(* List -- SML Basis Library *)

datatype list = datatype list

exception Empty

val null       : 'a list -> bool
val hd         : 'a list -> 'a                          (* Empty     *)
val tl         : 'a list -> 'a list                     (* Empty     *)
val last       : 'a list -> 'a                          (* Empty     *)

val nth        : 'a list * int -> 'a                    (* Subscript *)
val take       : 'a list * int -> 'a list               (* Subscript *)
val drop       : 'a list * int -> 'a list               (* Subscript *)

val length     : 'a list -> int 

val rev        : 'a list -> 'a list 

val @          : 'a list * '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 foldr      : ('a * 'b -> 'b) -> 'b -> 'a list -> 'b
val foldl      : ('a * 'b -> 'b) -> 'b -> 'a list -> 'b

val exists     : ('a -> bool) -> 'a list -> bool
val all        : ('a -> bool) -> 'a list -> bool

val collate    : ('a * 'a -> order) -> 'a list * 'a list -> order

val tabulate   : int * (int -> 'a) -> 'a list           (* Size      *)

val getItem    : 'a list -> ('a * 'a list) option

(* 
   ['a list] is the type of lists of elements of type 'a.

   [null xs] is true iff xs is nil.

   [hd xs] returns the first element of xs.  Raises Empty if xs is nil.

   [tl xs] returns all but the first element of xs.  
   Raises Empty if xs is nil.

   [last xs] returns the last element of xs.  Raises Empty if xs is nil.

   [nth(xs, i)] returns the i'th element of xs, counting from 0.
   Raises Subscript if i<0 or i>=length xs.

   [take(xs, i)] returns the first i elements of xs.  Raises Subscript
   if i<0 or i>length xs.

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

   [length xs] returns the number of elements in xs.

   [rev xs] returns the list of xs's elements, reversed.

   [xs @ ys] returns the list which is the concatenation of xs and ys.

   [concat xss] returns the list which is the concatenation of all the
   lists in xss.

   [revAppend(xs, ys)] is equivalent to rev xs @ ys, but more efficient. 

   [app f xs] applies f to the elements of xs, from left to right.

   [map f xs] applies f to each element x of xs, from left to
   right, and returns the list of f's results.
 
   [mapPartial f xs] applies f to each element x of xs, from left
   to right, and returns the list of those y's for which f(x)
   evaluated to SOME y.

   [find p xs] applies p to each element x of xs, from left to right,
   until p(x) evaluates to true; returns SOME x if such an x exists,
   otherwise NONE.

   [filter p xs] applies p to each element x of xs, from left to
   right, and returns the sublist of those x for which p(x) evaluated
   to true.

   [partition p xs] applies p to each element x of xs, from left
   to right, and returns a pair (pos, neg) where pos is the sublist
   of those x for which p(x) evaluated to true, and neg is the sublist of
   those for which p(x) evaluated to false.

   [foldr op% e xs] evaluates x1 % (x2 % ( ... % (x(n-1) % (xn % e)) ... ))
   where xs = [x1, x2, ..., x(n-1), xn], and % is taken to be infixed.

   [foldl op% e xs] evaluates xn % (x(n-1) % ( ... % (x2 % (x1 % e))))
   where xs = [x1, x2, ..., x(n-1), xn], and % is taken to be infixed.

   [exists p xs] applies p to each element x of xs, from left to
   right until p(x) evaluates to true; returns true if such an x
   exists, otherwise false.

   [all p xs] applies p to each element x of xs, from left to
   right until p(x) evaluates to false; returns false if such an x
   exists, otherwise true.

   [collate cmp (xs, ys)] returns LESS, EQUAL or GREATER according as
   xs precedes, equals or follows ys in the lexicographic ordering on
   lists induced by the ordering cmp on elements.

   [tabulate(n, f)] returns a list of length n whose elements are
   f(0), f(1), ..., f(n-1), created from left to right.  Raises Size
   if n<0.

   [getItem xs] attempts to extract an element from the list xs.  It
   returns NONE if xs is empty, and returns SOME (x, xr) if xs=x::xr.
   This can be used for scanning booleans, integers, reals, and so on
   from a list of characters.  For instance, to scan a decimal integer
   from a list cs of characters, compute 
        Int.scan StringCvt.DEC List.getItem cs
*)
