Multi-parameter type class

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The GHC Users Guide has a Multi Parameter Type Classes section.

About

Basically, type classes which can take multiple arguments, such as:

class Monad m => VarMonad m v where
  new :: a -> m (v a)
  get :: v a -> m a
  put :: v a -> a -> m ()

instance VarMonad IO IORef where ...
instance VarMonad (ST s) (STRef s) where ...

To enable them, use the {-# LANGUAGE MultiParamTypeClasses #-} pragma.

If you think of a single-parameter type class as a set of types, then a multi-parameter type class (MPTC) is a relation between types.

Naive use of MPTCs may result in ambiguity, so functional dependencies were developed as a method of resolving that ambiguity, declaring that some subset of the parameters is sufficient to determine the values of the others.

Some uses of MPTCs with functional dependencies can be replaced with type families. See functional dependencies vs. type families.

MPTCs are part of GHC2021.

The above example can even be implemented in plain Haskell 98.

Also see

The archived Haskell' page