WillNess

reverse xs = foldr (\x f rev -> f (x:rev)) id xs []

-- with  g = (\x f rev -> f (x:rev))  -- :

-- g a (g b (g c (g d id))) []
--      g b (g c (g d id)) [a]
--           g c (g d id) [b,a]
--                g d id [c,b,a]
--                    id [d,c,b,a]
--                       [d,c,b,a]

WillNess

http://stackoverflow.com/questions/20568276/implement-insert-in-haskell-with-foldr
  /20570385#20570385
----

You need a [paramorphism](http://stackoverflow.com/a/13317563/849891) for that:

    para  :: (a -> [a] -> b -> b) -> b -> [a] -> b
    foldr :: (a ->        b -> b) -> b -> [a] -> b
    
    para  c n (x : xs) = c x xs (para c n xs)

WillNess

{-# OPTIONS_GHC -O2 -fno-cse #-}
---------------------------------------------------------------------------------------------
----- Sieve of Eratosthenes Comparison Table --- Treefold Merge with Wheel by Will Ness -----

--- original linear-fold merging idea due to Richard Bird, in M. O'Neill JFP article
--- original tree-like folding idea due to Dave Bayer, on Haskell-cafe
--- double primes feed idea to prevent memoization/space leaks due to Melissa O'Neill
--- simplification of tree-folding formulation and wheel adaptation due to Will Ness

--- original Euler sieve one-liner due to Daniel Fischer on haskell-cafe

WillNess

{-# OPTIONS_GHC -O2 -fno-cse #-}
---------------------------------------------------------------------------------------------
----- Sieve of Eratosthenes Comparison Table --- Treefold Merge with Wheel by Will Ness -----

--- original linear-fold merging idea due to Richard Bird, in M. O'Neill JFP article
--- original tree-like folding idea due to Dave Bayer, on Haskell-cafe
--- double primes feed idea to prevent memoization/space leaks due to Melissa O'Neill
--- simplification of tree-folding formulation and wheel adaptation due to Will Ness

--- original Euler sieve one-liner due to Daniel Fischer on haskell-cafe

WillNess

zebra(X,HS):-         
  length(HS,5),
  member(H1,HS),  nation(H1,eng),     color(H1,red),
  member(H2,HS),  nation(H2,spa),     owns( H2,dog),            
  member(H3,HS),  drink( H3,coffee),  color(H3,green),         
  member(H4,HS),  nation(H4,ukr),     drink(H4,tea),
  member(H5,HS),  smoke( H5,oldgold), owns( H5,snails),   
  member(H6,HS),  smoke( H6,kools),   color(H6,yellow), 
  member(H7,HS),  smoke( H7,lucky),   drink(H7,orange),
  member(H8,HS),  nation(H8,jpn),     smoke(H8,parlamt),

WillNess

(define (rev lst)
  (if (or (null? lst)
          (null? (cdr lst)))
      lst
      (apply (lambda (x . xs)
               (apply (lambda (y . ys)
                        (cons y (rev (cons x (rev ys)))))
                      (rev xs)))
             lst)))

WillNess

(define (rplac1 xs a b)
  (let g ((xs xs) (f #f) (k (lambda (x y) x)))         ; http://ideone.com/AbWKxS
    (cond
      (f          (k xs f))                 ; shortcut!
      ((null? xs) (k xs f))                            ; http://stackoverflow.com/q/16550176/849891
      ((not (pair? xs))                                ; http://stackoverflow.com/q/16444290/849891
        (if (eq? xs a) (k b #t) (k xs f)))  ; not f!
      (else 
        (g (car xs)   f   (lambda (x f) 
        (g (cdr xs)   f   (lambda (y f) 

WillNess

s = filter (`notElem`s) x   -- NOT

s = foldr (\(n,a) r-> if (a `notElem` take n s) then a:r else r) [] $ zip [0..] x  -- not quite, yet

s = let a = [ [e | e `notElem` take n s] | (n,e) <- zip c x]   -- here it is!
        b = map length a     --       \
        c = scanl (+) 0 b    --        \
        s = concat a         -- _this_ `s` 
    in s

WillNess

primes = ($[3,5..]) $ (id &&& map (\x->[x*x,x*x+2*x..])

                     >>> second (foldi (\(x:xs)->(x:).union xs) []) 

                     >>> (2:).uncurry minus 


Prelude Saga Control.Arrow Control.Applicative> ($[3,5..]) $ (id&&&id) >>> second
 (map (\x->[x*x, x*x+2*x..])) >>> second (foldi (\(x:xs)->(x:).union xs) []) >>>
 (2:).uncurry minus >>> drop  160000 >>> take 10

WillNess

-- http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-26.html#%_thm_4.21

(\n. ((\fact. fact fact n)   (\ft k. if (= k 1) 1 (* k (ft ft (- k 1))))   ))

(\n. ( (\x g. g g x)  n  (\ft k. if (= k 1) 1 (* k (ft ft (- k 1))))   ))

(\g x. g g x)   (\ft k. if (= k 1) 1 (* k (ft ft (- k 1))))