moveKnight :: KnightPos -> [KnightPos]  
moveKnight (c,r) = filter onBoard  
    [(c+2,r-1),(c+2,r+1),(c-2,r-1),(c-2,r+1)  
    ,(c+1,r-2),(c+1,r+2),(c-1,r-2),(c-1,r+2)  
    ]  
    where onBoard (c,r) = c `elem` [1..8] && r `elem` [1..8] 

I know that this is a massively contrived situation, but they serve me as an exercise to understand language better.

moveKnight :: KnightPos -> [KnightPos]  
moveKnight (c,r) = filter onBoard  
    [(c+2,r-1),(c+2,r+1),(c-2,r-1),(c-2,r+1)  
    ,(c+1,r-2),(c+1,r+2),(c-1,r-2),(c-1,r+2)  
    ]  
    where onBoard (c,r) = c `elem` [1..8] && r `elem` [1..8]

I know that this is a massively contrived situation, but they serve me as an exercise to understand the language better.

So the above works correctly, but the code looks ugly and doesn't use advanced idioms, such as applicative style.

With applicative approach I don't know how to do it. I tried the below code, which generates 2 times more elements, because it doesn't know, that if you increment/decrement by 1 on the left side, you must do it by 2 on the right side:

[(,)] <*> ([(+), (-)] <*> [6] <*> [1, 2]) <*> ([(+), (-)] <*> [6] <*> [1, 2])
-- generates: [(7,7),(7,8),(7,5),(7,4),(8,7),(8,8),(8,5),(8,4),
--             (5,7),(5,8),(5,5),(5,4),(4,7),(4,8),(4,5),(4,4)]

• How to implement the generation of such list with applicative style?
• How to generalize it to arbitrary possible permutations?
• What intuitions, insights and lessons can I get from this exercise?

So the above works correctly, but the code looks ugly. Because every list comprehension is equivalent to a lift, the above code could be rewritten with liftA5:

liftA5 :: Applicative g => (a -> b -> c -> d -> e -> f) -> g a -> g b -> g c -> g d -> g e -> g f
liftA5 f a b c d e = f <$> a <*> b <*> c <*> d <*> e

liftA5 (\c r f g a -> (c `f` a, r `g` (invert a))) [6] [2] [(+), (-)] [(+), (-)] [1,2]

• Are there any way to generate the above list in a more elegant way?
• How to generalize it to arbitrary possible permutations? (So that my code could parametrized and not fixed to just numbers 1 and 2, or just + and -, etc)
• What intuitions, insights and lessons can I get from this exercise?