src/Pure/General/seq.ML
author wenzelm
Sat Jun 17 19:37:53 2006 +0200 (2006-06-17)
changeset 19912 4a3e35fd6e02
parent 19865 8e1cee9e03dc
child 20332 27e4f43a0c3e
permissions -rw-r--r--
added singleton;
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(*  Title:      Pure/General/seq.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Markus Wenzel, TU Munich
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Unbounded sequences implemented by closures.  RECOMPUTES if sequence
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is re-inspected.  Memoing, using polymorphic refs, was found to be
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slower!  (More GCs)
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*)
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signature SEQ =
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sig
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  type 'a seq
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  val make: (unit -> ('a * 'a seq) option) -> 'a seq
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  val pull: 'a seq -> ('a * 'a seq) option
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  val empty: 'a seq
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  val cons: 'a -> 'a seq -> 'a seq
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  val single: 'a -> 'a seq
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  val try: ('a -> 'b) -> 'a -> 'b seq
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  val hd: 'a seq -> 'a
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  val tl: 'a seq -> 'a seq
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  val chop: int -> 'a seq -> 'a list * 'a seq
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  val list_of: 'a seq -> 'a list
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  val of_list: 'a list -> 'a seq
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  val append: 'a seq -> 'a seq -> 'a seq
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  val mapp: ('a -> 'b) -> 'a seq -> 'b seq -> 'b seq
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  val interleave: 'a seq * 'a seq -> 'a seq
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  val filter: ('a -> bool) -> 'a seq -> 'a seq
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  val flat: 'a seq seq -> 'a seq
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  val map: ('a -> 'b) -> 'a seq -> 'b seq
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  val maps: ('a -> 'b seq) -> 'a seq -> 'b seq
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  val map_filter: ('a -> 'b option) -> 'a seq -> 'b seq
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  val lift: ('a -> 'b -> 'c) -> 'a seq -> 'b -> 'c seq
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  val lifts: ('a -> 'b -> 'c seq) -> 'a seq -> 'b -> 'c seq
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  val singleton: ('a list -> 'b list seq) -> 'a -> 'b seq
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  val print: (int -> 'a -> unit) -> int -> 'a seq -> unit
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  val it_right : ('a * 'b seq -> 'b seq) -> 'a seq * 'b seq -> 'b seq
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  val commute: 'a seq list -> 'a list seq
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  val map_list: ('a -> 'b seq) -> 'a list -> 'b list seq
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  val succeed: 'a -> 'a seq
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  val fail: 'a -> 'b seq
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  val THEN: ('a -> 'b seq) * ('b -> 'c seq) -> 'a -> 'c seq
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  val ORELSE: ('a -> 'b seq) * ('a -> 'b seq) -> 'a -> 'b seq
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  val APPEND: ('a -> 'b seq) * ('a -> 'b seq) -> 'a -> 'b seq
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  val EVERY: ('a -> 'a seq) list -> 'a -> 'a seq
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  val FIRST: ('a -> 'b seq) list -> 'a -> 'b seq
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  val TRY: ('a -> 'a seq) -> 'a -> 'a seq
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  val REPEAT: ('a -> 'a seq) -> 'a -> 'a seq
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  val REPEAT1: ('a -> 'a seq) -> 'a -> 'a seq
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  val INTERVAL: (int -> 'a -> 'a seq) -> int -> int -> 'a -> 'a seq
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  val DETERM: ('a -> 'b seq) -> 'a -> 'b seq
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end;
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structure Seq: SEQ =
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struct
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(** lazy sequences **)
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datatype 'a seq = Seq of unit -> ('a * 'a seq) option;
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(*the abstraction for making a sequence*)
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val make = Seq;
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(*return next sequence element as NONE or SOME (x, xq)*)
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fun pull (Seq f) = f ();
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(*the empty sequence*)
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val empty = Seq (fn () => NONE);
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(*prefix an element to the sequence -- use cons (x, xq) only if
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  evaluation of xq need not be delayed, otherwise use
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  make (fn () => SOME (x, xq))*)
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fun cons x xq = make (fn () => SOME (x, xq));
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fun single x = cons x empty;
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(*head and tail -- beware of calling the sequence function twice!!*)
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fun hd xq = #1 (the (pull xq))
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and tl xq = #2 (the (pull xq));
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(*partial function as procedure*)
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fun try f x =
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  (case Library.try f x of
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    SOME y => single y
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  | NONE => empty);
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(*the list of the first n elements, paired with rest of sequence;
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  if length of list is less than n, then sequence had less than n elements*)
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fun chop n xq =
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  if n <= 0 then ([], xq)
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  else
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    (case pull xq of
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      NONE => ([], xq)
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    | SOME (x, xq') => apfst (Library.cons x) (chop (n - 1) xq'));
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(*conversion from sequence to list*)
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fun list_of xq =
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  (case pull xq of
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    NONE => []
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  | SOME (x, xq') => x :: list_of xq');
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(*conversion from list to sequence*)
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fun of_list xs = fold_rev cons xs empty;
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(*sequence append:  put the elements of xq in front of those of yq*)
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fun append xq yq =
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  let
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    fun copy s =
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      make (fn () =>
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        (case pull s of
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          NONE => pull yq
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        | SOME (x, s') => SOME (x, copy s')))
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  in copy xq end;
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(*map over a sequence xq, append the sequence yq*)
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fun mapp f xq yq =
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  let
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    fun copy s =
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      make (fn () =>
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        (case pull s of
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          NONE => pull yq
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        | SOME (x, s') => SOME (f x, copy s')))
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  in copy xq end;
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(*interleave elements of xq with those of yq -- fairer than append*)
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fun interleave (xq, yq) =
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  make (fn () =>
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    (case pull xq of
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      NONE => pull yq
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    | SOME (x, xq') => SOME (x, interleave (yq, xq'))));
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(*filter sequence by predicate*)
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fun filter pred xq =
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  let
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    fun copy s =
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      make (fn () =>
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        (case pull s of
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          NONE => NONE
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        | SOME (x, s') => if pred x then SOME (x, copy s') else pull (copy s')));
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  in copy xq end;
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(*flatten a sequence of sequences to a single sequence*)
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fun flat xqq =
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  make (fn () =>
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    (case pull xqq of
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      NONE => NONE
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    | SOME (xq, xqq') => pull (append xq (flat xqq'))));
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(*map the function f over the sequence, making a new sequence*)
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fun map f xq =
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  make (fn () =>
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    (case pull xq of
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      NONE => NONE
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    | SOME (x, xq') => SOME (f x, map f xq')));
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fun maps f = flat o map f;
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fun map_filter f = maps (fn x => (case f x of NONE => empty | SOME y => single y));
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fun lift f xq y = map (fn x => f x y) xq;
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fun lifts f xq y = maps (fn x => f x y) xq;
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fun singleton f x = f [x] |> map (fn [y] => y | _ => raise Empty);
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(*print a sequence, up to "count" elements*)
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fun print print_elem count =
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  let
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    fun prnt k xq =
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      if k > count then ()
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      else
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        (case pull xq of
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          NONE => ()
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        | SOME (x, xq') => (print_elem k x; writeln ""; prnt (k + 1) xq'));
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  in prnt 1 end;
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(*accumulating a function over a sequence; this is lazy*)
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fun it_right f (xq, yq) =
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  let
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    fun its s =
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      make (fn () =>
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        (case pull s of
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          NONE => pull yq
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        | SOME (a, s') => pull (f (a, its s'))))
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  in its xq end;
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(*turn a list of sequences into a sequence of lists*)
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fun commute [] = single []
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  | commute (xq :: xqs) =
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      make (fn () =>
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        (case pull xq of
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          NONE => NONE
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        | SOME (x, xq') =>
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            (case pull (commute xqs) of
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              NONE => NONE
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            | SOME (xs, xsq) =>
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                SOME (x :: xs, append (map (Library.cons x) xsq) (commute (xq' :: xqs))))));
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fun map_list f = commute o List.map f;
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(** sequence functions **)      (*some code copied from Pure/tctical.ML*)
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fun succeed x = single x;
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fun fail _ = empty;
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fun op THEN (f, g) x = flat (map g (f x));
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fun op ORELSE (f, g) x =
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  (case pull (f x) of
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    NONE => g x
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  | some => make (fn () => some));
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fun op APPEND (f, g) x =
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  append (f x) (make (fn () => pull (g x)));
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fun EVERY fs = foldr THEN succeed fs;
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fun FIRST fs = foldr ORELSE fail fs;
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fun TRY f = ORELSE (f, succeed);
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fun REPEAT f =
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  let
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    fun rep qs x =
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      (case pull (f x) of
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        NONE => SOME (x, make (fn () => repq qs))
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      | SOME (x', q) => rep (q :: qs) x')
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    and repq [] = NONE
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      | repq (q :: qs) =
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          (case pull q of
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            NONE => repq qs
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          | SOME (x, q) => rep (q :: qs) x);
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  in fn x => make (fn () => rep [] x) end;
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fun REPEAT1 f = THEN (f, REPEAT f);
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fun INTERVAL f i j x =
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  if i > j then single x
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  else op THEN (f j, INTERVAL f i (j - 1)) x;
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fun DETERM f x =
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  (case pull (f x) of
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    NONE => empty
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  | SOME (x', _) => cons x' empty);
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end;