Why do I need annotation here?

In the following code:

type ParseResult<'a> =
    {
        Result : Option<'a>;
        Rest : string
    }

type Parser<'a> = string -> ParseResult<'a>

let ThenBind p (f : Option<'a> -> Parser<'b>) : Parser<'b> =
    fun input ->
        let r = p input
        match r.Result with
        | None -> { Result = None; Rest = input }
        | _ -> (f r.Result) r.Rest

      

        
        
        
      

    

With type annotation for f, the type for ThenBind is:

p:(string -> ParseResult<'a>) ->
f:(Option<'a> -> Parser<'b>) ->
input:string -> ParseResult<'b>

      

        
        
        
      

    

But without annotation, this:

p:(string -> ParseResult<'a>) ->
f:(Option<'a> -> string -> ParseResult<'b>) ->
input:string -> ParseResult<'b>

      

        
        
        
      

    

Why?