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List-Like Monoid Generation + -- * List-Like Monoid Production hunk ./doc/html/monoids/src/Data-Monoid-Combinators.html 225 -filterWith :: (Generator c, Elem c `Reducer` m) => (m -> n) -> (Elem c -> Bool) -> c -> n -filterWith f p = f . filter p -{-# INLINE filterWith #-} - --- | A specialization of 'filter' using the 'First' 'Monoid', analogous to 'Data.List.find' --- --- @ --- 'filterWith' 'getProduct' --- @ -find :: Generator c => (Elem c -> Bool) -> c -> Maybe (Elem c) -find = filterWith getFirst -{-# INLINE find #-} - --- | A generalization of 'Data.List.replicate' to an arbitrary 'Monoid'. Adapted from --- <http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html> -replicate :: (Monoid m, Integral n) => m -> n -> m -replicate x0 y0 - | y0 < 0 = mempty -- error "negative length" - | y0 == 0 = mempty - | otherwise = f x0 y0 - where - f x y - | even y = f (x `mappend` x) (y `quot` 2) - | y == 1 = x - | otherwise = g (x `mappend` x) ((y - 1) `quot` 2) x - g x y z - | even y = g (x `mappend` x) (y `quot` 2) z - | y == 1 = x `mappend` z - | otherwise = g (x `mappend` x) ((y - 1) `quot` 2) (x `mappend` z) -{-# INLINE replicate #-} - --- | A generalization of 'Data.List.cycle' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids. -cycle :: Monoid m => m -> m -cycle xs = xs' where xs' = xs `mappend` xs' - --- | A generalization of 'Data.List.repeat' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids. -repeat :: (e `Reducer` m) => e -> m -repeat x = xs where xs = cons x xs - -prop_replicate_right_distributive :: (Eq m, Monoid m, Arbitrary m, Integral n) => m -> n -> n -> Bool -prop_replicate_right_distributive m x y - = replicate m (x + y) == replicate m x `mappend` replicate m y +-- | Allows idiomatic specialization of filter by proving a function that will be used to transform the output +filterWith :: (Generator c, Elem c `Reducer` m) => (m -> n) -> (Elem c -> Bool) -> c -> n +filterWith f p = f . filter p +{-# INLINE filterWith #-} + +-- | A specialization of 'filter' using the 'First' 'Monoid', analogous to 'Data.List.find' +-- +-- @ +-- 'filterWith' 'getFirst' +-- @ +find :: Generator c => (Elem c -> Bool) -> c -> Maybe (Elem c) +find = filterWith getFirst +{-# INLINE find #-} + +-- | A generalization of 'Data.List.replicate' to an arbitrary 'Monoid'. Adapted from +-- <http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html> +replicate :: (Monoid m, Integral n) => m -> n -> m +replicate x0 y0 + | y0 < 0 = mempty -- error "negative length" + | y0 == 0 = mempty + | otherwise = f x0 y0 + where + f x y + | even y = f (x `mappend` x) (y `quot` 2) + | y == 1 = x + | otherwise = g (x `mappend` x) ((y - 1) `quot` 2) x + g x y z + | even y = g (x `mappend` x) (y `quot` 2) z + | y == 1 = x `mappend` z + | otherwise = g (x `mappend` x) ((y - 1) `quot` 2) (x `mappend` z) +{-# INLINE replicate #-} + +-- | A generalization of 'Data.List.cycle' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids. +cycle :: Monoid m => m -> m +cycle xs = xs' where xs' = xs `mappend` xs' + +-- | A generalization of 'Data.List.repeat' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids. +repeat :: (e `Reducer` m) => e -> m +repeat x = xs where xs = cons x xs + +prop_replicate_right_distributive :: (Eq m, Monoid m, Arbitrary m, Integral n) => m -> n -> n -> Bool +prop_replicate_right_distributive m x y + = replicate m (x + y) == replicate m x `mappend` replicate m y }