Polymonad programming in Haskell

Abstract

Polymonads were recently introduced by Hicks et al. as a unified approach to programming with different notions of monads. Their work was mainly focused on foundational aspects of the approach. In this article, we show how to incorporate the notion of polymonads into Haskell, which is the first time this has been done in a full-scale language. In particular, we show how polymonads can be represented in Haskell, give a justification of the representation through proofs in Agda, and provide a plugin for the Glasgow Haskell Compiler (GHC) that enables their use in practice. Finally, we demonstrate the utility of our system by means of examples concerned with session types and the parameterized effect monad. This work provides a common representation of a number of existing approaches to generalized monads in Haskell.

Fault tolerant functional reactive programming (functional pearl)

“…Their use and, especially, the possibility of combining different kinds of effects irrespective of their stacking order might ease the specification of mechanisms for fault tolerance at different architectural levels. We have explored the use of effect monads or graded monads , polymonads [Bracker and Nilsson 2015], and supermonads [Bracker and Nilsson 2016]. We have not explored the use of unconstrained indexed monads [Katsumata 2014; .…”

Supermonads: one notion to bind them all

“…A solution to this problem can be found in the work by Kmett [23,24] and the work on polymonads [9,16]. Both introduce a type class similar to the following: This way, when defining an instance, m, n and p can be partially applied versions of the type constructor in the instance head.…”

“…Type checker plugins have been used to implement type system extensions such as type level natural numbers [12] and units of measure [14]. We have previously used a plugin to integrate polymonads into Haskell [9]. We will content ourselves with a brief explanation here, referring the reader to the earlier work and the GHC documentation for details.…”

“…Polymonads [16] are similar to supermonads in that they also use a set of bind operations that allow a different type constructor in each position and that they also have a set of unary type constructors. In our previous work [9] we implemented a plugin for GHC that added type inference for polymonads to the compiler.…”

“…In earlier work [9], we successfully integrated polymonads [16] into Haskell to mitigate the above problems. While polymonads are very general in some ways, and have the benefit of being compositional, the polymonad theory in its current form does not allow non-phantom indices or constrained result types.…”