Derive an instance for an algebraic class. For example:

deriveInstance [t| (Num m, Num n) => Num (m, n) |]

To be able to derive an instance for a of class c, we need an instance of Algebra f a, where f is the signature of c.

deriveInstance will generate a signature for the class if there is no signature in scope.

Derive an instance for an algebraic class with a given partial implementation. For example:

deriveInstanceWith [t| Num n => Num (Integer -> n) |]
  [d|
    fromInteger x y = fromInteger (x + y)
  |]

Derive an instance for an algebraic class with a given partial implementation, but don't generate the signature. This is for when you want to derive several instances of the same class, but can't splice the results directly. In that case deriveSignature can't detect it has already generated the signature earlier.

Derive the instances for the superclasses too, all using the same context. Usually you'd want to do this manually since you can often give a stricter context, for example:

deriveSuperclassInstances [t| (Fractional m, Fractional n) => Fractional (m, n) |]

will derive an instance (Fractional m, Fractional n) => Num (m, n) while the instance only needs (Num m, Num n).

Derive a signature for an algebraic class. For example:

deriveSignature ''Monoid

The above would generate the following:

data MonoidSignature a = Op_mempty | Op_mappend a a | Op_mconcat [a]
  deriving (Functor, Foldable, Traversable, Eq, Ord)

type instance Signature Monoid = MonoidSignature

instance AlgebraSignature MonoidSignature where
  type Class MonoidSignature = Monoid
  evaluate Op_mempty = mempty
  evaluate (Op_mappend a b) = mappend a b
  evaluate (Op_mconcat ms) = mconcat ms

instance Show a => Show (MonoidSignature a) where
  showsPrec d Op_mempty          = showParen (d > 10) $ showString "mempty"
  showsPrec d (Op_mappend a1 a2) = showParen (d > 10) $ showString "mappend" . showChar ' ' . showsPrec 11 a1 . showChar ' ' . showsPrec 11 a2
  showsPrec d (Op_mconcat a1)    = showParen (d > 10) $ showString "mconcat" . showChar ' ' . showsPrec 11 a1

deriveSignature creates the signature data type and an instance for it of the AlgebraSignature class. DeriveTraversable is used the generate the Traversable instance of the signature.

This will do nothing if there is already a signature for the class in scope.