author | skalberg |
Fri, 04 Mar 2005 15:07:34 +0100 | |
changeset 15574 | b1d1b5bfc464 |
parent 15570 | 8d8c70b41bab |
child 15663 | 6e6233e8cf5e |
permissions | -rw-r--r-- |
14278 | 1 |
signature LAZY_SEQ = |
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sig |
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type 'a seq |
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(* From LIST *) |
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val null : 'a seq -> bool |
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val length : 'a seq -> int |
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val @ : 'a seq * 'a seq -> 'a 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 last : 'a seq -> 'a |
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val getItem : 'a seq -> ('a * 'a seq) option |
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val nth : 'a seq * int -> 'a |
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val take : 'a seq * int -> 'a seq |
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val drop : 'a seq * int -> 'a seq |
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val rev : 'a seq -> 'a seq |
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val concat : 'a seq seq -> 'a seq |
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val revAppend : 'a seq * 'a seq -> 'a seq |
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val app : ('a -> unit) -> 'a seq -> unit |
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val map : ('a -> 'b) -> 'a seq -> 'b seq |
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val mapPartial : ('a -> 'b option) -> 'a seq -> 'b seq |
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val find : ('a -> bool) -> 'a seq -> 'a option |
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val filter : ('a -> bool) -> 'a seq -> 'a seq |
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val partition : ('a -> bool) |
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-> 'a seq -> 'a seq * 'a seq |
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val foldl : ('a * 'b -> 'b) -> 'b -> 'a seq -> 'b |
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val foldr : ('a * 'b -> 'b) -> 'b -> 'a seq -> 'b |
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val exists : ('a -> bool) -> 'a seq -> bool |
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val all : ('a -> bool) -> 'a seq -> bool |
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val tabulate : int * (int -> 'a) -> 'a seq |
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val collate : ('a * 'a -> order) |
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-> 'a seq * 'a seq -> order |
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(* Miscellaneous *) |
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val cycle : ((unit ->'a seq) -> 'a seq) -> 'a seq |
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val iterates : ('a -> 'a) -> 'a -> 'a seq |
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val of_function: (unit -> 'a option) -> 'a seq |
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val of_string : string -> char seq |
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val of_instream: TextIO.instream -> char seq |
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(* From SEQ *) |
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val make: (unit -> ('a * 'a seq) option) -> 'a seq |
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val empty: 'a -> '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 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 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 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 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 LazySeq :> LAZY_SEQ = |
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struct |
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open Susp |
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datatype 'a seq = Seq of ('a * 'a seq) option susp |
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exception Empty |
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fun getItem (Seq s) = force s |
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fun make f = Seq (delay f) |
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fun null s = isSome (getItem s) |
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local |
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fun F n NONE = n |
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| F n (SOME(_,s)) = F (n+1) (getItem s) |
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in |
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fun length s = F 0 (getItem s) |
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end |
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fun s1 @ s2 = |
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let |
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fun F NONE = getItem s2 |
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| F (SOME(x,s1')) = SOME(x,F' s1') |
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and F' s = make (fn () => F (getItem s)) |
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in |
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F' s1 |
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end |
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local |
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fun F NONE = raise Empty |
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| F (SOME arg) = arg |
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in |
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fun hd s = #1 (F (getItem s)) |
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fun tl s = #2 (F (getItem s)) |
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end |
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local |
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fun F x NONE = x |
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| F _ (SOME(x,s)) = F x (getItem s) |
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fun G NONE = raise Empty |
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| G (SOME(x,s)) = F x (getItem s) |
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in |
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fun last s = G (getItem s) |
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end |
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local |
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fun F NONE _ = raise Subscript |
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| F (SOME(x,_)) 0 = x |
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| F (SOME(_,s)) n = F (getItem s) (n-1) |
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in |
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fun nth(s,n) = |
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if n < 0 |
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then raise Subscript |
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else F (getItem s) n |
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end |
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local |
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fun F NONE _ = raise Subscript |
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| F (SOME(x,s)) n = SOME(x,F' s (n-1)) |
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and F' s 0 = Seq (value NONE) |
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| F' s n = make (fn () => F (getItem s) n) |
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in |
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fun take (s,n) = |
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if n < 0 |
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then raise Subscript |
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else F' s n |
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end |
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local |
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fun F s 0 = s |
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| F NONE _ = raise Subscript |
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| F (SOME(_,s)) n = F (getItem s) (n-1) |
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in |
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fun drop (s,0) = s |
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| drop (s,n) = |
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if n < 0 |
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then raise Subscript |
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else make (fn () => F (getItem s) n) |
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end |
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local |
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fun F s NONE = s |
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| F s (SOME(x,s')) = F (SOME(x, Seq (value s))) (getItem s') |
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in |
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fun rev s = make (fn () => F NONE (getItem s)) |
14278 | 161 |
end |
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local |
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fun F s NONE = getItem s |
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| F s (SOME(x,s')) = F (Seq (value (SOME(x,s)))) (getItem s') |
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in |
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fun revAppend (s1,s2) = make (fn () => F s2 (getItem s1)) |
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end |
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local |
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fun F NONE = NONE |
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| F (SOME(s1,s2)) = |
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let |
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fun G NONE = F (getItem s2) |
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| G (SOME(x,s)) = SOME(x,make (fn () => G (getItem s))) |
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in |
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G (getItem s1) |
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end |
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in |
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fun concat s = make (fn () => F (getItem s)) |
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end |
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fun app f = |
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let |
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fun F NONE = () |
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| F (SOME(x,s)) = |
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(f x; |
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F (getItem s)) |
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in |
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F o getItem |
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end |
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fun map f = |
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let |
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fun F NONE = NONE |
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| F (SOME(x,s)) = SOME(f x,F' s) |
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and F' s = make (fn() => F (getItem s)) |
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in |
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F' |
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end |
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fun mapPartial f = |
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let |
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fun F NONE = NONE |
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| F (SOME(x,s)) = |
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(case f x of |
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SOME y => SOME(y,F' s) |
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| NONE => F (getItem s)) |
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and F' s = make (fn()=> F (getItem s)) |
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in |
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F' |
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end |
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fun find P = |
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let |
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fun F NONE = NONE |
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| F (SOME(x,s)) = |
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if P x |
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then SOME x |
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else F (getItem s) |
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in |
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F o getItem |
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end |
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(*fun filter p = mapPartial (fn x => if p x then SOME x else NONE)*) |
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fun filter P = |
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let |
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fun F NONE = NONE |
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| F (SOME(x,s)) = |
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if P x |
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then SOME(x,F' s) |
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else F (getItem s) |
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and F' s = make (fn () => F (getItem s)) |
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in |
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F' |
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end |
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fun partition f s = |
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let |
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val s' = map (fn x => (x,f x)) s |
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in |
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(mapPartial (fn (x,true) => SOME x | _ => NONE) s', |
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mapPartial (fn (x,false) => SOME x | _ => NONE) s') |
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end |
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fun exists P = |
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let |
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fun F NONE = false |
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| F (SOME(x,s)) = P x orelse F (getItem s) |
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14278 | 251 |
in |
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F o getItem |
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end |
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fun all P = |
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let |
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fun F NONE = true |
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| F (SOME(x,s)) = P x andalso F (getItem s) |
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in |
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F o getItem |
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end |
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(*fun tabulate f = map f (iterates (fn x => x + 1) 0)*) |
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fun tabulate (n,f) = |
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let |
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fun F n = make (fn () => SOME(f n,F (n+1))) |
14278 | 268 |
in |
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F n |
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end |
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fun collate c (s1,s2) = |
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let |
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fun F NONE _ = LESS |
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| F _ NONE = GREATER |
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| F (SOME(x,s1)) (SOME(y,s2)) = |
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(case c (x,y) of |
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LESS => LESS |
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| GREATER => GREATER |
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| EQUAL => F' s1 s2) |
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and F' s1 s2 = F (getItem s1) (getItem s2) |
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in |
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F' s1 s2 |
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end |
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||
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fun empty _ = Seq (value NONE) |
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fun single x = Seq(value (SOME(x,Seq (value NONE)))) |
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fun cons a = Seq(value (SOME a)) |
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14278 | 289 |
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fun cycle seqfn = |
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let |
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val knot = ref (Seq (value NONE)) |
14278 | 293 |
in |
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knot := seqfn (fn () => !knot); |
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!knot |
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end |
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||
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fun iterates f = |
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let |
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15531 | 300 |
fun F x = make (fn() => SOME(x,F (f x))) |
14278 | 301 |
in |
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F |
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end |
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fun interleave (s1,s2) = |
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let |
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15531 | 307 |
fun F NONE = getItem s2 |
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| F (SOME(x,s1')) = SOME(x,interleave(s2,s1')) |
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14278 | 309 |
in |
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make (fn()=> F (getItem s1)) |
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end |
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(* val force_all = app ignore *) |
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local |
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15531 | 316 |
fun F NONE = () |
317 |
| F (SOME(x,s)) = F (getItem s) |
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14278 | 318 |
in |
15026 | 319 |
fun force_all s = F (getItem s) |
14278 | 320 |
end |
321 |
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fun of_function f = |
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let |
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324 |
fun F () = case f () of |
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SOME x => SOME(x,make F) |
326 |
| NONE => NONE |
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14278 | 327 |
in |
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make F |
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end |
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||
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local |
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fun F [] = NONE |
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| F (x::xs) = SOME(x,F' xs) |
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and F' xs = make (fn () => F xs) |
335 |
in |
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fun of_list xs = F' xs |
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end |
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val of_string = of_list o String.explode |
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fun of_instream is = |
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let |
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val buffer : char list ref = ref [] |
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fun get_input () = |
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case !buffer of |
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(c::cs) => (buffer:=cs; |
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15531 | 347 |
SOME c) |
14278 | 348 |
| [] => (case String.explode (TextIO.input is) of |
15531 | 349 |
[] => NONE |
14278 | 350 |
| (c::cs) => (buffer := cs; |
15531 | 351 |
SOME c)) |
14278 | 352 |
in |
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of_function get_input |
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354 |
end |
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355 |
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356 |
local |
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15531 | 357 |
fun F k NONE = k [] |
358 |
| F k (SOME(x,s)) = F (fn xs => k (x::xs)) (getItem s) |
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14278 | 359 |
in |
360 |
fun list_of s = F (fn x => x) (getItem s) |
|
361 |
end |
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362 |
||
363 |
(* Adapted from seq.ML *) |
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364 |
||
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val succeed = single |
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fun fail _ = Seq (value NONE) |
14278 | 367 |
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368 |
(* fun op THEN (f, g) x = flat (map g (f x)) *) |
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369 |
||
370 |
fun op THEN (f, g) = |
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371 |
let |
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15531 | 372 |
fun F NONE = NONE |
373 |
| F (SOME(x,xs)) = |
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14278 | 374 |
let |
15531 | 375 |
fun G NONE = F (getItem xs) |
376 |
| G (SOME(y,ys)) = SOME(y,make (fn () => G (getItem ys))) |
|
14278 | 377 |
in |
378 |
G (getItem (g x)) |
|
379 |
end |
|
380 |
in |
|
381 |
fn x => make (fn () => F (getItem (f x))) |
|
382 |
end |
|
383 |
||
384 |
fun op ORELSE (f, g) x = |
|
385 |
make (fn () => |
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386 |
case getItem (f x) of |
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15531 | 387 |
NONE => getItem (g x) |
14278 | 388 |
| some => some) |
389 |
||
390 |
fun op APPEND (f, g) x = |
|
391 |
let |
|
392 |
fun copy s = |
|
393 |
case getItem s of |
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15531 | 394 |
NONE => getItem (g x) |
395 |
| SOME(x,xs) => SOME(x,make (fn () => copy xs)) |
|
14278 | 396 |
in |
397 |
make (fn () => copy (f x)) |
|
398 |
end |
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399 |
||
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
400 |
fun EVERY fs = foldr THEN succeed fs |
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
401 |
fun FIRST fs = foldr ORELSE fail fs |
14278 | 402 |
|
403 |
fun TRY f x = |
|
404 |
make (fn () => |
|
405 |
case getItem (f x) of |
|
15531 | 406 |
NONE => SOME(x,Seq (value NONE)) |
14278 | 407 |
| some => some) |
408 |
||
409 |
fun REPEAT f = |
|
410 |
let |
|
411 |
fun rep qs x = |
|
412 |
case getItem (f x) of |
|
15531 | 413 |
NONE => SOME(x, make (fn () => repq qs)) |
414 |
| SOME (x', q) => rep (q :: qs) x' |
|
415 |
and repq [] = NONE |
|
14278 | 416 |
| repq (q :: qs) = |
417 |
case getItem q of |
|
15531 | 418 |
NONE => repq qs |
419 |
| SOME (x, q) => rep (q :: qs) x |
|
14278 | 420 |
in |
421 |
fn x => make (fn () => rep [] x) |
|
422 |
end |
|
423 |
||
424 |
fun REPEAT1 f = THEN (f, REPEAT f); |
|
425 |
||
426 |
fun INTERVAL f i = |
|
427 |
let |
|
428 |
fun F j = |
|
429 |
if i > j |
|
430 |
then single |
|
431 |
else op THEN (f j, F (j - 1)) |
|
432 |
in F end |
|
433 |
||
434 |
fun DETERM f x = |
|
435 |
make (fn () => |
|
436 |
case getItem (f x) of |
|
15531 | 437 |
NONE => NONE |
438 |
| SOME (x', _) => SOME(x',Seq (value NONE))) |
|
14278 | 439 |
|
440 |
(*partial function as procedure*) |
|
441 |
fun try f x = |
|
442 |
make (fn () => |
|
443 |
case Library.try f x of |
|
15531 | 444 |
SOME y => SOME(y,Seq (value NONE)) |
445 |
| NONE => NONE) |
|
14278 | 446 |
|
447 |
(*functional to print a sequence, up to "count" elements; |
|
448 |
the function prelem should print the element number and also the element*) |
|
449 |
fun print prelem count seq = |
|
450 |
let |
|
451 |
fun pr k xq = |
|
452 |
if k > count |
|
453 |
then () |
|
454 |
else |
|
455 |
case getItem xq of |
|
15531 | 456 |
NONE => () |
457 |
| SOME (x, xq') => |
|
14278 | 458 |
(prelem k x; |
459 |
writeln ""; |
|
460 |
pr (k + 1) xq') |
|
461 |
in |
|
462 |
pr 1 seq |
|
463 |
end |
|
464 |
||
465 |
(*accumulating a function over a sequence; this is lazy*) |
|
466 |
fun it_right f (xq, yq) = |
|
467 |
let |
|
468 |
fun its s = |
|
469 |
make (fn () => |
|
470 |
case getItem s of |
|
15531 | 471 |
NONE => getItem yq |
472 |
| SOME (a, s') => getItem(f (a, its s'))) |
|
14278 | 473 |
in |
474 |
its xq |
|
475 |
end |
|
476 |
||
477 |
(*map over a sequence s1, append the sequence s2*) |
|
478 |
fun mapp f s1 s2 = |
|
479 |
let |
|
15531 | 480 |
fun F NONE = getItem s2 |
481 |
| F (SOME(x,s1')) = SOME(f x,F' s1') |
|
14278 | 482 |
and F' s = make (fn () => F (getItem s)) |
483 |
in |
|
484 |
F' s1 |
|
485 |
end |
|
486 |
||
487 |
(*turn a list of sequences into a sequence of lists*) |
|
488 |
local |
|
15531 | 489 |
fun F [] = SOME([],Seq (value NONE)) |
14278 | 490 |
| F (xq :: xqs) = |
491 |
case getItem xq of |
|
15531 | 492 |
NONE => NONE |
493 |
| SOME (x, xq') => |
|
14278 | 494 |
(case F xqs of |
15531 | 495 |
NONE => NONE |
496 |
| SOME (xs, xsq) => |
|
14278 | 497 |
let |
498 |
fun G s = |
|
499 |
make (fn () => |
|
500 |
case getItem s of |
|
15531 | 501 |
NONE => F (xq' :: xqs) |
502 |
| SOME(ys,ysq) => SOME(x::ys,G ysq)) |
|
14278 | 503 |
in |
15531 | 504 |
SOME (x :: xs, G xsq) |
14278 | 505 |
end) |
506 |
in |
|
507 |
fun commute xqs = make (fn () => F xqs) |
|
508 |
end |
|
509 |
||
510 |
(*the list of the first n elements, paired with rest of sequence; |
|
511 |
if length of list is less than n, then sequence had less than n elements*) |
|
512 |
fun chop (n, xq) = |
|
513 |
if n <= 0 |
|
514 |
then ([], xq) |
|
515 |
else |
|
516 |
case getItem xq of |
|
15531 | 517 |
NONE => ([], xq) |
518 |
| SOME (x, xq') => apfst (Library.cons x) (chop (n - 1, xq')) |
|
14278 | 519 |
|
520 |
fun foldl f e s = |
|
521 |
let |
|
15531 | 522 |
fun F k NONE = k e |
523 |
| F k (SOME(x,s)) = F (fn y => k (f(x,y))) (getItem s) |
|
14278 | 524 |
in |
525 |
F (fn x => x) (getItem s) |
|
526 |
end |
|
527 |
||
528 |
fun foldr f e s = |
|
529 |
let |
|
15531 | 530 |
fun F e NONE = e |
531 |
| F e (SOME(x,s)) = F (f(x,e)) (getItem s) |
|
14278 | 532 |
in |
533 |
F e (getItem s) |
|
534 |
end |
|
535 |
||
536 |
end |