-- elements that satisfy the predicate; i.e.,
-- filter p xs = [ x | x <- xs, p x]
filter :: (a -> Bool) -> [a] -> [a]
-{-# INLINE filter #-}
-filter p xs = build (\c n -> foldr (filterFB c p) n xs)
+filter = filterList
filterFB c p x r | p x = x `c` r
| otherwise = r
{-# RULES
+"filter" forall p xs. filter p xs = build (\c n -> foldr (filterFB c p) n xs)
"filterFB" forall c p q. filterFB (filterFB c p) q = filterFB c (\x -> p x && q x)
"filterList" forall p. foldr (filterFB (:) p) [] = filterList p
#-}
-- iterate f x returns an infinite list of repeated applications of f to x:
-- iterate f x == [x, f x, f (f x), ...]
iterate :: (a -> a) -> a -> [a]
-{-# INLINE iterate #-}
-iterate f x = build (\c _n -> iterateFB c f x)
+iterate = iterateList
iterateFB c f x = x `c` iterateFB c f (f x)
iterateList f x = x : iterateList f (f x)
{-# RULES
-"iterate" iterateFB (:) = iterateList
+"iterate" forall f x. iterate f x = build (\c _n -> iterateFB c f x)
+"iterateFB" iterateFB (:) = iterateList
#-}
-- repeat x is an infinite list, with x the value of every element.
repeat :: a -> [a]
-{-# INLINE repeat #-}
-repeat x = build (\c _n -> repeatFB c x)
+repeat = repeatList
repeatFB c x = xs where xs = x `c` xs
repeatList x = xs where xs = x : xs
{-# RULES
-"repeat" repeatFB (:) = repeatList
+"repeat" forall x. repeat x = build (\c _n -> repeatFB c x)
+"repeatFB" repeatFB (:) = repeatList
#-}
-- replicate n x is a list of length n with x the value of every element
\begin{code}
----------------------------------------------
zip :: [a] -> [b] -> [(a,b)]
-{-# INLINE zip #-}
-zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys)
+zip = zipList
zipFB c x y r = (x,y) `c` r
zipList _ _ = []
{-# RULES
-"zipList" foldr2 (zipFB (:)) [] = zipList
+"zip" forall xs ys. zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys)
+"zipList" foldr2 (zipFB (:)) [] = zipList
#-}
\end{code}
\begin{code}
----------------------------------------------
zipWith :: (a->b->c) -> [a]->[b]->[c]
-{-# INLINE zipWith #-}
-zipWith f xs ys = build (\c n -> foldr2 (zipWithFB c f) n xs ys)
+zipWith = zipWithList
+
zipWithFB c f x y r = (x `f` y) `c` r
zipWithList _ _ _ = []
{-# RULES
-"zipWithList" forall f. foldr2 (zipWithFB (:) f) [] = zipWithList f
+"zipWith" forall f xs ys. zipWith f xs ys = build (\c n -> foldr2 (zipWithFB c f) n xs ys)
+"zipWithList" forall f. foldr2 (zipWithFB (:) f) [] = zipWithList f
#-}
\end{code}