I have been given the following question as part of a college assignment. Due to the module being very short, we are using only a subset of Haskell, without any of the syntactic sugar or idiomatic shortcuts....I must write:

append xs ys : The list formed by joining the lists xs and ys, in that order

append (5:8:3:[]) (4:7:[]) => 5:8:3:4:7:[]

I understand the concept of how foldr works, but I am only starting off in Functional programming. I managed to write the following working solution (hidden for the benefit of others in my class...) :

However, I just can't for the life of me, explain what the hell is going on!? I wrote it by just fiddling around in the interpreter, for example, the following line :

foldr (\x -> \y -> x:y) [] (2:3:4:[])

which returned [2:3:4] , which led me to try,

foldr (\x -> \y -> x:y) (2:3:4:[]) (5:6:7:[])

which returned [5,6,7,2,3,4]

so I worked it out from there. I came to the correct solution through guess work and a bit of luck...

I am working from the following definition of foldr:

foldr = \f -> \s -> \xs -> if null xs then
                              s
                           else
                              f (head xs) (foldr f s (tail xs) )

Can someone baby step me through my correct solution? I can't seem to get it....I already have scoured the web, and also read a bunch of SE threads, such as How foldr works