Why is my F# vector add function using tail recursion not working?

Question

I cannot get this to work in F#. I am trying to write a tail recursive form of vector add and pass the previously calculated values using a. It is giving error "error FS0001: Type mismatch. Expecting a ''a'
but given a ''b list -> 'c list -> 'a list'
The types ''a' and ''b list -> 'c list -> 'a list' cannot be unified."

let rec vecadd a v1 v2 =
 match (v1, v2) with
 | ([], []) -> a
 | (h1::t1, h2::t2) -> vecadd a::h1+h2 t1 t2

Answer 1

First of all, you need to add parentheses around (a::h1+h2). Otherwise, the compiler thinks that you are calling vecadd with a as the argument and then prepending that to a list. Your code gets parsed as (vecadd a)::h1+h2 instead.

Once you add the parentheses, there is one more issue. In your recursive call, the argument a::h1+h2 is not right - the operator :: prepends a value to the front of a list and so it takes a value and a list of values. In your case, you are trying to use it to append a value to the end of the list.

You can fix this by using h1+h2::a to add the new element to the front of the list and then reversing the list before returning it in the [], [] case:

let rec vecadd a v1 v2 =
 match (v1, v2) with
 | ([], []) -> List.rev a
 | (h1::t1, h2::t2) -> vecadd (h1+h2::a) t1 t2