-- This rule is useful in cases like
-- head [y | (x,y) <- ps, x==t]
{-# RULES
-"head/build" forall g::forall b.(Bool->b->b)->b->b .
+"head/build" forall (g::forall b.(Bool->b->b)->b->b) .
head (build g) = g (\x _ -> x) badHead
-"head/augment" forall xs, g::forall b. (a->b->b) -> b -> b .
+"head/augment" forall xs (g::forall b. (a->b->b) -> b -> b) .
head (augment g xs) = g (\x _ -> x) (head xs)
#-}
-- 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
-"filterFB" forall c,p,q. filterFB (filterFB c p) q = filterFB c (\x -> p x && q x)
+"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
or (x:xs) = x || or xs
{-# RULES
-"and/build" forall g::forall b.(Bool->b->b)->b->b .
+"and/build" forall (g::forall b.(Bool->b->b)->b->b) .
and (build g) = g (&&) True
-"or/build" forall g::forall b.(Bool->b->b)->b->b .
+"or/build" forall (g::forall b.(Bool->b->b)->b->b) .
or (build g) = g (||) False
#-}
#endif
all _ [] = True
all p (x:xs) = p x && all p xs
{-# RULES
-"any/build" forall p, g::forall b.(a->b->b)->b->b .
+"any/build" forall p (g::forall b.(a->b->b)->b->b) .
any p (build g) = g ((||) . p) False
-"all/build" forall p, g::forall b.(a->b->b)->b->b .
+"all/build" forall p (g::forall b.(a->b->b)->b->b) .
all p (build g) = g ((&&) . p) True
#-}
#endif
-- foldr2 k z xs ys = foldr (foldr2_left k z) (\_ -> z) xs ys
-- foldr2 k z xs ys = foldr (foldr2_right k z) (\_ -> z) ys xs
{-# RULES
-"foldr2/left" forall k,z,ys,g::forall b.(a->b->b)->b->b .
+"foldr2/left" forall k z ys (g::forall b.(a->b->b)->b->b) .
foldr2 k z (build g) ys = g (foldr2_left k z) (\_ -> z) ys
-"foldr2/right" forall k,z,xs,g::forall b.(a->b->b)->b->b .
+"foldr2/right" forall k z xs (g::forall b.(a->b->b)->b->b) .
foldr2 k z xs (build g) = g (foldr2_right k z) (\_ -> z) xs
#-}
\end{code}
\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}