wenzelm@41
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(* Title: Pure/library.ML
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clasohm@0
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ID: $Id$
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wenzelm@233
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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wenzelm@16188
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Author: Markus Wenzel, TU Muenchen
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clasohm@0
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wenzelm@233
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Basic library: functions, options, pairs, booleans, lists, integers,
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haftmann@19596
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strings, lists as sets, balanced trees, orders, current directory, misc.
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wenzelm@21395
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wenzelm@21395
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See also General/basics.ML for the most fundamental concepts.
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clasohm@0
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*)
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clasohm@0
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wenzelm@21395
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infix 1 |>>>
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wenzelm@21395
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infix 2 ?
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wenzelm@21395
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infix 3 o oo ooo oooo
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wenzelm@21395
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infix 4 ~~ upto downto
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haftmann@20854
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infix orf andf \ \\ mem mem_int mem_string union union_int
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wenzelm@21395
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union_string inter inter_int inter_string subset subset_int subset_string
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wenzelm@5893
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wenzelm@15745
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signature BASIC_LIBRARY =
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wenzelm@4621
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sig
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wenzelm@4621
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(*functions*)
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wenzelm@16842
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val I: 'a -> 'a
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wenzelm@16842
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val K: 'a -> 'b -> 'a
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wenzelm@4621
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val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
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wenzelm@4621
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val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
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haftmann@21335
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val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
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wenzelm@21565
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val ? : bool * ('a -> 'a) -> 'a -> 'a
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wenzelm@16721
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val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
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wenzelm@16721
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val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
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wenzelm@16721
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val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
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wenzelm@16842
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val funpow: int -> ('a -> 'a) -> 'a -> 'a
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clasohm@1364
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wenzelm@18681
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(*exceptions*)
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wenzelm@18681
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exception EXCEPTION of exn * string
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wenzelm@18681
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val do_transform_failure: bool ref
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wenzelm@18681
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val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
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wenzelm@14868
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datatype 'a result = Result of 'a | Exn of exn
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wenzelm@14868
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val capture: ('a -> 'b) -> 'a -> 'b result
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wenzelm@14868
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val release: 'a result -> 'a
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wenzelm@14868
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val get_result: 'a result -> 'a option
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wenzelm@14868
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val get_exn: 'a result -> exn option
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wenzelm@4621
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wenzelm@18681
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(*errors*)
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wenzelm@19542
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exception SYS_ERROR of string
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wenzelm@19542
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val sys_error: string -> 'a
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wenzelm@18681
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exception ERROR of string
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wenzelm@18681
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val error: string -> 'a
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wenzelm@18681
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val cat_error: string -> string -> 'a
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wenzelm@18681
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val assert: bool -> string -> unit
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wenzelm@18681
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val deny: bool -> string -> unit
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wenzelm@18681
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val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
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wenzelm@18681
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wenzelm@4621
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(*pairs*)
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wenzelm@4621
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val pair: 'a -> 'b -> 'a * 'b
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wenzelm@4621
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val rpair: 'a -> 'b -> 'b * 'a
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wenzelm@4621
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val fst: 'a * 'b -> 'a
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wenzelm@4621
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val snd: 'a * 'b -> 'b
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haftmann@17498
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val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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haftmann@17498
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val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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haftmann@19454
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val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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wenzelm@4621
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val swap: 'a * 'b -> 'b * 'a
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wenzelm@4621
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val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
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wenzelm@4621
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val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
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wenzelm@4621
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val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
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wenzelm@4621
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wenzelm@4621
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(*booleans*)
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wenzelm@4621
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val equal: ''a -> ''a -> bool
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wenzelm@4621
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val not_equal: ''a -> ''a -> bool
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wenzelm@4621
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val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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wenzelm@4621
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val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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wenzelm@4621
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val exists: ('a -> bool) -> 'a list -> bool
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wenzelm@4621
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val forall: ('a -> bool) -> 'a list -> bool
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wenzelm@4621
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val set: bool ref -> bool
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wenzelm@4621
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val reset: bool ref -> bool
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wenzelm@4621
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val toggle: bool ref -> bool
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wenzelm@9118
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val change: 'a ref -> ('a -> 'a) -> unit
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wenzelm@4621
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val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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wenzelm@4621
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wenzelm@4621
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(*lists*)
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skalberg@15570
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exception UnequalLengths
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wenzelm@5285
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val single: 'a -> 'a list
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wenzelm@20882
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val the_single: 'a list -> 'a
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wenzelm@19273
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val singleton: ('a list -> 'b list) -> 'a -> 'b
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wenzelm@5904
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val apply: ('a -> 'a) list -> 'a -> 'a
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haftmann@18278
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val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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wenzelm@4956
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val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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wenzelm@19461
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val flat: 'a list list -> 'a list
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wenzelm@19424
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val unflat: 'a list list -> 'b list -> 'b list list
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haftmann@18441
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val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
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haftmann@18549
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val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
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wenzelm@21395
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val maps: ('a -> 'b list) -> 'a list -> 'b list
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wenzelm@19011
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val chop: int -> 'a list -> 'a list * 'a list
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nipkow@4713
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val dropwhile: ('a -> bool) -> 'a list -> 'a list
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haftmann@18278
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val nth: 'a list -> int -> 'a
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haftmann@18011
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val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
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wenzelm@18286
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val nth_list: 'a list list -> int -> 'a list
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haftmann@18514
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val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
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haftmann@18514
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val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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wenzelm@4621
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val split_last: 'a list -> 'a list * 'a
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wenzelm@4621
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val find_index: ('a -> bool) -> 'a list -> int
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wenzelm@4621
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val find_index_eq: ''a -> ''a list -> int
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wenzelm@4621
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val find_first: ('a -> bool) -> 'a list -> 'a option
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haftmann@19233
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val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
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wenzelm@4916
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val get_first: ('a -> 'b option) -> 'a list -> 'b option
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haftmann@19454
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val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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haftmann@18330
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val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
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haftmann@18330
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val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
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wenzelm@19799
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val zip_options: 'a list -> 'b option list -> ('a * 'b) list
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haftmann@18330
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val ~~ : 'a list * 'b list -> ('a * 'b) list
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haftmann@18330
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val split_list: ('a * 'b) list -> 'a list * 'b list
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wenzelm@4621
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val separate: 'a -> 'a list -> 'a list
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wenzelm@4621
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val replicate: int -> 'a -> 'a list
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wenzelm@18148
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val multiply: 'a list -> 'a list list -> 'a list list
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wenzelm@14792
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val product: 'a list -> 'b list -> ('a * 'b) list
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wenzelm@16129
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val filter: ('a -> bool) -> 'a list -> 'a list
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wenzelm@4621
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val filter_out: ('a -> bool) -> 'a list -> 'a list
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wenzelm@19483
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val map_filter: ('a -> 'b option) -> 'a list -> 'b list
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haftmann@18441
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val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
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wenzelm@4621
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val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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haftmann@20108
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val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
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wenzelm@4621
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val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
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wenzelm@12249
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val prefixes1: 'a list -> 'a list list
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wenzelm@19011
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val prefixes: 'a list -> 'a list list
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wenzelm@12249
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val suffixes1: 'a list -> 'a list list
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wenzelm@19011
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val suffixes: 'a list -> 'a list list
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wenzelm@4621
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wenzelm@4621
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(*integers*)
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paulson@15965
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val gcd: IntInf.int * IntInf.int -> IntInf.int
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paulson@15965
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val lcm: IntInf.int * IntInf.int -> IntInf.int
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wenzelm@4621
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val inc: int ref -> int
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wenzelm@4621
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val dec: int ref -> int
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wenzelm@4621
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val upto: int * int -> int list
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wenzelm@4621
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val downto: int * int -> int list
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wenzelm@4621
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val downto0: int list * int -> bool
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wenzelm@4621
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val radixpand: int * int -> int list
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wenzelm@4621
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val radixstring: int * string * int -> string
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wenzelm@4621
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val string_of_int: int -> string
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wenzelm@21942
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val signed_string_of_int: int -> string
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wenzelm@4621
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val string_of_indexname: string * int -> string
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wenzelm@20095
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val read_intinf: int -> string list -> IntInf.int * string list
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wenzelm@14826
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val read_int: string list -> int * string list
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wenzelm@14826
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val oct_char: string -> string
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wenzelm@4621
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wenzelm@4621
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(*strings*)
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haftmann@18011
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val nth_string: string -> int -> string
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wenzelm@16188
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val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
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wenzelm@6312
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val exists_string: (string -> bool) -> string -> bool
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wenzelm@16188
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val forall_string: (string -> bool) -> string -> bool
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wenzelm@4621
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val enclose: string -> string -> string -> string
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wenzelm@6642
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val unenclose: string -> string
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wenzelm@4621
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val quote: string -> string
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wenzelm@4621
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val space_implode: string -> string list -> string
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wenzelm@4621
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val commas: string list -> string
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wenzelm@4621
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val commas_quote: string list -> string
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wenzelm@4621
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val cat_lines: string list -> string
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wenzelm@4621
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val space_explode: string -> string -> string list
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wenzelm@14826
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val split_lines: string -> string list
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wenzelm@5942
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val prefix_lines: string -> string -> string
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wenzelm@7712
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val untabify: string list -> string list
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wenzelm@18681
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val prefix: string -> string -> string
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wenzelm@5285
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val suffix: string -> string -> string
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wenzelm@18681
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val unprefix: string -> string -> string
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wenzelm@5285
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val unsuffix: string -> string -> string
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wenzelm@10951
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val replicate_string: int -> string -> string
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wenzelm@14926
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val translate_string: (string -> string) -> string -> string
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wenzelm@4621
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wenzelm@16492
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(*lists as sets -- see also Pure/General/ord_list.ML*)
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wenzelm@18923
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val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
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wenzelm@18923
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val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
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wenzelm@18923
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val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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wenzelm@19301
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val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
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wenzelm@18923
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val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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wenzelm@4621
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val mem: ''a * ''a list -> bool
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wenzelm@4621
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val mem_int: int * int list -> bool
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wenzelm@4621
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val mem_string: string * string list -> bool
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wenzelm@4621
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val union: ''a list * ''a list -> ''a list
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wenzelm@4621
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val union_int: int list * int list -> int list
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wenzelm@4621
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val union_string: string list * string list -> string list
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wenzelm@4621
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val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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paulson@7090
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val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
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wenzelm@4621
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val inter: ''a list * ''a list -> ''a list
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wenzelm@4621
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val inter_int: int list * int list -> int list
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wenzelm@4621
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val inter_string: string list * string list -> string list
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wenzelm@4621
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val subset: ''a list * ''a list -> bool
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wenzelm@4621
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val subset_int: int list * int list -> bool
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wenzelm@4621
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val subset_string: string list * string list -> bool
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wenzelm@4621
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val eq_set: ''a list * ''a list -> bool
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wenzelm@4621
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val eq_set_string: string list * string list -> bool
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wenzelm@4621
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val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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wenzelm@19301
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val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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wenzelm@4621
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val \ : ''a list * ''a -> ''a list
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wenzelm@4621
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val \\ : ''a list * ''a list -> ''a list
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wenzelm@19046
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val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
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wenzelm@18966
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val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
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wenzelm@16878
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val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
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wenzelm@4621
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haftmann@17540
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(*lists as tables -- see also Pure/General/alist.ML*)
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wenzelm@12284
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val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
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wenzelm@4621
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val merge_lists: ''a list -> ''a list -> ''a list
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wenzelm@4692
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val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
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wenzelm@4621
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wenzelm@4621
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(*balanced trees*)
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wenzelm@4621
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203 |
exception Balance
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wenzelm@4621
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204 |
val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
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wenzelm@4621
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205 |
val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
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wenzelm@4621
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206 |
val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
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wenzelm@4621
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207 |
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wenzelm@4621
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208 |
(*orders*)
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wenzelm@18966
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209 |
val is_equal: order -> bool
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wenzelm@4621
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210 |
val rev_order: order -> order
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wenzelm@4621
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211 |
val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
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wenzelm@4621
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212 |
val int_ord: int * int -> order
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wenzelm@4621
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213 |
val string_ord: string * string -> order
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wenzelm@16676
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214 |
val fast_string_ord: string * string -> order
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wenzelm@16492
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215 |
val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
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wenzelm@4621
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216 |
val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
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wenzelm@4621
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217 |
val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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wenzelm@4621
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218 |
val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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wenzelm@4621
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219 |
val sort: ('a * 'a -> order) -> 'a list -> 'a list
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wenzelm@18427
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220 |
val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
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wenzelm@4621
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221 |
val sort_strings: string list -> string list
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wenzelm@4621
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222 |
val sort_wrt: ('a -> string) -> 'a list -> 'a list
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wenzelm@4621
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223 |
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berghofe@14106
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224 |
(*random numbers*)
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berghofe@14106
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225 |
exception RANDOM
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berghofe@14106
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226 |
val random: unit -> real
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berghofe@14106
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227 |
val random_range: int -> int -> int
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berghofe@14106
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228 |
val one_of: 'a list -> 'a
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berghofe@14106
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229 |
val frequency: (int * 'a) list -> 'a
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berghofe@14106
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230 |
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wenzelm@14826
|
231 |
(*current directory*)
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wenzelm@4621
|
232 |
val cd: string -> unit
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wenzelm@4621
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233 |
val pwd: unit -> string
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wenzelm@4621
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234 |
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wenzelm@4621
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235 |
(*misc*)
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wenzelm@19644
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236 |
val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
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wenzelm@4621
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237 |
val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
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wenzelm@4621
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238 |
val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
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wenzelm@4621
|
239 |
val gensym: string -> string
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wenzelm@4621
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240 |
val scanwords: (string -> bool) -> string list -> string list
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wenzelm@16439
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241 |
type stamp
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wenzelm@16439
|
242 |
val stamp: unit -> stamp
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wenzelm@16439
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243 |
type serial
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wenzelm@16439
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244 |
val serial: unit -> serial
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wenzelm@19512
|
245 |
val serial_string: unit -> string
|
wenzelm@16535
|
246 |
structure Object: sig type T end
|
wenzelm@4621
|
247 |
end;
|
wenzelm@4621
|
248 |
|
wenzelm@15745
|
249 |
signature LIBRARY =
|
skalberg@15570
|
250 |
sig
|
wenzelm@15745
|
251 |
include BASIC_LIBRARY
|
skalberg@15570
|
252 |
val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
|
skalberg@15570
|
253 |
val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
|
skalberg@15570
|
254 |
val take: int * 'a list -> 'a list
|
skalberg@15570
|
255 |
val drop: int * 'a list -> 'a list
|
skalberg@15570
|
256 |
val last_elem: 'a list -> 'a
|
skalberg@15570
|
257 |
val seq: ('a -> unit) -> 'a list -> unit
|
skalberg@15570
|
258 |
end;
|
skalberg@15570
|
259 |
|
wenzelm@15745
|
260 |
structure Library: LIBRARY =
|
clasohm@1364
|
261 |
struct
|
clasohm@0
|
262 |
|
wenzelm@21395
|
263 |
(* functions *)
|
clasohm@0
|
264 |
|
wenzelm@16842
|
265 |
fun I x = x;
|
wenzelm@16842
|
266 |
fun K x = fn _ => x;
|
wenzelm@233
|
267 |
fun curry f x y = f (x, y);
|
wenzelm@233
|
268 |
fun uncurry f (x, y) = f x y;
|
clasohm@0
|
269 |
|
wenzelm@21395
|
270 |
(*application and structured results -- old version*)
|
wenzelm@16705
|
271 |
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
|
wenzelm@16842
|
272 |
|
haftmann@17141
|
273 |
(*conditional application*)
|
wenzelm@21565
|
274 |
fun b ? f = fn x => if b then f x else x;
|
haftmann@17141
|
275 |
|
wenzelm@16721
|
276 |
(*composition with multiple args*)
|
wenzelm@16721
|
277 |
fun (f oo g) x y = f (g x y);
|
wenzelm@16721
|
278 |
fun (f ooo g) x y z = f (g x y z);
|
wenzelm@16721
|
279 |
fun (f oooo g) x y z w = f (g x y z w);
|
wenzelm@16721
|
280 |
|
wenzelm@233
|
281 |
(*function exponentiation: f(...(f x)...) with n applications of f*)
|
wenzelm@233
|
282 |
fun funpow n f x =
|
wenzelm@233
|
283 |
let fun rep (0, x) = x
|
wenzelm@233
|
284 |
| rep (n, x) = rep (n - 1, f x)
|
wenzelm@233
|
285 |
in rep (n, x) end;
|
clasohm@0
|
286 |
|
clasohm@0
|
287 |
|
wenzelm@17341
|
288 |
(* exceptions *)
|
wenzelm@17341
|
289 |
|
wenzelm@18681
|
290 |
val do_transform_failure = ref true;
|
wenzelm@18681
|
291 |
|
wenzelm@18681
|
292 |
fun transform_failure exn f x =
|
wenzelm@18681
|
293 |
if ! do_transform_failure then
|
wenzelm@18681
|
294 |
f x handle Interrupt => raise Interrupt | e => raise exn e
|
wenzelm@18681
|
295 |
else f x;
|
wenzelm@18681
|
296 |
|
wenzelm@17341
|
297 |
exception EXCEPTION of exn * string;
|
wenzelm@6959
|
298 |
|
wenzelm@14868
|
299 |
datatype 'a result =
|
wenzelm@14868
|
300 |
Result of 'a |
|
wenzelm@14868
|
301 |
Exn of exn;
|
wenzelm@14868
|
302 |
|
wenzelm@14868
|
303 |
fun capture f x = Result (f x) handle e => Exn e;
|
wenzelm@14868
|
304 |
|
wenzelm@14868
|
305 |
fun release (Result y) = y
|
wenzelm@14868
|
306 |
| release (Exn e) = raise e;
|
wenzelm@14868
|
307 |
|
skalberg@15531
|
308 |
fun get_result (Result x) = SOME x
|
skalberg@15531
|
309 |
| get_result _ = NONE;
|
wenzelm@14868
|
310 |
|
skalberg@15531
|
311 |
fun get_exn (Exn exn) = SOME exn
|
skalberg@15531
|
312 |
| get_exn _ = NONE;
|
wenzelm@14868
|
313 |
|
wenzelm@14868
|
314 |
|
wenzelm@18681
|
315 |
(* errors *)
|
wenzelm@18681
|
316 |
|
wenzelm@19542
|
317 |
exception SYS_ERROR of string;
|
wenzelm@19542
|
318 |
fun sys_error msg = raise SYS_ERROR msg;
|
wenzelm@19542
|
319 |
|
wenzelm@18681
|
320 |
exception ERROR of string;
|
wenzelm@18681
|
321 |
fun error msg = raise ERROR msg;
|
wenzelm@18681
|
322 |
|
wenzelm@18681
|
323 |
fun cat_error "" msg = error msg
|
wenzelm@18681
|
324 |
| cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
|
wenzelm@18681
|
325 |
|
wenzelm@18681
|
326 |
fun assert p msg = if p then () else error msg;
|
wenzelm@18681
|
327 |
fun deny p msg = if p then error msg else ();
|
wenzelm@18681
|
328 |
|
wenzelm@18681
|
329 |
fun assert_all pred list msg =
|
wenzelm@18681
|
330 |
let
|
wenzelm@18681
|
331 |
fun ass [] = ()
|
wenzelm@18681
|
332 |
| ass (x :: xs) = if pred x then ass xs else error (msg x);
|
wenzelm@18681
|
333 |
in ass list end;
|
wenzelm@18681
|
334 |
|
wenzelm@18681
|
335 |
|
wenzelm@21395
|
336 |
(* pairs *)
|
clasohm@0
|
337 |
|
wenzelm@233
|
338 |
fun pair x y = (x, y);
|
wenzelm@233
|
339 |
fun rpair x y = (y, x);
|
clasohm@0
|
340 |
|
wenzelm@233
|
341 |
fun fst (x, y) = x;
|
wenzelm@233
|
342 |
fun snd (x, y) = y;
|
wenzelm@233
|
343 |
|
haftmann@17498
|
344 |
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
|
haftmann@17498
|
345 |
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
|
haftmann@19454
|
346 |
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
|
wenzelm@233
|
347 |
|
wenzelm@233
|
348 |
fun swap (x, y) = (y, x);
|
wenzelm@233
|
349 |
|
wenzelm@4212
|
350 |
(*apply function to components*)
|
wenzelm@233
|
351 |
fun apfst f (x, y) = (f x, y);
|
wenzelm@233
|
352 |
fun apsnd f (x, y) = (x, f y);
|
wenzelm@4212
|
353 |
fun pairself f (x, y) = (f x, f y);
|
wenzelm@233
|
354 |
|
wenzelm@233
|
355 |
|
wenzelm@21395
|
356 |
(* booleans *)
|
wenzelm@233
|
357 |
|
wenzelm@21395
|
358 |
(*polymorphic equality*)
|
wenzelm@233
|
359 |
fun equal x y = x = y;
|
wenzelm@233
|
360 |
fun not_equal x y = x <> y;
|
wenzelm@233
|
361 |
|
wenzelm@21395
|
362 |
(*combining predicates*)
|
wenzelm@16721
|
363 |
fun p orf q = fn x => p x orelse q x;
|
wenzelm@16721
|
364 |
fun p andf q = fn x => p x andalso q x;
|
wenzelm@233
|
365 |
|
wenzelm@233
|
366 |
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
|
wenzelm@233
|
367 |
fun exists (pred: 'a -> bool) : 'a list -> bool =
|
wenzelm@233
|
368 |
let fun boolf [] = false
|
wenzelm@233
|
369 |
| boolf (x :: xs) = pred x orelse boolf xs
|
wenzelm@233
|
370 |
in boolf end;
|
wenzelm@233
|
371 |
|
wenzelm@233
|
372 |
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
|
wenzelm@233
|
373 |
fun forall (pred: 'a -> bool) : 'a list -> bool =
|
wenzelm@233
|
374 |
let fun boolf [] = true
|
wenzelm@233
|
375 |
| boolf (x :: xs) = pred x andalso boolf xs
|
wenzelm@233
|
376 |
in boolf end;
|
wenzelm@233
|
377 |
|
wenzelm@19644
|
378 |
|
wenzelm@380
|
379 |
(* flags *)
|
wenzelm@380
|
380 |
|
wenzelm@380
|
381 |
fun set flag = (flag := true; true);
|
wenzelm@380
|
382 |
fun reset flag = (flag := false; false);
|
wenzelm@380
|
383 |
fun toggle flag = (flag := not (! flag); ! flag);
|
wenzelm@380
|
384 |
|
wenzelm@9118
|
385 |
fun change r f = r := f (! r);
|
wenzelm@9118
|
386 |
|
wenzelm@18712
|
387 |
(*temporarily set flag during execution*)
|
wenzelm@2978
|
388 |
fun setmp flag value f x =
|
wenzelm@2958
|
389 |
let
|
wenzelm@2958
|
390 |
val orig_value = ! flag;
|
wenzelm@18712
|
391 |
val _ = flag := value;
|
wenzelm@18712
|
392 |
val result = capture f x;
|
wenzelm@18712
|
393 |
val _ = flag := orig_value;
|
wenzelm@18712
|
394 |
in release result end;
|
wenzelm@2958
|
395 |
|
wenzelm@19644
|
396 |
|
wenzelm@21395
|
397 |
|
wenzelm@233
|
398 |
(** lists **)
|
wenzelm@233
|
399 |
|
skalberg@15570
|
400 |
exception UnequalLengths;
|
wenzelm@233
|
401 |
|
wenzelm@5285
|
402 |
fun single x = [x];
|
wenzelm@233
|
403 |
|
wenzelm@20882
|
404 |
fun the_single [x] = x
|
wenzelm@20882
|
405 |
| the_single _ = raise Empty;
|
wenzelm@20882
|
406 |
|
wenzelm@20882
|
407 |
fun singleton f x = the_single (f [x]);
|
wenzelm@19273
|
408 |
|
wenzelm@5904
|
409 |
fun apply [] x = x
|
wenzelm@5904
|
410 |
| apply (f :: fs) x = apply fs (f x);
|
wenzelm@5904
|
411 |
|
wenzelm@233
|
412 |
|
wenzelm@21395
|
413 |
(* fold -- old versions *)
|
haftmann@16691
|
414 |
|
wenzelm@233
|
415 |
(*the following versions of fold are designed to fit nicely with infixes*)
|
wenzelm@233
|
416 |
|
wenzelm@233
|
417 |
(* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn
|
wenzelm@233
|
418 |
for operators that associate to the left (TAIL RECURSIVE)*)
|
wenzelm@233
|
419 |
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
|
wenzelm@233
|
420 |
let fun itl (e, []) = e
|
wenzelm@233
|
421 |
| itl (e, a::l) = itl (f(e, a), l)
|
wenzelm@233
|
422 |
in itl end;
|
wenzelm@233
|
423 |
|
wenzelm@233
|
424 |
(* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e))
|
wenzelm@233
|
425 |
for operators that associate to the right (not tail recursive)*)
|
wenzelm@233
|
426 |
fun foldr f (l, e) =
|
wenzelm@233
|
427 |
let fun itr [] = e
|
wenzelm@233
|
428 |
| itr (a::l) = f(a, itr l)
|
wenzelm@233
|
429 |
in itr l end;
|
wenzelm@233
|
430 |
|
wenzelm@233
|
431 |
(* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn))
|
wenzelm@233
|
432 |
for n > 0, operators that associate to the right (not tail recursive)*)
|
paulson@20443
|
433 |
fun foldr1 f [] = raise Empty
|
wenzelm@20510
|
434 |
| foldr1 f l =
|
paulson@20443
|
435 |
let fun itr [x] = x
|
wenzelm@20510
|
436 |
| itr (x::l) = f(x, itr l)
|
paulson@20443
|
437 |
in itr l end;
|
wenzelm@233
|
438 |
|
wenzelm@16705
|
439 |
fun foldl_map f =
|
wenzelm@16705
|
440 |
let
|
wenzelm@16705
|
441 |
fun fold_aux (x, []) = (x, [])
|
wenzelm@16705
|
442 |
| fold_aux (x, y :: ys) =
|
wenzelm@16705
|
443 |
let
|
wenzelm@16705
|
444 |
val (x', y') = f (x, y);
|
wenzelm@16705
|
445 |
val (x'', ys') = fold_aux (x', ys);
|
wenzelm@16705
|
446 |
in (x'', y' :: ys') end;
|
wenzelm@16705
|
447 |
in fold_aux end;
|
wenzelm@16705
|
448 |
|
wenzelm@233
|
449 |
|
wenzelm@233
|
450 |
(* basic list functions *)
|
wenzelm@233
|
451 |
|
wenzelm@20510
|
452 |
fun eq_list eq (list1, list2) =
|
haftmann@20348
|
453 |
let
|
wenzelm@20510
|
454 |
fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
|
wenzelm@20510
|
455 |
| eq_lst _ = true;
|
wenzelm@20510
|
456 |
in length list1 = length list2 andalso eq_lst (list1, list2) end;
|
haftmann@20348
|
457 |
|
wenzelm@19483
|
458 |
fun maps f [] = []
|
wenzelm@19483
|
459 |
| maps f (x :: xs) = f x @ maps f xs;
|
wenzelm@19483
|
460 |
|
wenzelm@21395
|
461 |
fun chop n xs = unfold_rev n dest xs;
|
wenzelm@19011
|
462 |
|
wenzelm@233
|
463 |
(*take the first n elements from a list*)
|
wenzelm@233
|
464 |
fun take (n, []) = []
|
wenzelm@233
|
465 |
| take (n, x :: xs) =
|
wenzelm@233
|
466 |
if n > 0 then x :: take (n - 1, xs) else [];
|
wenzelm@233
|
467 |
|
wenzelm@233
|
468 |
(*drop the first n elements from a list*)
|
wenzelm@233
|
469 |
fun drop (n, []) = []
|
wenzelm@233
|
470 |
| drop (n, x :: xs) =
|
wenzelm@233
|
471 |
if n > 0 then drop (n - 1, xs) else x :: xs;
|
wenzelm@233
|
472 |
|
nipkow@4713
|
473 |
fun dropwhile P [] = []
|
nipkow@4713
|
474 |
| dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
|
nipkow@4713
|
475 |
|
wenzelm@233
|
476 |
(*return nth element of a list, where 0 designates the first element;
|
wenzelm@18461
|
477 |
raise Subscript if list too short*)
|
haftmann@18011
|
478 |
fun nth xs i = List.nth (xs, i);
|
wenzelm@233
|
479 |
|
wenzelm@18461
|
480 |
fun nth_list xss i = nth xss i handle Subscript => [];
|
wenzelm@18461
|
481 |
|
haftmann@18011
|
482 |
fun nth_map 0 f (x :: xs) = f x :: xs
|
haftmann@18011
|
483 |
| nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
|
haftmann@18011
|
484 |
| nth_map _ _ [] = raise Subscript;
|
wenzelm@11773
|
485 |
|
haftmann@18514
|
486 |
fun map_index f =
|
haftmann@18514
|
487 |
let
|
haftmann@18514
|
488 |
fun mapp _ [] = []
|
haftmann@18514
|
489 |
| mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
|
haftmann@18514
|
490 |
in mapp 0 end;
|
haftmann@18514
|
491 |
|
haftmann@21118
|
492 |
fun fold_index f =
|
haftmann@21118
|
493 |
let
|
haftmann@21118
|
494 |
fun fold_aux _ [] y = y
|
haftmann@21118
|
495 |
| fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
|
haftmann@21118
|
496 |
in fold_aux 0 end;
|
haftmann@21118
|
497 |
|
skalberg@15570
|
498 |
val last_elem = List.last;
|
wenzelm@233
|
499 |
|
wenzelm@3762
|
500 |
(*rear decomposition*)
|
skalberg@15570
|
501 |
fun split_last [] = raise Empty
|
wenzelm@3762
|
502 |
| split_last [x] = ([], x)
|
wenzelm@3762
|
503 |
| split_last (x :: xs) = apfst (cons x) (split_last xs);
|
wenzelm@3762
|
504 |
|
wenzelm@4212
|
505 |
(*find the position of an element in a list*)
|
wenzelm@4212
|
506 |
fun find_index pred =
|
wenzelm@4212
|
507 |
let fun find _ [] = ~1
|
wenzelm@4212
|
508 |
| find n (x :: xs) = if pred x then n else find (n + 1) xs;
|
wenzelm@4212
|
509 |
in find 0 end;
|
wenzelm@3762
|
510 |
|
wenzelm@4224
|
511 |
fun find_index_eq x = find_index (equal x);
|
wenzelm@4212
|
512 |
|
wenzelm@4212
|
513 |
(*find first element satisfying predicate*)
|
skalberg@15531
|
514 |
fun find_first _ [] = NONE
|
wenzelm@4212
|
515 |
| find_first pred (x :: xs) =
|
skalberg@15531
|
516 |
if pred x then SOME x else find_first pred xs;
|
wenzelm@233
|
517 |
|
wenzelm@4916
|
518 |
(*get first element by lookup function*)
|
skalberg@15531
|
519 |
fun get_first _ [] = NONE
|
wenzelm@4916
|
520 |
| get_first f (x :: xs) =
|
wenzelm@4916
|
521 |
(case f x of
|
skalberg@15531
|
522 |
NONE => get_first f xs
|
wenzelm@4916
|
523 |
| some => some);
|
wenzelm@4916
|
524 |
|
haftmann@19233
|
525 |
fun get_index f =
|
haftmann@19233
|
526 |
let
|
haftmann@19233
|
527 |
fun get _ [] = NONE
|
wenzelm@19461
|
528 |
| get i (x :: xs) =
|
haftmann@19233
|
529 |
case f x
|
wenzelm@19461
|
530 |
of NONE => get (i + 1) xs
|
haftmann@19233
|
531 |
| SOME y => SOME (i, y)
|
haftmann@19233
|
532 |
in get 0 end;
|
haftmann@19233
|
533 |
|
skalberg@15531
|
534 |
val flat = List.concat;
|
wenzelm@233
|
535 |
|
wenzelm@12136
|
536 |
fun unflat (xs :: xss) ys =
|
wenzelm@19424
|
537 |
let val (ps, qs) = chop (length xs) ys
|
nipkow@13629
|
538 |
in ps :: unflat xss qs end
|
wenzelm@12136
|
539 |
| unflat [] [] = []
|
skalberg@15570
|
540 |
| unflat _ _ = raise UnequalLengths;
|
wenzelm@12136
|
541 |
|
wenzelm@21479
|
542 |
fun burrow f xss = unflat xss (f (flat xss));
|
haftmann@18359
|
543 |
|
haftmann@18549
|
544 |
fun fold_burrow f xss s =
|
haftmann@18549
|
545 |
apfst (unflat xss) (f (flat xss) s);
|
haftmann@18359
|
546 |
|
wenzelm@233
|
547 |
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
|
wenzelm@233
|
548 |
(proc x1; ...; proc xn) for side effects*)
|
skalberg@15570
|
549 |
val seq = List.app;
|
wenzelm@233
|
550 |
|
wenzelm@233
|
551 |
(*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*)
|
wenzelm@233
|
552 |
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
|
wenzelm@233
|
553 |
| separate _ xs = xs;
|
wenzelm@233
|
554 |
|
wenzelm@233
|
555 |
(*make the list [x, x, ..., x] of length n*)
|
wenzelm@233
|
556 |
fun replicate n (x: 'a) : 'a list =
|
wenzelm@233
|
557 |
let fun rep (0, xs) = xs
|
wenzelm@233
|
558 |
| rep (n, xs) = rep (n - 1, x :: xs)
|
wenzelm@233
|
559 |
in
|
skalberg@15570
|
560 |
if n < 0 then raise Subscript
|
wenzelm@233
|
561 |
else rep (n, [])
|
wenzelm@233
|
562 |
end;
|
wenzelm@233
|
563 |
|
wenzelm@14926
|
564 |
fun translate_string f = String.translate (f o String.str);
|
wenzelm@14926
|
565 |
|
wenzelm@4248
|
566 |
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
|
wenzelm@18148
|
567 |
fun multiply [] _ = []
|
wenzelm@18148
|
568 |
| multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
|
wenzelm@4248
|
569 |
|
wenzelm@14792
|
570 |
(*direct product*)
|
wenzelm@14792
|
571 |
fun product _ [] = []
|
wenzelm@14792
|
572 |
| product [] _ = []
|
wenzelm@14792
|
573 |
| product (x :: xs) ys = map (pair x) ys @ product xs ys;
|
wenzelm@14792
|
574 |
|
wenzelm@233
|
575 |
|
wenzelm@233
|
576 |
(* filter *)
|
wenzelm@233
|
577 |
|
wenzelm@233
|
578 |
(*copy the list preserving elements that satisfy the predicate*)
|
skalberg@15531
|
579 |
val filter = List.filter;
|
clasohm@0
|
580 |
fun filter_out f = filter (not o f);
|
wenzelm@19483
|
581 |
val map_filter = List.mapPartial;
|
wenzelm@233
|
582 |
|
wenzelm@233
|
583 |
|
wenzelm@233
|
584 |
(* lists of pairs *)
|
wenzelm@233
|
585 |
|
skalberg@15570
|
586 |
exception UnequalLengths;
|
skalberg@15570
|
587 |
|
haftmann@18330
|
588 |
fun map2 _ [] [] = []
|
haftmann@18330
|
589 |
| map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
|
haftmann@18330
|
590 |
| map2 _ _ _ = raise UnequalLengths;
|
wenzelm@380
|
591 |
|
haftmann@18330
|
592 |
fun fold2 f =
|
haftmann@18330
|
593 |
let
|
haftmann@18330
|
594 |
fun fold_aux [] [] z = z
|
haftmann@18330
|
595 |
| fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
|
haftmann@18330
|
596 |
| fold_aux _ _ _ = raise UnequalLengths;
|
haftmann@18330
|
597 |
in fold_aux end;
|
wenzelm@380
|
598 |
|
wenzelm@19799
|
599 |
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
|
wenzelm@19799
|
600 |
| zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
|
wenzelm@19799
|
601 |
| zip_options _ [] = []
|
wenzelm@19799
|
602 |
| zip_options [] _ = raise UnequalLengths;
|
wenzelm@4956
|
603 |
|
wenzelm@233
|
604 |
(*combine two lists forming a list of pairs:
|
wenzelm@233
|
605 |
[x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
|
wenzelm@233
|
606 |
fun [] ~~ [] = []
|
wenzelm@233
|
607 |
| (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
|
skalberg@15570
|
608 |
| _ ~~ _ = raise UnequalLengths;
|
wenzelm@233
|
609 |
|
wenzelm@233
|
610 |
(*inverse of ~~; the old 'split':
|
wenzelm@233
|
611 |
[(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*)
|
skalberg@15570
|
612 |
val split_list = ListPair.unzip;
|
wenzelm@233
|
613 |
|
wenzelm@233
|
614 |
|
wenzelm@233
|
615 |
(* prefixes, suffixes *)
|
wenzelm@233
|
616 |
|
haftmann@18441
|
617 |
fun is_prefix _ [] _ = true
|
haftmann@18441
|
618 |
| is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
|
haftmann@18441
|
619 |
| is_prefix eq _ _ = false;
|
wenzelm@233
|
620 |
|
wenzelm@233
|
621 |
(* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn])
|
wenzelm@233
|
622 |
where xi is the first element that does not satisfy the predicate*)
|
wenzelm@233
|
623 |
fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list =
|
wenzelm@233
|
624 |
let fun take (rxs, []) = (rev rxs, [])
|
wenzelm@255
|
625 |
| take (rxs, x :: xs) =
|
wenzelm@255
|
626 |
if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs)
|
wenzelm@233
|
627 |
in take([], xs) end;
|
wenzelm@233
|
628 |
|
haftmann@20108
|
629 |
fun chop_prefix eq ([], ys) = ([], ([], ys))
|
haftmann@20108
|
630 |
| chop_prefix eq (xs, []) = ([], (xs, []))
|
haftmann@20108
|
631 |
| chop_prefix eq (xs as x::xs', ys as y::ys') =
|
haftmann@20108
|
632 |
if eq (x, y) then
|
haftmann@20108
|
633 |
let val (ps', xys'') = chop_prefix eq (xs', ys')
|
haftmann@20108
|
634 |
in (x::ps', xys'') end
|
haftmann@20108
|
635 |
else ([], (xs, ys));
|
haftmann@20108
|
636 |
|
wenzelm@233
|
637 |
(* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn])
|
wenzelm@233
|
638 |
where xi is the last element that does not satisfy the predicate*)
|
wenzelm@233
|
639 |
fun take_suffix _ [] = ([], [])
|
wenzelm@233
|
640 |
| take_suffix pred (x :: xs) =
|
wenzelm@233
|
641 |
(case take_suffix pred xs of
|
wenzelm@233
|
642 |
([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
|
wenzelm@233
|
643 |
| (prfx, sffx) => (x :: prfx, sffx));
|
wenzelm@233
|
644 |
|
wenzelm@12249
|
645 |
fun prefixes1 [] = []
|
wenzelm@12249
|
646 |
| prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
|
wenzelm@12249
|
647 |
|
wenzelm@19011
|
648 |
fun prefixes xs = [] :: prefixes1 xs;
|
wenzelm@19011
|
649 |
|
wenzelm@12249
|
650 |
fun suffixes1 xs = map rev (prefixes1 (rev xs));
|
wenzelm@19011
|
651 |
fun suffixes xs = [] :: suffixes1 xs;
|
wenzelm@233
|
652 |
|
wenzelm@233
|
653 |
|
wenzelm@233
|
654 |
(** integers **)
|
wenzelm@233
|
655 |
|
wenzelm@16439
|
656 |
fun gcd (x, y) =
|
paulson@15965
|
657 |
let fun gxd x y : IntInf.int =
|
wenzelm@21859
|
658 |
if y = IntInf.fromInt 0 then x else gxd y (x mod y)
|
nipkow@10692
|
659 |
in if x < y then gxd y x else gxd x y end;
|
nipkow@10692
|
660 |
|
wenzelm@16439
|
661 |
fun lcm (x, y) = (x * y) div gcd (x, y);
|
nipkow@10692
|
662 |
|
wenzelm@2958
|
663 |
fun inc i = (i := ! i + 1; ! i);
|
wenzelm@2958
|
664 |
fun dec i = (i := ! i - 1; ! i);
|
wenzelm@233
|
665 |
|
wenzelm@233
|
666 |
|
wenzelm@233
|
667 |
(* lists of integers *)
|
wenzelm@233
|
668 |
|
wenzelm@233
|
669 |
(*make the list [from, from + 1, ..., to]*)
|
wenzelm@21859
|
670 |
fun (i upto j) =
|
wenzelm@21859
|
671 |
if i > j then [] else i :: (i + 1 upto j);
|
wenzelm@233
|
672 |
|
wenzelm@233
|
673 |
(*make the list [from, from - 1, ..., to]*)
|
wenzelm@21859
|
674 |
fun (i downto j) =
|
wenzelm@21859
|
675 |
if i < j then [] else i :: (i - 1 downto j);
|
wenzelm@233
|
676 |
|
wenzelm@233
|
677 |
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
|
wenzelm@233
|
678 |
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
|
wenzelm@233
|
679 |
| downto0 ([], n) = n = ~1;
|
wenzelm@233
|
680 |
|
wenzelm@233
|
681 |
|
wenzelm@233
|
682 |
(* convert integers to strings *)
|
wenzelm@233
|
683 |
|
wenzelm@233
|
684 |
(*expand the number in the given base;
|
wenzelm@233
|
685 |
example: radixpand (2, 8) gives [1, 0, 0, 0]*)
|
wenzelm@233
|
686 |
fun radixpand (base, num) : int list =
|
wenzelm@233
|
687 |
let
|
wenzelm@233
|
688 |
fun radix (n, tail) =
|
wenzelm@233
|
689 |
if n < base then n :: tail
|
wenzelm@233
|
690 |
else radix (n div base, (n mod base) :: tail)
|
wenzelm@233
|
691 |
in radix (num, []) end;
|
wenzelm@233
|
692 |
|
wenzelm@233
|
693 |
(*expands a number into a string of characters starting from "zerochar";
|
wenzelm@233
|
694 |
example: radixstring (2, "0", 8) gives "1000"*)
|
wenzelm@233
|
695 |
fun radixstring (base, zerochar, num) =
|
wenzelm@233
|
696 |
let val offset = ord zerochar;
|
wenzelm@233
|
697 |
fun chrof n = chr (offset + n)
|
wenzelm@233
|
698 |
in implode (map chrof (radixpand (base, num))) end;
|
wenzelm@233
|
699 |
|
wenzelm@233
|
700 |
|
paulson@3407
|
701 |
val string_of_int = Int.toString;
|
wenzelm@233
|
702 |
|
wenzelm@21942
|
703 |
fun signed_string_of_int i =
|
wenzelm@21942
|
704 |
if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
|
wenzelm@21942
|
705 |
|
paulson@3407
|
706 |
fun string_of_indexname (a,0) = a
|
paulson@3407
|
707 |
| string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
|
wenzelm@233
|
708 |
|
wenzelm@233
|
709 |
|
wenzelm@14826
|
710 |
(* read integers *)
|
wenzelm@14826
|
711 |
|
wenzelm@20095
|
712 |
fun read_intinf radix cs =
|
wenzelm@20095
|
713 |
let
|
wenzelm@20095
|
714 |
val zero = ord "0";
|
wenzelm@20095
|
715 |
val limit = zero + radix;
|
wenzelm@20095
|
716 |
fun scan (num, []) = (num, [])
|
wenzelm@20095
|
717 |
| scan (num, c :: cs) =
|
wenzelm@20095
|
718 |
if zero <= ord c andalso ord c < limit then
|
wenzelm@20095
|
719 |
scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
|
wenzelm@20095
|
720 |
else (num, c :: cs);
|
wenzelm@21859
|
721 |
in scan (IntInf.fromInt 0, cs) end;
|
wenzelm@14826
|
722 |
|
wenzelm@20095
|
723 |
fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
|
wenzelm@14826
|
724 |
|
wenzelm@20095
|
725 |
fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
|
wenzelm@14826
|
726 |
|
wenzelm@14826
|
727 |
|
wenzelm@14826
|
728 |
|
wenzelm@233
|
729 |
(** strings **)
|
wenzelm@233
|
730 |
|
wenzelm@16188
|
731 |
(* functions tuned for strings, avoiding explode *)
|
wenzelm@6312
|
732 |
|
haftmann@18011
|
733 |
fun nth_string str i =
|
wenzelm@6959
|
734 |
(case try String.substring (str, i, 1) of
|
skalberg@15531
|
735 |
SOME s => s
|
skalberg@15570
|
736 |
| NONE => raise Subscript);
|
wenzelm@6312
|
737 |
|
wenzelm@16188
|
738 |
fun fold_string f str x0 =
|
wenzelm@6282
|
739 |
let
|
wenzelm@6282
|
740 |
val n = size str;
|
wenzelm@16188
|
741 |
fun iter (x, i) =
|
wenzelm@16188
|
742 |
if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
|
wenzelm@16188
|
743 |
in iter (x0, 0) end;
|
wenzelm@6282
|
744 |
|
wenzelm@14968
|
745 |
fun exists_string pred str =
|
wenzelm@14968
|
746 |
let
|
wenzelm@14968
|
747 |
val n = size str;
|
wenzelm@14968
|
748 |
fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
|
wenzelm@14968
|
749 |
in ex 0 end;
|
wenzelm@6312
|
750 |
|
wenzelm@16188
|
751 |
fun forall_string pred = not o exists_string (not o pred);
|
wenzelm@16188
|
752 |
|
lcp@512
|
753 |
(*enclose in brackets*)
|
lcp@512
|
754 |
fun enclose lpar rpar str = lpar ^ str ^ rpar;
|
wenzelm@6642
|
755 |
fun unenclose str = String.substring (str, 1, size str - 2);
|
wenzelm@255
|
756 |
|
wenzelm@233
|
757 |
(*simple quoting (does not escape special chars)*)
|
lcp@512
|
758 |
val quote = enclose "\"" "\"";
|
wenzelm@233
|
759 |
|
wenzelm@4212
|
760 |
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
|
wenzelm@233
|
761 |
fun space_implode a bs = implode (separate a bs);
|
wenzelm@233
|
762 |
|
wenzelm@255
|
763 |
val commas = space_implode ", ";
|
wenzelm@380
|
764 |
val commas_quote = commas o map quote;
|
wenzelm@255
|
765 |
|
wenzelm@233
|
766 |
(*concatenate messages, one per line, into a string*)
|
wenzelm@255
|
767 |
val cat_lines = space_implode "\n";
|
wenzelm@233
|
768 |
|
wenzelm@4212
|
769 |
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
|
wenzelm@3832
|
770 |
fun space_explode _ "" = []
|
paulson@21899
|
771 |
| space_explode sep s = String.fields (fn c => str c = sep) s;
|
wenzelm@3832
|
772 |
|
wenzelm@3832
|
773 |
val split_lines = space_explode "\n";
|
wenzelm@3832
|
774 |
|
wenzelm@14826
|
775 |
fun prefix_lines "" txt = txt
|
wenzelm@14826
|
776 |
| prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
|
wenzelm@14826
|
777 |
|
wenzelm@7712
|
778 |
fun untabify chs =
|
wenzelm@7712
|
779 |
let
|
wenzelm@7712
|
780 |
val tab_width = 8;
|
wenzelm@7712
|
781 |
|
wenzelm@7712
|
782 |
fun untab (_, "\n") = (0, ["\n"])
|
wenzelm@9118
|
783 |
| untab (pos, "\t") =
|
wenzelm@9118
|
784 |
let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
|
wenzelm@7712
|
785 |
| untab (pos, c) = (pos + 1, [c]);
|
wenzelm@7712
|
786 |
in
|
wenzelm@19301
|
787 |
if not (exists (fn c => c = "\t") chs) then chs
|
wenzelm@7712
|
788 |
else flat (#2 (foldl_map untab (0, chs)))
|
wenzelm@7712
|
789 |
end;
|
wenzelm@7712
|
790 |
|
wenzelm@18681
|
791 |
fun prefix prfx s = prfx ^ s;
|
wenzelm@16188
|
792 |
fun suffix sffx s = s ^ sffx;
|
wenzelm@5285
|
793 |
|
wenzelm@18681
|
794 |
fun unprefix prfx s =
|
wenzelm@18681
|
795 |
if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
|
wenzelm@18681
|
796 |
else raise Fail "unprefix";
|
wenzelm@18681
|
797 |
|
wenzelm@16188
|
798 |
fun unsuffix sffx s =
|
wenzelm@17061
|
799 |
if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
|
wenzelm@17061
|
800 |
else raise Fail "unsuffix";
|
wenzelm@5285
|
801 |
|
wenzelm@10951
|
802 |
fun replicate_string 0 _ = ""
|
wenzelm@10951
|
803 |
| replicate_string 1 a = a
|
wenzelm@10951
|
804 |
| replicate_string k a =
|
wenzelm@10951
|
805 |
if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
|
wenzelm@10951
|
806 |
else replicate_string (k div 2) (a ^ a) ^ a;
|
wenzelm@10951
|
807 |
|
wenzelm@233
|
808 |
|
wenzelm@16492
|
809 |
(** lists as sets -- see also Pure/General/ord_list.ML **)
|
wenzelm@233
|
810 |
|
wenzelm@18923
|
811 |
(*canonical member, insert, remove*)
|
wenzelm@18923
|
812 |
fun member eq list x =
|
wenzelm@18923
|
813 |
let
|
wenzelm@18923
|
814 |
fun memb [] = false
|
wenzelm@18923
|
815 |
| memb (y :: ys) = eq (x, y) orelse memb ys;
|
wenzelm@18923
|
816 |
in memb list end;
|
wenzelm@233
|
817 |
|
wenzelm@18923
|
818 |
fun insert eq x xs = if member eq xs x then xs else x :: xs;
|
wenzelm@18923
|
819 |
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
|
berghofe@1576
|
820 |
|
wenzelm@19301
|
821 |
fun subtract eq = fold (remove eq);
|
wenzelm@19301
|
822 |
|
wenzelm@18923
|
823 |
fun merge _ ([], ys) = ys
|
wenzelm@18923
|
824 |
| merge eq (xs, ys) = fold_rev (insert eq) ys xs;
|
berghofe@1576
|
825 |
|
wenzelm@18923
|
826 |
(*old-style infixes*)
|
wenzelm@18923
|
827 |
fun x mem xs = member (op =) xs x;
|
wenzelm@18923
|
828 |
fun (x: int) mem_int xs = member (op =) xs x;
|
wenzelm@18923
|
829 |
fun (x: string) mem_string xs = member (op =) xs x;
|
wenzelm@233
|
830 |
|
wenzelm@233
|
831 |
|
wenzelm@233
|
832 |
(*union of sets represented as lists: no repetitions*)
|
wenzelm@233
|
833 |
fun xs union [] = xs
|
wenzelm@233
|
834 |
| [] union ys = ys
|
haftmann@20854
|
835 |
| (x :: xs) union ys = xs union (insert (op =) x ys);
|
wenzelm@233
|
836 |
|
paulson@2175
|
837 |
(*union of sets, optimized version for ints*)
|
berghofe@1576
|
838 |
fun (xs:int list) union_int [] = xs
|
berghofe@1576
|
839 |
| [] union_int ys = ys
|
haftmann@20854
|
840 |
| (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
|
berghofe@1576
|
841 |
|
paulson@2175
|
842 |
(*union of sets, optimized version for strings*)
|
berghofe@1576
|
843 |
fun (xs:string list) union_string [] = xs
|
berghofe@1576
|
844 |
| [] union_string ys = ys
|
haftmann@20854
|
845 |
| (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
|
berghofe@1576
|
846 |
|
wenzelm@233
|
847 |
(*generalized union*)
|
wenzelm@233
|
848 |
fun gen_union eq (xs, []) = xs
|
wenzelm@233
|
849 |
| gen_union eq ([], ys) = ys
|
wenzelm@18923
|
850 |
| gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
|
wenzelm@233
|
851 |
|
wenzelm@233
|
852 |
|
wenzelm@233
|
853 |
(*intersection*)
|
wenzelm@233
|
854 |
fun [] inter ys = []
|
wenzelm@233
|
855 |
| (x :: xs) inter ys =
|
wenzelm@233
|
856 |
if x mem ys then x :: (xs inter ys) else xs inter ys;
|
wenzelm@233
|
857 |
|
paulson@2175
|
858 |
(*intersection, optimized version for ints*)
|
berghofe@1576
|
859 |
fun ([]:int list) inter_int ys = []
|
berghofe@1576
|
860 |
| (x :: xs) inter_int ys =
|
berghofe@1576
|
861 |
if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
|
berghofe@1576
|
862 |
|
paulson@2175
|
863 |
(*intersection, optimized version for strings *)
|
berghofe@1576
|
864 |
fun ([]:string list) inter_string ys = []
|
berghofe@1576
|
865 |
| (x :: xs) inter_string ys =
|
berghofe@1576
|
866 |
if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
|
berghofe@1576
|
867 |
|
paulson@7090
|
868 |
(*generalized intersection*)
|
paulson@7090
|
869 |
fun gen_inter eq ([], ys) = []
|
wenzelm@12284
|
870 |
| gen_inter eq (x::xs, ys) =
|
wenzelm@18923
|
871 |
if member eq ys x then x :: gen_inter eq (xs, ys)
|
wenzelm@18923
|
872 |
else gen_inter eq (xs, ys);
|
paulson@7090
|
873 |
|
wenzelm@233
|
874 |
|
wenzelm@233
|
875 |
(*subset*)
|
wenzelm@233
|
876 |
fun [] subset ys = true
|
wenzelm@233
|
877 |
| (x :: xs) subset ys = x mem ys andalso xs subset ys;
|
wenzelm@233
|
878 |
|
paulson@2175
|
879 |
(*subset, optimized version for ints*)
|
wenzelm@16439
|
880 |
fun ([]: int list) subset_int ys = true
|
berghofe@1576
|
881 |
| (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
|
berghofe@1576
|
882 |
|
paulson@2175
|
883 |
(*subset, optimized version for strings*)
|
wenzelm@16439
|
884 |
fun ([]: string list) subset_string ys = true
|
berghofe@1576
|
885 |
| (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
|
berghofe@1576
|
886 |
|
wenzelm@4363
|
887 |
(*set equality*)
|
wenzelm@4363
|
888 |
fun eq_set (xs, ys) =
|
wenzelm@4363
|
889 |
xs = ys orelse (xs subset ys andalso ys subset xs);
|
wenzelm@4363
|
890 |
|
paulson@2182
|
891 |
(*set equality for strings*)
|
wenzelm@16439
|
892 |
fun eq_set_string ((xs: string list), ys) =
|
berghofe@1576
|
893 |
xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
|
berghofe@1576
|
894 |
|
wenzelm@18923
|
895 |
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
|
paulson@2182
|
896 |
|
wenzelm@19301
|
897 |
fun gen_eq_set eq (xs, ys) =
|
haftmann@20348
|
898 |
eq_list eq (xs, ys) orelse
|
wenzelm@19301
|
899 |
(gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
|
wenzelm@19301
|
900 |
|
wenzelm@265
|
901 |
|
wenzelm@233
|
902 |
(*removing an element from a list WITHOUT duplicates*)
|
wenzelm@233
|
903 |
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
|
wenzelm@233
|
904 |
| [] \ x = [];
|
paulson@2243
|
905 |
fun ys \\ xs = foldl (op \) (ys,xs);
|
clasohm@0
|
906 |
|
clasohm@0
|
907 |
|
wenzelm@233
|
908 |
(*makes a list of the distinct members of the input; preserves order, takes
|
wenzelm@233
|
909 |
first of equal elements*)
|
wenzelm@19046
|
910 |
fun distinct eq lst =
|
wenzelm@233
|
911 |
let
|
wenzelm@233
|
912 |
fun dist (rev_seen, []) = rev rev_seen
|
wenzelm@233
|
913 |
| dist (rev_seen, x :: xs) =
|
wenzelm@18923
|
914 |
if member eq rev_seen x then dist (rev_seen, xs)
|
wenzelm@233
|
915 |
else dist (x :: rev_seen, xs);
|
wenzelm@19046
|
916 |
in dist ([], lst) end;
|
wenzelm@233
|
917 |
|
wenzelm@255
|
918 |
(*returns a list containing all repeated elements exactly once; preserves
|
wenzelm@255
|
919 |
order, takes first of equal elements*)
|
wenzelm@18966
|
920 |
fun duplicates eq lst =
|
wenzelm@255
|
921 |
let
|
wenzelm@255
|
922 |
fun dups (rev_dups, []) = rev rev_dups
|
wenzelm@255
|
923 |
| dups (rev_dups, x :: xs) =
|
wenzelm@18923
|
924 |
if member eq rev_dups x orelse not (member eq xs x) then
|
wenzelm@255
|
925 |
dups (rev_dups, xs)
|
wenzelm@255
|
926 |
else dups (x :: rev_dups, xs);
|
wenzelm@18966
|
927 |
in dups ([], lst) end;
|
wenzelm@255
|
928 |
|
wenzelm@16878
|
929 |
fun has_duplicates eq =
|
wenzelm@16878
|
930 |
let
|
wenzelm@16878
|
931 |
fun dups [] = false
|
wenzelm@16878
|
932 |
| dups (x :: xs) = member eq xs x orelse dups xs;
|
wenzelm@16878
|
933 |
in dups end;
|
wenzelm@16878
|
934 |
|
wenzelm@255
|
935 |
|
haftmann@19119
|
936 |
(** association lists -- legacy operations **)
|
clasohm@0
|
937 |
|
wenzelm@12284
|
938 |
fun gen_merge_lists _ xs [] = xs
|
wenzelm@12284
|
939 |
| gen_merge_lists _ [] ys = ys
|
haftmann@20951
|
940 |
| gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys;
|
clasohm@0
|
941 |
|
wenzelm@12284
|
942 |
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
|
haftmann@20951
|
943 |
fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs;
|
wenzelm@233
|
944 |
|
wenzelm@233
|
945 |
|
wenzelm@233
|
946 |
(** balanced trees **)
|
wenzelm@233
|
947 |
|
wenzelm@233
|
948 |
exception Balance; (*indicates non-positive argument to balancing fun*)
|
wenzelm@233
|
949 |
|
wenzelm@233
|
950 |
(*balanced folding; avoids deep nesting*)
|
wenzelm@233
|
951 |
fun fold_bal f [x] = x
|
wenzelm@233
|
952 |
| fold_bal f [] = raise Balance
|
wenzelm@233
|
953 |
| fold_bal f xs =
|
wenzelm@19474
|
954 |
let val (ps, qs) = chop (length xs div 2) xs
|
nipkow@13629
|
955 |
in f (fold_bal f ps, fold_bal f qs) end;
|
wenzelm@233
|
956 |
|
wenzelm@233
|
957 |
(*construct something of the form f(...g(...(x)...)) for balanced access*)
|
wenzelm@233
|
958 |
fun access_bal (f, g, x) n i =
|
wenzelm@233
|
959 |
let fun acc n i = (*1<=i<=n*)
|
wenzelm@233
|
960 |
if n=1 then x else
|
wenzelm@233
|
961 |
let val n2 = n div 2
|
wenzelm@233
|
962 |
in if i<=n2 then f (acc n2 i)
|
wenzelm@233
|
963 |
else g (acc (n-n2) (i-n2))
|
wenzelm@233
|
964 |
end
|
wenzelm@233
|
965 |
in if 1<=i andalso i<=n then acc n i else raise Balance end;
|
wenzelm@233
|
966 |
|
wenzelm@233
|
967 |
(*construct ALL such accesses; could try harder to share recursive calls!*)
|
wenzelm@233
|
968 |
fun accesses_bal (f, g, x) n =
|
wenzelm@233
|
969 |
let fun acc n =
|
wenzelm@233
|
970 |
if n=1 then [x] else
|
wenzelm@233
|
971 |
let val n2 = n div 2
|
wenzelm@233
|
972 |
val acc2 = acc n2
|
wenzelm@233
|
973 |
in if n-n2=n2 then map f acc2 @ map g acc2
|
wenzelm@233
|
974 |
else map f acc2 @ map g (acc (n-n2)) end
|
wenzelm@233
|
975 |
in if 1<=n then acc n else raise Balance end;
|
wenzelm@233
|
976 |
|
wenzelm@233
|
977 |
|
wenzelm@233
|
978 |
|
wenzelm@2506
|
979 |
(** orders **)
|
wenzelm@2506
|
980 |
|
wenzelm@18966
|
981 |
fun is_equal EQUAL = true
|
wenzelm@18966
|
982 |
| is_equal _ = false;
|
wenzelm@18966
|
983 |
|
wenzelm@4445
|
984 |
fun rev_order LESS = GREATER
|
wenzelm@4445
|
985 |
| rev_order EQUAL = EQUAL
|
wenzelm@4445
|
986 |
| rev_order GREATER = LESS;
|
wenzelm@4445
|
987 |
|
wenzelm@4479
|
988 |
(*assume rel is a linear strict order*)
|
wenzelm@4445
|
989 |
fun make_ord rel (x, y) =
|
wenzelm@4445
|
990 |
if rel (x, y) then LESS
|
wenzelm@4445
|
991 |
else if rel (y, x) then GREATER
|
wenzelm@4445
|
992 |
else EQUAL;
|
wenzelm@4445
|
993 |
|
wenzelm@15051
|
994 |
val int_ord = Int.compare;
|
wenzelm@15051
|
995 |
val string_ord = String.compare;
|
wenzelm@2506
|
996 |
|
wenzelm@16676
|
997 |
fun fast_string_ord (s1, s2) =
|
wenzelm@16676
|
998 |
(case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
|
wenzelm@16676
|
999 |
|
wenzelm@16492
|
1000 |
fun option_ord ord (SOME x, SOME y) = ord (x, y)
|
wenzelm@16492
|
1001 |
| option_ord _ (NONE, NONE) = EQUAL
|
wenzelm@16492
|
1002 |
| option_ord _ (NONE, SOME _) = LESS
|
wenzelm@16492
|
1003 |
| option_ord _ (SOME _, NONE) = GREATER;
|
wenzelm@16492
|
1004 |
|
wenzelm@4343
|
1005 |
(*lexicographic product*)
|
wenzelm@4343
|
1006 |
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
|
wenzelm@4343
|
1007 |
(case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
|
wenzelm@4343
|
1008 |
|
wenzelm@4343
|
1009 |
(*dictionary order -- in general NOT well-founded!*)
|
wenzelm@16984
|
1010 |
fun dict_ord elem_ord (x :: xs, y :: ys) =
|
wenzelm@16984
|
1011 |
(case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
|
wenzelm@16984
|
1012 |
| dict_ord _ ([], []) = EQUAL
|
wenzelm@4343
|
1013 |
| dict_ord _ ([], _ :: _) = LESS
|
wenzelm@16984
|
1014 |
| dict_ord _ (_ :: _, []) = GREATER;
|
wenzelm@4343
|
1015 |
|
wenzelm@4343
|
1016 |
(*lexicographic product of lists*)
|
wenzelm@4343
|
1017 |
fun list_ord elem_ord (xs, ys) =
|
wenzelm@16676
|
1018 |
(case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
|
wenzelm@4343
|
1019 |
|
wenzelm@2506
|
1020 |
|
wenzelm@4621
|
1021 |
(* sorting *)
|
wenzelm@4621
|
1022 |
|
wenzelm@18427
|
1023 |
(*quicksort -- stable, i.e. does not reorder equal elements*)
|
wenzelm@18427
|
1024 |
fun quicksort unique ord =
|
wenzelm@4621
|
1025 |
let
|
wenzelm@16878
|
1026 |
fun qsort [] = []
|
wenzelm@16878
|
1027 |
| qsort (xs as [_]) = xs
|
wenzelm@18427
|
1028 |
| qsort (xs as [x, y]) =
|
wenzelm@18427
|
1029 |
(case ord (x, y) of
|
wenzelm@18427
|
1030 |
LESS => xs
|
wenzelm@18427
|
1031 |
| EQUAL => if unique then [x] else xs
|
wenzelm@18427
|
1032 |
| GREATER => [y, x])
|
wenzelm@16878
|
1033 |
| qsort xs =
|
haftmann@18011
|
1034 |
let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
|
wenzelm@16878
|
1035 |
in qsort lts @ eqs @ qsort gts end
|
wenzelm@4621
|
1036 |
and part _ [] = ([], [], [])
|
wenzelm@4621
|
1037 |
| part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
|
wenzelm@4621
|
1038 |
and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
|
wenzelm@18427
|
1039 |
| add EQUAL x (lts, [], gts) = (lts, [x], gts)
|
wenzelm@18427
|
1040 |
| add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
|
wenzelm@4621
|
1041 |
| add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
|
wenzelm@4621
|
1042 |
in qsort end;
|
wenzelm@4621
|
1043 |
|
wenzelm@18427
|
1044 |
fun sort ord = quicksort false ord;
|
wenzelm@18427
|
1045 |
fun sort_distinct ord = quicksort true ord;
|
wenzelm@18427
|
1046 |
|
wenzelm@4621
|
1047 |
val sort_strings = sort string_ord;
|
wenzelm@4621
|
1048 |
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
|
wenzelm@4621
|
1049 |
|
wenzelm@4621
|
1050 |
|
wenzelm@2506
|
1051 |
|
berghofe@14106
|
1052 |
(** random numbers **)
|
berghofe@14106
|
1053 |
|
berghofe@14106
|
1054 |
exception RANDOM;
|
berghofe@14106
|
1055 |
|
berghofe@14618
|
1056 |
fun rmod x y = x - y * Real.realFloor (x / y);
|
berghofe@14106
|
1057 |
|
berghofe@14106
|
1058 |
local
|
berghofe@14106
|
1059 |
val a = 16807.0;
|
berghofe@14106
|
1060 |
val m = 2147483647.0;
|
berghofe@14106
|
1061 |
val random_seed = ref 1.0;
|
berghofe@14106
|
1062 |
in
|
berghofe@14106
|
1063 |
|
berghofe@14106
|
1064 |
fun random () =
|
berghofe@14106
|
1065 |
let val r = rmod (a * !random_seed) m
|
berghofe@14106
|
1066 |
in (random_seed := r; r) end;
|
berghofe@14106
|
1067 |
|
berghofe@14106
|
1068 |
end;
|
berghofe@14106
|
1069 |
|
berghofe@14106
|
1070 |
fun random_range l h =
|
berghofe@14106
|
1071 |
if h < l orelse l < 0 then raise RANDOM
|
berghofe@14106
|
1072 |
else l + Real.floor (rmod (random ()) (real (h - l + 1)));
|
berghofe@14106
|
1073 |
|
haftmann@18011
|
1074 |
fun one_of xs = nth xs (random_range 0 (length xs - 1));
|
berghofe@14106
|
1075 |
|
berghofe@14106
|
1076 |
fun frequency xs =
|
berghofe@14106
|
1077 |
let
|
berghofe@14106
|
1078 |
val sum = foldl op + (0, map fst xs);
|
wenzelm@17756
|
1079 |
fun pick n ((k: int, x) :: xs) =
|
berghofe@14106
|
1080 |
if n <= k then x else pick (n - k) xs
|
berghofe@14106
|
1081 |
in pick (random_range 1 sum) xs end;
|
berghofe@14106
|
1082 |
|
berghofe@14106
|
1083 |
|
wenzelm@14826
|
1084 |
(** current directory **)
|
wenzelm@233
|
1085 |
|
paulson@2243
|
1086 |
val cd = OS.FileSys.chDir;
|
wenzelm@2317
|
1087 |
val pwd = OS.FileSys.getDir;
|
paulson@2243
|
1088 |
|
berghofe@3606
|
1089 |
|
wenzelm@19644
|
1090 |
|
wenzelm@4621
|
1091 |
(** misc **)
|
wenzelm@233
|
1092 |
|
wenzelm@19644
|
1093 |
fun divide_and_conquer decomp x =
|
wenzelm@19644
|
1094 |
let val (ys, recomb) = decomp x
|
wenzelm@19644
|
1095 |
in recomb (map (divide_and_conquer decomp) ys) end;
|
wenzelm@19644
|
1096 |
|
clasohm@0
|
1097 |
|
wenzelm@233
|
1098 |
(*Partition a list into buckets [ bi, b(i+1), ..., bj ]
|
clasohm@0
|
1099 |
putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*)
|
clasohm@0
|
1100 |
fun partition_list p i j =
|
wenzelm@233
|
1101 |
let fun part k xs =
|
wenzelm@233
|
1102 |
if k>j then
|
clasohm@0
|
1103 |
(case xs of [] => []
|
skalberg@15570
|
1104 |
| _ => raise Fail "partition_list")
|
clasohm@0
|
1105 |
else
|
wenzelm@19691
|
1106 |
let val (ns, rest) = List.partition (p k) xs;
|
wenzelm@233
|
1107 |
in ns :: part(k+1)rest end
|
clasohm@0
|
1108 |
in part i end;
|
clasohm@0
|
1109 |
|
wenzelm@19691
|
1110 |
fun partition_eq (eq:'a * 'a -> bool) =
|
wenzelm@19691
|
1111 |
let
|
wenzelm@19691
|
1112 |
fun part [] = []
|
wenzelm@19691
|
1113 |
| part (x :: ys) =
|
wenzelm@19691
|
1114 |
let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
|
wenzelm@19691
|
1115 |
in (x::xs)::(part xs') end
|
wenzelm@19691
|
1116 |
in part end;
|
wenzelm@19691
|
1117 |
|
wenzelm@19691
|
1118 |
|
clasohm@0
|
1119 |
|
wenzelm@233
|
1120 |
(* generating identifiers *)
|
clasohm@0
|
1121 |
|
paulson@4063
|
1122 |
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
|
clasohm@0
|
1123 |
local
|
paulson@4063
|
1124 |
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
|
paulson@4063
|
1125 |
fun char i = if i<26 then chr (ord "A" + i)
|
wenzelm@5904
|
1126 |
else if i<52 then chr (ord "a" + i - 26)
|
wenzelm@5904
|
1127 |
else if i<62 then chr (ord"0" + i - 52)
|
wenzelm@5904
|
1128 |
else if i=62 then "_"
|
wenzelm@5904
|
1129 |
else (*i=63*) "'";
|
paulson@4063
|
1130 |
|
paulson@4063
|
1131 |
val charVec = Vector.tabulate (64, char);
|
paulson@4063
|
1132 |
|
wenzelm@5904
|
1133 |
fun newid n =
|
wenzelm@5904
|
1134 |
let
|
wenzelm@4284
|
1135 |
in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end;
|
paulson@2003
|
1136 |
|
wenzelm@4284
|
1137 |
val seedr = ref 0;
|
paulson@4063
|
1138 |
|
clasohm@0
|
1139 |
in
|
wenzelm@4284
|
1140 |
|
wenzelm@12346
|
1141 |
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
|
clasohm@0
|
1142 |
|
paulson@4063
|
1143 |
end;
|
paulson@4063
|
1144 |
|
paulson@4063
|
1145 |
|
wenzelm@233
|
1146 |
(* lexical scanning *)
|
clasohm@0
|
1147 |
|
wenzelm@233
|
1148 |
(*scan a list of characters into "words" composed of "letters" (recognized by
|
wenzelm@233
|
1149 |
is_let) and separated by any number of non-"letters"*)
|
wenzelm@233
|
1150 |
fun scanwords is_let cs =
|
wenzelm@233
|
1151 |
let fun scan1 [] = []
|
wenzelm@233
|
1152 |
| scan1 cs =
|
wenzelm@233
|
1153 |
let val (lets, rest) = take_prefix is_let cs
|
wenzelm@233
|
1154 |
in implode lets :: scanwords is_let rest end;
|
wenzelm@233
|
1155 |
in scan1 (#2 (take_prefix (not o is_let) cs)) end;
|
clasohm@0
|
1156 |
|
wenzelm@4212
|
1157 |
|
wenzelm@16439
|
1158 |
(* stamps and serial numbers *)
|
wenzelm@16439
|
1159 |
|
wenzelm@16439
|
1160 |
type stamp = unit ref;
|
wenzelm@16439
|
1161 |
val stamp: unit -> stamp = ref;
|
wenzelm@16439
|
1162 |
|
wenzelm@16439
|
1163 |
type serial = int;
|
wenzelm@16439
|
1164 |
local val count = ref 0
|
wenzelm@16439
|
1165 |
in fun serial () = inc count end;
|
wenzelm@16439
|
1166 |
|
wenzelm@19512
|
1167 |
val serial_string = string_of_int o serial;
|
wenzelm@19512
|
1168 |
|
wenzelm@16535
|
1169 |
|
wenzelm@16535
|
1170 |
(* generic objects *)
|
wenzelm@16535
|
1171 |
|
wenzelm@16535
|
1172 |
(*note that the builtin exception datatype may be extended by new
|
wenzelm@16535
|
1173 |
constructors at any time*)
|
wenzelm@16535
|
1174 |
structure Object = struct type T = exn end;
|
wenzelm@16535
|
1175 |
|
clasohm@1364
|
1176 |
end;
|
clasohm@1364
|
1177 |
|
wenzelm@15745
|
1178 |
structure BasicLibrary: BASIC_LIBRARY = Library;
|
wenzelm@15745
|
1179 |
open BasicLibrary;
|