Inferences in term logic can all be represented in the monadic predicate calculus. The validities of monadic predicate calculus with identity are decidable, however. According to Peirce, a genuinely monadic predicate characteristically expresses quality. One application for this monadic list is representing nondeterministic computation. Many symbols denote both monadic and dyadic functions, interpreted according to use. Thus, this forgetful functor is not monadic. Adding a single binary relation symbol to monadic logic, however, results in an undecidable logic. This explanation would predict a monadic effect, although weaker than the dyadic one. An elementary version of polyadic algebra is described in monadic Boolean algebra. In Haskell, the function is a monadic operator. There are also characterizations based on an equivalent form of automata and monadic second-order logic. One says a category is an "algebraic category" if it is monadic over formula 43. Monadic topology has a central repository that all collected data is fed into. Frequently concept testing surveys are described as either monadic, sequential monadic or comparative. Its type system includes dependent types, monadic effects, and refinement types.