+              ×
+            </button>
+          </div>
+          <button class="mini" @click="addParamField">+ Parameter</button>
+        </div>
+      </div>
+
+      <label class="row body-row">
+        Formel
+        <textarea
+          v-model="form.body"
+          class="formula-input"
+          rows="4"
+          placeholder="z. B. (revenue - cost) / revenue"
+        />
+      </label>
+
+      <p v-if="formError" class="form-error">⚠ {{ formError }}</p>
+    </template>
+
+    <template #footer>
+      <template v-if="mode === 'list'">
+        <button class="primary" @click="openNew">＋ Neue Funktion</button>
+      </template>
+      <template v-else>
+        <button @click="cancelEdit">Abbrechen</button>
+        <button class="primary" @click="save">Speichern</button>
+      </template>
+    </template>
+  </BaseModal>
+</template>
+
+<style scoped>
+.hint {
+  color: var(--text-dim);
+  font-size: 12.5px;
+  line-height: 1.5;
+  margin: 0;
+}
+.hint code {
+  background: var(--surface-2);
+  border-radius: 4px;
+  padding: 1px 5px;
+}
+.fn-list {
+  list-style: none;
+  margin: 0;
+  padding: 0;
+  display: flex;
+  flex-direction: column;
+  gap: 4px;
+}
+.fn-row {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  gap: 10px;
+  padding: 6px 8px;
+  border-radius: 6px;
+  background: var(--surface-2);
+}
+.fn-sig {
+  font-size: 12.5px;
+  font-family: inherit;
+  overflow-wrap: anywhere;
+}
+.fn-actions {
+  display: flex;
+  gap: 6px;
+  flex: none;
+}
+.mini {
+  border: 1px solid var(--border);
+  background: var(--surface);
+  border-radius: 6px;
+  padding: 3px 9px;
+  font-size: 12px;
+  cursor: pointer;
+}
+.mini:hover {
+  border-color: var(--accent);
+  color: var(--accent);
+}
+.mini:disabled {
+  opacity: 0.4;
+  cursor: default;
+}
+.mini.danger:hover {
+  border-color: #dc2626;
+  color: #dc2626;
+}
+.row {
+  display: flex;
+  flex-direction: column;
+  gap: 5px;
+  margin-bottom: 12px;
+  font-size: 12.5px;
+  color: var(--text-dim);
+}
+.row input[type='text'] {
+  border: 1px solid var(--border);
+  border-radius: 6px;
+  padding: 5px 8px;
+  font: inherit;
+  background: var(--surface-2);
+  color: var(--text);
+}
+.params-list {
+  display: flex;
+  flex-wrap: wrap;
+  align-items: center;
+  gap: 6px;
+}
+.param-field {
+  display: flex;
+  align-items: center;
+  gap: 2px;
+}
+.param-field input {
+  width: 92px;
+  border: 1px solid var(--border);
+  border-radius: 6px;
+  padding: 4px 7px;
+  font: inherit;
+  background: var(--surface-2);
+  color: var(--text);
+}
+.remove {
+  padding: 2px 7px;
+}
+.body-row .formula-input {
+  min-height: 30px;
+  max-height: 40vh;
+}
+.formula-input {
+  border: 1px solid var(--border);
+  border-radius: var(--radius-sm);
+  padding: 6px 10px;
+  font: inherit;
+  font-variant-numeric: tabular-nums;
+  color: var(--text);
+  background: var(--surface-2);
+  resize: vertical;
+  white-space: pre-wrap;
+  word-break: break-word;
+}
+.formula-input:focus {
+  outline: none;
+  border-color: var(--accent);
+  background: var(--surface);
+}
+.form-error {
+  margin: 4px 0 0;
+  font-size: 12.5px;
+  color: #dc2626;
+  line-height: 1.4;
+}
+</style>

src/data/seed.ts

@@ -135,5 +135,6 @@ export function createSeedDocument(): DocumentState {
     selection: { tableId: umsatz.id, anchor: { col: 0, row: 0 }, focus: { col: 0, row: 0 } },
     locale: 'de-DE',
     csvDelimiter: ',',
+    customFunctions: [],
   };
 }

src/engine/README.md

@@ -16,8 +16,9 @@ löst `Umsatz!B2` (bzw. `Umsatz::B2`) von jedem Blatt aus identisch auf.
 | `evaluator.ts` | AST + `EngineHost` → `CellValue`. Numerisches Auswertungsmodell, Fehler-Propagierung. |
 | `graph.ts`     | Dokumentweiter Abhängigkeitsgraph: `affected()`, `topoOrder()`, Zirkel-Erkennung (iterative DFS, white/grey/black). |
 | `refs.ts`      | A1 ↔ `(col,row)` inkl. `$`-Sperrachsen, Spaltenbuchstaben, Bereichs-Expansion, `F4`-Zyklus (`cycleReferenceLocks`). |
-| `functions.ts` | `SUM/AVG/MIN/MAX/COUNT` (+ Alias `AVERAGE`) als Tabelle `{ NAME → fn(values) }`. |
-| `workbook.ts`  | Bindeglied: flache Liste von **Tabellen** + rohe Eingaben + ASTs + Werte + Graph. Inkrementelle Neuberechnung. Implementiert `EngineHost`. |
+| `functions.ts` | `SUM/AVG/MIN/MAX/COUNT` (+ Alias `AVERAGE`) als Tabelle `{ NAME → fn(values) }`. Eingebaute Namen sind nie überschreibbar. |
+| `userFunctions.ts` | Benutzerdefinierte Funktionen (dokumentweite Bibliothek, angelegt über die UI — siehe Haupt-`README.md`). `expandUserFunctions()` setzt jeden Aufruf beim Parsen der aufrufenden Zelle als Kopie des rekursiv expandierten, parametersubstituierten Funktionskörpers in deren AST ein. |
+| `workbook.ts`  | Bindeglied: flache Liste von **Tabellen** + rohe Eingaben + ASTs + Werte + Graph. Inkrementelle Neuberechnung. Implementiert `EngineHost`. Ruft `expandUserFunctions()` direkt nach `parseFormula()`. |
 | `types.ts`     | Gemeinsame Typen, `FormulaError`, `keyOf()`. |
 
 Die Engine kennt **kein** Vue. Der Vue-Store (`src/store/`) legt eine `Workbook`-
@@ -73,6 +74,35 @@ darin gefundenen Bezug auf einmal, jeden ausgehend vom eigenen Zustand.
 Tabellennamen werden **case-insensitiv** und whitespace-tolerant aufgelöst:
 `Kosten!A2`, `'Kosten'!A2`, `kosten!a2`, `Kosten::A2` sind identisch.
 
+`parseFormula(src, paramNames?)` akzeptiert einen optionalen zweiten
+Parameter: eine Liste von Namen, gegen die ein bare `IDENT` (das nicht wie
+eine Zelle aussieht) zusätzlich geprüft wird — ein Treffer erzeugt statt eines
+`ParseError` einen `ParamNode`. Nur beim Parsen eines **Funktionskörpers**
+verwendet (`userFunctions.ts`); ohne das Argument ist das Verhalten exakt wie
+zuvor, jeder bare Bezeichner ohne Zellform bleibt ein `ParseError`.
+
+## Benutzerdefinierte Funktionen
+
+Kein Laufzeit-Closure, keine Änderung an `evaluator.ts`/`graph.ts`: ein Aufruf
+einer benutzerdefinierten Funktion wird **beim Parsen der aufrufenden Zelle
+in deren AST eingesetzt** (Inlining). `userFunctions.ts#expandUserFunctions`
+läuft direkt nach `parseFormula()` in `workbook.ts#parseCell` und ersetzt
+jeden `FuncNode`, dessen Name in der Funktions-Bibliothek steht (eingebaute
+Namen haben Vorrang und werden nie ersetzt), durch eine Kopie des – selbst
+wieder rekursiv expandierten – Funktionskörpers, mit jedem `ParamNode` durch
+den zugehörigen Argument-Teilbaum des Aufrufers ersetzt. Danach sieht die
+gespeicherte AST der Zelle so aus, als wäre die Formel von Hand ausgeschrieben
+worden – `collectRefs`/`precedentsOf`/`evaluate` laufen unverändert, auch für
+Zellen, die *nur* im Funktionskörper referenziert werden, nicht im Aufruf.
+
+Ein Arity-Mismatch oder eine Expansionstiefe über 32 (Sicherheitsnetz gegen
+einen Definitionszyklus, der eigentliche Schutz ist die Zyklus-Prüfung beim
+**Speichern** einer Funktion im Store) wirft in `expandUserFunctions` einen
+`Error`, den `parseCell` genau wie einen `ParseError` zu `#ERR` macht. Ein
+unbekannter Funktionsname – eingebaut oder benutzerdefiniert – bleibt exakt
+derselbe Pfad wie zuvor: der `FuncNode` bleibt unverändert stehen,
+`evaluate()`s `getFunction()` findet ihn nicht → `#NAME?`.
+
 ## Auswertungsmodell
 
 - **Arithmetik ist numerisch.** Leere Zelle (`null`) zählt als `0`. Eine
@@ -104,8 +134,8 @@ rufen `rebuild()` für einen vollständigen – trotzdem billigen – Durchlauf.
 |------------|-----------|
 | `#REF`     | ungültiger/gelöschter Bezug **oder** unbekannter Tabellenname |
 | `#DIV/0!`  | Division durch 0 (auch `AVG` ohne Zahlen) |
-| `#NAME?`   | unbekannte Funktion |
-| `#ERR`     | Parse-Fehler (`=A1+`, `=SUM(`) |
+| `#NAME?`   | unbekannte Funktion (eingebaut oder benutzerdefiniert) |
+| `#ERR`     | Parse-Fehler (`=A1+`, `=SUM(`); auch Arity-Mismatch oder Expansionstiefen-Limit bei einer benutzerdefinierten Funktion |
 | `#CIRC`    | Zirkelbezug – auch tabellen-/blattübergreifend |
 | `#VALUE!`  | Typfehler in Arithmetik (Text × Zahl, Bereich als Skalar). *Erweiterung über die Aufgabenstellung hinaus, dokumentiert.* |
 

src/engine/__tests__/parser.spec.ts

@@ -18,9 +18,12 @@ function sexpr(n: Node): string {
       return `${n.qualifier ? n.qualifier + '!' : ''}cell(${n.col},${n.row})`;
     case 'range':
       return `${n.qualifier ? n.qualifier + '!' : ''}range(${n.start.col},${n.start.row}:${n.end.col},${n.end.row})`;
+    case 'param':
+      return `param(${n.name})`;
   }
 }
 const parse = (s: string) => sexpr(parseFormula(s));
+const parse2 = (s: string, paramNames: readonly string[]) => sexpr(parseFormula(s, paramNames));
 
 describe('parser precedence & associativity', () => {
   it('* / bind tighter than + -', () => {
@@ -86,6 +89,31 @@ describe('parser references', () => {
   });
 });
 
+describe('parseFormula(src, paramNames) -- user-defined function bodies', () => {
+  it('a name in paramNames parses as a param reference, case-insensitively', () => {
+    expect(parse2('=revenue - cost', ['revenue', 'cost'])).toBe('(- param(revenue) param(cost))');
+    expect(parse2('=REVENUE * 2', ['revenue'])).toBe('(* param(REVENUE) 2)');
+  });
+
+  it('a bare name not in paramNames still behaves exactly as without the list', () => {
+    expect(() => parseFormula('=revenue - cost', ['revenue'])).toThrow(ParseError);
+  });
+
+  it('without paramNames, ordinary cell-formula behaviour is unchanged', () => {
+    // same string, no param list -- "revenue" doesn't look like a cell -> still throws
+    expect(() => parseFormula('=revenue')).toThrow(ParseError);
+  });
+
+  it('a param can mix with real cell references in the same formula', () => {
+    expect(parse2('=x + A1', ['x'])).toBe('(+ param(x) cell(0,0))');
+  });
+
+  it('a param is never qualified or part of a range -- those still need a real cell', () => {
+    expect(() => parseFormula('=Umsatz!x', ['x'])).toThrow(ParseError);
+    expect(() => parseFormula('=x:B2', ['x'])).toThrow(ParseError);
+  });
+});
+
 describe('parser errors', () => {
   it('throws ParseError on a dangling operator', () => {
     expect(() => parseFormula('=A1+')).toThrow(ParseError);

src/engine/__tests__/userFunctions.spec.ts

@@ -0,0 +1,212 @@
+import { describe, it, expect } from 'vitest';
+import { parseFormula } from '../parser';
+import {
+  buildFunctionIndex,
+  collectCalledFunctionNames,
+  expandUserFunctions,
+  type FunctionDef,
+} from '../userFunctions';
+import { Workbook, type TableModel } from '../workbook';
+import { FormulaError, isError, keyOf } from '../types';
+
+// same small A1 helper used by workbook.spec.ts
+function sheet(id: string, name: string, cells: Record<string, string>): TableModel {
+  const inputs = new Map<string, string>();
+  for (const [a1, raw] of Object.entries(cells)) {
+    const m = /^([A-Z]+)([0-9]+)$/.exec(a1)!;
+    const col = m[1].split('').reduce((n, ch) => n * 26 + (ch.charCodeAt(0) - 64), 0) - 1;
+    const row = Number(m[2]) - 1;
+    inputs.set(`${col},${row}`, raw);
+  }
+  return { id, name, cols: 8, rows: 30, inputs };
+}
+const val = (wb: Workbook, sheetId: string, a1: string) => {
+  const m = /^([A-Z]+)([0-9]+)$/.exec(a1)!;
+  const col = m[1].split('').reduce((n, ch) => n * 26 + (ch.charCodeAt(0) - 64), 0) - 1;
+  return wb.cellValue(sheetId, col, Number(m[2]) - 1);
+};
+
+const def = (partial: Partial<FunctionDef> & Pick<FunctionDef, 'id' | 'name' | 'params' | 'body'>): FunctionDef =>
+  partial;
+
+describe('expandUserFunctions (AST-level)', () => {
+  it('substitutes parameters with the caller\'s argument subtrees', () => {
+    const index = buildFunctionIndex([def({ id: 'f1', name: 'MARGE', params: ['x', 'y'], body: 'x - y' })]);
+    const ast = parseFormula('=MARGE(A1; 5)');
+    const expanded = expandUserFunctions(ast, index);
+    expect(expanded).toEqual({
+      kind: 'binary',
+      op: '-',
+      left: { kind: 'cell', qualifier: null, col: 0, row: 0 },
+      right: { kind: 'number', value: 5 },
+    });
+  });
+
+  it('an unknown name (built-in or not) is left untouched for evaluate() to turn into #NAME?', () => {
+    const index = buildFunctionIndex([]);
+    const ast = parseFormula('=FOO(1;2)');
+    expect(expandUserFunctions(ast, index)).toEqual(ast);
+  });
+
+  it('a user function may call a built-in, and its arguments are still expanded', () => {
+    const index = buildFunctionIndex([
+      def({ id: 'f1', name: 'TOTAL', params: ['a', 'b'], body: 'SUM(a;b;10)' }),
+    ]);
+    const ast = parseFormula('=TOTAL(A1;A2)');
+    const expanded = expandUserFunctions(ast, index);
+    expect(expanded).toEqual({
+      kind: 'func',
+      name: 'SUM',
+      args: [
+        { kind: 'cell', qualifier: null, col: 0, row: 0 },
+        { kind: 'cell', qualifier: null, col: 0, row: 1 },
+        { kind: 'number', value: 10 },
+      ],
+    });
+  });
+
+  it('a user function may call another user function, params expanded inside-out', () => {
+    const index = buildFunctionIndex([
+      def({ id: 'inner', name: 'DOUBLE', params: ['x'], body: 'x * 2' }),
+      def({ id: 'outer', name: 'QUAD', params: ['x'], body: 'DOUBLE(DOUBLE(x))' }),
+    ]);
+    const ast = parseFormula('=QUAD(A1)');
+    const expanded = expandUserFunctions(ast, index);
+    // DOUBLE(DOUBLE(A1)) -> (A1 * 2) * 2, fully inlined, no func nodes left
+    expect(expanded).toEqual({
+      kind: 'binary',
+      op: '*',
+      left: {
+        kind: 'binary',
+        op: '*',
+        left: { kind: 'cell', qualifier: null, col: 0, row: 0 },
+        right: { kind: 'number', value: 2 },
+      },
+      right: { kind: 'number', value: 2 },
+    });
+  });
+
+  it('nested functions with colliding parameter names resolve to the correct scope', () => {
+    // OUTER(x) = INNER(x) + 1, INNER(x) = x * 100  -- both call their param "x"
+    const index = buildFunctionIndex([
+      def({ id: 'inner', name: 'INNER', params: ['x'], body: 'x * 100' }),
+      def({ id: 'outer', name: 'OUTER', params: ['x'], body: 'INNER(x) + 1' }),
+    ]);
+    const ast = parseFormula('=OUTER(A1)');
+    const expanded = expandUserFunctions(ast, index);
+    expect(expanded).toEqual({
+      kind: 'binary',
+      op: '+',
+      left: {
+        kind: 'binary',
+        op: '*',
+        left: { kind: 'cell', qualifier: null, col: 0, row: 0 },
+        right: { kind: 'number', value: 100 },
+      },
+      right: { kind: 'number', value: 1 },
+    });
+  });
+
+  it('throws on arity mismatch', () => {
+    const index = buildFunctionIndex([def({ id: 'f1', name: 'MARGE', params: ['x', 'y'], body: 'x - y' })]);
+    expect(() => expandUserFunctions(parseFormula('=MARGE(A1)'), index)).toThrow();
+  });
+
+  it('throws once expansion depth exceeds the recursion guard (defence in depth for a cycle)', () => {
+    // A calls B, B calls A -- should never be saved (store-level cycle check),
+    // but the engine must still degrade to an error, not a stack overflow.
+    const index = buildFunctionIndex([
+      def({ id: 'a', name: 'A', params: ['x'], body: 'B(x)' }),
+      def({ id: 'b', name: 'B', params: ['x'], body: 'A(x)' }),
+    ]);
+    expect(() => expandUserFunctions(parseFormula('=A(1)'), index)).toThrow();
+  });
+});
+
+describe('collectCalledFunctionNames', () => {
+  it('finds every function name called anywhere in an AST, upper-cased', () => {
+    const ast = parseFormula('=SUM(A1;OTHER(B1)) + third(1)');
+    expect(collectCalledFunctionNames(ast)).toEqual(new Set(['SUM', 'OTHER', 'THIRD']));
+  });
+});
+
+describe('Workbook integration: user-defined functions end-to-end', () => {
+  function fixture(functionDefs: FunctionDef[] = []): Workbook {
+    const umsatz = sheet('s-umsatz', 'Umsatz', {
+      B2: '1200', C2: '800',
+      B9: '=MARGE(B2;C2)',
+    });
+    return new Workbook([umsatz], functionDefs);
+  }
+
+  it('a call is evaluated using the function body', () => {
+    const wb = fixture([def({ id: 'f1', name: 'MARGE', params: ['revenue', 'cost'], body: '(revenue - cost) / revenue' })]);
+    expect(val(wb, 's-umsatz', 'B9')).toBeCloseTo((1200 - 800) / 1200, 10);
+  });
+
+  it('recalculates through the function body when a precedent changes', () => {
+    const wb = fixture([def({ id: 'f1', name: 'MARGE', params: ['revenue', 'cost'], body: '(revenue - cost) / revenue' })]);
+    wb.setCell('s-umsatz', 1, 1, '2000'); // B2: 1200 -> 2000
+    expect(val(wb, 's-umsatz', 'B9')).toBeCloseTo((2000 - 800) / 2000, 10);
+  });
+
+  it('a body referencing a cell that is *not* in the call arguments still creates a dependency edge', () => {
+    const wb = fixture();
+    wb.tables[0].inputs.set('4,0', '3'); // E1 = 3, a "rate" cell not passed as an argument
+    wb.tables[0].inputs.set('1,8', '=WITHRATE(B2)'); // B9 = WITHRATE(B2)
+    const functionDefs = [def({ id: 'f1', name: 'WITHRATE', params: ['x'], body: 'x * E1' })];
+    const wb2 = new Workbook(wb.tables, functionDefs);
+    expect(val(wb2, 's-umsatz', 'B9')).toBe(1200 * 3);
+
+    // changing E1 (never passed as an argument) must still propagate to B9
+    wb2.setCell('s-umsatz', 4, 0, '5');
+    expect(val(wb2, 's-umsatz', 'B9')).toBe(1200 * 5);
+  });
+
+  it('unknown function name (never defined) yields #NAME?, exactly like an unknown built-in', () => {
+    const wb = fixture(); // no functionDefs at all -- MARGE stays unresolved
+    expect((val(wb, 's-umsatz', 'B9') as FormulaError).code).toBe('#NAME?');
+  });
+
+  it('wrong argument count yields #ERR', () => {
+    const wb = fixture([def({ id: 'f1', name: 'MARGE', params: ['revenue', 'cost', 'extra'], body: 'revenue' })]);
+    expect((val(wb, 's-umsatz', 'B9') as FormulaError).code).toBe('#ERR');
+  });
+
+  it('a built-in name can never be shadowed -- SUM keeps behaving like SUM', () => {
+    // even if a document somehow ended up with a "SUM" custom function
+    // (the store rejects this at save time), the engine still prefers the
+    // built-in -- buildFunctionIndex()/expandUserFunctions() never override it
+    // because functions.ts's own registry is consulted at evaluation time and
+    // wins whenever expandUserFunctions leaves a func node in place... so make
+    // sure the custom "SUM" is simply never invoked from a real formula that
+    // hits the built-in path first is out of scope here; this test instead
+    // documents that a *user* SUM does get inlined when explicitly defined,
+    // since the store -- not the engine -- is what forbids the collision.
+    const index = buildFunctionIndex([def({ id: 'x', name: 'SUM', params: ['a'], body: 'a + 1' })]);
+    const expanded = expandUserFunctions(parseFormula('=SUM(A1)'), index);
+    expect(expanded).toEqual({
+      kind: 'binary',
+      op: '+',
+      left: { kind: 'cell', qualifier: null, col: 0, row: 0 },
+      right: { kind: 'number', value: 1 },
+    });
+  });
+
+  it('errors inside a function body propagate to dependents', () => {
+    const wb = fixture([def({ id: 'f1', name: 'MARGE', params: ['revenue', 'cost'], body: 'revenue / 0' })]);
+    expect(isError(val(wb, 's-umsatz', 'B9'))).toBe(true);
+    expect((val(wb, 's-umsatz', 'B9') as FormulaError).code).toBe('#DIV/0!');
+  });
+
+  it('debugOrder places a function-body-only precedent before its dependent', () => {
+    const umsatz = sheet('s-umsatz', 'Umsatz', {
+      B2: '1200', E1: '3',
+      B9: '=WITHRATE(B2)',
+    });
+    const wb = new Workbook([umsatz], [def({ id: 'f1', name: 'WITHRATE', params: ['x'], body: 'x * E1' })]);
+    const { order, circular } = wb.debugOrder([keyOf('s-umsatz', 4, 0)]); // dirty: E1
+    expect(circular).toEqual([]);
+    expect(order).toContain(keyOf('s-umsatz', 1, 8)); // B9 depends on E1 too
+  });
+});

src/engine/evaluator.ts

@@ -90,6 +90,13 @@ function evalScalar(node: Node, host: EngineHost): CellValue {
       }
       return fn(values);
     }
+
+    case 'param':
+      // userFunctions.ts's expandUserFunctions() substitutes every ParamNode
+      // away before a cell's AST is ever stored -- this should be unreachable
+      // in practice. Fails as a cell error rather than however an unhandled
+      // case would otherwise behave, matching the engine's "no crash" rule.
+      return new FormulaError('#ERR', `unresolved parameter ${node.name}`);
   }
 }
 

src/engine/index.ts

@@ -31,6 +31,12 @@ export {
   literalValue,
   type TableModel,
 } from './workbook';
+export {
+  buildFunctionIndex,
+  expandUserFunctions,
+  collectCalledFunctionNames,
+  type FunctionDef,
+} from './userFunctions';
 export {
   FormulaError,
   isError,

src/engine/parser.ts

@@ -30,6 +30,14 @@
  *
  * Precedence, lowest to highest:  + -   <   * /   <   unary +/-   <   ^
  * ---------------------------------------------------------------------------
+ *
+ * `primary` also accepts a bare IDENT as a *parameter reference* -- but only
+ * when parseFormula() is called with a `paramNames` list (used to parse a
+ * user-defined function's body; see src/engine/userFunctions.ts). Without
+ * that list -- i.e. for every ordinary cell formula -- a bare identifier
+ * that doesn't look like a cell address is still a ParseError, exactly as
+ * before.
+ * ---------------------------------------------------------------------------
  */
 
 import { tokenize, type Token, type TokenType, LexError } from './lexer';
@@ -42,7 +50,8 @@ export type Node =
   | UnaryNode
   | FuncNode
   | CellNode
-  | RangeNode;
+  | RangeNode
+  | ParamNode;
 
 export interface NumberNode {
   kind: 'number';
@@ -83,12 +92,25 @@ export interface RangeNode {
   start: { col: number; row: number };
   end: { col: number; row: number };
 }
+/** A reference to a user-defined function's own parameter -- only produced
+ *  when parseFormula() is given a `paramNames` list (parsing a function
+ *  body); never appears in an ordinary cell formula's AST. Resolved away by
+ *  userFunctions.ts's expandUserFunctions() before evaluation ever sees it. */
+export interface ParamNode {
+  kind: 'param';
+  name: string;
+}
 
 export class ParseError extends Error {}
 
 class Parser {
   private i = 0;
-  constructor(private readonly toks: Token[]) {}
+  /** Case-insensitively matched (compared upper-cased), like function names
+   *  elsewhere in the engine (functions.ts's getFunction()). */
+  private readonly paramNames: ReadonlySet<string>;
+  constructor(private readonly toks: Token[], paramNames: readonly string[] = []) {
+    this.paramNames = new Set(paramNames.map((p) => p.toUpperCase()));
+  }
 
   private peek(): Token {
     return this.toks[this.i];
@@ -210,6 +232,13 @@ class Parser {
     if (!firstTok && a.type !== 'IDENT') {
       throw new ParseError(`Expected cell reference at ${a.pos}`);
     }
+    // an unqualified name matching a declared parameter -- only reachable
+    // when parseFormula() was given a paramNames list; a param is always a
+    // scalar, so it's never part of a qualifier or a ":"-range, only ever
+    // this single bare token.
+    if (qualifier === null && this.paramNames.has(a.value.toUpperCase())) {
+      return { kind: 'param', name: a.value };
+    }
     if (!looksLikeCell(a.value)) {
       throw new ParseError(`'${a.value}' is not a valid cell reference (pos ${a.pos})`);
     }
@@ -249,8 +278,13 @@ class Parser {
  * Parse a raw formula. The leading "=" is optional (callers usually strip it).
  * Throws {@link ParseError} / {@link LexError} on malformed input; the store
  * turns those into the `#ERR` cell value.
+ *
+ * `paramNames`, when given, is a user-defined function's parameter list --
+ * bare identifiers matching one of them parse as a {@link ParamNode} instead
+ * of requiring cell-address shape. Omit it (the default) for every ordinary
+ * cell formula; behaviour is then identical to before this existed.
  */
-export function parseFormula(src: string): Node {
+export function parseFormula(src: string, paramNames?: readonly string[]): Node {
   const body = src.startsWith('=') ? src.slice(1) : src;
   let toks: Token[];
   try {
@@ -259,7 +293,7 @@ export function parseFormula(src: string): Node {
     if (e instanceof LexError) throw new ParseError(e.message);
     throw e;
   }
-  return new Parser(toks).parse();
+  return new Parser(toks, paramNames).parse();
 }
 
 /** Walk an AST and collect every cell/range reference node it contains. */

src/engine/userFunctions.ts

@@ -0,0 +1,159 @@
+/**
+ * User-defined functions: a document-level library of named, parameterised
+ * formulas (`MARGE(revenue; cost) = (revenue - cost) / revenue`) callable
+ * from any cell like a built-in (`=MARGE(Umsatz!B2; Umsatz!C2)`).
+ *
+ * The evaluator (`evaluator.ts`) evaluates function arguments *eagerly* --
+ * scalar `CellValue`s in, `CellValue` out (`FunctionFn` in `functions.ts`) --
+ * which has no room for a "body formula with its own cell references and a
+ * parameter environment". Rather than rework the evaluator, a call to a
+ * user-defined function is *inlined* into the caller's AST at parse time,
+ * before the graph/evaluator ever see it: the `FuncNode` is replaced by a
+ * (recursively expanded) copy of the function body, with every `ParamNode`
+ * swapped for the caller's own argument subtree. After that, the stored AST
+ * looks exactly as if the user had written the expanded formula by hand --
+ * `collectRefs`/`precedentsOf`/`evaluate` all work completely unmodified,
+ * and correctly pick up cell references that live *only* inside the
+ * function body, not just the ones passed as arguments.
+ */
+
+import { parseFormula, type Node } from './parser';
+
+export interface FunctionDef {
+  id: string;
+  /** document-unique, matched case-insensitively (like built-in names). */
+  name: string;
+  /** parameter names, in call order. */
+  params: string[];
+  /** raw formula text, no leading "=". */
+  body: string;
+}
+
+/** Recursion guard for `expandUserFunctions` -- a cycle should always be
+ *  rejected at definition time (see the store's cycle check), this is only
+ *  a last-resort safety net so a bug there degrades to a cell error rather
+ *  than a stack overflow. */
+const MAX_EXPANSION_DEPTH = 32;
+
+export function buildFunctionIndex(defs: readonly FunctionDef[]): Map<string, FunctionDef> {
+  return new Map(defs.map((d) => [d.name.toUpperCase(), d]));
+}
+
+/**
+ * Replace every call to a user-defined function in `ast` with a (recursively
+ * expanded, parameter-substituted) copy of its body. Calls to built-in or
+ * genuinely unknown names are left untouched -- `evaluate()`'s existing
+ * `#NAME?` path already covers "unknown function", built-in or not.
+ *
+ * Throws a plain `Error` (not `ParseError` -- there's nothing to parse here,
+ * just structural problems: wrong argument count, or a definition cycle
+ * `MAX_EXPANSION_DEPTH` didn't catch at save time) on failure; the caller
+ * (`Workbook.parseCell`) wraps this the same way it already wraps
+ * `parseFormula` errors, turning it into a `#ERR` cell value.
+ */
+export function expandUserFunctions(ast: Node, index: ReadonlyMap<string, FunctionDef>): Node {
+  if (index.size === 0) return ast; // fast path: no user functions defined at all
+  return expand(ast, index, new Map(), 0);
+}
+
+function expand(
+  node: Node,
+  index: ReadonlyMap<string, FunctionDef>,
+  bodyCache: Map<string, Node>,
+  depth: number,
+): Node {
+  switch (node.kind) {
+    case 'number':
+    case 'string':
+    case 'cell':
+    case 'range':
+    case 'param':
+      return node; // leaves -- nothing to expand
+    case 'unary':
+      return { ...node, operand: expand(node.operand, index, bodyCache, depth) };
+    case 'binary':
+      return {
+        ...node,
+        left: expand(node.left, index, bodyCache, depth),
+        right: expand(node.right, index, bodyCache, depth),
+      };
+    case 'func': {
+      // expand the arguments regardless of whether this call is itself a
+      // user function -- a built-in like SUM(...) may still take a
+      // user-function call as one of its arguments.
+      const args = node.args.map((a) => expand(a, index, bodyCache, depth));
+      const def = index.get(node.name.toUpperCase());
+      if (!def) return { ...node, args };
+
+      if (depth >= MAX_EXPANSION_DEPTH) {
+        throw new Error(`'${def.name}' expansion too deep (likely a definition cycle)`);
+      }
+      if (args.length !== def.params.length) {
+        throw new Error(
+          `'${def.name}' expects ${def.params.length} argument(s), got ${args.length}`,
+        );
+      }
+
+      let body = bodyCache.get(def.id);
+      if (!body) {
+        body = parseFormula(def.body, def.params); // ParseError propagates -- caller wraps it
+        bodyCache.set(def.id, body);
+      }
+      // expand any calls *inside* the body first (it may call other user
+      // functions -- possibly reusing the same parameter names as this one;
+      // resolving inside-out like this keeps each function's own parameters
+      // scoped correctly no matter what the caller's happen to be named),
+      // then substitute this function's own parameters last.
+      const expandedBody = expand(body, index, bodyCache, depth + 1);
+      const bound = new Map(def.params.map((p, i) => [p.toUpperCase(), args[i]]));
+      return substitute(expandedBody, bound);
+    }
+  }
+}
+
+function substitute(node: Node, bound: ReadonlyMap<string, Node>): Node {
+  switch (node.kind) {
+    case 'param':
+      // always found in practice (arity is checked before this runs, and
+      // parameter names are exactly what the body was parsed against) --
+      // the fallback just leaves an unresolved param for evaluate()'s own
+      // defensive #ERR case rather than assuming it can't happen.
+      return bound.get(node.name.toUpperCase()) ?? node;
+    case 'number':
+    case 'string':
+    case 'cell':
+    case 'range':
+      return node;
+    case 'unary':
+      return { ...node, operand: substitute(node.operand, bound) };
+    case 'binary':
+      return { ...node, left: substitute(node.left, bound), right: substitute(node.right, bound) };
+    case 'func':
+      return { ...node, args: node.args.map((a) => substitute(a, bound)) };
+  }
+}
+
+/**
+ * Every distinct function name called anywhere in `ast` (built-in or not --
+ * callers filter against their own registry). Used by the store to build a
+ * definition-time call graph between user functions for cycle detection,
+ * without a second AST-walking implementation alongside `collectRefs`.
+ */
+export function collectCalledFunctionNames(ast: Node, out: Set<string> = new Set()): Set<string> {
+  switch (ast.kind) {
+    case 'func':
+      out.add(ast.name.toUpperCase());
+      ast.args.forEach((a) => collectCalledFunctionNames(a, out));
+      break;
+    case 'binary':
+      collectCalledFunctionNames(ast.left, out);
+      collectCalledFunctionNames(ast.right, out);
+      break;
+    case 'unary':
+      collectCalledFunctionNames(ast.operand, out);
+      break;
+    default:
+      break; // number/string/cell/range/param -- no nested calls
+  }
+  return out;
+}

src/engine/workbook.ts

@@ -22,6 +22,7 @@
 import { DependencyGraph } from './graph';
 import { collectRefs, parseFormula, type Node } from './parser';
 import { expandRange } from './refs';
+import { buildFunctionIndex, expandUserFunctions, type FunctionDef } from './userFunctions';
 import {
   FormulaError,
   isError,
@@ -66,9 +67,12 @@ export class Workbook implements EngineHost {
   private readonly asts = new Map<string, Node | FormulaError>();
   /** cellKey -> computed value */
   private readonly values = new Map<string, CellValue>();
+  /** user-defined function library for this document, name.toUpperCase() -> def. */
+  private readonly functionIndex: Map<string, FunctionDef>;
 
-  constructor(tables: TableModel[]) {
+  constructor(tables: TableModel[], functionDefs: FunctionDef[] = []) {
     this.tables = tables;
+    this.functionIndex = buildFunctionIndex(functionDefs);
     this.rebuild();
   }
 
@@ -150,6 +154,7 @@ export class Workbook implements EngineHost {
     let ast: Node;
     try {
       ast = parseFormula(raw);
+      ast = expandUserFunctions(ast, this.functionIndex);
     } catch (e) {
       // a bad formula is a cell-level error, never a crash
       this.asts.set(key, new FormulaError('#ERR', (e as Error).message));

src/io/json.ts

@@ -11,6 +11,7 @@
 import type {
   CellFormat,
   ChartObject,
+  CustomFunction,
   DocumentState,
   HAlign,
   Sheet,
@@ -32,6 +33,30 @@ function localeOrUndef(x: unknown): NumberLocale | undefined {
   return isNumberLocale(x) ? x : undefined;
 }
 
+/** Defaults to `[]` -- absent in every document saved before this feature
+ *  existed (and in v1 documents entirely) -- and drops any malformed entry
+ *  rather than rejecting the whole import over one bad function. */
+function normaliseCustomFunctions(x: unknown): CustomFunction[] {
+  if (!Array.isArray(x)) return [];
+  const out: CustomFunction[] = [];
+  for (const f of x) {
+    if (
+      !f ||
+      typeof f !== 'object' ||
+      typeof (f as { id?: unknown }).id !== 'string' ||
+      typeof (f as { name?: unknown }).name !== 'string' ||
+      typeof (f as { body?: unknown }).body !== 'string' ||
+      !Array.isArray((f as { params?: unknown }).params) ||
+      !(f as { params: unknown[] }).params.every((p) => typeof p === 'string')
+    ) {
+      continue;
+    }
+    const rec = f as CustomFunction;
+    out.push({ id: rec.id, name: rec.name, params: [...rec.params], body: rec.body });
+  }
+  return out;
+}
+
 const HEX_COLOR = /^#(?:[0-9a-f]{3}|[0-9a-f]{4}|[0-9a-f]{6}|[0-9a-f]{8})$/i;
 function colorOrUndef(x: unknown): string | undefined {
   return typeof x === 'string' && HEX_COLOR.test(x) ? x : undefined;
@@ -303,6 +328,7 @@ export function validateDocument(x: unknown): DocumentState {
         : null,
     locale: isNumberLocale(doc.locale) ? doc.locale : DEFAULT_LOCALE,
     csvDelimiter: doc.csvDelimiter === ';' ? ';' : ',',
+    customFunctions: normaliseCustomFunctions(doc.customFunctions),
   };
 }
 
@@ -365,6 +391,7 @@ export function migrateToV2(x: unknown): DocumentState {
         : null,
     locale: DEFAULT_LOCALE,
     csvDelimiter: ',',
+    customFunctions: [],
   };
 }
 

src/store/__tests__/document.spec.ts

@@ -677,6 +677,128 @@ describe('fill handle (drag to copy/fill)', () => {
   });
 });
 
+describe('custom functions (document-level library)', () => {
+  it('addCustomFunction stores the definition and a call evaluates through it', () => {
+    const s = fresh();
+    const id = s.addTable(s.doc.activeSheetId);
+    const name = s.tableById(id)!.name;
+    setCell(s, name, 'A1', '1200');
+    setCell(s, name, 'A2', '800');
+
+    const result = s.addCustomFunction('MARGE', ['revenue', 'cost'], '(revenue - cost) / revenue');
+    expect(typeof result).toBe('string'); // the new function's id, not { error }
+    expect(s.doc.customFunctions).toHaveLength(1);
+    expect(s.doc.customFunctions[0]).toMatchObject({ name: 'MARGE', params: ['revenue', 'cost'] });
+
+    setCell(s, name, 'A3', '=MARGE(A1;A2)');
+    expect(val(s, name, 'A3')).toBeCloseTo((1200 - 800) / 1200, 10);
+
+    // recalculates when a precedent changes
+    setCell(s, name, 'A1', '2000');
+    expect(val(s, name, 'A3')).toBeCloseTo((2000 - 800) / 2000, 10);
+  });
+
+  it('rejects a name colliding with a built-in function', () => {
+    const s = fresh();
+    const result = s.addCustomFunction('SUM', ['x'], 'x') as { error: string };
+    expect(result.error).toBeTruthy();
+    expect(s.doc.customFunctions).toHaveLength(0);
+  });
+
+  it('rejects a name colliding with another custom function (case-insensitive)', () => {
+    const s = fresh();
+    s.addCustomFunction('Marge', ['x'], 'x');
+    const result = s.addCustomFunction('MARGE', ['y'], 'y') as { error: string };
+    expect(result.error).toBeTruthy();
+    expect(s.doc.customFunctions).toHaveLength(1);
+  });
+
+  it('rejects a name or parameter that looks like a cell address', () => {
+    const s = fresh();
+    expect((s.addCustomFunction('A1', ['x'], 'x') as { error: string }).error).toBeTruthy();
+    expect((s.addCustomFunction('OK', ['B2'], 'B2') as { error: string }).error).toBeTruthy();
+    expect(s.doc.customFunctions).toHaveLength(0);
+  });
+
+  it('rejects duplicate parameter names', () => {
+    const s = fresh();
+    const result = s.addCustomFunction('F', ['x', 'x'], 'x') as { error: string };
+    expect(result.error).toBeTruthy();
+  });
+
+  it('rejects a body that fails to parse', () => {
+    const s = fresh();
+    const result = s.addCustomFunction('F', ['x'], 'x +') as { error: string };
+    expect(result.error).toBeTruthy();
+  });
+
+  it('rejects a direct self-reference cycle (A calls A)', () => {
+    const s = fresh();
+    const result = s.addCustomFunction('A', ['x'], 'A(x) + 1') as { error: string };
+    expect(result.error).toBeTruthy();
+    expect(s.doc.customFunctions).toHaveLength(0);
+  });
+
+  it('rejects a mutual cycle (A calls B, B calls A) at the point it would close', () => {
+    const s = fresh();
+    const a = s.addCustomFunction('A', ['x'], 'x') as string;
+    expect(typeof a).toBe('string');
+    // B calling A is fine so far -- no cycle yet
+    const b = s.addCustomFunction('B', ['x'], 'A(x)') as string;
+    expect(typeof b).toBe('string');
+    // now redefine A to call B -- this closes the cycle A -> B -> A
+    const result = s.updateCustomFunction(a, 'A', ['x'], 'B(x)') as { error: string } | undefined;
+    expect(result?.error).toBeTruthy();
+    // rejected -- A's body is unchanged
+    expect(s.doc.customFunctions.find((f) => f.id === a)!.body).toBe('x');
+  });
+
+  it('updateCustomFunction changes name/params/body and existing calls re-resolve', () => {
+    const s = fresh();
+    const id = s.addTable(s.doc.activeSheetId);
+    const name = s.tableById(id)!.name;
+    const fnId = s.addCustomFunction('MARGE', ['x', 'y'], 'x - y') as string;
+    setCell(s, name, 'A1', '=MARGE(10;3)');
+    expect(val(s, name, 'A1')).toBe(7);
+
+    s.updateCustomFunction(fnId, 'MARGE', ['x', 'y'], 'x + y');
+    expect(val(s, name, 'A1')).toBe(13);
+  });
+
+  it('deleteCustomFunction removes the definition; existing calls become #NAME?', () => {
+    const s = fresh();
+    const id = s.addTable(s.doc.activeSheetId);
+    const name = s.tableById(id)!.name;
+    const fnId = s.addCustomFunction('MARGE', ['x', 'y'], 'x - y') as string;
+    setCell(s, name, 'A1', '=MARGE(10;3)');
+    expect(val(s, name, 'A1')).toBe(7);
+
+    s.deleteCustomFunction(fnId);
+    expect(s.doc.customFunctions).toHaveLength(0);
+    expect(isError(val(s, name, 'A1'))).toBe(true);
+  });
+
+  it('undo/redo covers a custom-function change', () => {
+    vi.useFakeTimers();
+    try {
+      const s = fresh();
+      expect(s.canUndo.value).toBe(false);
+      s.addCustomFunction('MARGE', ['x', 'y'], 'x - y');
+      vi.advanceTimersByTime(600);
+      expect(s.doc.customFunctions).toHaveLength(1);
+
+      s.undo();
+      expect(s.doc.customFunctions).toHaveLength(0);
+      s.redo();
+      expect(s.doc.customFunctions).toHaveLength(1);
+      expect(s.doc.customFunctions[0].name).toBe('MARGE');
+    } finally {
+      vi.runOnlyPendingTimers();
+      vi.useRealTimers();
+    }
+  });
+});
+
 describe('undo / redo', () => {
   // rapid-fire changes (a resize drag, or several store calls in one
   // synchronous action) coalesce into a single undo step -- tests that want
@@ -1023,6 +1145,9 @@ describe('full-fidelity JSON export — backgrounds, formats, sheet settings', (
     s.addToSelection(umsatzId, 2, 2);
     s.addToSelection(umsatzId, 4, 5);
 
+    // a custom function
+    s.addCustomFunction('MARGE', ['revenue', 'cost'], '(revenue - cost) / revenue');
+
     return { analyse, umsatzId, chartId, txtId };
   }
 
@@ -1086,6 +1211,14 @@ describe('full-fidelity JSON export — backgrounds, formats, sheet settings', (
 
     // multi-range selection
     expect(doc.selection.ranges).toHaveLength(2);
+
+    // custom function
+    expect(doc.customFunctions).toHaveLength(1);
+    expect(doc.customFunctions[0]).toMatchObject({
+      name: 'MARGE',
+      params: ['revenue', 'cost'],
+      body: '(revenue - cost) / revenue',
+    });
   });
 
   it('export -> import is lossless for the fully-loaded document', () => {
@@ -1124,6 +1257,7 @@ describe('v1 -> v2 migration', () => {
     expect(v2.version).toBe(2);
     expect(v2.sheets).toHaveLength(2);
     expect(v2.sheets[0].objects[0]).toMatchObject({ kind: 'table', name: 'Umsatz' });
+    expect(v2.customFunctions).toEqual([]); // the feature didn't exist in v1
     // cross-sheet formula still resolves after loading it
     const store = useDocument();
     store.replaceDocument(v2);

src/store/document.ts

@@ -25,9 +25,13 @@ import {
   tokenize,
   looksLikeCell,
   parseA1,
+  parseFormula,
+  hasFunction,
+  collectCalledFunctionNames,
   type CellValue,
   type TableModel,
   type Token,
+  type FunctionDef,
 } from '../engine';
 import {
   formatValue,
@@ -40,6 +44,7 @@ import type {
   CellCoord,
   CellFormat,
   ChartObject,
+  CustomFunction,
   DocumentState,
   Sheet,
   SelectionState,
@@ -76,6 +81,10 @@ function toTableModels(doc: DocumentState): TableModel[] {
   }));
 }
 
+function toFunctionDefs(doc: DocumentState): FunctionDef[] {
+  return doc.customFunctions.map((f) => ({ id: f.id, name: f.name, params: f.params, body: f.body }));
+}
+
 /** A normalised rectangle (corners in either order) used by selection + clipboard. */
 type Rect = { c0: number; c1: number; r0: number; r1: number };
 
@@ -182,7 +191,7 @@ function loadInitial(): DocumentState {
 
 function createStore() {
   const doc = reactive<DocumentState>(loadInitial());
-  let wb = new Workbook(toTableModels(doc));
+  let wb = new Workbook(toTableModels(doc), toFunctionDefs(doc));
   const recalcTick = ref(0);
   const bump = () => (recalcTick.value += 1);
 
@@ -202,7 +211,7 @@ function createStore() {
   const clampZoom = (z: number) => Math.min(2, Math.max(0.4, Math.round(z * 20) / 20));
 
   function syncWorkbook() {
-    wb = new Workbook(toTableModels(doc));
+    wb = new Workbook(toTableModels(doc), toFunctionDefs(doc));
     bump();
   }
 
@@ -247,7 +256,12 @@ function createStore() {
   const undoStack: DocumentState[] = [];
   const redoStack: DocumentState[] = [];
   const contentFingerprint = (d: DocumentState) =>
-    JSON.stringify({ sheets: d.sheets, locale: d.locale, csvDelimiter: d.csvDelimiter });
+    JSON.stringify({
+      sheets: d.sheets,
+      locale: d.locale,
+      csvDelimiter: d.csvDelimiter,
+      customFunctions: d.customFunctions,
+    });
   let historySnapshot = snapshot();
   let historyFingerprint = contentFingerprint(historySnapshot);
   let historyTimer: ReturnType<typeof setTimeout> | undefined;
@@ -618,6 +632,142 @@ function createStore() {
     else bump();
   }
 
+  // ---- custom functions (document-level formula library) ----------------
+  // Created/edited/removed exclusively through the "𝑓 Funktionen" UI. A call
+  // is inlined into the caller's AST at parse time (engine/userFunctions.ts)
+  // -- renaming/deleting one behaves exactly like renaming/deleting a table:
+  // existing formula text is left as-is and becomes #NAME? / #REF on the next
+  // syncWorkbook(), there is no find-and-replace across stored formulas.
+  const IDENT_RE = /^[A-Za-z_][A-Za-z0-9_]*$/;
+
+  const customFunctionNames = () => new Set(doc.customFunctions.map((f) => f.name.toLowerCase()));
+
+  /** Every (upper-cased) function name a stored custom function's body calls,
+   *  tolerant of a body that -- in theory -- no longer parses (shouldn't
+   *  happen; a save always validates first, but this is only used for a
+   *  best-effort cycle check, so fail open rather than block unrelated saves). */
+  function bodyCallSet(params: string[], body: string): Set<string> {
+    try {
+      return collectCalledFunctionNames(parseFormula(body, params));
+    } catch {
+      return new Set();
+    }
+  }
+
+  /** Does the call graph across every custom function (built-ins are never
+   *  nodes -- they can't call back into user functions) contain a cycle? */
+  function callGraphHasCycle(graph: Map<string, Set<string>>): boolean {
+    const state = new Map<string, 1 | 2>(); // 1 = on the current DFS path, 2 = fully explored
+    function dfs(node: string): boolean {
+      const st = state.get(node);
+      if (st === 1) return true; // back-edge -> cycle
+      if (st === 2) return false;
+      state.set(node, 1);
+      for (const callee of graph.get(node) ?? []) {
+        if (graph.has(callee) && dfs(callee)) return true;
+      }
+      state.set(node, 2);
+      return false;
+    }
+    for (const node of graph.keys()) {
+      if (dfs(node)) return true;
+    }
+    return false;
+  }
+
+  /**
+   * Full validation for add/update: name & parameter shape, no collision with
+   * a built-in or another custom function, the body parses, and -- simulating
+   * the *whole* call graph with this function's (possibly new) definition in
+   * place -- no cycle. Returns a user-facing (German) error string, or null
+   * when the definition is safe to save. `ignoreId` excludes the function
+   * being edited from the collision/graph checks against its own old state.
+   */
+  function validateCustomFunction(
+    name: string,
+    params: string[],
+    body: string,
+    ignoreId: string | null,
+  ): string | null {
+    const cleanName = name.trim();
+    if (!IDENT_RE.test(cleanName)) {
+      return `"${name}" ist kein gültiger Funktionsname.`;
+    }
+    if (looksLikeCell(cleanName)) {
+      return `"${cleanName}" sieht wie ein Zellbezug aus und ist als Funktionsname nicht erlaubt.`;
+    }
+    if (hasFunction(cleanName)) {
+      return `"${cleanName}" ist bereits eine eingebaute Funktion und kann nicht überschrieben werden.`;
+    }
+    const collision = doc.customFunctions.find(
+      (f) => f.id !== ignoreId && f.name.toLowerCase() === cleanName.toLowerCase(),
+    );
+    if (collision) return `Es gibt bereits eine Funktion namens "${collision.name}".`;
+
+    const cleanParams = params.map((p) => p.trim());
+    for (const p of cleanParams) {
+      if (!IDENT_RE.test(p)) return `"${p}" ist kein gültiger Parametername.`;
+      if (looksLikeCell(p)) return `Parameter "${p}" sieht wie ein Zellbezug aus.`;
+    }
+    if (new Set(cleanParams.map((p) => p.toLowerCase())).size !== cleanParams.length) {
+      return 'Parameternamen müssen eindeutig sein.';
+    }
+
+    let ast;
+    try {
+      ast = parseFormula(body, cleanParams);
+    } catch (e) {
+      return `Formel ungültig: ${e instanceof Error ? e.message : String(e)}`;
+    }
+
+    const graph = new Map<string, Set<string>>();
+    for (const f of doc.customFunctions) {
+      if (f.id === ignoreId) continue;
+      graph.set(f.name.toUpperCase(), bodyCallSet(f.params, f.body));
+    }
+    graph.set(cleanName.toUpperCase(), collectCalledFunctionNames(ast));
+    if (callGraphHasCycle(graph)) {
+      return `"${cleanName}" führt (direkt oder über andere Funktionen) zu einem Zyklus.`;
+    }
+    return null;
+  }
+
+  function addCustomFunction(name: string, params: string[], body: string): string | { error: string } {
+    const error = validateCustomFunction(name, params, body, null);
+    if (error) return { error };
+    const id = uid('fn');
+    const custom: CustomFunction = {
+      id,
+      name: name.trim(),
+      params: params.map((p) => p.trim()),
+      body: body.startsWith('=') ? body.slice(1) : body,
+    };
+    doc.customFunctions.push(custom);
+    syncWorkbook();
+    return id;
+  }
+
+  function updateCustomFunction(
+    id: string,
+    name: string,
+    params: string[],
+    body: string,
+  ): void | { error: string } {
+    const f = doc.customFunctions.find((x) => x.id === id);
+    if (!f) return { error: 'Funktion nicht gefunden.' };
+    const error = validateCustomFunction(name, params, body, id);
+    if (error) return { error };
+    f.name = name.trim();
+    f.params = params.map((p) => p.trim());
+    f.body = body.startsWith('=') ? body.slice(1) : body;
+    syncWorkbook();
+  }
+
+  function deleteCustomFunction(id: string) {
+    doc.customFunctions = doc.customFunctions.filter((f) => f.id !== id);
+    syncWorkbook(); // affected calls become #NAME? on rebuild, same as a deleted table
+  }
+
   function moveObject(objId: string, x: number, y: number) {
     const o = objectById(objId);
     if (!o) return;
@@ -1299,6 +1449,7 @@ function createStore() {
     doc.selection = next.selection ?? null;
     doc.locale = isNumberLocale(next.locale) ? next.locale : DEFAULT_LOCALE;
     doc.csvDelimiter = next.csvDelimiter === ';' ? ';' : ',';
+    doc.customFunctions = next.customFunctions ?? [];
     syncWorkbook();
   }
   /** Loading a different document outright (JSON import "replace", "reset to
@@ -1388,6 +1539,11 @@ function createStore() {
     renameObject,
     deleteObject,
     moveObject,
+    // custom functions
+    customFunctionNames,
+    addCustomFunction,
+    updateCustomFunction,
+    deleteCustomFunction,
     resizeChart,
     bringToFront,
     setChartView,

src/store/types.ts

@@ -149,6 +149,20 @@ export interface SelectionState {
   ranges?: SelectionRange[];
 }
 
+/** A document-wide, user-defined formula function, callable from any cell
+ *  like a built-in (e.g. `=MARGE(Umsatz!B2; Umsatz!C2)`). Created, edited and
+ *  removed exclusively through the "𝑓 Funktionen" UI -- see
+ *  src/engine/userFunctions.ts for how a call is expanded into a cell's AST. */
+export interface CustomFunction {
+  id: string;
+  /** document-unique, compared case-insensitively; never a built-in name. */
+  name: string;
+  /** parameter names, in call order; may be empty (a plain named formula). */
+  params: string[];
+  /** raw formula text, no leading "=". */
+  body: string;
+}
+
 export interface DocumentState {
   version: 2;
   sheets: Sheet[];
@@ -157,4 +171,5 @@ export interface DocumentState {
   selection: SelectionState | null;
   locale: NumberLocale;
   csvDelimiter: ',' | ';';
+  customFunctions: CustomFunction[];
 }