-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Conversions between algebraic classes and F-algebras.
--   
--   Algebraic classes are type classes where all the methods return a
--   value of the same type, which is also the class parameter. Examples
--   from <tt>base</tt> are <tt>Num</tt> and <tt>Monoid</tt>.
--   
--   F-algebras are functions <tt>f a -&gt; a</tt>, where the functor
--   <tt>f</tt> is called the signature, and the type <tt>a</tt> the
--   carrier.
--   
--   This package relates these 2 concepts, and can create conversions
--   between the two using Template Haskell. More specifically, it can
--   generate:
--   
--   <ul>
--   <li>signatures from algebraic classes</li>
--   <li>instances of algebraic classes from F-algebras.</li>
--   </ul>
--   
--   This is useful because type classes are more commonly used in Haskell
--   than F-algebras, but F-algebras are easier to work with, because they
--   are just functions.
@package algebraic-classes
@version 0.1


module Data.Algebra.Internal
class Traversable f => AlgebraSignature f where type family Class f :: * -> Constraint
evaluate :: (AlgebraSignature f, Class f b) => f b -> b
class Algebra f a
algebra :: (Algebra f a, AlgebraSignature f) => f a -> a


module Data.Algebra.TH

-- | Derive an instance for an algebraic class. For example:
--   
--   <pre>
--   deriveInstance [t| (Num m, Num n) =&gt; Num (m, n) |]
--   </pre>
--   
--   To be able to derive an instance for <tt>a</tt> of class <tt>c</tt>,
--   we need an instance of <tt><a>Algebra</a> f a</tt>, where <tt>f</tt>
--   is the signature of <tt>c</tt>.
--   
--   <a>deriveInstance</a> will generate a signature for the class if there
--   is no signature in scope.
deriveInstance :: Q Type -> Q [Dec]

-- | Derive a signature for an algebraic class. For exaple:
--   
--   <pre>
--   deriveSignature ''Num
--   </pre>
--   
--   <a>deriveSignature</a> creates the signature data type and an instance
--   for it of the <a>AlgebraSignature</a> class. <tt>DeriveFunctor</tt> is
--   used the generate the <a>Functor</a> instance of the signature.
--   
--   This will do nothing if there is already a signature for the class in
--   scope.
deriveSignature :: Name -> Q [Dec]
data SignatureTH
SignatureTH :: Name -> Name -> [OperationTH] -> SignatureTH
signatureName :: SignatureTH -> Name
typeVarName :: SignatureTH -> Name
operations :: SignatureTH -> [OperationTH]
data OperationTH
OperationTH :: Name -> Name -> [Type] -> OperationTH
functionName :: OperationTH -> Name
operationName :: OperationTH -> Name
arguments :: OperationTH -> [Type]
getSignatureInfo :: Name -> Q SignatureTH
buildSignatureDataType :: SignatureTH -> [Dec]
signatureInstance :: Name -> SignatureTH -> [Dec]


module Data.Algebra
class Traversable f => AlgebraSignature f where type family Class f :: * -> Constraint
evaluate :: (AlgebraSignature f, Class f b) => f b -> b
class Algebra f a
algebra :: (Algebra f a, AlgebraSignature f) => f a -> a

-- | Derive an instance for an algebraic class. For example:
--   
--   <pre>
--   deriveInstance [t| (Num m, Num n) =&gt; Num (m, n) |]
--   </pre>
--   
--   To be able to derive an instance for <tt>a</tt> of class <tt>c</tt>,
--   we need an instance of <tt><a>Algebra</a> f a</tt>, where <tt>f</tt>
--   is the signature of <tt>c</tt>.
--   
--   <a>deriveInstance</a> will generate a signature for the class if there
--   is no signature in scope.
deriveInstance :: Q Type -> Q [Dec]

-- | Derive a signature for an algebraic class. For exaple:
--   
--   <pre>
--   deriveSignature ''Num
--   </pre>
--   
--   <a>deriveSignature</a> creates the signature data type and an instance
--   for it of the <a>AlgebraSignature</a> class. <tt>DeriveFunctor</tt> is
--   used the generate the <a>Functor</a> instance of the signature.
--   
--   This will do nothing if there is already a signature for the class in
--   scope.
deriveSignature :: Name -> Q [Dec]

-- | The <a>Monoid</a> signature has this <a>AlgebraSignature</a> instance:
--   
--   <pre>
--   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
--   </pre>
data MonoidSignature a
Op_mempty :: MonoidSignature a
Op_mappend :: a -> a -> MonoidSignature a
Op_mconcat :: [a] -> MonoidSignature a
instance Functor MonoidSignature
instance Foldable MonoidSignature
instance Traversable MonoidSignature
instance Show a => Show (MonoidSignature a)
instance AlgebraSignature MonoidSignature
instance (Class f b) => Algebra f (a -> b)
instance (Class f m, Class f n) => Algebra f (m, n)
instance Algebra f ()