mysql错误(hy000):无法添加外键约束

我正在尝试为一个简单的在线商店创建一个MySQL模式。我现有的表格如下:

• user -用户信息
• address -用户地址信息
• product -产品信息
• purchase -由用户创建和购买的购物图

我使用以下SQL代码创建了这些表:

CREATE TABLE user(
    user_id INT AUTO_INCREMENT,
    first_name VARCHAR(20) NOT NULL, 
    middle_name VARCHAR(20) NOT NULL, 
    last_name VARCHAR(20) NOT NULL, 
    email VARCHAR(40) NOT NULL UNIQUE,
    password VARCHAR(255) NOT NULL, 
    registered BOOLEAN NOT NULL, 
    phone VARCHAR(12),
    PRIMARY KEY(user_id)
);

CREATE TABLE product(
    product_id INT AUTO_INCREMENT,
    name VARCHAR(40) NOT NULL UNIQUE,
    price DECIMAL(5,2) NOT NULL,
    description VARCHAR(100) UNIQUE,
    PRIMARY KEY(product_id)
);

CREATE TABLE address(
    user_id INT,
    address_id INT,
    city VARCHAR(15) NOT NULL,
    district VARCHAR(20) NOT NULL,
    details VARCHAR(50) NOT NULL,
    is_default BOOLEAN NOT NULL,
    FOREIGN KEY(user_id) REFERENCES user(user_id) ON DELETE CASCADE,
    PRIMARY KEY(user_id, address_id)
);

CREATE TABLE purchase(
    purchase_id INT AUTO_INCREMENT,
    user_id INT,
    total_price DECIMAL(8,2) NOT NULL,
    state ENUM('placed', 'paid', 'shipped', 'received', 'completed', 'cancelled') DEFAULT 'placed',
    user_name VARCHAR(40) NOT NULL,
    full_address VARCHAR(85) NOT NULL,
    FOREIGN KEY(user_id) REFERENCES user(user_id) ON DELETE SET NULL,
    PRIMARY KEY(purchase_id)
);

现在,我正试图创建一个最终的表来存储购物图中的单个项目,如下所示:

CREATE TABLE purchase_item(
    purchase_id INT,
    product_id INT,
    product_name VARCHAR(40) NOT NULL,
    amount DECIMAL(4,2) NOT NULL,
    price DECIMAL(8,2) NOT NULL,
    FOREIGN KEY(purchase_id) REFERENCES purchase(purchase_id) ON DELETE CASCADE,
    FOREIGN KEY(product_id) REFERENCES product(product_id) ON DELETE SET NULL,
    PRIMARY KEY(purchase_id, product_id)
);

但我得到以下错误:

ERROR 1215 (HY000): Cannot add foreign key constraint

如果我按以下方式更新产品的外键,则不会出现任何错误:

FOREIGN KEY(product_id) REFERENCES product(product_id) ON DELETE CASCADE,

我想要 purchase_item 如果相应的 购买 会被删除,但不会在相应的 产品 获取删除。