18.S996S13 Project: In search of a Monad

For programmers, Monads are a well-known way to represent an abstract data structure, but without knowing its true nature. Admittedly, the definition of Monads in Category Theory is too subtle and obscure so makes people to avoid from trying to understand them. In this paper, we attempt to explore popular Monads in a purely functional programming language, Haskell, with a Category-theoretic mindset. Starting from the definition of Monads, we describe how they are defined and implemented in Haskell. In particular, we classify Monads by their implementation style, and it turns out that a common fallacy of using Monad metaphors can be understood in this vein. Also, we explain why IO Monad is particularly important in Haskell and what its role is, in a programmer’s perspective. Furthermore, we design a new Monad, called S Monad, in order to represent the system call abstractions, and shed light on a future Haskell OS using S Monad to represent the system call abstractions.