Infinite type error when defining zip with foldr only; can it be fixed?

(for the context to this see this recent SO entry).

I tried to come up with the definition of zip using foldr only:

zipp :: [a] -> [b] -> [(a,b)]zipp xs ys = zip1 xs (zip2 ys)  where     -- zip1 :: [a] -> tq -> [(a,b)]          -- zip1 xs :: tr ~ tq -> [(a,b)]     zip1 xs q = foldr (\ x r q -> q x r ) n xs q                        -------- c --------     n    q  = []     -- zip2 :: [b] -> a -> tr -> [(a,b)]     -- zip2 ys :: tq ~ a -> tr -> [(a,b)]     zip2 ys x r = foldr (\ y q x r -> (x,y) : r q ) m ys x r                           ---------- k --------------     m  x r  = []{-      zipp [x1,x2,x3] [y1,y2,y3,y4]    = c x1 (c x2 (c xn n)) (k y1 (k y2 (k y3 (k y4 m))))           ---------------       ----------------------            r                    q    = k y1 (k y2 (k y3 (k y4 m))) x1 (c x2 (c xn n))           ----------------------    ---------------           q                         r-}

It "works" on paper, but gives two "infinite type" errors:

Occurs check: cannot construct the infinite type:  t1 ~ (a -> t1 -> [(a, b)]) -> [(a, b)]             -- trOccurs check: cannot construct the infinite type:  t0 ~ a -> (t0 -> [(a, b)]) -> [(a, b)]             -- tq

Evidently, each type tr, tq, depends on the other, in a circular manner.

Is there any way to make it work, by some type sorcery or something?

I use Haskell Platform 2014.2.0.0 with GHCi 7.8.3 on Win7.