# [plt-scheme] HTDP 21.1.2 - trying to put it together

Starting from the top with all the rough working
We have
;map: (X -> Y) [listof X] -> [listof Y]
;fold: (A B -> B) B [listof A] -> B
We want to implement map in terms of fold which means we want fold to
produce [listof Y]
substituting [listof Y] for B in folds result
;fold (A B -> B) B [listof A] -> [listof Y]
...and all other places within folds contract
;fold (A [listof Y] -> [listof Y]) [listof Y] [listof A] -> [listof Y]
thus far defining map in terms of fold gives us
(define (map f a-list)
(fold someFunc someValue a-list))
but we know that the result of applying map to an empty list should be an
empty list
hence we substitute someValue with empty
(define (map f a-list)
(fold someFunc empty a-list))
Now to define someFunc.
Well its contract must conform to
;someFunc: X [listof Y] -> [listof Y]
If we plug in Y for X and consider that Y is supposed to result from
applying (the function we are mapping) to X
then someFunc begins to look like this
(define (someFunc f aloy)
(..... f ..... (first aloy) (rest aloy))
where f is a function with a contract
(X -> Y)
To produce a list as required by the contract we have to use cons
somewhere.
I would have said
(define (someFunc f aloy)
(cons (f first aloy) (rest aloy)))
but it's not right - is it.