---
name: "List"
section: "3o"
platform: "linux"
package: "ocaml"
version: "5.5.0-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/List/3o"
---

# List(3o)

List operations.

## NAME

List - List operations.

## Module

Module   List

## Documentation

Module **List**\
  :  **sig end**

List operations.

Some functions are flagged as not tail-recursive.  A tail-recursive function uses constant stack space, while a non-tail-recursive function uses stack space proportional to the length of its list argument, which can be a problem with very long lists.  When the function takes several list arguments, an approximate formula giving stack usage (in some unspecified constant unit) is shown in parentheses.

The above considerations can usually be ignored if your lists are not longer than about 10000 elements.

The labeled version of this module can be used as described in the **StdLabels** module.

*type* **'a** *t* =  **'a list** =\
  \| \[\]\
  \| (::) **of** **'a \* 'a list**

An alias for the type of lists.

*val length* :  **'a list -\> int**

Return the length (number of elements) of the given list.

*val compare\_lengths* :  **'a list -\> 'b list -\> int**

Compare the lengths of two lists.  **compare\_lengths l1 l2** is equivalent to  **compare (length l1) (length l2)** , except that the computation stops after reaching the end of the shortest list.

**Since** 4.05

*val compare\_length\_with* :  **'a list -\> int -\> int**

Compare the length of a list to an integer.  **compare\_length\_with l len** is equivalent to  **compare (length l) len** , except that the computation stops after at most  **len** iterations on the list.

**Since** 4.05

*val is\_empty* :  **'a list -\> bool**

**is\_empty l** is true if and only if  **l** has no elements. It is equivalent to **compare\_length\_with l 0 = 0** .

**Since** 5.1

*val cons* :  **'a -\> 'a list -\> 'a list**

**cons x xs** is  **x :: xs**

**Since** 4.03 (4.05 in ListLabels)

*val singleton* :  **'a -\> 'a list**

**singleton x** returns the one-element list  **\[x\]** .

**Since** 5.4

*val hd* :  **'a list -\> 'a**

Return the first element of the given list.

**Raises Failure** if the list is empty.

*val tl* :  **'a list -\> 'a list**

Return the given list without its first element.

**Raises Failure** if the list is empty.

*val nth* :  **'a list -\> int -\> 'a**

Return the  **n** -th element of the given list. The first element (head of the list) is at position 0.

**Raises Failure** if the list is too short.

**Raises Invalid\_argument** if  **n** is negative.

*val nth\_opt* :  **'a list -\> int -\> 'a option**

Return the  **n** -th element of the given list. The first element (head of the list) is at position 0. Return  **None** if the list is too short.

**Since** 4.05

**Raises Invalid\_argument** if  **n** is negative.

*val rev* :  **'a list -\> 'a list**

List reversal.

*val init* :  **int -\> (int -\> 'a) -\> 'a list**

**init len f** is  **\[f 0; f 1; ...; f (len-1)\]** , evaluated left to right.

**Since** 4.06

**Raises Invalid\_argument** if  **len \< 0** .

*val append* :  **'a list -\> 'a list -\> 'a list**

**append l0 l1** appends  **l1** to  **l0** . Same function as the infix operator  **@** .

**Since** 5.1 this function is tail-recursive.

*val rev\_append* :  **'a list -\> 'a list -\> 'a list**

**rev\_append l1 l2** reverses  **l1** and concatenates it with  **l2** . This is equivalent to  **(** **List.rev** **l1) @ l2** .

*val concat* :  **'a list list -\> 'a list**

Concatenate a list of lists. The elements of the argument are all concatenated together (in the same order) to give the result. Not tail-recursive (length of the argument + length of the longest sub-list).

*val flatten* :  **'a list list -\> 'a list**

Same as  **List.concat** . Not tail-recursive (length of the argument + length of the longest sub-list).

### Comparison

*val equal* :  **('a -\> 'a -\> bool) -\> 'a list -\> 'a list -\> bool**

**equal eq \[a1; ...; an\] \[b1; ..; bm\]** holds when the two input lists have the same length, and for each pair of elements  **ai** ,  **bi** at the same position we have **eq ai bi** .

Note: the  **eq** function may be called even if the lists have different length. If you know your equality function is costly, you may want to check  **List.compare\_lengths** first.

**Since** 4.12

*val compare* :  **('a -\> 'a -\> int) -\> 'a list -\> 'a list -\> int**

**compare cmp \[a1; ...; an\] \[b1; ...; bm\]** performs a lexicographic comparison of the two input lists, using the same  **'a -\> 'a -\> int** interface as  **compare** :

\- **a1 :: l1** is smaller than  **a2 :: l2** (negative result) if  **a1** is smaller than  **a2** , or if they are equal (0 result) and  **l1** is smaller than  **l2**

\-the empty list  **\[\]** is strictly smaller than non-empty lists

Note: the  **cmp** function will be called even if the lists have different lengths.

**Since** 4.12

### Iterators

*val iter* :  **('a -\> unit) -\> 'a list -\> unit**

**iter f \[a1; ...; an\]** applies function  **f** in turn to **\[a1; ...; an\]** . It is equivalent to **f a1; f a2; ...; f an** .

*val iteri* :  **(int -\> 'a -\> unit) -\> 'a list -\> unit**

Same as  **List.iter** , but the function is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

**Since** 4.00

*val map* :  **('a -\> 'b) -\> 'a list -\> 'b list**

**map f \[a1; ...; an\]** applies function  **f** to  **a1, ..., an** , and builds the list  **\[f a1; ...; f an\]** with the results returned by  **f** .

*val mapi* :  **(int -\> 'a -\> 'b) -\> 'a list -\> 'b list**

Same as  **List.map** , but the function is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

**Since** 4.00

*val rev\_map* :  **('a -\> 'b) -\> 'a list -\> 'b list**

**rev\_map f l** gives the same result as **List.rev** **(** **List.map** **f l)** , but is more efficient.

*val filter\_map* :  **('a -\> 'b option) -\> 'a list -\> 'b list**

**filter\_map f l** applies  **f** to every element of  **l** , filters out the  **None** elements and returns the list of the arguments of the  **Some** elements.

**Since** 4.08

*val filter\_mapi* :  **(int -\> 'a -\> 'b option) -\> 'a list -\> 'b list**

Same as  **List.filter\_map** , but the function is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

**Since** 5.5

*val concat\_map* :  **('a -\> 'b list) -\> 'a list -\> 'b list**

**concat\_map f l** gives the same result as **List.concat** **(** **List.map** **f l)** . Tail-recursive.

**Since** 4.10

*val fold\_left\_map* :  **('acc -\> 'a -\> 'acc \* 'b) -\> 'acc -\> 'a list -\> 'acc \* 'b list**

**fold\_left\_map** is  a combination of  **fold\_left** and  **map** that threads an accumulator through calls to  **f** .

**Since** 4.11

*val fold\_left* :  **('acc -\> 'a -\> 'acc) -\> 'acc -\> 'a list -\> 'acc**

**fold\_left f init \[b1; ...; bn\]** is **f (... (f (f init b1) b2) ...) bn** .

*val fold\_right* :  **('a -\> 'acc -\> 'acc) -\> 'a list -\> 'acc -\> 'acc**

**fold\_right f \[a1; ...; an\] init** is **f a1 (f a2 (... (f an init) ...))** . Not tail-recursive.

### Iterators on two lists

*val iter2* :  **('a -\> 'b -\> unit) -\> 'a list -\> 'b list -\> unit**

**iter2 f \[a1; ...; an\] \[b1; ...; bn\]** calls in turn **f a1 b1; ...; f an bn** .

**Raises Invalid\_argument** if the two lists are determined to have different lengths.

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

**map2 f \[a1; ...; an\] \[b1; ...; bn\]** is **\[f a1 b1; ...; f an bn\]** .

**Raises Invalid\_argument** if the two lists are determined to have different lengths.

*val rev\_map2* :  **('a -\> 'b -\> 'c) -\> 'a list -\> 'b list -\> 'c list**

**rev\_map2 f l1 l2** gives the same result as **List.rev** **(** **List.map2** **f l1 l2)** , but is more efficient.

*val fold\_left2* :  **('acc -\> 'a -\> 'b -\> 'acc) -\> 'acc -\> 'a list -\> 'b list -\> 'acc**

**fold\_left2 f init \[a1; ...; an\] \[b1; ...; bn\]** is **f (... (f (f init a1 b1) a2 b2) ...) an bn** .

**Raises Invalid\_argument** if the two lists are determined to have different lengths.

*val fold\_right2* :  **('a -\> 'b -\> 'acc -\> 'acc) -\> 'a list -\> 'b list -\> 'acc -\> 'acc**

**fold\_right2 f \[a1; ...; an\] \[b1; ...; bn\] init** is **f a1 b1 (f a2 b2 (... (f an bn init) ...))** .

**Raises Invalid\_argument** if the two lists are determined to have different lengths. Not tail-recursive.

### List scanning

*val for\_all* :  **('a -\> bool) -\> 'a list -\> bool**

**for\_all f \[a1; ...; an\]** checks if all elements of the list satisfy the predicate  **f** . That is, it returns **(f a1) && (f a2) && ... && (f an)** for a non-empty list and **true** if the list is empty.

*val exists* :  **('a -\> bool) -\> 'a list -\> bool**

**exists f \[a1; ...; an\]** checks if at least one element of the list satisfies the predicate  **f** . That is, it returns **(f a1) \|\| (f a2) \|\| ... \|\| (f an)** for a non-empty list and **false** if the list is empty.

*val for\_all2* :  **('a -\> 'b -\> bool) -\> 'a list -\> 'b list -\> bool**

Same as  **List.for\_all** , but for a two-argument predicate.

**Raises Invalid\_argument** if the two lists are determined to have different lengths.

*val exists2* :  **('a -\> 'b -\> bool) -\> 'a list -\> 'b list -\> bool**

Same as  **List.exists** , but for a two-argument predicate.

**Raises Invalid\_argument** if the two lists are determined to have different lengths.

*val mem* :  **'a -\> 'a list -\> bool**

**mem a set** is true if and only if  **a** is equal to an element of  **set** .

*val memq* :  **'a -\> 'a list -\> bool**

Same as  **List.mem** , but uses physical equality instead of structural equality to compare list elements.

### List searching

*val find* :  **('a -\> bool) -\> 'a list -\> 'a**

**find f l** returns the first element of the list  **l** that satisfies the predicate  **f** .

**Raises Not\_found** if there is no value that satisfies  **f** in the list  **l** .

*val find\_opt* :  **('a -\> bool) -\> 'a list -\> 'a option**

**find f l** returns the first element of the list  **l** that satisfies the predicate  **f** . Returns  **None** if there is no value that satisfies  **f** in the list  **l** .

**Since** 4.05

*val find\_index* :  **('a -\> bool) -\> 'a list -\> int option**

**find\_index f xs** returns  **Some i** , where  **i** is the index of the first element of the list  **xs** that satisfies  **f x** , if there is such an element.

It returns  **None** if there is no such element.

**Since** 5.1

*val find\_map* :  **('a -\> 'b option) -\> 'a list -\> 'b option**

**find\_map f l** applies  **f** to the elements of  **l** in order, and returns the first result of the form  **Some v** , or  **None** if none exist.

**Since** 4.10

*val find\_mapi* :  **(int -\> 'a -\> 'b option) -\> 'a list -\> 'b option**

Same as  **find\_map** , but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

**Since** 5.1

*val filter* :  **('a -\> bool) -\> 'a list -\> 'a list**

**filter f l** returns all the elements of the list  **l** that satisfy the predicate  **f** . The order of the elements in the input list is preserved.

*val find\_all* :  **('a -\> bool) -\> 'a list -\> 'a list**

**find\_all** is another name for  **List.filter** .

*val filteri* :  **(int -\> 'a -\> bool) -\> 'a list -\> 'a list**

Same as  **List.filter** , but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

**Since** 4.11

### List manipulation

*val take* :  **int -\> 'a list -\> 'a list**

**take n l** returns the prefix of  **l** of length  **n** , or a copy of  **l** if  **n \> length l** . This is the empty list if  **n** is negative.

Warning. In version 5.3 only, this function raises **Invalid\_argument** for negative  **n** values.

**Since** 5.3

*val drop* :  **int -\> 'a list -\> 'a list**

**drop n l** returns the suffix of  **l** after  **n** elements, or  **\[\]** if  **n \> length l** . This is  **l** if  **n** is negative.

Warning. In version 5.3 only, this function raises **Invalid\_argument** for negative  **n** values.

**Since** 5.3

*val take\_while* :  **('a -\> bool) -\> 'a list -\> 'a list**

**take\_while p l** is the longest (possibly empty) prefix of  **l** containing only elements that satisfy  **p** .

**Since** 5.3

*val drop\_while* :  **('a -\> bool) -\> 'a list -\> 'a list**

**drop\_while p l** is the longest (possibly empty) suffix of  **l** starting at the first element that does not satisfy  **p** .

**Since** 5.3

*val partition* :  **('a -\> bool) -\> 'a list -\> 'a list \* 'a list**

**partition f l** returns a pair of lists  **(l1, l2)** , where **l1** is the list of all the elements of  **l** that satisfy the predicate  **f** , and  **l2** is the list of all the elements of  **l** that do not satisfy  **f** . The order of the elements in the input list is preserved.

*val partition\_map* :  **('a -\> ('b, 'c) Either.t) -\> 'a list -\> 'b list \* 'c list**

**partition\_map f l** returns a pair of lists  **(l1, l2)** such that, for each element  **x** of the input list  **l** :

\-if  **f x** is  **Left y1** , then  **y1** is in  **l1** , and

\-if  **f x** is  **Right y2** , then  **y2** is in  **l2** .

The output elements are included in  **l1** and  **l2** in the same relative order as the corresponding input elements in  **l** .

In particular,  **partition\_map (fun x -\> if f x then Left x else Right x) l** is equivalent to  **partition f l** .

**Since** 4.12

### Association lists

*val assoc* :  **'a -\> ('a \* 'b) list -\> 'b**

**assoc a l** returns the value associated with key  **a** in the list of pairs  **l** . That is, **assoc a \[ ...; (a,b); ...\] = b** if  **(a,b)** is the leftmost binding of  **a** in list  **l** .

**Raises Not\_found** if there is no value associated with  **a** in the list  **l** .

*val assoc\_opt* :  **'a -\> ('a \* 'b) list -\> 'b option**

**assoc\_opt a l** returns the value associated with key  **a** in the list of pairs  **l** . That is, **assoc\_opt a \[ ...; (a,b); ...\] = Some b** if  **(a,b)** is the leftmost binding of  **a** in list  **l** . Returns  **None** if there is no value associated with  **a** in the list  **l** .

**Since** 4.05

*val assq* :  **'a -\> ('a \* 'b) list -\> 'b**

Same as  **List.assoc** , but uses physical equality instead of structural equality to compare keys.

*val assq\_opt* :  **'a -\> ('a \* 'b) list -\> 'b option**

Same as  **List.assoc\_opt** , but uses physical equality instead of structural equality to compare keys.

**Since** 4.05

*val mem\_assoc* :  **'a -\> ('a \* 'b) list -\> bool**

Same as  **List.assoc** , but simply return  **true** if a binding exists, and  **false** if no bindings exist for the given key.

*val mem\_assq* :  **'a -\> ('a \* 'b) list -\> bool**

Same as  **List.mem\_assoc** , but uses physical equality instead of structural equality to compare keys.

*val remove\_assoc* :  **'a -\> ('a \* 'b) list -\> ('a \* 'b) list**

**remove\_assoc a l** returns the list of pairs  **l** without the first pair with key  **a** , if any. Not tail-recursive.

*val remove\_assq* :  **'a -\> ('a \* 'b) list -\> ('a \* 'b) list**

Same as  **List.remove\_assoc** , but uses physical equality instead of structural equality to compare keys. Not tail-recursive.

### Lists of pairs

*val split* :  **('a \* 'b) list -\> 'a list \* 'b list**

Transform a list of pairs into a pair of lists: **split \[(a1,b1); ...; (an,bn)\]** is  **(\[a1; ...; an\], \[b1; ...; bn\])** . Not tail-recursive.

*val split\_map* :  **('c -\> 'a \* 'b) -\> 'c list -\> 'a list \* 'b list**

**split\_map f l** is equivalent to  **split (map f l)** but avoids allocating intermediate lists.

**Since** 5.5

    Not tail-recursive.

*val combine* :  **'a list -\> 'b list -\> ('a \* 'b) list**

Transform a pair of lists into a list of pairs: **combine \[a1; ...; an\] \[b1; ...; bn\]** is **\[(a1,b1); ...; (an,bn)\]** .

**Raises Invalid\_argument** if the two lists have different lengths. Not tail-recursive.

### Sorting

*val sort* :  **('a -\> 'a -\> int) -\> 'a list -\> 'a list**

Sort a list in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see Array.sort for a complete specification). For example, **compare** is a suitable comparison function. The resulting list is sorted in increasing order. **List.sort** is guaranteed to run in constant heap space (in addition to the size of the result list) and logarithmic stack space.

The current implementation uses Merge Sort. It runs in constant heap space and logarithmic stack space.

*val stable\_sort* :  **('a -\> 'a -\> int) -\> 'a list -\> 'a list**

Same as  **List.sort** , but the sorting algorithm is guaranteed to be stable (i.e. elements that compare equal are kept in their original order).

The current implementation uses Merge Sort. It runs in constant heap space and logarithmic stack space.

*val fast\_sort* :  **('a -\> 'a -\> int) -\> 'a list -\> 'a list**

Same as  **List.sort** or  **List.stable\_sort** , whichever is faster on typical input.

*val sort\_uniq* :  **('a -\> 'a -\> int) -\> 'a list -\> 'a list**

Same as  **List.sort** , but also remove duplicates: if multiple elements compare equal, keep only the first.

**Before5.4** the element kept was not necessarily the first one.

**Since** 4.02 (4.03 in ListLabels)

*val merge* :  **('a -\> 'a -\> int) -\> 'a list -\> 'a list -\> 'a list**

Merge two lists: Assuming that  **l1** and  **l2** are sorted according to the comparison function  **cmp** ,  **merge cmp l1 l2** will return a sorted list containing all the elements of  **l1** and  **l2** . If several elements compare equal, the elements of  **l1** will be before the elements of  **l2** . Not tail-recursive (sum of the lengths of the arguments).

### Lists and Sequences

*val to\_seq* :  **'a list -\> 'a Seq.t**

Iterate on the list.

**Since** 4.07

*val of\_seq* :  **'a Seq.t -\> 'a list**

Create a list from a sequence.

**Since** 4.07