> fmap id == id
> fmap (f . g) == fmap f . fmap g
-The instances of 'Functor' for lists, 'Maybe' and 'IO' defined in the "Prelude"
-satisfy these laws.
+The instances of 'Functor' for lists, 'Data.Maybe.Maybe' and 'System.IO.IO'
+defined in the "Prelude" satisfy these laws.
-}
class Functor f where
fmap :: (a -> b) -> f a -> f b
-{- | The 'Monad' class defines the basic operations over a /monad/.
+{- | The 'Monad' class defines the basic operations over a /monad/,
+a concept from a branch of mathematics known as /category theory/.
+From the perspective of a Haskell programmer, however, it is best to
+think of a monad as an /abstract datatype/ of actions.
+Haskell's @do@ expressions provide a convenient syntax for writing
+monadic expressions.
+
+Minimal complete definition: '>>=' and 'return'.
+
Instances of 'Monad' should satisfy the following laws:
> return a >>= k == k a
> fmap f xs == xs >>= return . f
-The instances of 'Monad' for lists, 'Maybe' and 'IO' defined in the "Prelude"
-satisfy these laws.
+The instances of 'Monad' for lists, 'Data.Maybe.Maybe' and 'System.IO.IO'
+defined in the "Prelude" satisfy these laws.
-}
class Monad m where
+ -- | Sequentially compose two actions, passing any value produced
+ -- by the first as an argument to the second.
(>>=) :: forall a b. m a -> (a -> m b) -> m b
+ -- | Sequentially compose two actions, discarding any value produced
+ -- by the first, like sequencing operators (such as the semicolon)
+ -- in imperative languages.
(>>) :: forall a b. m a -> m b -> m b
-- Explicit for-alls so that we know what order to
-- give type arguments when desugaring
+
+ -- | Inject a value into the monadic type.
return :: a -> m a
+ -- | Fail with a message. This operation is not part of the
+ -- mathematical definition of a monad, but is invoked on pattern-match
+ -- failure in a @do@ expression.
fail :: String -> m a
m >> k = m >>= \_ -> k
"foldr/augment" forall k z xs (g::forall b. (a->b->b) -> b -> b) .
foldr k z (augment g xs) = g k (foldr k z xs)
-"foldr/id" foldr (:) [] = \x->x
-"foldr/app" [1] forall xs ys. foldr (:) ys xs = xs ++ ys
+"foldr/id" foldr (:) [] = \x -> x
+"foldr/app" [1] forall ys. foldr (:) ys = \xs -> xs ++ ys
-- Only activate this from phase 1, because that's
-- when we disable the rule that expands (++) into foldr
type String = [Char]
{-| The character type 'Char' is an enumeration whose values represent
-Unicode (or equivalently ISO 10646) characters.
+Unicode (or equivalently ISO\/IEC 10646) characters
+(see <http://www.unicode.org/> for details).
This set extends the ISO 8859-1 (Latin-1) character set
(the first 256 charachers), which is itself an extension of the ASCII
character set (the first 128 characters).
lazy :: a -> a
lazy x = x
--- | Assertion function. This simply ignores its boolean argument.
+-- Assertion function. This simply ignores its boolean argument.
-- The compiler may rewrite it to @('assertError' line)@.
+-- | If the first argument evaluates to 'True', then the result is the
+-- second argument. Otherwise an 'AssertionFailed' exception is raised,
+-- containing a 'String' with the source file and line number of the
+-- call to 'assert'.
+--
+-- Assertions can normally be turned on or off with a compiler flag
+-- (for GHC, assertions are normally on unless optimisation is turned on
+-- with @-O@ or the @-fignore-asserts@
+-- option is given). When assertions are turned off, the first
+-- argument to 'assert' is ignored, and the second argument is
+-- returned as the result.
+
-- SLPJ: in 5.04 etc 'assert' is in GHC.Prim,
-- but from Template Haskell onwards it's simply
-- defined here in Base.lhs
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