I know it's supposed to be pseudo code and most likely it's something like sprintf "% world %d" "hello" 42 but I got a little confused by the type list being backwards from what I expected
This paragraph shows that with a format string with an int format specifer, and then a string format specifier, the token list shows is exactly that, and the type it returns is a function that takes an Int and a String as input and returns a new string.
> For example, if the format string was "%d %s", the tokenization would be [IntFormat, NormalChar ' ', StrFormat], so the resulting type would be Int -> String -> String`. This might be confusing because it's a post-order traversal of the list, and might feel kind of backwards.
Isn't that exactly the order you'd expect?
I'm confused why it's called backwards, and why they say "post-order" traversal of a list, since I'm only used to hearing about traversing trees that way.
Isn't Int -> String -> String a shorthand for Int -> (String -> String)?
Thus I would have assumed the first argument to the result of sprintf "%s %d" would be an integer, then a string and the final result would be a string.
But the invocation would be sprintf "%s %d" "hello" 42, wouldn't it?
Yes. Though I find it more convenient think of it as a function with multiple arguments and not a function that returns another function.
> Thus I would have assumed the first argument to the result of sprintf "%s %d" would be an integer, then a string and the final result would be a string.
Why assume that? (Not rhetorical.) Wouldn't that be like if in C, you had to write the arguments in reverse order of the format string, like this?
printf("%s %d!\n", 5, "hi");> Wouldn't that be like if in C, you had to write the arguments in reverse order of the format string, like this?
Exactly and that's not what we want
Let's go through this step by step:
sprintf "%s %d" returns a function, taking a string and returning a function taking an integer and returning a string, right?
sprintf "%s %d" "hello" returns a function taking an integer, returning a string, right?
sprintf "%s %d" "hello" 42 returns a string, right?
Thus my intuition of the return type of sprintf "%s %d" would be string -> (int -> string) not int -> (string -> string)
The "backwards" in the article is referring to the way the list is processed by the recursive function. The list and the resulting type are in the correct/intuitive order. I also found this sentence confusing.
By the way, thinking of a function of type a->b->c as a->(b->c) is technically correct and useful in certain cases, for example, when you are currying. But in most cases you can just read this as a function taking two arguments of types a and b, returning something of type c.