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(* Title: Pure/General/seq.ML
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Author: Markus Wenzel, TU Munich
Unbounded sequences implemented by closures. RECOMPUTES if sequence
is re-inspected. Memoing, using polymorphic refs, was found to be
slower! (More GCs)
*)
signature SEQ =
sig
type 'a seq
val make: (unit -> ('a * 'a seq) option) -> 'a seq
val pull: 'a seq -> ('a * 'a seq) option
val empty: 'a seq
val cons: 'a -> 'a seq -> 'a seq
val single: 'a -> 'a seq
val try: ('a -> 'b) -> 'a -> 'b seq
val hd: 'a seq -> 'a
val tl: 'a seq -> 'a seq
val chop: int -> 'a seq -> 'a list * 'a seq
val take: int -> 'a seq -> 'a seq
val list_of: 'a seq -> 'a list
val of_list: 'a list -> 'a seq
val append: 'a seq -> 'a seq -> 'a seq
val mapp: ('a -> 'b) -> 'a seq -> 'b seq -> 'b seq
val interleave: 'a seq * 'a seq -> 'a seq
val filter: ('a -> bool) -> 'a seq -> 'a seq
val flat: 'a seq seq -> 'a seq
val map: ('a -> 'b) -> 'a seq -> 'b seq
val maps: ('a -> 'b seq) -> 'a seq -> 'b seq
val map_filter: ('a -> 'b option) -> 'a seq -> 'b seq
val lift: ('a -> 'b -> 'c) -> 'a seq -> 'b -> 'c seq
val lifts: ('a -> 'b -> 'c seq) -> 'a seq -> 'b -> 'c seq
val singleton: ('a list -> 'b list seq) -> 'a -> 'b seq
val print: (int -> 'a -> unit) -> int -> 'a seq -> unit
val it_right : ('a * 'b seq -> 'b seq) -> 'a seq * 'b seq -> 'b seq
datatype 'a result = Result of 'a | Error of unit -> string
val make_results: 'a seq -> 'a result seq
val filter_results: 'a result seq -> 'a seq
val maps_results: ('a -> 'b result seq) -> 'a result seq -> 'b result seq
val maps_result: ('a -> 'b seq) -> 'a result seq -> 'b result seq
val map_result: ('a -> 'b) -> 'a result seq -> 'b result seq
val first_result: string -> 'a result seq -> 'a * 'a seq
val the_result: string -> 'a result seq -> 'a
val succeed: 'a -> 'a seq
val fail: 'a -> 'b seq
val THEN: ('a -> 'b seq) * ('b -> 'c seq) -> 'a -> 'c seq
val ORELSE: ('a -> 'b seq) * ('a -> 'b seq) -> 'a -> 'b seq
val APPEND: ('a -> 'b seq) * ('a -> 'b seq) -> 'a -> 'b seq
val EVERY: ('a -> 'a seq) list -> 'a -> 'a seq
val FIRST: ('a -> 'b seq) list -> 'a -> 'b seq
val TRY: ('a -> 'a seq) -> 'a -> 'a seq
val REPEAT: ('a -> 'a seq) -> 'a -> 'a seq
val REPEAT1: ('a -> 'a seq) -> 'a -> 'a seq
val INTERVAL: (int -> 'a -> 'a seq) -> int -> int -> 'a -> 'a seq
val DETERM: ('a -> 'b seq) -> 'a -> 'b seq
end;
structure Seq: SEQ =
struct
(** lazy sequences **)
datatype 'a seq = Seq of unit -> ('a * 'a seq) option;
(*the abstraction for making a sequence*)
val make = Seq;
(*return next sequence element as NONE or SOME (x, xq)*)
fun pull (Seq f) = f ();
(*the empty sequence*)
val empty = Seq (fn () => NONE);
(*prefix an element to the sequence -- use cons (x, xq) only if
evaluation of xq need not be delayed, otherwise use
make (fn () => SOME (x, xq))*)
fun cons x xq = make (fn () => SOME (x, xq));
fun single x = cons x empty;
(*head and tail -- beware of calling the sequence function twice!!*)
fun hd xq = #1 (the (pull xq))
and tl xq = #2 (the (pull xq));
(*partial function as procedure*)
fun try f x =
(case Basics.try f x of
SOME y => single y
| NONE => empty);
(*the list of the first n elements, paired with rest of sequence;
if length of list is less than n, then sequence had less than n elements*)
fun chop n xq =
if n <= (0 : int) then ([], xq)
else
(case pull xq of
NONE => ([], xq)
| SOME (x, xq') => apfst (Basics.cons x) (chop (n - 1) xq'));
(*truncate the sequence after n elements*)
fun take n xq =
if n <= (0 : int) then empty
else make (fn () =>
(Option.map o apsnd) (take (n - 1)) (pull xq));
(*conversion from sequence to list*)
fun list_of xq =
(case pull xq of
NONE => []
| SOME (x, xq') => x :: list_of xq');
(*conversion from list to sequence*)
fun of_list xs = fold_rev cons xs empty;
(*sequence append: put the elements of xq in front of those of yq*)
fun append xq yq =
let
fun copy s =
make (fn () =>
(case pull s of
NONE => pull yq
| SOME (x, s') => SOME (x, copy s')))
in copy xq end;
(*map over a sequence xq, append the sequence yq*)
fun mapp f xq yq =
let
fun copy s =
make (fn () =>
(case pull s of
NONE => pull yq
| SOME (x, s') => SOME (f x, copy s')))
in copy xq end;
(*interleave elements of xq with those of yq -- fairer than append*)
fun interleave (xq, yq) =
make (fn () =>
(case pull xq of
NONE => pull yq
| SOME (x, xq') => SOME (x, interleave (yq, xq'))));
(*filter sequence by predicate*)
fun filter pred xq =
let
fun copy s =
make (fn () =>
(case pull s of
NONE => NONE
| SOME (x, s') => if pred x then SOME (x, copy s') else pull (copy s')));
in copy xq end;
(*flatten a sequence of sequences to a single sequence*)
fun flat xqq =
make (fn () =>
(case pull xqq of
NONE => NONE
| SOME (xq, xqq') => pull (append xq (flat xqq'))));
(*map the function f over the sequence, making a new sequence*)
fun map f xq =
make (fn () =>
(case pull xq of
NONE => NONE
| SOME (x, xq') => SOME (f x, map f xq')));
fun maps f xq =
make (fn () =>
(case pull xq of
NONE => NONE
| SOME (x, xq') => pull (append (f x) (maps f xq'))));
fun map_filter f = maps (fn x => (case f x of NONE => empty | SOME y => single y));
fun lift f xq y = map (fn x => f x y) xq;
fun lifts f xq y = maps (fn x => f x y) xq;
fun singleton f x = f [x] |> map (fn [y] => y | _ => raise List.Empty);
(*print a sequence, up to "count" elements*)
fun print print_elem count =
let
fun prnt (k: int) xq =
if k > count then ()
else
(case pull xq of
NONE => ()
| SOME (x, xq') => (print_elem k x; writeln ""; prnt (k + 1) xq'));
in prnt 1 end;
(*accumulating a function over a sequence; this is lazy*)
fun it_right f (xq, yq) =
let
fun its s =
make (fn () =>
(case pull s of
NONE => pull yq
| SOME (a, s') => pull (f (a, its s'))))
in its xq end;
(* embedded errors *)
datatype 'a result = Result of 'a | Error of unit -> string;
fun make_results xq = map Result xq;
fun filter_results xq = map_filter (fn Result x => SOME x | Error _ => NONE) xq;
fun maps_results f xq =
make (fn () =>
(case pull xq of
NONE => NONE
| SOME (Result x, xq') => pull (append (f x) (maps_results f xq'))
| SOME (Error msg, xq') => SOME (Error msg, maps_results f xq')));
fun maps_result f = maps_results (map Result o f);
fun map_result f = maps_result (single o f);
(*first result or first error within sequence*)
fun first_result default_msg seq =
let
fun result opt_msg xq =
(case (opt_msg, pull xq) of
(_, SOME (Result x, xq')) => (x, filter_results xq')
| (SOME _, SOME (Error _, xq')) => result opt_msg xq'
| (NONE, SOME (Error msg, xq')) => result (SOME msg) xq'
| (SOME msg, NONE) => error (msg ())
| (NONE, NONE) => error (if default_msg = "" then "Empty result sequence" else default_msg));
in result NONE seq end;
fun the_result default_msg seq = #1 (first_result default_msg seq);
(** sequence functions **) (*cf. Pure/tactical.ML*)
fun succeed x = single x;
fun fail _ = empty;
fun op THEN (f, g) x = maps g (f x);
fun op ORELSE (f, g) x =
(case pull (f x) of
NONE => g x
| some => make (fn () => some));
fun op APPEND (f, g) x =
append (f x) (make (fn () => pull (g x)));
fun EVERY fs = fold_rev (curry op THEN) fs succeed;
fun FIRST fs = fold_rev (curry op ORELSE) fs fail;
fun TRY f = ORELSE (f, succeed);
fun REPEAT f =
let
fun rep qs x =
(case pull (f x) of
NONE => SOME (x, make (fn () => repq qs))
| SOME (x', q) => rep (q :: qs) x')
and repq [] = NONE
| repq (q :: qs) =
(case pull q of
NONE => repq qs
| SOME (x, q) => rep (q :: qs) x);
in fn x => make (fn () => rep [] x) end;
fun REPEAT1 f = THEN (f, REPEAT f);
fun INTERVAL f (i: int) j x =
if i > j then single x
else op THEN (f j, INTERVAL f i (j - 1)) x;
fun DETERM f x =
(case pull (f x) of
NONE => empty
| SOME (x', _) => cons x' empty);
end;
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