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(* ListPair -- SML Basis Library *) val zip : 'a list * 'b list -> ('a * 'b) list val unzip : ('a * 'b) list -> 'a list * 'b list val map : ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list val app : ('a * 'b -> unit) -> 'a list * 'b list -> unit val all : ('a * 'b -> bool) -> 'a list * 'b list -> bool val exists : ('a * 'b -> bool) -> 'a list * 'b list -> bool val foldr : ('a * 'b * 'c -> 'c) -> 'c -> 'a list * 'b list -> 'c val foldl : ('a * 'b * 'c -> 'c) -> 'c -> 'a list * 'b list -> 'c val allEq : ('a * 'b -> bool) -> 'a list * 'b list -> bool exception UnequalLengths val zipEq : ('a list * 'b list) -> ('a * 'b) list val mapEq : ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list val appEq : ('a * 'b -> 'c) -> 'a list * 'b list -> unit val foldrEq : ('a * 'b * 'c -> 'c) -> 'c -> 'a list * 'b list -> 'c val foldlEq : ('a * 'b * 'c -> 'c) -> 'c -> 'a list * 'b list -> 'c (* These functions process pairs (xs, ys) of lists. There are three groups of functions: * zip, map, app, all, exists, foldr and foldl raise no exception when the argument lists are found to be of unequal length; the excess elements from the longer list are simply disregarded. * zipEq, mapEq, appEq, foldrEq and foldlEq raise exception UnequalLengths when the argument lists are found to be of unequal length. * allEq raises no exception but returns false if the lists are found to have unequal lengths (after traversing the lists). [zip(xs, ys)] returns the list of pairs of corresponding elements from xs and ys. [unzipxys] returns a pair (xs, ys), where xs is the list of first components of xys, and ys is the list of second components from xys. Hence zip (unzip xys) has the same result and effect as xys. [mapf (xs, ys)] applies function f to the pairs of corresponding elements of xs and ys from left to right and returns the list of results. Hence map f (xs, ys) has the same result and effect as List.map f (zip (xs, ys)). [appf (xs, ys)] applies function f to the pairs of corresponding elements of xs and ys from left to right and returns (). Hence app f (xs, ys) has the same result and effect as List.app f (zip (xs, ys)). [allp (xs, ys)] applies predicate p to the pairs of corresponding elements of xs and ys from left to right until p evaluates to false or one or both lists is exhausted; returns true if p is true of all such pairs; otherwise false. Hence all p (xs, ys) has the same result and effect as List.all p (zip (xs, ys)). [existsp (xs, ys)] applies predicate p to the pairs of corresponding elements of xs and ys from left to right until p evaluates to true or one or both lists is exhausted; returns true if p is true of any such pair; otherwise false. Hence exists p (xs, ys) has the same result and effect as List.exists p (zip (xs, ys)). Also, exists p (xs, ys) is equivalent to not(all (not o p) (xs, ys)). [foldrf e (xs, ys)] evaluates f(x1, y1, f(x2, y2, f(..., f(xn, yn, e)))) where xs = [x1, x2, ..., x(n-1), xn, ...], ys = [y1, y2, ..., y(n-1), yn, ...], and n = min(length xs, length ys). Equivalent to List.foldr (fn ((x, y), r) => f(x, y, r)) e (zip(xs, ys)). [foldlf e (xs, ys)] evaluates f(xn, yn, f( ..., f(x2, y2, f(x1, y1, e)))) where xs = [x1, x2, ..., x(n-1), xn, ...], ys = [y1, y2, ..., y(n-1), yn, ...], and n = min(length xs, length ys). Equivalent to List.foldl (fn ((x, y), r) => f(x, y, r)) e (zip(xs, ys)). [zipEq(xs, ys)] returns the list of pairs of corresponding elements from xs and ys. Raises UnequalLengths if xs and ys do not have the same length. [mapEqf (xs, ys)] applies function f to pairs of corresponding elements of xs and ys from left to right, and then returns the list of results if xs and ys have the same length, otherwise raises UnequalLengths. If f has no side effects and terminates, then it is equivalent to List.map f (zipEq (xs, ys)). [appEqf (xs, ys)] applies function f to pairs of corresponding elements of xs and ys from left to right, and then raises UnequalLengths if xs and ys have the same length. [foldrEqf e (xs, ys)] raises UnequalLengths if xs and ys do not have the same length. Otherwise evaluates f(x1, y1, f(x2, y2, f(..., f(xn, yn, e)))) where xs = [x1, x2, ..., x(n-1), xn], ys = [y1, y2, ..., y(n-1), yn], and n = length xs = length ys. Equivalent to List.foldr (fn ((x,y),r) => f(x,y,r)) e (zipEq(xs, ys)). [foldlEqf e (xs, ys)] evaluates f(xn, yn, f( ..., f(x2, y2, f(x1, y1, e)))) where xs = [x1, x2, ..., x(n-1), xn, ...], ys = [y1, y2, ..., y(n-1), yn, ...], and n = min(length xs, length ys). Then raises UnequalLengths if xs and ys do not have the same length. If f has no side effects and terminates normally, then it is equivalent to List.foldl (fn ((x,y),r) => f(x,y,r)) e (zipEq(xs, ys)). [allEqp (xs, ys)] works as all p (xs, ys) but returns false if xs and ys do not have the same length. Equivalent to all p (xs, ys) andalso length xs = length ys. *)

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