How to define map using foldr?

Question

I've recently began studying Haskell and in one of my assignments I've got an exercise which asks to define the map function in terms of foldr, and I can't for the life of me figure out how to do this. I've searched stack overflow for solutions and came across this one:

How would you define map and filter using foldr in Haskell?

However here the solution involves using lambdas, which I haven't covered yet and I assume that because of this the exercise should be doable without lambdas (although you never know).

I guess what confuses me the most is that map takes in a unary function (e.g. +1), whereas foldr takes a binary function (e.g. +), and I don't really see how to make these two work together.

Answer 1

foldr is actually easy: Given a list (written with : and []) like

a : (b : (c : (d : [])))

then applying foldr h x to it will replace every : with `h` and [] with x:

a `h` (b `h` (c `h` (d `h` x)))

Compare that with what map f would to the list:

f a : (f b : (f c : (f d : [])))

This should guide you in choosing h and x so that foldr h x = map f.