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Summary

Instances generated using DerivingVia are accepted even though equivalent handwritten instances are rejected due to violation of the (liberal) coverage condition.

Steps to reproduce

This module demonstrates the problem:

{-# LANGUAGE DerivingVia #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleInstances #-}

module DerivingViaBug where

class C a b | b -> a

newtype A t a = A a
instance C t (A t a)

data T = T
  deriving (C a) via (A () T)

The above program is accepted. But if we write the C a T instance manually, rather than deriving it, the program is rejected:

data T = T
instance C a T

src/DerivingViaBug.hs:13:10: error:
    • Illegal instance declaration for ‘C a T’
        The coverage condition fails in class ‘C’
          for functional dependency: ‘b -> a’
        Reason: lhs type ‘T’ does not determine rhs type ‘a’
        Un-determined variable: a
    • In the instance declaration for ‘C a T’
   |
13 | instance C a T
   |          ^^^^^

Expected behavior

The simplest solution to this problem would be to reject the derived instance. However, this introduces a bit of an inconsistency between functional dependencies and associated types. Consider the following similar program, which uses associated types instead of functional dependencies:

{-# LANGUAGE DerivingVia #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE UndecidableInstances #-}

module DerivingViaBug where

class C a where
  type F a

newtype A t a = A a
instance C (A t a) where
  type F (A t a) = t

data T = T
  deriving (C) via (A () T)

This program is accepted, and the behavior is reasonable. The derived instance is

instance C T where
  type F T = F (A () T)

so F T is ultimately (). To achieve analogous behavior for functional dependencies, it seems like a reasonable derived instance could be

instance C () T

which can be constructed by applying the substitution {t ↦ (), a ↦ T} to the original C t (A t a) instance declaration. I haven’t thought about it enough to say whether or not that would cause more problems than it would solve, however.

Environment

• GHC version used: 8.6.5
• Operating System: macOS 10.14.5 (18F132)
• System Architecture: x86_64