src/Pure/library.ML
author wenzelm
Sat Jan 18 19:15:12 2014 +0100 (2014-01-18)
changeset 55033 8e8243975860
parent 52271 6f3771c00280
child 56038 0e2dec666152
permissions -rw-r--r--
support for nested text cartouches;
clarified Symbol.is_symbolic: exclude \<open> and \<close>;
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(*  Title:      Pure/library.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Markus Wenzel, TU Muenchen
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Basic library: functions, pairs, booleans, lists, integers,
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strings, lists as sets, orders, current directory, misc.
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See also General/basics.ML for the most fundamental concepts.
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*)
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infix 2 ?
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infix 3 o oo ooo oooo
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infix 4 ~~ upto downto
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infix orf andf
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signature BASIC_LIBRARY =
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sig
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  (*functions*)
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  val undefined: 'a -> 'b
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  val I: 'a -> 'a
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  val K: 'a -> 'b -> 'a
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  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
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  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
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  val ? : bool * ('a -> 'a) -> 'a -> 'a
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  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
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  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
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  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
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  val funpow: int -> ('a -> 'a) -> 'a -> 'a
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  val funpow_yield: int -> ('a -> 'b * 'a) -> 'a -> 'b list * 'a
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  (*user errors*)
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  exception ERROR of string
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  val error: string -> 'a
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  val cat_error: string -> string -> 'a
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  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
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  (*pairs*)
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  val pair: 'a -> 'b -> 'a * 'b
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  val rpair: 'a -> 'b -> 'b * 'a
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  val fst: 'a * 'b -> 'a
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  val snd: 'a * 'b -> 'b
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  val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val swap: 'a * 'b -> 'b * 'a
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  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
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  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
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  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
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  (*booleans*)
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  val equal: ''a -> ''a -> bool
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  val not_equal: ''a -> ''a -> bool
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  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val exists: ('a -> bool) -> 'a list -> bool
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  val forall: ('a -> bool) -> 'a list -> bool
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  val setmp_CRITICAL: 'a Unsynchronized.ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val setmp_thread_data: 'a Universal.tag -> 'a -> 'a -> ('b -> 'c) -> 'b -> 'c
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  (*lists*)
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  val single: 'a -> 'a list
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  val the_single: 'a list -> 'a
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  val singleton: ('a list -> 'b list) -> 'a -> 'b
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  val yield_singleton: ('a list -> 'c -> 'b list * 'c) -> 'a -> 'c -> 'b * 'c
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  val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option
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  val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option
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  val foldl1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val eq_list: ('a * 'a -> bool) -> 'a list * 'a list -> bool
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  val maps: ('a -> 'b list) -> 'a list -> 'b list
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  val filter: ('a -> bool) -> 'a list -> 'a list
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  val filter_out: ('a -> bool) -> 'a list -> 'a list
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  val map_filter: ('a -> 'b option) -> 'a list -> 'b list
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  val take: int -> 'a list -> 'a list
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  val drop: int -> 'a list -> 'a list
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  val chop: int -> 'a list -> 'a list * 'a list
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  val chop_groups: int -> 'a list -> 'a list list
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  val nth: 'a list -> int -> 'a
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  val nth_list: 'a list list -> int -> 'a list
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  val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
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  val nth_drop: int -> 'a list -> 'a list
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  val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
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  val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val map_range: (int -> 'a) -> int -> 'a list
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  val fold_range: (int -> 'a -> 'a) -> int -> 'a -> 'a
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  val split_last: 'a list -> 'a list * 'a
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  val find_first: ('a -> bool) -> 'a list -> 'a option
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  val find_index: ('a -> bool) -> 'a list -> int
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  val get_first: ('a -> 'b option) -> 'a list -> 'b option
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  val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
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  val flat: 'a list list -> 'a list
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  val unflat: 'a list list -> 'b list -> 'b list list
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  val grouped: int -> (('a list -> 'b list) -> 'c list list -> 'd list list) ->
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    ('a -> 'b) -> 'c list -> 'd list
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  val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
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  val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
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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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  val separate: 'a -> 'a list -> 'a list
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  val surround: 'a -> 'a list -> 'a list
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  val replicate: int -> 'a -> 'a list
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  val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
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  val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
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  val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
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  val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
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  val fold_rev2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
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  val forall2: ('a -> 'b -> bool) -> 'a list -> 'b list -> bool
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  val map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list
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  val zip_options: 'a list -> 'b option list -> ('a * 'b) list
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  val ~~ : 'a list * 'b list -> ('a * 'b) list
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  val split_list: ('a * 'b) list -> 'a list * 'b list
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  val burrow_fst: ('a list -> 'b list) -> ('a * 'c) list -> ('b * 'c) list
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  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
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  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
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  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val prefixes1: 'a list -> 'a list list
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  val prefixes: 'a list -> 'a list list
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  val suffixes1: 'a list -> 'a list list
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  val suffixes: 'a list -> 'a list list
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  (*integers*)
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  val upto: int * int -> int list
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  val downto: int * int -> int list
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  val radixpand: int * int -> int list
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  val radixstring: int * string * int -> string
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  val string_of_int: int -> string
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  val signed_string_of_int: int -> string
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  val string_of_indexname: string * int -> string
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  val read_radix_int: int -> string list -> int * string list
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  val read_int: string list -> int * string list
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  val oct_char: string -> string
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  (*strings*)
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  val nth_string: string -> int -> string
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  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
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  val exists_string: (string -> bool) -> string -> bool
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  val forall_string: (string -> bool) -> string -> bool
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  val first_field: string -> string -> (string * string) option
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  val enclose: string -> string -> string -> string
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  val unenclose: string -> string
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  val quote: string -> string
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  val cartouche: string -> string
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  val space_implode: string -> string list -> string
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  val commas: string list -> string
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  val commas_quote: string list -> string
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  val cat_lines: string list -> string
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  val space_explode: string -> string -> string list
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  val split_lines: string -> string list
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  val prefix_lines: string -> string -> string
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  val prefix: string -> string -> string
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  val suffix: string -> string -> string
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  val unprefix: string -> string -> string
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  val unsuffix: string -> string -> string
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  val trim_line: string -> string
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  val replicate_string: int -> string -> string
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  val translate_string: (string -> string) -> string -> string
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  val match_string: string -> string -> bool
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  (*reals*)
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  val string_of_real: real -> string
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  val signed_string_of_real: real -> string
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  (*lists as sets -- see also Pure/General/ord_list.ML*)
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  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
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  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
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  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
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  val union: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
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  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
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  val inter: ('a * 'b -> bool) -> 'b list -> 'a list -> 'a list
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  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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  val subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val eq_set: ('a * 'a -> bool) -> 'a list * 'a list -> bool
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  val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
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  val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
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  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
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  val map_transpose: ('a list -> 'b) -> 'a list list -> 'b list
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  (*lists as multisets*)
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  val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val combine: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
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  val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  (*orders*)
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  val is_equal: order -> bool
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  val rev_order: order -> order
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  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
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  val bool_ord: bool * bool -> order
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  val int_ord: int * int -> order
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  val string_ord: string * string -> order
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  val fast_string_ord: string * string -> order
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  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
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  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
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  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val sort: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_strings: string list -> string list
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  val sort_wrt: ('a -> string) -> 'a list -> 'a list
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  val tag_list: int -> 'a list -> (int * 'a) list
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  val untag_list: (int * 'a) list -> 'a list
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  val order_list: (int * 'a) list -> 'a list
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  (*random numbers*)
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  exception RANDOM
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  val random: unit -> real
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  val random_range: int -> int -> int
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  (*misc*)
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  val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
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  val divide_and_conquer': ('a -> 'b -> ('a list * ('c list * 'b -> 'c * 'b)) * 'b) ->
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    'a -> 'b -> 'c * 'b
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  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
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  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
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  type serial = int
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  val serial: unit -> serial
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  val serial_string: unit -> string
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  eqtype stamp
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  val stamp: unit -> stamp
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  structure Any: sig type T = exn end
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  val cd: string -> unit
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  val pwd: unit -> string
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  val getenv: string -> string
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  val getenv_strict: string -> string
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end;
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signature LIBRARY =
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sig
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  include BASIC_LIBRARY
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  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
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  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
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end;
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structure Library: LIBRARY =
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struct
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(* functions *)
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fun undefined _ = raise Match;
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fun I x = x;
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fun K x = fn _ => x;
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fun curry f x y = f (x, y);
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fun uncurry f (x, y) = f x y;
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(*conditional application*)
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fun b ? f = fn x => if b then f x else x;
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(*composition with multiple args*)
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fun (f oo g) x y = f (g x y);
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fun (f ooo g) x y z = f (g x y z);
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fun (f oooo g) x y z w = f (g x y z w);
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(*function exponentiation: f (... (f x) ...) with n applications of f*)
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fun funpow (0 : int) _ = I
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  | funpow n f = f #> funpow (n - 1) f;
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fun funpow_yield (0 : int) _ x = ([], x)
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  | funpow_yield n f x = x |> f ||>> funpow_yield (n - 1) f |>> op ::;
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(* user errors *)
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exception ERROR of string;
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fun error msg = raise ERROR msg;
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fun cat_error "" msg = error msg
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  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
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fun assert_all pred list msg =
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  let
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    fun ass [] = ()
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      | ass (x :: xs) = if pred x then ass xs else error (msg x);
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  in ass list end;
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(* pairs *)
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fun pair x y = (x, y);
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fun rpair x y = (y, x);
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fun fst (x, y) = x;
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fun snd (x, y) = y;
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fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
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fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
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fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
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fun swap (x, y) = (y, x);
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fun apfst f (x, y) = (f x, y);
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   292
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   293
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   294
wenzelm@233
   295
wenzelm@21395
   296
(* booleans *)
wenzelm@233
   297
wenzelm@21395
   298
(*polymorphic equality*)
wenzelm@233
   299
fun equal x y = x = y;
wenzelm@233
   300
fun not_equal x y = x <> y;
wenzelm@233
   301
wenzelm@21395
   302
(*combining predicates*)
wenzelm@16721
   303
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   304
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   305
wenzelm@25752
   306
val exists = List.exists;
wenzelm@25752
   307
val forall = List.all;
clasohm@0
   308
wenzelm@19644
   309
wenzelm@380
   310
(* flags *)
wenzelm@380
   311
wenzelm@32966
   312
fun setmp_CRITICAL flag value f x =
wenzelm@39616
   313
  NAMED_CRITICAL "setmp" (fn () => Unsynchronized.setmp flag value f x);
wenzelm@23932
   314
wenzelm@25797
   315
fun setmp_thread_data tag orig_data data f x =
wenzelm@26079
   316
  uninterruptible (fn restore_attributes => fn () =>
wenzelm@26079
   317
    let
wenzelm@28122
   318
      val _ = Thread.setLocal (tag, data);
wenzelm@26079
   319
      val result = Exn.capture (restore_attributes f) x;
wenzelm@28122
   320
      val _ = Thread.setLocal (tag, orig_data);
wenzelm@26079
   321
    in Exn.release result end) ();
wenzelm@25797
   322
wenzelm@19644
   323
wenzelm@21395
   324
wenzelm@233
   325
(** lists **)
wenzelm@233
   326
wenzelm@5285
   327
fun single x = [x];
wenzelm@233
   328
wenzelm@20882
   329
fun the_single [x] = x
wenzelm@47060
   330
  | the_single _ = raise List.Empty;
wenzelm@20882
   331
wenzelm@20882
   332
fun singleton f x = the_single (f [x]);
wenzelm@19273
   333
haftmann@25061
   334
fun yield_singleton f x = f [x] #>> the_single;
haftmann@25061
   335
wenzelm@25058
   336
fun perhaps_apply funs arg =
wenzelm@25058
   337
  let
wenzelm@25058
   338
    fun app [] res = res
wenzelm@25058
   339
      | app (f :: fs) (changed, x) =
wenzelm@25058
   340
          (case f x of
wenzelm@25058
   341
            NONE => app fs (changed, x)
wenzelm@25058
   342
          | SOME x' => app fs (true, x'));
wenzelm@25058
   343
  in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   344
wenzelm@25058
   345
fun perhaps_loop f arg =
wenzelm@25058
   346
  let
wenzelm@25058
   347
    fun loop (changed, x) =
wenzelm@25058
   348
      (case f x of
wenzelm@25058
   349
        NONE => (changed, x)
wenzelm@25058
   350
      | SOME x' => loop (true, x'));
wenzelm@25058
   351
  in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   352
wenzelm@233
   353
wenzelm@21395
   354
(* fold -- old versions *)
haftmann@16691
   355
wenzelm@233
   356
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   357
wenzelm@233
   358
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   359
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   360
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   361
  let fun itl (e, [])  = e
wenzelm@233
   362
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   363
  in  itl end;
wenzelm@233
   364
wenzelm@233
   365
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   366
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   367
fun foldr f (l, e) =
wenzelm@233
   368
  let fun itr [] = e
wenzelm@233
   369
        | itr (a::l) = f(a, itr l)
wenzelm@233
   370
  in  itr l  end;
wenzelm@233
   371
berghofe@25681
   372
(*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
berghofe@25681
   373
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@47060
   374
fun foldl1 f [] = raise List.Empty
berghofe@25681
   375
  | foldl1 f (x :: xs) = foldl f (x, xs);
berghofe@25681
   376
wenzelm@233
   377
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   378
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@47060
   379
fun foldr1 f [] = raise List.Empty
wenzelm@20510
   380
  | foldr1 f l =
paulson@20443
   381
      let fun itr [x] = x
wenzelm@20510
   382
            | itr (x::l) = f(x, itr l)
paulson@20443
   383
      in  itr l  end;
wenzelm@233
   384
wenzelm@233
   385
wenzelm@233
   386
(* basic list functions *)
wenzelm@233
   387
wenzelm@20510
   388
fun eq_list eq (list1, list2) =
wenzelm@42403
   389
  pointer_eq (list1, list2) orelse
wenzelm@42403
   390
    let
wenzelm@42403
   391
      fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@42403
   392
        | eq_lst _ = true;
wenzelm@42403
   393
    in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   394
wenzelm@19483
   395
fun maps f [] = []
wenzelm@19483
   396
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   397
haftmann@25538
   398
val filter = List.filter;
haftmann@25538
   399
fun filter_out f = filter (not o f);
haftmann@25538
   400
val map_filter = List.mapPartial;
haftmann@25538
   401
haftmann@33955
   402
fun take (0: int) xs = []
haftmann@33955
   403
  | take _ [] = []
haftmann@34059
   404
  | take n (x :: xs) = x :: take (n - 1) xs;
haftmann@33955
   405
haftmann@33955
   406
fun drop (0: int) xs = xs
haftmann@33955
   407
  | drop _ [] = []
haftmann@34059
   408
  | drop n (x :: xs) = drop (n - 1) xs;
haftmann@33955
   409
wenzelm@24593
   410
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   411
  | chop _ [] = ([], [])
wenzelm@23220
   412
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   413
wenzelm@46891
   414
fun chop_groups n list =
wenzelm@46891
   415
  (case chop (Int.max (n, 1)) list of
wenzelm@46891
   416
    ([], _) => []
wenzelm@46891
   417
  | (g, rest) => g :: chop_groups n rest);
wenzelm@46891
   418
wenzelm@46891
   419
wenzelm@233
   420
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   421
  raise Subscript if list too short*)
haftmann@18011
   422
fun nth xs i = List.nth (xs, i);
wenzelm@233
   423
wenzelm@43278
   424
fun nth_list xss i = nth xss i handle General.Subscript => [];
wenzelm@18461
   425
haftmann@18011
   426
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   427
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
wenzelm@24593
   428
  | nth_map (_: int) _ [] = raise Subscript;
wenzelm@11773
   429
haftmann@24846
   430
fun nth_drop n xs =
haftmann@24846
   431
  List.take (xs, n) @ List.drop (xs, n + 1);
haftmann@24846
   432
haftmann@18514
   433
fun map_index f =
haftmann@18514
   434
  let
haftmann@52271
   435
    fun map_aux (_: int) [] = []
haftmann@52271
   436
      | map_aux i (x :: xs) = f (i, x) :: map_aux (i + 1) xs
haftmann@52271
   437
  in map_aux 0 end;
haftmann@18514
   438
haftmann@21118
   439
fun fold_index f =
haftmann@21118
   440
  let
wenzelm@24593
   441
    fun fold_aux (_: int) [] y = y
haftmann@52271
   442
      | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y)
haftmann@21118
   443
  in fold_aux 0 end;
haftmann@21118
   444
haftmann@33063
   445
fun map_range f i =
haftmann@33063
   446
  let
haftmann@52271
   447
    fun map_aux (k: int) =
haftmann@52271
   448
      if k < i then f k :: map_aux (k + 1) else []
haftmann@52271
   449
  in map_aux 0 end;
haftmann@52271
   450
haftmann@52271
   451
fun fold_range f i =
haftmann@52271
   452
  let
haftmann@52271
   453
    fun fold_aux (k: int) y =
haftmann@52271
   454
      if k < i then fold_aux (k + 1) (f k y) else y
haftmann@52271
   455
  in fold_aux 0 end;
haftmann@52271
   456
haftmann@33063
   457
wenzelm@3762
   458
(*rear decomposition*)
wenzelm@47060
   459
fun split_last [] = raise List.Empty
wenzelm@3762
   460
  | split_last [x] = ([], x)
wenzelm@3762
   461
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   462
wenzelm@46891
   463
(*find first element satisfying predicate*)
wenzelm@46891
   464
val find_first = List.find;
wenzelm@46891
   465
ballarin@29209
   466
(*find position of first element satisfying a predicate*)
wenzelm@4212
   467
fun find_index pred =
wenzelm@24593
   468
  let fun find (_: int) [] = ~1
wenzelm@4212
   469
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   470
  in find 0 end;
wenzelm@3762
   471
wenzelm@4916
   472
(*get first element by lookup function*)
skalberg@15531
   473
fun get_first _ [] = NONE
wenzelm@4916
   474
  | get_first f (x :: xs) =
wenzelm@4916
   475
      (case f x of
skalberg@15531
   476
        NONE => get_first f xs
wenzelm@4916
   477
      | some => some);
wenzelm@4916
   478
haftmann@19233
   479
fun get_index f =
haftmann@19233
   480
  let
wenzelm@24593
   481
    fun get (_: int) [] = NONE
wenzelm@19461
   482
      | get i (x :: xs) =
wenzelm@46838
   483
          (case f x of
wenzelm@46838
   484
            NONE => get (i + 1) xs
wenzelm@46838
   485
          | SOME y => SOME (i, y))
haftmann@19233
   486
  in get 0 end;
haftmann@19233
   487
skalberg@15531
   488
val flat = List.concat;
wenzelm@233
   489
wenzelm@12136
   490
fun unflat (xs :: xss) ys =
wenzelm@19424
   491
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   492
      in ps :: unflat xss qs end
wenzelm@12136
   493
  | unflat [] [] = []
wenzelm@40722
   494
  | unflat _ _ = raise ListPair.UnequalLengths;
wenzelm@12136
   495
wenzelm@46891
   496
fun grouped n comb f = chop_groups n #> comb (map f) #> flat;
wenzelm@46891
   497
wenzelm@21479
   498
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   499
wenzelm@24864
   500
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   501
haftmann@18549
   502
fun fold_burrow f xss s =
haftmann@18549
   503
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   504
wenzelm@233
   505
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   506
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   507
  | separate _ xs = xs;
wenzelm@233
   508
wenzelm@25980
   509
fun surround s (x :: xs) = s :: x :: surround s xs
wenzelm@25980
   510
  | surround s [] = [s];
wenzelm@25980
   511
wenzelm@233
   512
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   513
fun replicate (n: int) x =
wenzelm@233
   514
  let fun rep (0, xs) = xs
wenzelm@233
   515
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   516
  in
skalberg@15570
   517
    if n < 0 then raise Subscript
wenzelm@233
   518
    else rep (n, [])
wenzelm@233
   519
  end;
wenzelm@233
   520
wenzelm@4248
   521
wenzelm@25549
   522
(* direct product *)
wenzelm@25549
   523
haftmann@25538
   524
fun map_product f _ [] = []
haftmann@25538
   525
  | map_product f [] _ = []
haftmann@25538
   526
  | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
wenzelm@233
   527
haftmann@25538
   528
fun fold_product f _ [] z = z
haftmann@25538
   529
  | fold_product f [] _ z = z
haftmann@25538
   530
  | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
wenzelm@233
   531
wenzelm@25549
   532
wenzelm@25549
   533
(* lists of pairs *)
wenzelm@233
   534
haftmann@18330
   535
fun map2 _ [] [] = []
haftmann@18330
   536
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
wenzelm@40722
   537
  | map2 _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   538
wenzelm@23220
   539
fun fold2 f [] [] z = z
wenzelm@23220
   540
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@40722
   541
  | fold2 f _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   542
wenzelm@40721
   543
fun fold_rev2 f [] [] z = z
wenzelm@40721
   544
  | fold_rev2 f (x :: xs) (y :: ys) z = f x y (fold_rev2 f xs ys z)
wenzelm@40722
   545
  | fold_rev2 f _ _ _ = raise ListPair.UnequalLengths;
wenzelm@40721
   546
haftmann@40564
   547
fun forall2 P [] [] = true
haftmann@40564
   548
  | forall2 P (x :: xs) (y :: ys) = P x y andalso forall2 P xs ys
wenzelm@40733
   549
  | forall2 P _ _ = raise ListPair.UnequalLengths;
haftmann@40564
   550
haftmann@25943
   551
fun map_split f [] = ([], [])
haftmann@25943
   552
  | map_split f (x :: xs) =
haftmann@25943
   553
      let
haftmann@25943
   554
        val (y, w) = f x;
haftmann@25943
   555
        val (ys, ws) = map_split f xs;
haftmann@25943
   556
      in (y :: ys, w :: ws) end;
haftmann@25943
   557
wenzelm@19799
   558
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   559
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   560
  | zip_options _ [] = []
wenzelm@40722
   561
  | zip_options [] _ = raise ListPair.UnequalLengths;
wenzelm@4956
   562
wenzelm@233
   563
(*combine two lists forming a list of pairs:
wenzelm@233
   564
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   565
fun [] ~~ [] = []
wenzelm@233
   566
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@40722
   567
  | _ ~~ _ = raise ListPair.UnequalLengths;
wenzelm@233
   568
wenzelm@233
   569
(*inverse of ~~; the old 'split':
wenzelm@233
   570
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   571
val split_list = ListPair.unzip;
wenzelm@233
   572
haftmann@28347
   573
fun burrow_fst f xs = split_list xs |>> f |> op ~~;
haftmann@28347
   574
wenzelm@233
   575
wenzelm@233
   576
(* prefixes, suffixes *)
wenzelm@233
   577
haftmann@18441
   578
fun is_prefix _ [] _ = true
haftmann@18441
   579
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   580
  | is_prefix eq _ _ = false;
wenzelm@233
   581
wenzelm@233
   582
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   583
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   584
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   585
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   586
        | take (rxs, x :: xs) =
wenzelm@255
   587
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   588
  in  take([], xs)  end;
wenzelm@233
   589
haftmann@20108
   590
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   591
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   592
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   593
      if eq (x, y) then
haftmann@20108
   594
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   595
        in (x :: ps', xys'') end
haftmann@20108
   596
      else ([], (xs, ys));
haftmann@20108
   597
wenzelm@233
   598
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   599
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   600
fun take_suffix _ [] = ([], [])
wenzelm@233
   601
  | take_suffix pred (x :: xs) =
wenzelm@233
   602
      (case take_suffix pred xs of
wenzelm@233
   603
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   604
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   605
wenzelm@12249
   606
fun prefixes1 [] = []
wenzelm@12249
   607
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   608
wenzelm@19011
   609
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   610
wenzelm@12249
   611
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   612
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   613
wenzelm@23220
   614
wenzelm@23220
   615
wenzelm@233
   616
(** integers **)
wenzelm@233
   617
wenzelm@233
   618
(* lists of integers *)
wenzelm@233
   619
wenzelm@233
   620
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   621
fun ((i: int) upto j) =
wenzelm@21859
   622
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   623
wenzelm@233
   624
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   625
fun ((i: int) downto j) =
wenzelm@21859
   626
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   627
wenzelm@233
   628
wenzelm@233
   629
(* convert integers to strings *)
wenzelm@233
   630
wenzelm@233
   631
(*expand the number in the given base;
wenzelm@233
   632
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   633
fun radixpand (base, num) : int list =
wenzelm@233
   634
  let
wenzelm@233
   635
    fun radix (n, tail) =
wenzelm@233
   636
      if n < base then n :: tail
wenzelm@233
   637
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   638
  in radix (num, []) end;
wenzelm@233
   639
wenzelm@233
   640
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   641
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   642
fun radixstring (base, zerochar, num) =
wenzelm@233
   643
  let val offset = ord zerochar;
wenzelm@233
   644
      fun chrof n = chr (offset + n)
wenzelm@233
   645
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   646
wenzelm@233
   647
wenzelm@41492
   648
local
wenzelm@41492
   649
  val zero = ord "0";
wenzelm@41494
   650
  val small = 10000: int;
wenzelm@41492
   651
  val small_table = Vector.tabulate (small, Int.toString);
wenzelm@41492
   652
in
wenzelm@41492
   653
wenzelm@41492
   654
fun string_of_int i =
wenzelm@41492
   655
  if i < 0 then Int.toString i
wenzelm@41492
   656
  else if i < 10 then chr (zero + i)
wenzelm@41492
   657
  else if i < small then Vector.sub (small_table, i)
wenzelm@41492
   658
  else Int.toString i;
wenzelm@41492
   659
wenzelm@41492
   660
end;
wenzelm@233
   661
wenzelm@21942
   662
fun signed_string_of_int i =
wenzelm@21942
   663
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   664
wenzelm@23220
   665
fun string_of_indexname (a, 0) = a
wenzelm@23220
   666
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   667
wenzelm@233
   668
wenzelm@14826
   669
(* read integers *)
wenzelm@14826
   670
wenzelm@24630
   671
fun read_radix_int radix cs =
wenzelm@20095
   672
  let
wenzelm@20095
   673
    val zero = ord "0";
wenzelm@20095
   674
    val limit = zero + radix;
wenzelm@20095
   675
    fun scan (num, []) = (num, [])
wenzelm@20095
   676
      | scan (num, c :: cs) =
wenzelm@50637
   677
          if zero <= ord c andalso ord c < limit then
wenzelm@50637
   678
            scan (radix * num + (ord c - zero), cs)
wenzelm@50637
   679
          else (num, c :: cs);
wenzelm@24630
   680
  in scan (0, cs) end;
wenzelm@14826
   681
wenzelm@24630
   682
val read_int = read_radix_int 10;
wenzelm@14826
   683
wenzelm@40627
   684
fun oct_char s = chr (#1 (read_radix_int 8 (raw_explode s)));
wenzelm@14826
   685
wenzelm@14826
   686
wenzelm@14826
   687
wenzelm@233
   688
(** strings **)
wenzelm@233
   689
wenzelm@16188
   690
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   691
haftmann@18011
   692
fun nth_string str i =
wenzelm@6959
   693
  (case try String.substring (str, i, 1) of
skalberg@15531
   694
    SOME s => s
skalberg@15570
   695
  | NONE => raise Subscript);
wenzelm@6312
   696
wenzelm@16188
   697
fun fold_string f str x0 =
wenzelm@6282
   698
  let
wenzelm@6282
   699
    val n = size str;
wenzelm@16188
   700
    fun iter (x, i) =
wenzelm@16188
   701
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   702
  in iter (x0, 0) end;
wenzelm@6282
   703
wenzelm@14968
   704
fun exists_string pred str =
wenzelm@14968
   705
  let
wenzelm@14968
   706
    val n = size str;
wenzelm@14968
   707
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   708
  in ex 0 end;
wenzelm@6312
   709
wenzelm@16188
   710
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   711
wenzelm@28025
   712
fun first_field sep str =
wenzelm@28022
   713
  let
wenzelm@28025
   714
    val n = size sep;
wenzelm@28022
   715
    val len = size str;
wenzelm@28022
   716
    fun find i =
wenzelm@28022
   717
      if i + n > len then NONE
wenzelm@28025
   718
      else if String.substring (str, i, n) = sep then SOME i
wenzelm@28022
   719
      else find (i + 1);
wenzelm@28025
   720
  in
wenzelm@28025
   721
    (case find 0 of
wenzelm@28025
   722
      NONE => NONE
wenzelm@28025
   723
    | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
wenzelm@28025
   724
  end;
wenzelm@28022
   725
lcp@512
   726
(*enclose in brackets*)
lcp@512
   727
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   728
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   729
wenzelm@233
   730
(*simple quoting (does not escape special chars)*)
lcp@512
   731
val quote = enclose "\"" "\"";
wenzelm@233
   732
wenzelm@55033
   733
val cartouche = enclose "\\<open>" "\\<close>";
wenzelm@55033
   734
wenzelm@233
   735
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   736
wenzelm@255
   737
val commas = space_implode ", ";
wenzelm@380
   738
val commas_quote = commas o map quote;
wenzelm@255
   739
wenzelm@255
   740
val cat_lines = space_implode "\n";
wenzelm@233
   741
wenzelm@4212
   742
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   743
fun space_explode _ "" = []
paulson@21899
   744
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   745
wenzelm@3832
   746
val split_lines = space_explode "\n";
wenzelm@3832
   747
wenzelm@14826
   748
fun prefix_lines "" txt = txt
wenzelm@14826
   749
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   750
wenzelm@18681
   751
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   752
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   753
wenzelm@18681
   754
fun unprefix prfx s =
wenzelm@18681
   755
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   756
  else raise Fail "unprefix";
wenzelm@18681
   757
wenzelm@16188
   758
fun unsuffix sffx s =
wenzelm@17061
   759
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   760
  else raise Fail "unsuffix";
wenzelm@5285
   761
wenzelm@47499
   762
val trim_line = perhaps (try (unsuffix "\n"));
wenzelm@47499
   763
wenzelm@24593
   764
fun replicate_string (0: int) _ = ""
wenzelm@10951
   765
  | replicate_string 1 a = a
wenzelm@10951
   766
  | replicate_string k a =
wenzelm@10951
   767
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   768
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   769
haftmann@31250
   770
fun translate_string f = String.translate (f o String.str);
haftmann@31250
   771
kleing@29882
   772
(*crude matching of str against simple glob pat*)
kleing@29882
   773
fun match_string pat str =
kleing@29882
   774
  let
kleing@29882
   775
    fun match [] _ = true
kleing@29882
   776
      | match (p :: ps) s =
kleing@29882
   777
          size p <= size s andalso
kleing@29882
   778
            (case try (unprefix p) s of
kleing@29882
   779
              SOME s' => match ps s'
kleing@29882
   780
            | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
kleing@29882
   781
  in match (space_explode "*" pat) str end;
wenzelm@23220
   782
wenzelm@35976
   783
wenzelm@41516
   784
(** reals **)
wenzelm@41516
   785
wenzelm@41516
   786
val string_of_real = Real.fmt (StringCvt.GEN NONE);
wenzelm@41516
   787
wenzelm@41516
   788
fun signed_string_of_real x =
wenzelm@41516
   789
  if x < 0.0 then "-" ^ string_of_real (~ x) else string_of_real x;
wenzelm@41516
   790
wenzelm@41516
   791
wenzelm@35976
   792
wenzelm@16492
   793
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   794
wenzelm@26439
   795
(* canonical operations *)
wenzelm@26439
   796
wenzelm@18923
   797
fun member eq list x =
wenzelm@18923
   798
  let
wenzelm@18923
   799
    fun memb [] = false
wenzelm@18923
   800
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   801
  in memb list end;
berghofe@1576
   802
wenzelm@18923
   803
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   804
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   805
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   806
haftmann@33049
   807
fun inter eq xs = filter (member eq xs);
haftmann@33049
   808
haftmann@33042
   809
fun union eq = fold (insert eq);
wenzelm@19301
   810
fun subtract eq = fold (remove eq);
wenzelm@19301
   811
wenzelm@30572
   812
fun merge eq (xs, ys) =
wenzelm@30572
   813
  if pointer_eq (xs, ys) then xs
wenzelm@30572
   814
  else if null xs then ys
wenzelm@30572
   815
  else fold_rev (insert eq) ys xs;
clasohm@0
   816
wenzelm@26439
   817
haftmann@33050
   818
(* subset and set equality *)
haftmann@33050
   819
haftmann@33038
   820
fun subset eq (xs, ys) = forall (member eq ys) xs;
berghofe@1576
   821
haftmann@33038
   822
fun eq_set eq (xs, ys) =
haftmann@20348
   823
  eq_list eq (xs, ys) orelse
haftmann@33038
   824
    (subset eq (xs, ys) andalso subset (eq o swap) (ys, xs));
wenzelm@19301
   825
wenzelm@265
   826
wenzelm@233
   827
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   828
  first of equal elements*)
wenzelm@19046
   829
fun distinct eq lst =
wenzelm@233
   830
  let
wenzelm@233
   831
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   832
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   833
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   834
          else dist (x :: rev_seen, xs);
wenzelm@19046
   835
  in dist ([], lst) end;
wenzelm@233
   836
wenzelm@255
   837
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   838
  order, takes first of equal elements*)
wenzelm@18966
   839
fun duplicates eq lst =
wenzelm@255
   840
  let
wenzelm@255
   841
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   842
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   843
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   844
            dups (rev_dups, xs)
wenzelm@255
   845
          else dups (x :: rev_dups, xs);
wenzelm@18966
   846
  in dups ([], lst) end;
wenzelm@255
   847
wenzelm@16878
   848
fun has_duplicates eq =
wenzelm@16878
   849
  let
wenzelm@16878
   850
    fun dups [] = false
wenzelm@16878
   851
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   852
  in dups end;
wenzelm@16878
   853
wenzelm@255
   854
haftmann@32352
   855
(* matrices *)
haftmann@32352
   856
haftmann@32352
   857
fun map_transpose f xss =
haftmann@32352
   858
  let
wenzelm@40722
   859
    val n =
wenzelm@40722
   860
      (case distinct (op =) (map length xss) of
wenzelm@40722
   861
        [] => 0
haftmann@32352
   862
      | [n] => n
wenzelm@40722
   863
      | _ => raise ListPair.UnequalLengths);
haftmann@33206
   864
  in map_range (fn m => f (map (fn xs => nth xs m) xss)) n end;
haftmann@32352
   865
haftmann@32352
   866
wenzelm@23220
   867
nipkow@22142
   868
(** lists as multisets **)
nipkow@22142
   869
haftmann@33078
   870
fun remove1 eq x [] = []
haftmann@33078
   871
  | remove1 eq x (y :: ys) = if eq (x, y) then ys else y :: remove1 eq x ys;
nipkow@22142
   872
haftmann@33078
   873
fun combine eq xs ys = fold (remove1 eq) ys xs @ ys;
wenzelm@233
   874
haftmann@33079
   875
fun submultiset _ ([], _)  = true
haftmann@33079
   876
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
haftmann@33079
   877
clasohm@0
   878
clasohm@0
   879
wenzelm@2506
   880
(** orders **)
wenzelm@2506
   881
wenzelm@18966
   882
fun is_equal EQUAL = true
wenzelm@18966
   883
  | is_equal _ = false;
wenzelm@18966
   884
wenzelm@4445
   885
fun rev_order LESS = GREATER
wenzelm@4445
   886
  | rev_order EQUAL = EQUAL
wenzelm@4445
   887
  | rev_order GREATER = LESS;
wenzelm@4445
   888
wenzelm@4479
   889
(*assume rel is a linear strict order*)
wenzelm@4445
   890
fun make_ord rel (x, y) =
wenzelm@4445
   891
  if rel (x, y) then LESS
wenzelm@4445
   892
  else if rel (y, x) then GREATER
wenzelm@4445
   893
  else EQUAL;
wenzelm@4445
   894
wenzelm@25224
   895
fun bool_ord (false, true) = LESS
wenzelm@25224
   896
  | bool_ord (true, false) = GREATER
wenzelm@25224
   897
  | bool_ord _ = EQUAL;
wenzelm@25224
   898
wenzelm@15051
   899
val int_ord = Int.compare;
wenzelm@15051
   900
val string_ord = String.compare;
wenzelm@2506
   901
wenzelm@16676
   902
fun fast_string_ord (s1, s2) =
wenzelm@43793
   903
  if pointer_eq (s1, s2) then EQUAL
wenzelm@43793
   904
  else (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   905
wenzelm@16492
   906
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   907
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   908
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   909
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   910
wenzelm@4343
   911
(*lexicographic product*)
wenzelm@4343
   912
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   913
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   914
wenzelm@4343
   915
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   916
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   917
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   918
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   919
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   920
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   921
wenzelm@4343
   922
(*lexicographic product of lists*)
wenzelm@4343
   923
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   924
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   925
wenzelm@2506
   926
wenzelm@4621
   927
(* sorting *)
wenzelm@4621
   928
wenzelm@48271
   929
(*stable mergesort -- preserves order of equal elements*)
wenzelm@48271
   930
fun mergesort unique ord =
wenzelm@4621
   931
  let
wenzelm@48271
   932
    fun merge (xs as x :: xs') (ys as y :: ys') =
wenzelm@48271
   933
          (case ord (x, y) of
wenzelm@48271
   934
            LESS => x :: merge xs' ys
wenzelm@48271
   935
          | EQUAL =>
wenzelm@48271
   936
              if unique then merge xs ys'
wenzelm@48271
   937
              else x :: merge xs' ys
wenzelm@48271
   938
          | GREATER => y :: merge xs ys')
wenzelm@48271
   939
      | merge [] ys = ys
wenzelm@48271
   940
      | merge xs [] = xs;
wenzelm@48271
   941
wenzelm@48271
   942
    fun merge_all [xs] = xs
wenzelm@48271
   943
      | merge_all xss = merge_all (merge_pairs xss)
wenzelm@48271
   944
    and merge_pairs (xs :: ys :: xss) = merge xs ys :: merge_pairs xss
wenzelm@48271
   945
      | merge_pairs xss = xss;
wenzelm@48271
   946
wenzelm@48271
   947
    fun runs (x :: y :: xs) =
wenzelm@18427
   948
          (case ord (x, y) of
wenzelm@48271
   949
             LESS => ascending y [x] xs
wenzelm@48271
   950
           | EQUAL =>
wenzelm@48271
   951
               if unique then runs (x :: xs)
wenzelm@48271
   952
               else ascending y [x] xs
wenzelm@48271
   953
           | GREATER => descending y [x] xs)
wenzelm@48271
   954
      | runs xs = [xs]
wenzelm@4621
   955
wenzelm@48271
   956
    and ascending x xs (zs as y :: ys) =
wenzelm@48271
   957
          (case ord (x, y) of
wenzelm@48271
   958
             LESS => ascending y (x :: xs) ys
wenzelm@48271
   959
           | EQUAL =>
wenzelm@48271
   960
               if unique then ascending x xs ys
wenzelm@48271
   961
               else ascending y (x :: xs) ys
wenzelm@48271
   962
           | GREATER => rev (x :: xs) :: runs zs)
wenzelm@48271
   963
      | ascending x xs [] = [rev (x :: xs)]
wenzelm@48271
   964
wenzelm@48271
   965
    and descending x xs (zs as y :: ys) =
wenzelm@48271
   966
          (case ord (x, y) of
wenzelm@48271
   967
             GREATER => descending y (x :: xs) ys
wenzelm@48271
   968
           | EQUAL =>
wenzelm@48271
   969
               if unique then descending x xs ys
wenzelm@48271
   970
               else (x :: xs) :: runs zs
wenzelm@48271
   971
           | LESS => (x :: xs) :: runs zs)
wenzelm@48271
   972
      | descending x xs [] = [x :: xs];
wenzelm@48271
   973
wenzelm@48271
   974
  in merge_all o runs end;
wenzelm@48271
   975
wenzelm@48271
   976
fun sort ord = mergesort false ord;
wenzelm@48271
   977
fun sort_distinct ord = mergesort true ord;
wenzelm@18427
   978
wenzelm@4621
   979
val sort_strings = sort string_ord;
wenzelm@44617
   980
fun sort_wrt key xs = sort (string_ord o pairself key) xs;
wenzelm@4621
   981
wenzelm@4621
   982
wenzelm@30558
   983
(* items tagged by integer index *)
wenzelm@30558
   984
wenzelm@30558
   985
(*insert tags*)
wenzelm@30558
   986
fun tag_list k [] = []
haftmann@30570
   987
  | tag_list k (x :: xs) = (k:int, x) :: tag_list (k + 1) xs;
wenzelm@30558
   988
wenzelm@30558
   989
(*remove tags and suppress duplicates -- list is assumed sorted!*)
wenzelm@30558
   990
fun untag_list [] = []
wenzelm@30558
   991
  | untag_list [(k: int, x)] = [x]
wenzelm@30558
   992
  | untag_list ((k, x) :: (rest as (k', x') :: _)) =
wenzelm@30558
   993
      if k = k' then untag_list rest
wenzelm@30558
   994
      else x :: untag_list rest;
wenzelm@30558
   995
wenzelm@30558
   996
(*return list elements in original order*)
wenzelm@30558
   997
fun order_list list = untag_list (sort (int_ord o pairself fst) list);
wenzelm@30558
   998
wenzelm@30558
   999
wenzelm@2506
  1000
berghofe@14106
  1001
(** random numbers **)
berghofe@14106
  1002
berghofe@14106
  1003
exception RANDOM;
berghofe@14106
  1004
berghofe@14618
  1005
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1006
berghofe@14106
  1007
local
berghofe@14106
  1008
  val a = 16807.0;
berghofe@14106
  1009
  val m = 2147483647.0;
wenzelm@32737
  1010
  val random_seed = Unsynchronized.ref 1.0;
berghofe@14106
  1011
in
berghofe@14106
  1012
wenzelm@23922
  1013
fun random () = CRITICAL (fn () =>
wenzelm@23922
  1014
  let val r = rmod (a * ! random_seed) m
wenzelm@23922
  1015
  in (random_seed := r; r) end);
berghofe@14106
  1016
berghofe@14106
  1017
end;
berghofe@14106
  1018
berghofe@14106
  1019
fun random_range l h =
berghofe@14106
  1020
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1021
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1022
berghofe@14106
  1023
wenzelm@23220
  1024
wenzelm@4621
  1025
(** misc **)
wenzelm@233
  1026
wenzelm@19644
  1027
fun divide_and_conquer decomp x =
wenzelm@19644
  1028
  let val (ys, recomb) = decomp x
wenzelm@19644
  1029
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1030
wenzelm@32978
  1031
fun divide_and_conquer' decomp x s =
wenzelm@32978
  1032
  let val ((ys, recomb), s') = decomp x s
wenzelm@32978
  1033
  in recomb (fold_map (divide_and_conquer' decomp) ys s') end;
wenzelm@32978
  1034
clasohm@0
  1035
wenzelm@233
  1036
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1037
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1038
fun partition_list p i j =
wenzelm@37851
  1039
  let
wenzelm@37851
  1040
    fun part (k: int) xs =
wenzelm@37851
  1041
      if k > j then
wenzelm@37851
  1042
        (case xs of
wenzelm@37851
  1043
          [] => []
wenzelm@37851
  1044
        | _ => raise Fail "partition_list")
wenzelm@37851
  1045
      else
wenzelm@37851
  1046
        let val (ns, rest) = List.partition (p k) xs
wenzelm@37851
  1047
        in ns :: part (k + 1) rest end;
wenzelm@37851
  1048
  in part (i: int) end;
clasohm@0
  1049
wenzelm@37851
  1050
fun partition_eq (eq: 'a * 'a -> bool) =
wenzelm@19691
  1051
  let
wenzelm@19691
  1052
    fun part [] = []
wenzelm@19691
  1053
      | part (x :: ys) =
wenzelm@19691
  1054
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@37851
  1055
          in (x :: xs) :: part xs' end;
wenzelm@19691
  1056
  in part end;
wenzelm@19691
  1057
wenzelm@19691
  1058
wenzelm@45626
  1059
(* serial numbers and abstract stamps *)
wenzelm@16439
  1060
wenzelm@16439
  1061
type serial = int;
wenzelm@25702
  1062
val serial = Multithreading.serial;
wenzelm@19512
  1063
val serial_string = string_of_int o serial;
wenzelm@19512
  1064
wenzelm@45626
  1065
datatype stamp = Stamp of serial;
wenzelm@45626
  1066
fun stamp () = Stamp (serial ());
wenzelm@45626
  1067
wenzelm@16535
  1068
wenzelm@51368
  1069
(* values of any type *)
wenzelm@16535
  1070
wenzelm@16535
  1071
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1072
  constructors at any time*)
wenzelm@51368
  1073
structure Any = struct type T = exn end;
wenzelm@16535
  1074
wenzelm@43603
  1075
wenzelm@43603
  1076
(* current directory *)
wenzelm@43603
  1077
wenzelm@43603
  1078
val cd = OS.FileSys.chDir;
wenzelm@43603
  1079
val pwd = OS.FileSys.getDir;
wenzelm@43603
  1080
wenzelm@43603
  1081
wenzelm@43603
  1082
(* getenv *)
wenzelm@43603
  1083
wenzelm@43603
  1084
fun getenv x =
wenzelm@43603
  1085
  (case OS.Process.getEnv x of
wenzelm@43603
  1086
    NONE => ""
wenzelm@43603
  1087
  | SOME y => y);
wenzelm@43603
  1088
wenzelm@43603
  1089
fun getenv_strict x =
wenzelm@43603
  1090
  (case getenv x of
wenzelm@43603
  1091
    "" => error ("Undefined Isabelle environment variable: " ^ quote x)
wenzelm@43603
  1092
  | y => y);
wenzelm@43603
  1093
clasohm@1364
  1094
end;
clasohm@1364
  1095
wenzelm@32188
  1096
structure Basic_Library: BASIC_LIBRARY = Library;
wenzelm@32188
  1097
open Basic_Library;
wenzelm@40722
  1098