MySQL Error (HY000): Cannot add foreign key constraint - mysql

Question

I'm trying to create a MySQL schema for a simple online shop. My existing tables are as follows:
user — user info
address — address info for users
product — product info
purchase — a shopping chart created and purchased by a user
I've created these tables using the following SQL code:
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)
);
Now I'm trying to create a final table to store individual items in a shopping chart like this:
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)
);
But I get the following error:
ERROR 1215 (HY000): Cannot add foreign key constraint
I don't any errors if I update the foreign key for products as follows:
FOREIGN KEY(product_id) REFERENCES product(product_id) ON DELETE CASCADE,
I want the purchase_item to be deleted if the corresponding purchase gets deleted, but not when the corresponding product gets deleted.

Answer 1

https://dev.mysql.com/doc/refman/8.0/en/create-table-foreign-keys.html says:
If you specify a SET NULL action, make sure that you have not declared the columns in the child table as NOT NULL.
But your purchase_item.product_id column is part of that table's primary key, which implicitly makes the column NOT NULL.
You cannot use the SET NULL action for the primary key on that column.