Recursive OCaml function not working - list

I'm using the following code to try and put the average of consecutive numbers in an integer list into a new list:
let newList = []
let rec average2 xs =
match xs with
| [] -> newList
| x :: [] -> newList
| x :: x' :: [xs] -> append newList [((x + x')/2)] average2 x' :: [xs];;
but I keep getting the following error and don't understand why:
Error: This function has type 'a list -> 'a list -> 'a list It is applied to too many arguments; maybe you forgot a `;'.

You're passing the average2 function to the append function instead of calling it in the last line. Also, newList is empty and does not get mutated nor read from. You can just add a new head to the list when returning it.
Change it to
((x + x')/2) :: (average2 x' :: [xs])

Related

F#: Create a list that contains the head of all the lists, in the list

I am trying to create a function that takes the head of all the lists in the list ([[]]). So far I've found out how to take all the first ints of all the lists in the list, but I can't seem to make that into a list in the same function.
let isTable (llst : list<list<'a>>) : bool =
List.forall (fun (elem : list<'a>) -> not elem.IsEmpty && elem.Length = elem.Length) llst
let a = [[1;2;3];[4;5;6]]
printfn "%A" (isTable a)
List.iter (fun x -> printfn "%A " (List.head x)) a
Can anyone help here?
You can use List.map to apply List.head that you already found to each list.
let a = [[1;2;3];[4;5;6]]
let collectHeads l = List.map List.head l
printfn "%A" (collectHeads a) // [1,4]
Unlike List.head, List.map is a higher order function and expects a function as a parameter. Expected function should take an element of the list's type and return another element. It happens that List.head does just that: it takes a list as input and return's it's head as resulting element.

F# filtering sublist

Here is an input list: [[10;2;10]; [10;50;10]; [10;1;10]].
How would I filter the second element of each sub-list?
Below is my code and when I output the result I get [[10;50;10]] but what I want is [2;50;1]. Is there anyway to fix my code? I am really trying to understand F#. Thanks for the help in advance.
let sub =
let input = [[10;2;10]; [10;50;10]; [10;1;10]]
let findIndex input elem = input |> List.findIndex ((=) elem)
let q = input |> List.filter(fun elem -> findIndex input elem = 1)
printfn "%A" q
The following will get the expected result:
let second (x:List<int>) = x.[1]
let q = List.map second input
List.map is a higher order function that makes a new list by applying a function (the first argument, here the function second that returns the second element of a list) to a list (here input):
[ [10;2;10]; [10;50;10]; [10;1;10] ]
| | |
second second second <--- mapping function
| | |
V V V
[ 2 ; 50 ; 1 ]
Use List.map, not List.filter
List.filter keeps/removes items from an input list based on the function you give it, e.g. List.filter (fun x -> x % 2 = 0) myList would keep only the even numbers in myList. You can get an idea of this functionality based on its type signature, which is val filter: ('a -> bool) -> 'a list -> 'a list, meaning it takes a function (that takes an 'a and returns a boolean: ('a -> bool)), then takes a list, and returns a list of the same type.
List.map, on the other hand, transforms each element of a list into whatever you want, based on a function you give it. In your case you would use it like so:
let input = [[10;2;10]; [10;50;10]; [10;1;10]]
let result = input |> List.map (fun numbers -> numbers.[1])
printfn "%A" result
The signature of List.map is val map: ('a -> 'b) -> 'a list -> 'b list, meaning it takes a function that maps 'as to 'bs (in your case, this would map int lists to ints), takes a list of the first thing, and returns a list of the second thing.
Use List.map and List.tryIndex
Note that if any of the sub-lists are too short, the program will crash. If this is a concern, you can use a safe version of myList.[i]; namely List.tryIndex, which returns None if the item was not found. Try this out:
// Note the last sublist
let input = [[10;2;10]; [10;50;10]; [10;1;10]; [-1]]
let result : int option list = input |> List.map (fun numbers -> List.tryIndex 1 numbers)
printfn "%A" result
// This prints:
// [Some 2; Some 50; Some 1; None]

Unknown Type Error in OCaml

I'm attempting to create a new list of all the unique items from another list. My in_list function works properly and returns a value saying whether or not the value is found in the seen_list, but I can't for the life of me get this to compile.
let uniq x = match in_list x seen_list with
| true -> seen_list
| false -> seen_list#[x]
| _ -> seen_list
;;
List.iter uniq check_list;;
The problem is some sort of type error. Here it is:
Error: This expression has type int -> int list
but an expression was expected of type int -> unit
Type int list is not compatible with type unit
In essence you want to take the result returned by uniq and pass it as the list for the next call of uniq. To do this, you need to use a fold, or write your own recursion. The purpose of List.iter is just to call an imperative function for each element of a list. It doesn't combine the answers in any way. That's why you're getting a type error—your function isn't imperative. I.e., it doesn't return unit.
Perhaps this is what you want:
let rec uniq_list lst =
match lst with
| [] -> []
| x :: xs ->
let r = uniq_list xs in
if in_list x r then r else x :: r
Or, using List.fold_right (equivalent to the recursive function above):
let uniq_list lst =
List.fold_right
(fun x r -> if in_list x r then r else x :: r)
lst
[]
Or using List.fold_left which is tail-recursive:
let uniq_list lst =
List.fold_left
(fun r x -> if in_list x r then r else x :: r)
[]
lst
By the way, your in_list is equivalent to the standard library function List.mem.

Appending two lists

So this is one way to append two lists:
let rec append l1 l2 =
match l1 with
| h :: t -> h :: append t l2
| [] -> l2
But I am trying to write a tail-recursive version of append. (solve the problem before calling the recursive function).
This is my code so far, but when I try to add append in the first if statement the code becomes faulty for weird reasons.
let list1 = [1;2;3;4]
let list2 = [5;6;7;8]
let rec append lista listb =
match listb with
| h :: taillist -> if taillist != [] then
begin
lista # [h];
(* I cant put an append recursive call here because it causes error*)
end else
append lista taillist;
| [] -> lista;;
append list1 list2;;
The easiest way to transform a non tail-recursive list algorithm into a tail-recursive one, is to use an accumulator. Consider rewriting your code using a third list, that will accumulate the result. Use cons (i.e., ::) to prepend new elements to the third list, finally you will have a result of concatenation. Next, you need just to reverse it with List.rev et voila.
For the sake of completeness, there is a tail-recursive append:
let append l1 l2 =
let rec loop acc l1 l2 =
match l1, l2 with
| [], [] -> List.rev acc
| [], h :: t -> loop (h :: acc) [] t
| h :: t, l -> loop (h :: acc) t l
in
loop [] l1 l2
I would recommend to solve 99 problems to learn this idiom.
A couple of comments on your code:
It seems like cheating to define a list append function using #, since this is already a function that appends two lists :-)
Your code is written as if OCaml were an imperative language; i.e., you seem to expect the expression lista # [h] to modify the value of lista. But OCaml doesn't work that way. Lists in OCaml are immutable, and lista # [h] just calculates a new value without changing any previous values. You would need to pass this new value in your recursive call.
As #ivg says, the most straightforward way to solve your problem is using an accumulator, with a list reversal at the end. This is a common idiom in a language with immutable lists.
A version using constant stack space, implemented with a couple of standard functions (you'll get a tail-recursive solution after unfolding the definitions):
let append xs ys = List.rev_append (List.rev xs) ys
Incidentally, some OCaml libraries implement the append function in a pretty sophisticated way:
(1) see core_list0.ml in the Core_kernel library: search for "slow_append" and "count_append"
(2) or batList.mlv in the Batteries library.
An alternative tail-recursive solution (F#) leveraging continuations :
let concat x =
let rec concat f = function
| ([], x) -> f x
| (x1::x2, x3) -> concat (fun x4 -> f (x1::x4)) (x2, x3)
concat id x
I think the best way to go about it, like some have said would be to reverse the first list, then recursively add the head to the front of list2, but the top comment with code uses an accumulator, when you can get the same result without it by :: to the second list instead of an accumulator
let reverse list =
let rec reverse_helper acc list =
match list with
| [] -> acc
| h::t -> reverse_helper (h::acc) t in
reverse_helper [] lst;;
let append list1 list2 =
let rec append_helper list1_rev list2 =
match list1_rev with
| [] -> list2
| h :: t -> append_helper t (h::lst2) in
append_helper (reverse lst1) lst2;;
A possible answer to your question could be the following code :
let append list1 list2 =
let rec aux acc list1 list2 = match list1, list2 with
| [], [] -> List.rev(acc)
| head :: tail, [] -> aux (head :: acc) tail []
| [], head :: tail -> aux (head :: acc) [] tail
| head :: tail, head' :: tail' -> aux (head :: acc) tail (head' :: tail')
in aux [] list1 list2;
It's pretty similar to the code given by another one of the commenters on your post, but this one is more exhaustive, as I added a case for if list2 is empty from the beginning and list1 isn't
Here is a simpler solution:
let rec apptr l k =
let ln = List.rev l in
let rec app ln k acc = match ln with
| [] -> acc
| h::t -> app t k (h::acc) in
app ln k k
;;
let rec append (mylist: 'a list) (myotherlist : 'a list ): 'a list =
match mylist with
| [] -> myotherlist
| a :: rest -> a :: append rest myotherlist

Error in code to flatten a list in Ocaml

Hello All I am trying to flatten a list in Ocaml. I am a newbie so please pardon me if my mistake is dumb
So for example, if input is [[1];[2;3];[4]] I should end up with [1;2;3;4].
The idea I am trying to use is as follows
Iterate through the list from the right (Using fold_right) with accumaltor = []
The pseudo code is as follows
func flatten(list, accumalator)
For each item from right to left in list
If Item is a scalar then n :: accumalator
Else fi Item is a list of form head :: tail then
head :: flatten (tail, accumalator).
I think that theoretically the algorithm is correct, but please let me know if you disagree.
Now to my OCaml code to implement this algorithm
let rec flatten acc x =
match x with
n -> n :: acc
| [x] -> x :: acc
| head :: remainder ->
head :: ( my_flat acc remainder )
and my_flat = List.fold_right flatten
;;
my_flat [] [[1];[2;3];[4]]
The Error I get is the following
Error: This expression has type 'a but an expression was expected of type
'a list
The error occurs on the line that reads head :: ( my_flat acc remainder ) in the last pattern in the match statement
Any help is appreciated.
In OCaml, all the elements of a list must be the same type. Thus the value [1; [2; 3]; 4] is invalid all by itself. It contains two elements that are of type int and one element of type int list. In essence, your statement of the problem to be solved is impossible.
$ ocaml312
Objective Caml version 3.12.0
# [1; [2; 3]; 4];;
Characters 4-10:
[1; [2; 3]; 4];;
^^^^^^
Error: This expression has type 'a list
but an expression was expected of type int
This sounds like a homework problem, so I'll just say that restricting yourself to lists that are valid in OCaml may make it easier to solve.
Edit
OK, the problem can now be solved!
The essence of the reported type error is something like this. You have your accumulated result acc (of type int list in the example). You want to add the list x (also of type int list) to it. You've broken x into head (an int) and remainder (an int list). As you can see, remainder is not a suitable argument for your my_flat function. It wants an int list list, i.e., a list of lists of ints. In fact, your recursive call should almost certainly go to flatten and not to my_flat.
Another problem I see: the arguments of List.fold_right are: a function, a list, and a starting value. In your test call to my_flat, you're supplying the last two in the other order. The empty list [] is your starting value.
I hope this is enough to get you going. Since you're just starting out with OCaml there will probably be another problem or two before it works.
Edit 2
Here are a couple more comments, which might be spoilers if you're still working on your own solution....
A tidier version of your function my_flat is in the OCaml standard library under the name List.flatten. It's interesting to look at the implementation:
let rec flatten = function
[] -> []
| l::r -> l # flatten r
I'd call this a very elegant solution, but unfortunately it's not tail recursive. So it will consume some (linear) amount of stack space, and might even crash for a very long list.
Here's one based on the same idea, using the standard FP accumulator trick to get tail recursive behavior (as noted by Thomas):
let flatten2 ll =
let rec go acc = function
| [] -> List.rev acc
| l :: r -> go (List.rev_append l acc) r
in
go [] ll
As is often the case, the tail recursive version accumulates the result in reverse order, and reverses it at the end.
You can start by writing directly your algorithm, by decomposing the base cases of your input value, ie. the input list is either empty, or the head of the input list is empty, or the head of the input list has a head and a tail:
let rec flatten = function
| [] -> []
| [] :: t -> flatten t
| (x::y) :: t -> x :: (flatten (y::t))
You can then optimize the function, because this code is not tail-recursive and thus will crash when lists become too big. So you can rewrite this by using the usual technique:
let flatten list =
let rec aux accu = function
| [] -> accu
| [] :: t -> aux accu t
| (x::y) :: t -> aux (x::accu) (y::t) in
List.rev (aux [] list)
So my advice is: start by decomposing your problem based on the input types, and then later use accumulators to optimize your code.
I like this one, where the auxiliary function takes the accumulator, the first element of the list of lists, and the rest of the list of lists, it is clearer for me :
let flatten list =
let rec aux acc list1 list2 =
match list1 with
| x :: tail -> aux (x :: acc) tail list2
| [] ->
match list2 with
| [] -> List.rev acc
| x :: tail -> aux acc x tail
in
aux [] [] list
Thanks for all your help
Here is the code I used to solve this problem
let flatten list =
let rec flatten_each acc x =
match x with
[] -> acc
| head :: remainder -> head :: ( flatten_each acc remainder )
in
List.fold_right flatten_each ( List.rev list ) []
;;
Edit: as pointed out by Thomas this solution is not tail recursive. Tail recursive version is below
let flatten list =
let rec flatten_each acc x =
match x with
[] -> acc
| head :: remainder -> (flatten_each (acc # [head]) remainder )
in
List.fold_right flatten_each list []
;;