### 5.13  Module List

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.

val length : ('a, 'b) list -> 'b int
Return the length (number of elements) of the given list.

val hd : ('a, 'b) list -{'c | Failure: 'c |}-> 'a
with 'b < level('a), 'c
Return the first element of the given list. Raise Failure "hd" if the list is empty.

val tl : ('a, 'b) list -{'c | Failure: 'c |}-> ('a, 'b) list
with 'b < 'c
Return the given list without its first element. Raise Failure "tl" if the list is empty.

val nth : ('a, 'b) list ->
'b int -{'c | Invalid_argument: 'c; Failure: 'c |}-> 'a
with 'b < level('a), 'c
Return the n-th element of the given list. The first element (head of the list) is at position 0. Raise Failure "nth" if the list is too short.

val rev : ('a, 'b) list -> ('a, 'b) list
List reversal.

val append : ('a, 'b) list -> ('a, 'b) list -> ('a, 'b) list
Catenate two lists. Same function as the infix operator @. Not tail-recursive (length of the first argument). The @ operator is not tail-recursive either.

val rev_append : ('a, 'b) list -> ('a, 'b) list -> ('a, 'b) list
List.rev_append l1 l2 reverses l1 and concatenates it to l2.

This is equivalent to List.rev l1 @ l2, but rev_append is tail-recursive and more efficient.

val concat : (('a, 'b) list, 'b) list -> ('a, 'b) list
Concatenate a list of lists. Not tail-recursive (length of the argument + length of the longest sub-list).

val flatten : (('a, 'b) list, 'b) list -> ('a, 'b) list
Flatten a list of lists. Not tail-recursive (length of the argument + length of the longest sub-list).

#### 5.13.1  Iterators

val iter : ('a -{'b | 'c | 'b}-> 'd) -> ('a, 'b) list -{'b | 'c |}-> unit
with content('c) < 'b
List.iter f [a1; ...; an] applies function f in turn to a1; ...; an. It is equivalent to begin f a1; f a2; ...; f an; () end.

val map : ('a -{'b | 'c | 'd}-> 'e) ->
('a, 'f) list -{'b | 'c |}-> ('e, 'f) list
with content('c), 'd, 'f < 'b
and  'd < level('e)
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. Not tail-recursive.

val rev_map : ('a -{'b | 'c | 'd}-> 'e) ->
('a, 'f) list -{'b | 'c |}-> ('e, 'f) list
with content('c), 'd, 'f < 'b
and  'd < level('e)
List.rev_map f l gives the same result as List.rev (List.map f l), but is tail-recursive and more efficient.

val fold_left : ('a -{'b | 'c | 'd}-> 'e -{'f | 'g | 'h}-> 'a) ->
'a -> ('e, 'i) list -{'b | 'g |}-> 'j
with content('c), 'd, content('g), 'i < 'b
and  'b, content('c), 'd, content('g), 'h, 'i < 'f
and  'c < 'g
and  'd, 'h, 'i < level('j)
and  'a < 'j
and  'd, 'h < level('a)
List.fold_left f a [b1; ...; bn] is f (... (f (f a b1) b2) ...) bn.

val fold_right : ('a -{'b | 'c | 'd}-> 'e -{'f | 'g | 'h}-> 'i) ->
('a, 'd) list -> 'i -{'b | 'g |}-> 'i
with content('c), 'd, content('g) < 'b
and  'b, content('c), 'd, content('g), 'h < 'f
and  'c < 'g
and  'd, 'h < level('e)
and  'i < 'e
and  'd, 'h < level('i)
List.fold_right f [a1; ...; an] b is f a1 (f a2 (... (f an b) ...)). Not tail-recursive.

#### 5.13.2  Iterators on two lists

val iter2 : ('a -{'b | Invalid_argument: 'c; 'd | 'e}->
'f -{'g | Invalid_argument: 'c; 'h | 'g}-> 'i) ->
('a, 'c) list ->
('f, 'c) list -{'c | Invalid_argument: 'j; 'h |}-> unit
with 'c, content('d), content('h) < 'j
and  'c, content('d), 'e, content('h) < 'b
and  'c, content('d), 'e, content('h) < 'g
and  'd < 'h
List.iter2 f [a1; ...; an] [b1; ...; bn] calls in turn f a1 b1; ...; f an bn. Raise Invalid_argument if the two lists have different lengths.

#### 5.13.3  List scanning

val for_all : ('a -{'b | 'c | 'd}-> 'e bool) ->
('a, 'd) list -{'b | 'c |}-> 'e bool
with 'd < 'b, 'e
and  content('c) < 'b
for_all p [a1; ...; an] checks if all elements of the list satisfy the predicate p. That is, it returns (p a1) && (p a2) && ... && (p an).

val exists : ('a -{'b | 'c | 'd}-> 'e bool) ->
('a, 'd) list -{'b | 'c |}-> 'e bool
with 'd < 'b, 'e
and  content('c) < 'b
exists p [a1; ...; an] checks if at least one element of the list satisfies the predicate p. That is, it returns (p a1) || (p a2) || ... || (p an).

val mem : 'a -> ('a, 'b) list -> 'b bool
with content('a) < 'b
mem a l is true if and only if a is equal to an element of l.

val memq : 'a -> ('a, 'b) list -> 'b bool
with content('a) < 'b
Same as List.mem, but uses physical equality instead of structural equality to compare list elements.

#### 5.13.4  List searching

val find : ('a -{'b | Not_found: 'c; 'd | 'e}-> 'e bool) ->
('a, 'e) list -{'f | Not_found: 'c; 'd |}-> 'g
with 'a < 'g
and  'f < 'b, 'c
and  'e < 'b, 'c, level('g)
find p l returns the first element of the list l that satisfies the predicate p. Raise Not_found if there is no value that satisfies p in the list l.

val filter : ('a -{'b | 'c | 'd}-> 'd bool) ->
('a, 'd) list -{'b | 'c |}-> ('a, 'd) list
with 'd < 'b
filter p l returns all the elements of the list l that satisfy the predicate p. The order of the elements in the input list is preserved.

val find_all : ('a -{'b | 'c | 'd}-> 'd bool) ->
('a, 'd) list -{'b | 'c |}-> ('a, 'd) list
with 'd < 'b
find_all is another name for List.filter.

val partition : ('a -{'b | 'c | 'd}-> 'e bool) ->
('a, 'e) list -{'b | 'c |}-> ('a, 'e) list * ('a, 'e) list
with 'e < 'b
and  'd < 'b, 'e
partition p l returns a pair of lists (l1, l2), where l1 is the list of all the elements of l that satisfy the predicate p, and l2 is the list of all the elements of l that do not satisfy p. The order of the elements in the input list is preserved.

#### 5.13.5  Association lists

val assoc : 'a -> ('a * 'b, 'c) list -{'d | Not_found: 'd |}-> 'b
with content('a) < level('b), 'd
and  'c < level('b), 'd
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. Raise Not_found if there is no value associated with a in the list l.

val mem_assoc : 'a -> ('a * 'b, 'c) list -> 'c bool
with content('a) < 'c
Same as List.assoc, but simply return true if a binding exists, and false if no bindings exist for the given key.

val remove_assoc : 'a -> ('a * 'b, 'c) list -> ('a * 'b, 'c) list
with content('a) < 'c
remove_assoc a l returns the list of pairs l without the first pair with key a, if any. Not tail-recursive.

#### 5.13.6  Lists of pairs

val split : ('a * 'b, 'c) list -> ('a, 'c) list * ('b, 'c) list
Transform a list of pairs into a pair of lists:

split [(a1,b1); ...; (an,bn)] is ([a1; ...; an], [b1; ...; bn]). Not tail-recursive.

#### 5.13.7  Sorting

val sort : ('a -{'b | 'c | 'd}-> 'a -{'e | 'c | 'f}-> 'g int) ->
('a, 'h) list -{'i | 'c |}-> ('a, 'h) list
with 'd, 'f, 'g < level('a)
and  content('c), 'd, 'f, 'h, 'i < 'e
and  content('c), 'd, 'h, 'i < 'b
Sort a list in increasing order according to a comparison function. The comparison function must return 0 if it arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller. For example, the compare function 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 and is the same as List.stable_sort.

val stable_sort : ('a -{'b | 'c | 'd}-> 'a -{'e | 'c | 'f}-> 'g int) ->
('a, 'h) list -{'i | 'c |}-> ('a, 'h) list
with 'd, 'f, 'g < level('a)
and  content('c), 'd, 'f, 'h, 'i < 'e
and  content('c), 'd, 'h, 'i < 'b
Same as List.sort, but the sorting algorithm is stable.

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