The Standard ML Basis Library

The `List` structure

Synopsis

signature LIST structure List :> LIST

The List structure provides a collection of utility functions for manipulating polymorphic lists, traditionally an important datatype in functional programming.

Following the concrete syntax provided by the list :: operator, the head of a list appears leftmost. Thus, a traversal of a list from left to right starts with the head, then recurses on the tail. In addition, as a sequence type, a list has an indexing of its elements, with the head having index 0, the second element having index 1, etc.

Interface

datatype 'a list = nil | :: of 'a * 'a list exception Empty val null : 'a list -> bool val length : 'a list -> int val @ : 'a list * 'a list -> 'a list val hd : 'a list -> 'a val tl : 'a list -> 'a list val last : 'a list -> 'a val getItem : 'a list -> ('a * 'a list) option val nth : 'a list * int -> 'a val take : 'a list * int -> 'a list val drop : 'a list * int -> 'a list val rev : 'a list -> 'a list val concat : 'a list list -> 'a list val revAppend : 'a list * 'a list -> 'a list val app : ('a -> unit) -> 'a list -> unit val map : ('a -> 'b) -> 'a list -> 'b list val mapPartial : ('a -> 'b option) -> 'a list -> 'b list val find : ('a -> bool) -> 'a list -> 'a option val filter : ('a -> bool) -> 'a list -> 'a list val partition : ('a -> bool) -> 'a list -> 'a list * 'a list val foldl : ('a * 'b -> 'b) -> 'b -> 'a list -> 'b val foldr : ('a * 'b -> 'b) -> 'b -> 'a list -> 'b val exists : ('a -> bool) -> 'a list -> bool val all : ('a -> bool) -> 'a list -> bool val tabulate : int * (int -> 'a) -> 'a list val collate : ('a * 'a -> order) -> 'a list * 'a list -> order

Description

exception Empty

This exception indicates that an empty list was given as an argument to a function requiring a non-empty list.

null l

returns true if the list l is empty.

length l

returns the number of elements in the list l.

l1 @ l2

returns the list that is the concatenation of l1 and l2.

hd l

returns the first element of l. It raises Empty if l is nil.

tl l

returns all but the first element of l. It raises Empty if l is nil.

last l

returns the last element of l. It raises Empty if l is nil.

getItem l

returns NONE if the list is empty, and SOME(hd l,tl l) otherwise. This function is particularly useful for creating value readers from lists of characters. For example, Int.scan StringCvt.DEC getItem has the type

(int,char list) StringCvt.reader

and can be used to scan decimal integers from lists of characters.

nth (l, i)

returns the i^(th) element of the list l, counting from 0. It raises Subscript if i < 0 or i >= length l. We have nth(l,0) = hd l, ignoring exceptions.

take (l, i)

returns the first i elements of the list l. It raises Subscript if i < 0 or i > length l. We have take(l, length l) = l.

drop (l, i)

returns what is left after dropping the first i elements of the list l. It raises Subscript if i < 0 or i > length l. It holds that take(l, i) @ drop(l, i) = l when 0 <= i <= length l. We also have drop(l, length l) = [].

rev l

returns a list consisting of l's elements in reverse order.

concat l

returns the list that is the concatenation of all the lists in l in order.

concat[l1,l2,...ln] = l1 @ l2 @ ... @ ln

revAppend (l1, l2)

returns (rev l1) @ l2.

app f l

applies f to the elements of l, from left to right.

map f l

applies f to each element of l from left to right, returning the list of results.

mapPartial f l

applies f to each element of l from left to right, returning a list of results, with SOME stripped, where f was defined. f is not defined for an element of l if f applied to the element returns NONE. The above expression is equivalent to:

((map valOf) o (filter isSome) o (map f)) l

find f l

applies f to each element x of the list l, from left to right, until f x evaluates to true. It returns SOME(x) if such an x exists; otherwise it returns NONE.

filter f l

applies f to each element x of l, from left to right, and returns the list of those x for which f x evaluated to true, in the same order as they occurred in the argument list.

partition f l

applies f to each element x of l, from left to right, and returns a pair (pos, neg) where pos is the list of those x for which f x evaluated to true, and neg is the list of those for which f x evaluated to false. The elements of pos and neg retain the same relative order they possessed in l.

foldl f init [x1, x2, ..., xn]

returns

f(xn,...,f(x2, f(x1, init))...)

or init if the list is empty.

foldr f init [x1, x2, ..., xn]

returns

f(x1, f(x2, ..., f(xn, init)...))

or init if the list is empty.

exists f l

applies f to each element x of the list l, from left to right, until f x evaluates to true; it returns true if such an x exists and false otherwise.

all f l

applies f to each element x of the list l, from left to right, until f x evaluates to false; it returns false if such an x exists and true otherwise. It is equivalent to not(exists (not o f) l)).

tabulate (n, f)

returns a list of length n equal to [f(0), f(1), ..., f(n-1)], created from left to right. It raises Size if n < 0.

collate f (l1, l2)

performs lexicographic comparison of the two lists using the given ordering f on the list elements.

Discussion

The list type is considered primitive and is defined in the top-level environment. It is rebound here for consistency.

Rationale:

Lists are usually supported with a large collection of library functions. Here, we provide a somewhat smaller collection of operations that reflect common usage. We feel the collection is moderately complete, in that most programs will not need to define additional list operations. We have tried to adopt names that reflect a consensus from various existing libraries and texts. We have avoided functions relying on equality types.
Different SML implementations may still desire to provide list utility library modules, though if the design of List is right, they should be small.

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Generated April 12, 2004
Last Modified May 24, 2000
Comments to John Reppy.

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