OCaml: List mapping a function with 2 inputs

Question

I have a function sqrt which takes 2 floating point values, tolerance and number and gives out square root of the number within the specified tolerance. I use approximation method to do it.

let rec sqrt_rec approx tol number =
..................;;
let sqrt tol x = sqrt_rec (x/.2.0) tol x;;

I've another function map which takes a function and a list and applies the function to all elements of the list.

let rec map f l = 
match l with
[] -> []
| h::t -> f h::map f t;;

Now I'm trying to create another function all_sqrt which basically takes 1 floating point value, 1 floating point list and maps function sqrt to all the elements.

let all_sqrt tol_value ip_list = List.map sqrt tol_value ip_list;;

It is obviously giving me error. I tried making tol_value also a list but it still throws up error. Error: This function is applied to too many arguments; maybe you forgot a `;'

I believe i'm doing mapping wrong.

Answer 1

The List module contains

val map2 : ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list

which is used like this:

let all_sqrt tol_value ip_list = List.map2 sqrt tol_value ip_list

Answer 2

This sounds like homework, since you say you are limited to certain functions in your solution. So I'll try to give just some suggestions, not an answer.

You want to use the same tolerance for all the values in your list. Imagine if there was a way to combine the tolerance with your sqrt function to produce a new function that takes just one parameter. You have something of the type float -> float -> float, and you somehow want to supply just the first float. This would give you back a function of type float -> float. (As Wes pointed out, this works because your sqrt function is defined in Curried form.)

All I can say is that FP languages like OCaml (and Haskell) are exceptionally good at doing exactly this. In fact, it's kind of hard not to do it as long as you mind the precedences of various things. (I.e., think about the parentheses.)

Answer 3

I don't know O'Caml, but I do know Haskell, and it looks to me like you are applying map to 3 arguments "sqrt tol_value ip_list" map only takes two arguments, and is of the type ('a -> 'b) -> 'a list -> 'b list which means it accepts a function (functions only take one input and return one output), and a list, and returns a new list.

http://en.wikipedia.org/wiki/Currying