Recursive function in ML - sml

This is curried function that examines only the first two list elements.
fun inn list f = f(hd(list), hd(tl(list)));
What I would like to know is any ways that I can go through the rest of the list elements.
I don't know how I make it recursive.
Can anybody help me?

First remark: never use hd and tl. Use pattern matching instead.
I don't now what exactly you want your function to do, but here is one that iterates over a list and applies f to every element:
fun iter f l =
case l of
[] => ()
| x::xs => (f x; iter f xs)
which can be written more concisely as
fun iter f [] = ()
| iter f (x::xs) = (f x; iter f xs)
For what's it worth, this very function is available in the standard basis library under the name List.app.

Related

Simpler way to implement map function in OCaml

I know List.map uses recursion, I'm just wondering if there's a simpler way to implement map function without using recursion.
I know for reverse, I can simplify it into:
(* given *)
type 'a list =
| []
| (::) of 'a * 'a list
let nil : 'a list = []
let cons (hd : 'a) (tl : 'a list): 'a list = hd :: tl
let reverse (ls : 'a list): 'a list =
List.fold_left (Fun.flip cons) [] ls
Right now I'm thinking about using ##(the application operator), %(the function composition operator), and maybe Fun.flip or List.fold_left to do it, can anyone give me some hint about that?
I have tried the following, but OCaml raised an error about it.
List.fold_left (fun x -> f x) [] ls
List.fold_left uses recursion, so presumably you're looking to avoid use of the rec keyword, rather than recursion at all.
You note in comments trying:
List.fold_left (fun x -> f x) [] ls
But the function passed to List.fold_left must take two arguments: the initial state, and the first element of the list. Fun.flip cons worked in your reverse function because it does take two arguments.
Note: fun x -> f x is the same as writing f.
If you initial state is a list, you need to do something to that list in the function you pass to List.fold_left, like adding the result of f x to the front of it. Since this builds the list backwards, you will need to reverse the result. This is where ## will come in handy.
let map f lst =
List.(
rev ## fold_left (fun i x -> f x :: i) [] lst
)

Non-recursive way to reverse a list in a purely functional way?

I'm working in OCaml and need to write a function
let rev lst = ...
which reverses the list lst without using recursion. I don't think I can use iterative methods either, like a for-loop. And I can't use List library functions. And I can't define some kind of data structure that allows me to interface with the elements in reverse order. It has to be a very from-bare-OCaml implementation.
Given these constraints I really can't think of any way to do this. I really don't even know where to start. The only two things in my bag of tricks, when dealing with arbitrary lists, are recursion and iteration.
The only loophole I can see here is to define another function that uses recursion, and then have rev use it such that rev itself is not recursive. List.fold_left is easy enough to reimplement such that your rev function also doesn't use any functions from the List module. This should satisfy the requirements.
let rec foldl f i =
function
| [] -> i
| x::xs -> foldl f (f i x) xs
And then rev:
let rev lst = foldl (fun i x -> x::i) [] lst
If you feel like being clever, you could reimplement Fun.flip as well, and create a cons function. Both simple enough.
let flip f a b = f b a
let cons a b = a :: b
let rev lst = foldl (flip cons) [] lst

F# return list of list lengths

I am to use combinators and no for/while loops, recursion or defined library functions from F#'s List module, except constructors :: and []
Ideally I want to implement map
I am trying to write a function called llength that returns the list of the lengths of the sublists. For example llength [[1;2;3];[1;2];[1;2;3]] should return [3;2,3]. I also have function length that returns the length of a list.
let Tuple f = fun a b -> f (a, b)
let length l : int =
List.fold (Tuple (fst >> (+) 1)) 0 l
currently have
let llength l : int list =
List.map (length inner list) list
Not sure how I should try accessing my sublists with my restraints and should I use my other method on each sublist? any help is greatly appreciated, thanks!
Since this is homework, I don't want to just give you a fully coded solution, but here are some hints:
First, since fold is allowed you could implement map via fold. The folding function would take the list accumulated "so far" and prepend the next element transformed with mapping function. The result will come out reversed though (fold traverses forward, but you prepend at every step), so perhaps that wouldn't work for you if you're not allowed List.rev.
Second - the most obvious, fundamental way: naked recursion. Here's the way to think about it: (1) when the argument is an empty list, result should be an empty list; (2) when the argument is a non-empty list, the result should be length of the argument's head prepended to the list of lengths of the argument's tail, which can be calculated recursively. Try to write that down in F#, and there will be your solution.
Since you can use some functions that basically have a loop (fold, filter ...), there might be some "cheated & dirty" ways to implement map. For example, via filter:
let mymap f xs =
let mutable result = []
xs
|> List.filter (fun x ->
result <- f x :: result
true)
|> ignore
result |> List.rev
Note that List.rev is required as explained in the other answer.

Lwt and recursive functions

Is it ok to use Lwt.return as the final call in a recursive function?
I have a function that compiles fine but does not run properly and it looks like the function f below. Please assume that there is no issue with any function provided as g in this example, I am basically just trying to find out if it is ok to have a function with the following form or if there is a better/simpler (and Lwt compliant) way of doing the following:
let rec f (x : string list) (g : string -> unit Lwt.t) =
match List.length x with
| 0 -> Lwt.return ()
| _ -> g (List.hd x) >>= fun () -> f (List.tl x) g
;;
val f : string list -> (string -> unit Lwt.t) -> unit Lwt.t = <fun>
I am pretty sure that I am doing it wrong. But the actual function I am using is much more complex than this example so I am having a difficult time debugging it.
First of all the correct way of dealing with lists in OCaml is deconstructing them with pattern matching, like this:
let rec f (xs : string list) (g : string -> unit Lwt.t) =
match xs with
| [] -> return ()
| x :: xs -> g x >>= fun () -> f xs g
The next step would be notice, that you're actually just perform iteration over a list. There is a Lwt_list.iter_s for this:
let f g xs = Lwt_list.iter_s g xs
That can simplified even more
let f = Lwt_list.iter_s
That means, that you even do not need to write such function, since it is already there.
And finally, there was no issues with recursion in your original implementation. The function that you've provided was tail recursive.
It depends whether g returns an lwt thread that is already computed such as return () or scheduled and woken up later by the lwt scheduler. In the former case, it's possible that the call to fun () -> f (List.tl x) g is made right away instead of being scheduled for later, and that could grow the stack depending on what optimizations are happening.
I don't think your code should rely on such tricky behavior. For this particular example, as suggested in #ivg's answer, you should use the functions from the Lwt_list module.
It's a good idea to look at the implementation of the Lwt_list module to see how it's done. The same advice goes for the OCaml standard library as well.

Recursion over lists in Haskell

For instance, i have a list like ['a','b','c','d','e'].
I want to do something like this:
First do something with the first two elements, f 'a' 'b'
Then do the same thing with the return value of f and next element in the list, result = f 'a' 'b', lets say like f result 'c'. Then f resultof(result 'c') 'd' and so on.
How can i do something like this?
First let's consider that function f that you have. It takes some sort of accumulated value, a plain value, and combines them into a result. So, in the type signature, we'll say a for the type of the accumulated value, v for the type of the value, and r for the type of the result.
f :: a -> v -> r
Now we want to create a folding function that uses f and a list of values.
someFold :: (a -> v -> r) -> [v] -> ?
What should it return? It should yield something of the resultant type r, right? Notice now that a and r should actually be the same type, since we keep feeding the result of f into it's first argument again.
someFold :: (a -> v -> a) -> [v] -> a
Now one thing's missing. How do you get the very first a? There are two ways to look at that. Either you just pick the first value, in which case a is the same type as v, or you specify a base value, so a could actually be different than v. Let's go with the latter, since that's more interesting. Let's also decide to move left to right in this list. (That's what you need, right?)
someFold :: (a -> v -> a) -> a -> [v] -> a
So...how do we implement it? It'll be recursive, so let's start with the base cases.
someFold f acc [] = acc
If we hit the end of the list, then we've accumulated enough, right? That was easy. So how about the recursive case? From what you said, at each step we should apply f to the "accumulated value so far" as the first argument, and the "first value of the list" as the second. f acc x. Then we keep folding, using that as our new "accumulated" value.
someFold f acc (x:xs) = someFold f (f acc x) xs
Easy, right? But...what if we want to do like you said and start the function by taking the first two values of the list? Also easy. Just take the first element, and call it the original "base" accumulator!
someFold1 :: (v -> v -> v) -> [v] -> v
someFold1 f (x:xs) = someFold f x xs
Notice that since a is the same type as v for this special case, the function someFold1 has a very amusing type signature. If you understood this explanation, then congrats. We've just implemented foldl and foldl1.
Prelude> foldl1 min "abcde" -- "abcde" is sugar for ['a','b','c','d','e']
'a'
In real code, you should actually use foldl' and friends.
Sounds like homework. Take a look at folds.
In this case, the problem with a fold is, that it usually processes on element at a time. You could try to manually roll a fold.
Assume, you have your function f, that gets two elements at a time and the accumulator (the result of the last iteration) fed. Then you function looks like this:
fold2 :: (a -> a -> b -> b) -> [a] -> b -> b
fold2 f accum (x:y:zs) = fold2 f (f x y) zs
fold2 _ accum [] = accum
fold2 _ _ _ = error "odd number of elements"
Try to understand this. fold2 shaves the top two elements of the list of and feeds it into f. The result this is then passed as the new accumulator to the recursive call. This is done until the list is empty.