Fruit ketchup Fruit ketchup Fruit ketchup is a condiment prepared using fruit as a primary ingredient. Various fruits are used in its preparation, and it is also used as a spread and marinade, among other uses. Banana ketchup is a type of fruit ketchup that is common in the Philippines. Some companies mass-produce fruit ketchup, such as Philippines-based Jufran, and Chups, a small company based in Washington, D.C., United States. Fruit ketchup is composed primarily of fruit, and is prepared with fruits such as apples, pears, peaches, currants, grapes, cranberries, cherries and plums, among others. Tropical fruits used in its preparation can
History of type theory History of type theory The type theory was initially created to avoid paradoxes in a variety of formal logics and rewrite systems. Later, type theory referred to a class of formal systems, some of which can serve as alternatives to naive set theory as a foundation for all mathematics. It has been tied to formal mathematics since "Principia Mathematica" to today's proof assistants. In a letter to Gottlob Frege (1902) Russell announced his discovery of the paradox in Frege's Begriffsschrift. Frege promptly responded, acknowledging the problem and proposing a solution in a technical discussion of "levels". To quote Frege: Incidentally,