Polymonadic Programming

Monads are a popular tool for the working functional programmer to structure effectful computations. This paper presents polymonads, a generalization of monads. Polymonads give the familiar monadic bind the more general type forall a,b. L a -> (a -> M b) -> N b, to compose computations with three different kinds of effects, rather than just one. Polymonads subsume monads and parameterized monads, and can express other constructions, including precise type-and-effect systems and information flow tracking; more generally, polymonads correspond to Tate's productoid semantic model. We show how to equip a core language (called lambda-PM) with syntactic support for programming with polymonads. Type inference and elaboration in lambda-PM allows programmers to write polymonadic code directly in an ML-like syntax--our algorithms compute principal types and produce elaborated programs wherein the binds appear explicitly. Furthermore, we prove that the elaboration is coherent: no matter which (type-correct) binds are chosen, the elaborated program's semantics will be the same. Pleasingly, the inferred types are easy to read: the polymonad laws justify (sometimes dramatic) simplifications, but with no effect on a type's generality.Comment: In Proceedings MSFP 2014, arXiv:1406.153

Polymonad programming in Haskell

Polymonads were recently introduced by Hicks et al. as a unified approach to programming with different notions of monads. Their work was mainly focussed 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

Polymonad programming in Haskell

Polymonads were recently introduced by Hicks et al. as a unified approach to programming with different notions of monads. Their work was mainly focussed 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

Supermonads: one notion to bind them all

Several popular generalizations of monads have been implemented in Haskell. Unfortunately, because the shape of the associated type constructors do not match the standard Haskell monad interface, each such implementation provides its own type class and versions of associated library functions. Furthermore, simultaneous use of different monadic notions can be cumbersome as it in general is necessary to be explicit about which notion is used where. In this paper we introduce supermonads: an encoding of monadic notions that captures several different generalizations along with a version of the standard library of monadic functions that work uniformly with all of them. As standard Haskell type inference does not work for supermonads due to their generality, our supermonad implementation is accompanied with a language extension, in the form of a plugin for the Glasgow Haskell Compiler (GHC), that allows type inference for supermonads, obviating the need for manual annotations