Creating char Trie in OCaml - functional-programming

Question

I'm trying to build an initial Trie structure in OCaml where the edges are the char. So the string "ESK" would be mapped as:
[('E', [('S', [('K', [])])])]
My definition for this is:
type trie = Trie of (char * trie) list
However, on implementing an add function with:
let rec add_string str =
let key = String.get str 0 in
if String.length str = 1 then
(key, empty_trie) :: []
else
(key, add_string (tail str)) :: []
for add (tail str) the compiler gives me:
Error: This expression has type (char * trie) list
but an expression was expected of type trie
I'm a bit puzzled by this as I have not defined a trie as (char * trie) list?
tail is simply let tail str = String.slice str 1 (String.length str) and empty_trie is let empty_trie = Trie([])

Answer 1

Note that a more idiomatic way of writing the function would be
let rec add_string str =
let key = str.[0] in
if String.length str = 1 then
Trie [key, empty_trie]
else
Trie [key, add_string (tail str)]
Then there are two problems left with add_string: first it reallocates a new string at each iteration. It is simpler and more efficient to keep track of the current position:
let add_string str =
let rec add_string_aux pos str =
if pos = String.length str then empty_trie
else
let key = str.[pos] in
Trie [key, add_string_aux (pos+1) str] in
add_string_aux 0 str
The second problem is that the function is ill-named since it does not add a string to an existing trie but build a trie from a string: from_string or of_string might be better names.

Answer 2

Resolved. Trie should be explicitly used:
let rec add_string str =
let key = String.get str 0 in
if String.length str = 1 then
(key, empty_trie) :: []
else
(key, Trie (add_string (tail str))) :: []
This will result in add_string "ESK" producing:
(char * trie) list = [('E', Trie [('S', Trie [('K', Trie [])])])]