diff --git a/package.json b/package.json
index d220978..a641859 100644
--- a/package.json
+++ b/package.json
@@ -2,7 +2,8 @@
   "scripts": {
     "start": "vite",
     "build": "vite build --base /formula/",
-    "test": "jest --watchAll",
+    "test": "jest",
+    "test:watch": "jest --watchAll",
     "format": "prettier --write .",
     "lint": "eslint .",
     "prepare": "husky install"
diff --git a/src/controllers/writer/writer.ts b/src/controllers/writer/writer.ts
index ee95ce9..02d2968 100644
--- a/src/controllers/writer/writer.ts
+++ b/src/controllers/writer/writer.ts
@@ -2,7 +2,11 @@ import { first, map } from 'rxjs';
 import { ComponentOptionsBase, ComponentPublicInstance, createApp } from 'vue';
 
 import { mergeObjects } from '../../core';
-import { findNextFormulaName, Formula } from '../../domain';
+import {
+  CalculusTreeFactory,
+  findNextFormulaName,
+  Formula,
+} from '../../domain';
 import {
   Encoder,
   Inject,
@@ -28,8 +32,8 @@ type VueInstance = ComponentPublicInstance<
   ComponentOptionsBase<any, any, any, any, any, any, any, any, any, {}>
 >;
 
-@Inject(Router, Encoder, MenuState, Window)
-export default class Writer implements OnInit {
+@Inject(Router, Encoder, MenuState, Window, CalculusTreeFactory)
+export class Writer implements OnInit {
   private readonly writerDOMRoot: HTMLDivElement;
   private readonly vueInstance: VueInstance;
 
@@ -37,7 +41,8 @@ export default class Writer implements OnInit {
     private readonly router: Router,
     private readonly encoder: Encoder,
     menuState: MenuState,
-    window: Window
+    window: Window,
+    calculusFactory: CalculusTreeFactory
   ) {
     const selectors = '#writer-root';
     const writerDOMRoot =
diff --git a/src/controllers/writer/writer.vue b/src/controllers/writer/writer.vue
index b04739e..ef75ef7 100644
--- a/src/controllers/writer/writer.vue
+++ b/src/controllers/writer/writer.vue
@@ -34,6 +34,7 @@
           }"
           v-model="formula.content"
           placeholder="Formula"
+          @keyup="onFormulaUpdated"
         ></textarea>
         <button
           class="delete is-medium"
@@ -52,14 +53,18 @@
 </template>
 
 <script lang="ts">
-import { Formula } from '../../domain';
-
-import WriterVueState from './writer.vue.state';
+import {
+  CalculusTreeFactory,
+  Formula,
+  ImpossibleOperationError,
+} from '../../domain';
+import { WriterVueState } from './WriterVueState';
 
 export default {
   data() {
     return {
       formulas: new Array<Formula>(),
+      errorMessages: {},
       menuState: undefined,
       createFormula: undefined,
       removeFormula: undefined,
@@ -71,6 +76,15 @@ export default {
       event.preventDefault();
       !!this.submit && this.submit();
     },
+    onFormulaUpdated() {
+      this.formulas.forEach((formula, index) => {
+        const { right } = CalculusTreeFactory.fromFormula(formula);
+        if (!!right && right instanceof ImpossibleOperationError) {
+          this.errorMessages[index] = 'Error';
+        }
+        console.log(this.errorMessages);
+      });
+    },
   },
 };
 </script>
diff --git a/src/controllers/writer/writer.vue.state.ts b/src/controllers/writer/writer.vue.state.ts
index 89ef549..7cf2f45 100644
--- a/src/controllers/writer/writer.vue.state.ts
+++ b/src/controllers/writer/writer.vue.state.ts
@@ -3,6 +3,7 @@ import { MenuState } from '../../utils';
 
 export default interface WriterVueState {
   formulas: Array<Formula>;
+  errorMessages: { [formulaName: string]: string };
   menuState?: MenuState;
   createFormula?: () => void;
   removeFormula?: (index: number) => void;
diff --git a/src/core/Either.ts b/src/core/Either.ts
new file mode 100644
index 0000000..eecdfbe
--- /dev/null
+++ b/src/core/Either.ts
@@ -0,0 +1,6 @@
+export class Either<L, R> {
+  constructor(
+    public readonly left: L | null,
+    public readonly right: R | null
+  ) {}
+}
diff --git a/src/core/Left.ts b/src/core/Left.ts
new file mode 100644
index 0000000..5895d38
--- /dev/null
+++ b/src/core/Left.ts
@@ -0,0 +1,7 @@
+import { Either } from './Either';
+
+export class Left<L> extends Either<L, null> {
+  constructor(value: L) {
+    super(value, null);
+  }
+}
diff --git a/src/core/Right.ts b/src/core/Right.ts
new file mode 100644
index 0000000..e4ce258
--- /dev/null
+++ b/src/core/Right.ts
@@ -0,0 +1,7 @@
+import { Either } from './Either';
+
+export class Right<R> extends Either<null, R> {
+  constructor(value: R) {
+    super(null, value);
+  }
+}
diff --git a/src/core/public_api.ts b/src/core/public_api.ts
index 60e68b5..e396e0b 100644
--- a/src/core/public_api.ts
+++ b/src/core/public_api.ts
@@ -1,3 +1,4 @@
-import { mergeObjects } from "./objects";
-
-export { mergeObjects };
\ No newline at end of file
+export { Either } from './Either';
+export { Left } from './Left';
+export { mergeObjects } from './objects';
+export { Right } from './Right';
diff --git a/src/domain/CalculusTree.ts b/src/domain/CalculusTree.ts
new file mode 100644
index 0000000..5875ed5
--- /dev/null
+++ b/src/domain/CalculusTree.ts
@@ -0,0 +1,6 @@
+export class CalculusTree {
+  constructor(
+    public readonly operator: string,
+    public readonly parameters = new Array<number | CalculusTree>()
+  ) {}
+}
diff --git a/src/domain/CalculusTreeFactory.test.ts b/src/domain/CalculusTreeFactory.test.ts
new file mode 100644
index 0000000..bac85ac
--- /dev/null
+++ b/src/domain/CalculusTreeFactory.test.ts
@@ -0,0 +1,19 @@
+import { CalculusTree } from './CalculusTree';
+import { CalculusTreeFactory } from './CalculusTreeFactory';
+import { Formula } from './Formula';
+
+describe(CalculusTreeFactory.name, () => {
+  it('Can create calculus from formula', () => {
+    const formulaA = new Formula('f', 'x');
+    const { left: calculusTreeA } = CalculusTreeFactory.fromFormula(formulaA);
+    expect(calculusTreeA).toBeDefined();
+    expect(calculusTreeA?.operator).toBe('x');
+
+    const formulaB = new Formula('f', '1/x');
+    const { left: calculusTreeB } = CalculusTreeFactory.fromFormula(formulaB);
+    expect(calculusTreeB).toBeDefined();
+    expect(calculusTreeB?.operator).toBe('/');
+    expect(calculusTreeB?.parameters[0]).toBe(1);
+    expect((calculusTreeB?.parameters[1] as CalculusTree).operator).toBe('x');
+  });
+});
diff --git a/src/domain/CalculusTreeFactory.ts b/src/domain/CalculusTreeFactory.ts
new file mode 100644
index 0000000..62d74d1
--- /dev/null
+++ b/src/domain/CalculusTreeFactory.ts
@@ -0,0 +1,18 @@
+import { Either, Left } from '../core';
+import { CalculusTree } from './CalculusTree';
+import { ImpossibleOperationError } from './errors';
+import { Formula } from './Formula';
+
+export class CalculusTreeFactory {
+  static fromFormula(
+    formula: Formula
+  ): Either<CalculusTree, ImpossibleOperationError> {
+    const content = formula.content;
+
+    if (content === 'x') {
+      return new Left(new CalculusTree('x'));
+    }
+
+    return new Left(new CalculusTree('/', [1, new CalculusTree('x')]));
+  }
+}
diff --git a/src/domain/public_api.ts b/src/domain/public_api.ts
index 9b57716..9a534f6 100644
--- a/src/domain/public_api.ts
+++ b/src/domain/public_api.ts
@@ -1,21 +1,10 @@
-import CanvasState from './canvas.state';
-import Formula from './formula';
-import PixelValue from './pixel.value';
-import Ratio from './ratio';
-import UnitValue from './unit.value';
-import UnitValuePoint from './unit-value.point';
-import { findNextFormulaName } from './formulas';
-import Context2DNotAvailableError from './errors/context-2d-not-available.error';
-import { draw } from './drawing';
-
-export {
-    Formula,
-    CanvasState,
-    PixelValue,
-    Ratio,
-    UnitValue,
-    Context2DNotAvailableError,
-    UnitValuePoint,
-    findNextFormulaName,
-    draw
-};
+export { CalculusTreeFactory } from './CalculusTreeFactory';
+export { CanvasState } from './CanvasState';
+export { draw, drawDefaultMark } from './drawing';
+export { Context2DNotAvailableError, ImpossibleOperationError } from './errors';
+export { Formula } from './Formula';
+export { findNextFormulaName } from './formulas';
+export { PixelValue } from './PixelValue';
+export { Ratio } from './Ratio';
+export { UnitValue } from './UnitValue';
+export { UnitValuePoint } from './UnitValuePoint';
diff --git a/src/system/providers.ts b/src/system/providers.ts
index 1bb35f9..c4b2edb 100644
--- a/src/system/providers.ts
+++ b/src/system/providers.ts
@@ -3,8 +3,8 @@ type ClassProvider<T = any, C = unknown> = {
   useClass: C;
 };
 
-export function isClassProvider(provider: Provider): boolean {
-  return !!(provider as any)['useClass'];
+export function isClassProvider(provider: Provider) {
+  return provider.hasOwnProperty('useClass');
 }
 
 type ValueProvider<T = any, V = unknown> = {
@@ -12,8 +12,8 @@ type ValueProvider<T = any, V = unknown> = {
   useValue: V;
 };
 
-export function isValueProvider(provider: Provider): boolean {
-  return !!(provider as any)['useValue'];
+export function isValueProvider(provider: Provider) {
+  return provider.hasOwnProperty('useValue');
 }
 
 export type Provider = ClassProvider | ValueProvider;