What is incumbent upon one who vowed not to eat a specific food, and if he ate from it, he would pray 100 rak'ahs, then he ate from the food and did not fulfill his vow?

Undertaking a vow is disliked (makrooh). If you utter a vow formula, such as: "It is for Allah upon me," or "I vowed to pray a hundred rak'ahs if I eat from this food," and then you eat from it, this is a vow of contention (nathr lajaj), and you have the choice between fulfilling the vow (praying a hundred rak'ahs) or offering an expiation for a broken oath (kaffarat yameen).

However, if your vow formula does not contain the word "vow" or anything that signifies commitment, then this is not a vow but rather a promise, and you are not obligated to do anything by eating from the food.