Monads and Martingales

This talk will first introduce monads, and explain how they are used to model computation in the Haskell programming language.  By parameterizing a monad by an abstract type, we can obtain a model for a stateful computation, where the abstract state is the type parameter.  Through the use of a binary predicate type "Before" on the abstract state types, we show how to encode the state at some present "time" (or space-time point) being available for computation at a later "time."  The concept of a martingale is also described in the monadic setting.  This formalism is applied to the foundations of relativity, probabilistic modeling in purely functional settings, and functional reactive programming.