typescript-fp

name

typescript-fp

description

Master functional programming in TypeScript with type-safe patterns, strict typing, advanced type system features, discriminated unions, mapped types, conditional types, and functional patterns. Use when writing TypeScript code with functional paradigms, type-safe error handling with Option/Either types, implementing type-safe composition, leveraging TypeScript's type system for functional patterns, or ensuring compile-time safety in functional code.

Functional Programming in TypeScript

The Zen of Functional Programming in TypeScript

Types are truth The type system is your first and best test; trust it, extend it, let it guide refactoring.

Functions, not methods Favor pure, standalone functions over mutating methods. Logic and data are better apart.

Compose, don't construct Build complex behavior by wiring small functions, not by inheritance or sprawling classes.

Immutability is clarity Changing data increases entropy; prefer readonly and new values.

Explicit is safety Encode nullable, optional, and error-prone states as explicit types: Option, Either, custom unions.

Pipelines flow clearly Use composition (pipe, flow) to make data transformations readable and reasoned about at a glance.

Effects are contained Push side effects to the edge. Pure in the middle, async/io only when necessary and clearly isolated.

Type errors are friends If code doesn't type-check, it's not safe—fix it at compile time, not at runtime.

Libraries are bridges Leverage fp-ts, purify, and effect libraries—they bring the best of ML/Haskell/Scala worlds without leaving TypeScript.

The simplest solution wins If achievable by composing two pure functions, resist the urge for classes, frameworks, or lifecycles.

There is no 'any' in zen Avoid any: prefer unknown, never, or expressive unions. Demand and supply information with care.

Pattern match with safety Discriminated unions and pattern matching are clearer than chains of if/else or error-prone casts.

Refactor fearlessly Small, pure, and well-typed functions invite confident change—use types as a foundation for safety.

Embrace strictness strict: true and linting are not obstacles—they are the clearest guides on the path to quality.

TypeScript Configuration for FP

tsconfig.json

{
  "compilerOptions": {
    "strict": true,
    "strictNullChecks": true,
    "strictFunctionTypes": true,
    "strictBindCallApply": true,
    "strictPropertyInitialization": true,
    "noImplicitAny": true,
    "noImplicitThis": true,
    "noImplicitReturns": true,
    "noFallthroughCasesInSwitch": true,
    "noUncheckedIndexedAccess": true,
    "exactOptionalPropertyTypes": true,
    "noPropertyAccessFromIndexSignature": true,
    "allowUnusedLabels": false,
    "allowUnreachableCode": false,
    "target": "ES2022",
    "lib": ["ES2022"],
    "module": "ES2022",
    "moduleResolution": "bundler"
  }
}

ESLint Configuration

module.exports = {
  extends: [
    'eslint:recommended',
    'plugin:@typescript-eslint/recommended',
    'plugin:functional/recommended'
  ],
  plugins: ['@typescript-eslint', 'functional'],
  rules: {
    'functional/no-let': 'error',
    'functional/no-loop-statement': 'error',
    'functional/no-mutation': 'error',
    'functional/prefer-readonly-type': 'error',
    'functional/immutable-data': 'error',
    'functional/no-throw-statement': 'error',
    'functional/no-class': 'warn',
    'functional/no-this': 'warn',
    '@typescript-eslint/no-explicit-any': 'error',
    'prefer-const': 'error'
  }
};

Type System Features for FP

Advanced Type Utilities

// Readonly deeply nested structures
type DeepReadonly<T> = T extends Primitive
  ? T
  : T extends Array<infer U>
  ? ReadonlyArray<DeepReadonly<U>>
  : T extends Map<infer K, infer V>
  ? ReadonlyMap<DeepReadonly<K>, DeepReadonly<V>>
  : T extends Set<infer U>
  ? ReadonlySet<DeepReadonly<U>>
  : { readonly [K in keyof T]: DeepReadonly<T[K]> };

type Primitive = string | number | boolean | bigint | symbol | null | undefined;

// Extract function return type
type ReturnTypeOf<F> = F extends (...args: any[]) => infer R ? R : never;

// Extract function argument types
type ArgumentsOf<F> = F extends (...args: infer A) => any ? A : never;

// Make specific properties optional
type PartialBy<T, K extends keyof T> = Omit<T, K> & Partial<Pick<T, K>>;

// Make specific properties required
type RequiredBy<T, K extends keyof T> = Omit<T, K> & Required<Pick<T, K>>;

// Union to intersection
type UnionToIntersection<U> = 
  (U extends any ? (k: U) => void : never) extends 
  (k: infer I) => void ? I : never;

// Get keys where value type matches
type KeysOfType<T, V> = {
  [K in keyof T]: T[K] extends V ? K : never;
}[keyof T];

// NonEmptyArray type
type NonEmptyArray<T> = [T, ...T[]];

// Brand types for type safety
declare const brand: unique symbol;
type Brand<T, B> = T & { readonly [brand]: B };

type UserId = Brand<string, 'UserId'>;
type Email = Brand<string, 'Email'>;

const makeUserId = (id: string): UserId => id as UserId;
const makeEmail = (email: string): Email => email as Email;

Discriminated Unions

// Basic discriminated union
type Shape =
  | { kind: 'circle'; radius: number }
  | { kind: 'rectangle'; width: number; height: number }
  | { kind: 'square'; size: number };

const area = (shape: Shape): number => {
  switch (shape.kind) {
    case 'circle':
      return Math.PI * shape.radius ** 2;
    case 'rectangle':
      return shape.width * shape.height;
    case 'square':
      return shape.size ** 2;
  }
};

// Result type with discriminated union
type Result<E, A> =
  | { readonly _tag: 'Left'; readonly left: E }
  | { readonly _tag: 'Right'; readonly right: A };

const Left = <E, A = never>(left: E): Result<E, A> => 
  ({ _tag: 'Left', left });

const Right = <A, E = never>(right: A): Result<E, A> => 
  ({ _tag: 'Right', right });

// Type-safe pattern matching
const matchResult = <E, A, B>(
  result: Result<E, A>,
  patterns: {
    Left: (error: E) => B;
    Right: (value: A) => B;
  }
): B =>
  result._tag === 'Left' 
    ? patterns.Left(result.left) 
    : patterns.Right(result.right);

Mapped Types

// Make all properties optional recursively
type DeepPartial<T> = T extends Primitive
  ? T
  : T extends Array<infer U>
  ? Array<DeepPartial<U>>
  : T extends ReadonlyArray<infer U>
  ? ReadonlyArray<DeepPartial<U>>
  : { [K in keyof T]?: DeepPartial<T[K]> };

// Make all properties readonly recursively
type DeepReadonlyMap<T> = {
  readonly [K in keyof T]: DeepReadonly<T[K]>;
};

// Pick properties that are functions
type FunctionProperties<T> = Pick<T, KeysOfType<T, Function>>;

// Pick properties that are not functions
type NonFunctionProperties<T> = Pick<T, Exclude<keyof T, KeysOfType<T, Function>>>;

// Convert all methods to readonly functions
type ReadonlyMethods<T> = {
  readonly [K in keyof T]: T[K] extends (...args: infer A) => infer R
    ? (...args: A) => R
    : T[K];
};

Conditional Types

// Unwrap Promise type
type Awaited<T> = T extends Promise<infer U> ? Awaited<U> : T;

// Check if type is exactly a certain type
type IsExact<T, U> = 
  (<G>() => G extends T ? 1 : 2) extends 
  (<G>() => G extends U ? 1 : 2) ? true : false;

// Filter nullable values from union
type NonNullableFields<T> = {
  [K in keyof T]: NonNullable<T[K]>;
};

// Conditional required fields
type RequiredFields<T> = {
  [K in keyof T as T[K] extends Required<T>[K] ? K : never]: T[K];
};

// Conditional optional fields
type OptionalFields<T> = {
  [K in keyof T as T[K] extends Required<T>[K] ? never : K]: T[K];
};

Option Type Implementation

// Option type definition
type Option<A> =
  | { readonly _tag: 'None' }
  | { readonly _tag: 'Some'; readonly value: A };

// Constructors
const None = <A = never>(): Option<A> => ({ _tag: 'None' });

const Some = <A>(value: A): Option<A> => ({ _tag: 'Some', value });

// Type guards
const isNone = <A>(opt: Option<A>): opt is { _tag: 'None' } => 
  opt._tag === 'None';

const isSome = <A>(opt: Option<A>): opt is { _tag: 'Some'; value: A } => 
  opt._tag === 'Some';

// Core operations
const map = <A, B>(opt: Option<A>, f: (a: A) => B): Option<B> =>
  isSome(opt) ? Some(f(opt.value)) : None();

const flatMap = <A, B>(opt: Option<A>, f: (a: A) => Option<B>): Option<B> =>
  isSome(opt) ? f(opt.value) : None();

const getOrElse = <A>(opt: Option<A>, defaultValue: A): A =>
  isSome(opt) ? opt.value : defaultValue;

const fold = <A, B>(
  opt: Option<A>,
  onNone: () => B,
  onSome: (a: A) => B
): B =>
  isSome(opt) ? onSome(opt.value) : onNone();

// Convert from nullable
const fromNullable = <A>(value: A | null | undefined): Option<A> =>
  value == null ? None() : Some(value);

// Convert to nullable
const toNullable = <A>(opt: Option<A>): A | null =>
  isSome(opt) ? opt.value : null;

// Filter
const filter = <A>(opt: Option<A>, pred: (a: A) => boolean): Option<A> =>
  isSome(opt) && pred(opt.value) ? opt : None();

// Chaining operations
const pipe = <A>(opt: Option<A>) => ({
  map: <B>(f: (a: A) => B) => pipe(map(opt, f)),
  flatMap: <B>(f: (a: A) => Option<B>) => pipe(flatMap(opt, f)),
  filter: (pred: (a: A) => boolean) => pipe(filter(opt, pred)),
  getOrElse: (defaultValue: A): A => getOrElse(opt, defaultValue),
  fold: <B>(onNone: () => B, onSome: (a: A) => B): B => 
    fold(opt, onNone, onSome)
});

// Usage example
const safeDivide = (a: number, b: number): Option<number> =>
  b === 0 ? None() : Some(a / b);

const result = pipe(safeDivide(10, 2))
  .map(x => x * 2)
  .filter(x => x > 5)
  .getOrElse(0);

Either Type Implementation

// Either type definition
type Either<E, A> =
  | { readonly _tag: 'Left'; readonly left: E }
  | { readonly _tag: 'Right'; readonly right: A };

// Constructors
const Left = <E, A = never>(left: E): Either<E, A> => 
  ({ _tag: 'Left', left });

const Right = <A, E = never>(right: A): Either<E, A> => 
  ({ _tag: 'Right', right });

// Type guards
const isLeft = <E, A>(either: Either<E, A>): either is { _tag: 'Left'; left: E } =>
  either._tag === 'Left';

const isRight = <E, A>(either: Either<E, A>): either is { _tag: 'Right'; right: A } =>
  either._tag === 'Right';

// Core operations
const mapEither = <E, A, B>(
  either: Either<E, A>,
  f: (a: A) => B
): Either<E, B> =>
  isRight(either) ? Right(f(either.right)) : either;

const mapLeft = <E, A, F>(
  either: Either<E, A>,
  f: (e: E) => F
): Either<F, A> =>
  isLeft(either) ? Left(f(either.left)) : either;

const flatMapEither = <E, A, B>(
  either: Either<E, A>,
  f: (a: A) => Either<E, B>
): Either<E, B> =>
  isRight(either) ? f(either.right) : either;

const foldEither = <E, A, B>(
  either: Either<E, A>,
  onLeft: (e: E) => B,
  onRight: (a: A) => B
): B =>
  isLeft(either) ? onLeft(either.left) : onRight(either.right);

const getOrElseEither = <E, A>(
  either: Either<E, A>,
  onLeft: (e: E) => A
): A =>
  isLeft(either) ? onLeft(either.left) : either.right;

const swap = <E, A>(either: Either<E, A>): Either<A, E> =>
  isLeft(either) ? Right(either.left) : Left(either.right);

// Try-catch wrapper
const tryCatch = <A>(
  f: () => A,
  onError: (error: unknown) => Error = e => 
    e instanceof Error ? e : new Error(String(e))
): Either<Error, A> => {
  try {
    return Right(f());
  } catch (error) {
    return Left(onError(error));
  }
};

// Async variant
const tryCatchAsync = async <A>(
  f: () => Promise<A>,
  onError: (error: unknown) => Error = e => 
    e instanceof Error ? e : new Error(String(e))
): Promise<Either<Error, A>> => {
  try {
    return Right(await f());
  } catch (error) {
    return Left(onError(error));
  }
};

// Chaining operations
const pipeEither = <E, A>(either: Either<E, A>) => ({
  map: <B>(f: (a: A) => B) => pipeEither(mapEither(either, f)),
  mapLeft: <F>(f: (e: E) => F) => pipeEither(mapLeft(either, f)),
  flatMap: <B>(f: (a: A) => Either<E, B>) => pipeEither(flatMapEither(either, f)),
  fold: <B>(onLeft: (e: E) => B, onRight: (a: A) => B): B => 
    foldEither(either, onLeft, onRight),
  getOrElse: (onLeft: (e: E) => A): A => 
    getOrElseEither(either, onLeft),
  swap: () => pipeEither(swap(either))
});

// Usage example
const parseJSON = <A>(json: string): Either<Error, A> =>
  tryCatch(() => JSON.parse(json));

const validateUser = (data: unknown): Either<Error, User> => {
  if (typeof data !== 'object' || data === null) {
    return Left(new Error('Invalid data'));
  }
  // Validation logic...
  return Right(data as User);
};

const result = pipeEither(parseJSON<unknown>(jsonString))
  .flatMap(validateUser)
  .map(user => ({ ...user, name: user.name.toUpperCase() }))
  .fold(
    error => `Error: ${error.message}`,
    user => `Success: ${user.name}`
  );

Function Composition Utilities

// Compose (right-to-left)
function compose<A, B>(f: (a: A) => B): (a: A) => B;
function compose<A, B, C>(
  f: (b: B) => C,
  g: (a: A) => B
): (a: A) => C;
function compose<A, B, C, D>(
  f: (c: C) => D,
  g: (b: B) => C,
  h: (a: A) => B
): (a: A) => D;
function compose(...fns: Function[]): Function {
  return (x: any) => fns.reduceRight((acc, fn) => fn(acc), x);
}

// Pipe (left-to-right)
function pipe<A>(a: A): A;
function pipe<A, B>(a: A, f: (a: A) => B): B;
function pipe<A, B, C>(
  a: A,
  f: (a: A) => B,
  g: (b: B) => C
): C;
function pipe<A, B, C, D>(
  a: A,
  f: (a: A) => B,
  g: (b: B) => C,
  h: (c: C) => D
): D;
function pipe(a: any, ...fns: Function[]): any {
  return fns.reduce((acc, fn) => fn(acc), a);
}

// Flow (function composition)
function flow<A, B>(f: (a: A) => B): (a: A) => B;
function flow<A, B, C>(
  f: (a: A) => B,
  g: (b: B) => C
): (a: A) => C;
function flow<A, B, C, D>(
  f: (a: A) => B,
  g: (b: B) => C,
  h: (c: C) => D
): (a: A) => D;
function flow(...fns: Function[]): Function {
  return (x: any) => fns.reduce((acc, fn) => fn(acc), x);
}

// Usage examples
const double = (n: number): number => n * 2;
const increment = (n: number): number => n + 1;
const toString = (n: number): string => n.toString();

const processNumber = flow(double, increment, toString);
processNumber(5); // "11"

const result = pipe(
  5,
  double,
  increment,
  toString
); // "11"

Async/Promise Utilities

// TaskEither for async operations with error handling
type TaskEither<E, A> = () => Promise<Either<E, A>>;

const taskEitherOf = <E, A>(value: A): TaskEither<E, A> =>
  async () => Right(value);

const taskEitherFromPromise = <A>(
  promise: () => Promise<A>,
  onError: (error: unknown) => Error
): TaskEither<Error, A> =>
  async () => tryCatchAsync(promise, onError);

const mapTaskEither = <E, A, B>(
  task: TaskEither<E, A>,
  f: (a: A) => B
): TaskEither<E, B> =>
  async () => {
    const either = await task();
    return mapEither(either, f);
  };

const flatMapTaskEither = <E, A, B>(
  task: TaskEither<E, A>,
  f: (a: A) => TaskEither<E, B>
): TaskEither<E, B> =>
  async () => {
    const either = await task();
    if (isLeft(either)) return either;
    return f(either.right)();
  };

// Parallel execution
const sequenceTaskEither = <E, A>(
  tasks: readonly TaskEither<E, A>[]
): TaskEither<E, readonly A[]> =>
  async () => {
    const results = await Promise.all(tasks.map(t => t()));
    const lefts = results.filter(isLeft);
    if (lefts.length > 0) return lefts[0];
    return Right(results.map(r => (r as any).right));
  };

// Usage example
const fetchUser = (id: number): TaskEither<Error, User> =>
  taskEitherFromPromise(
    () => fetch(`/api/users/${id}`).then(r => r.json()),
    e => new Error(`Failed to fetch user: ${e}`)
  );

const processUser = flow(
  fetchUser,
  te => mapTaskEither(te, user => ({ ...user, processed: true }))
);

Lens Pattern for Immutable Updates

// Lens type
type Lens<S, A> = {
  get: (s: S) => A;
  set: (a: A) => (s: S) => S;
};

// Create lens
const lens = <S, A>(
  get: (s: S) => A,
  set: (a: A) => (s: S) => S
): Lens<S, A> => ({ get, set });

// Modify through lens
const modify = <S, A>(
  lens: Lens<S, A>,
  f: (a: A) => A
): ((s: S) => S) =>
  s => lens.set(f(lens.get(s)))(s);

// Compose lenses
const composeLens = <S, A, B>(
  outer: Lens<S, A>,
  inner: Lens<A, B>
): Lens<S, B> =>
  lens(
    s => inner.get(outer.get(s)),
    b => s => outer.set(inner.set(b)(outer.get(s)))(s)
  );

// Property lens helper
const prop = <S, K extends keyof S>(key: K): Lens<S, S[K]> =>
  lens(
    s => s[key],
    value => s => ({ ...s, [key]: value })
  );

// Usage example
type Address = { street: string; city: string };
type Person = { name: string; address: Address };

const addressLens = prop<Person, 'address'>('address');
const cityLens = prop<Address, 'city'>('city');
const personCityLens = composeLens(addressLens, cityLens);

const person: Person = {
  name: 'John',
  address: { street: '123 Main St', city: 'NYC' }
};

const updatedPerson = modify(personCityLens, () => 'LA')(person);

Validation Pattern

// Validation type
type Validation<E, A> = Either<readonly E[], A>;

const success = <E, A>(value: A): Validation<E, A> => Right(value);
const failure = <E, A>(errors: readonly E[]): Validation<E, A> => Left(errors);

// Applicative validation (accumulates errors)
const validateApply = <E, A, B>(
  vf: Validation<E, (a: A) => B>,
  va: Validation<E, A>
): Validation<E, B> => {
  if (isLeft(vf) && isLeft(va)) {
    return Left([...vf.left, ...va.left]);
  }
  if (isLeft(vf)) return vf as any;
  if (isLeft(va)) return va as any;
  return Right(vf.right(va.right));
};

// Validation builder
const validate = <A>(value: A) => ({
  check: <E>(
    pred: (a: A) => boolean,
    error: E
  ): Validation<E, A> =>
    pred(value) ? success(value) : failure([error]),
  
  checkAsync: async <E>(
    pred: (a: A) => Promise<boolean>,
    error: E
  ): Promise<Validation<E, A>> =>
    (await pred(value)) ? success(value) : failure([error])
});

// Combine validations
const combineValidations = <E, A extends readonly any[]>(
  ...validations: { [K in keyof A]: Validation<E, A[K]> }
): Validation<E, A> => {
  const errors: E[] = [];
  const values: any[] = [];
  
  for (const v of validations) {
    if (isLeft(v)) {
      errors.push(...v.left);
    } else {
      values.push(v.right);
    }
  }
  
  return errors.length > 0 ? Left(errors) : Right(values as any);
};

// Usage example
type ValidationError = { field: string; message: string };

const validateEmail = (email: string): Validation<ValidationError, string> =>
  validate(email)
    .check(
      e => e.includes('@'),
      { field: 'email', message: 'Must contain @' }
    );

const validateAge = (age: number): Validation<ValidationError, number> =>
  validate(age)
    .check(
      a => a >= 18,
      { field: 'age', message: 'Must be 18 or older' }
    );

const validateUser = (email: string, age: number) =>
  combineValidations(
    validateEmail(email),
    validateAge(age)
  );

Best Practices

1. Always use readonly for immutability

// Good
type User = {
  readonly id: string;
  readonly name: string;
  readonly tags: readonly string[];
};

// Better - utility type
type Immutable<T> = {
  readonly [K in keyof T]: T[K] extends object 
    ? Immutable<T[K]> 
    : T[K];
};

2. Avoid any - use unknown or never

// Bad
const parse = (json: string): any => JSON.parse(json);

// Good
const parse = (json: string): unknown => JSON.parse(json);

// Better - with type guard
const parseUser = (json: string): Either<Error, User> => {
  const result = tryCatch(() => JSON.parse(json));
  return flatMapEither(result, data => {
    if (isUser(data)) return Right(data);
    return Left(new Error('Invalid user data'));
  });
};

3. Use discriminated unions for state

// Good
type AsyncData<E, A> =
  | { status: 'idle' }
  | { status: 'loading' }
  | { status: 'error'; error: E }
  | { status: 'success'; data: A };

// Can't access data in wrong state
const renderData = (state: AsyncData<Error, string>): string => {
  switch (state.status) {
    case 'idle': return 'Not started';
    case 'loading': return 'Loading...';
    case 'error': return state.error.message; // Type-safe
    case 'success': return state.data; // Type-safe
  }
};

4. Leverage type inference

// Let TypeScript infer types
const numbers = [1, 2, 3, 4, 5]; // inferred as number[]
const doubled = numbers.map(n => n * 2); // inferred as number[]

// Explicit when necessary
const parseNumbers = (strs: string[]): number[] =>
  strs.map(s => parseInt(s, 10));

5. Use const assertions for literals

// Mutable array of string literals
const colors = ['red', 'green', 'blue'];
// Type: string[]

// Immutable tuple of literal types
const colors = ['red', 'green', 'blue'] as const;
// Type: readonly ["red", "green", "blue"]

// Object with literal types
const config = {
  apiUrl: 'https://api.example.com',
  timeout: 5000
} as const;
// Type: { readonly apiUrl: "https://api.example.com"; readonly timeout: 5000 }

6. Prefer type over interface for data

// Type - better for FP
type Point = {
  readonly x: number;
  readonly y: number;
};

// Type allows unions
type Shape = Circle | Rectangle | Square;

// Type allows mapped types
type Readonly<T> = { readonly [K in keyof T]: T[K] };

Common Patterns

Railway-Oriented Programming

// Chain operations that can fail
const processUser = flow(
  parseJSON<unknown>,
  flatMapEither(validateUser),
  mapEither(normalizeUser),
  flatMapEither(saveUser),
  mapEither(formatResponse)
);

const result = processUser(jsonString);

Builder Pattern with Types

type Builder<T> = {
  readonly build: () => T;
};

const userBuilder = () => {
  let name: string | undefined;
  let age: number | undefined;
  
  return {
    withName: (n: string) => (name = n, builder),
    withAge: (a: number) => (age = a, builder),
    build: (): Either<string, User> => {
      if (!name) return Left('Name required');
      if (!age) return Left('Age required');
      return Right({ name, age });
    }
  };
};

Testing

import { describe, it, expect } from 'vitest';

describe('Option', () => {
  it('maps over Some', () => {
    const opt = Some(5);
    const result = map(opt, n => n * 2);
    expect(result).toEqual(Some(10));
  });
  
  it('maps over None', () => {
    const opt = None<number>();
    const result = map(opt, n => n * 2);
    expect(result).toEqual(None());
  });
  
  it('flatMaps Some to Some', () => {
    const opt = Some(5);
    const result = flatMap(opt, n => Some(n * 2));
    expect(result).toEqual(Some(10));
  });
  
  it('flatMaps Some to None', () => {
    const opt = Some(5);
    const result = flatMap(opt, () => None());
    expect(result).toEqual(None());
  });
});

// Property-based testing
import fc from 'fast-check';

describe('Option laws', () => {
  it('satisfies functor identity', () => {
    fc.assert(
      fc.property(fc.integer(), n => {
        const opt = Some(n);
        const mapped = map(opt, x => x);
        expect(mapped).toEqual(opt);
      })
    );
  });
  
  it('satisfies functor composition', () => {
    const f = (n: number) => n * 2;
    const g = (n: number) => n + 1;
    
    fc.assert(
      fc.property(fc.integer(), n => {
        const opt = Some(n);
        const composed = map(map(opt, g), f);
        const direct = map(opt, x => f(g(x)));
        expect(composed).toEqual(direct);
      })
    );
  });
});

Performance Optimization

// Memoization with WeakMap for object keys
const memoizeObject = <K extends object, V>(
  fn: (key: K) => V
): ((key: K) => V) => {
  const cache = new WeakMap<K, V>();
  return (key: K): V => {
    if (!cache.has(key)) {
      cache.set(key, fn(key));
    }
    return cache.get(key)!;
  };
};

// Lazy evaluation for expensive operations
const lazyMap = <A, B>(
  arr: readonly A[],
  f: (a: A) => B
): (() => readonly B[]) => {
  let cached: readonly B[] | null = null;
  return () => {
    if (cached === null) {
      cached = arr.map(f);
    }
    return cached;
  };
};

// Batching async operations
const batchPromises = <A, B>(
  items: readonly A[],
  fn: (item: A) => Promise<B>,
  batchSize: number
): Promise<readonly B[]> => {
  const batches: A[][] = [];
  for (let i = 0; i < items.length; i += batchSize) {
    batches.push(items.slice(i, i + batchSize) as A[]);
  }
  
  return batches.reduce(
    async (acc, batch) => {
      const results = await acc;
      const batchResults = await Promise.all(batch.map(fn));
      return [...results, ...batchResults];
    },
    Promise.resolve([] as readonly B[])
  );
};