As always, please include a contract, a purpose, examples, and tests for each function.
Define tail-recursive functions to
In comments briefly explain what makes your functions tail-recursive. The functions may take extra parameters (compared to their non-tail-recursive versions).
map
Write map-tail: a tail-recursive version
of map. map-tail takes a list, a function
applicable to list elements, and an accumulator list (i.e. the list of
results). Just as a regular map, it returns a list of
results of applying the function to each element of the list.
Define a function map1 that takes a list and a function
and calls map-tail with the list, the function, and the
initial value of the accumulator list. map1 should work
exactly as the pre-defined map. Test your function to
make sure that this is the case.
This is how map is implemented in Scheme/Racket.