Task: Text Categorization
Input (English): Any system like this one must neglect one of three objectives or lose strong normalization according to Girard's paradox. A polymorphic variety of this system is referred to as System F. Related systems include one developed by Coquand and Huet and the intuitionist theory of Per Martin-Lof. Permitting actions such as alpha, beta, and eta conversion, research on this system inspired the development of domain theory. Inductive types may be added to it via Mogensen-Scott encoding, and defining under this system the function k to take x and give not x x, then applying that function to k, is the Kleene-Rosser paradox. System F corresponds to second-order propositional logic, and natural deduction may be interpreted as a "typed" version of this system, by the Curry-Howard correspondence. For 10 points, name this formal system, which can compute the same set of functions as a certain kind of machine according to the Church-Turing thesis.
Output (English): Science