src/Pure/library.ML
author wenzelm
Thu Aug 15 16:02:47 2019 +0200 (9 months ago)
changeset 70533 031620901fcd
parent 70464 2d6a489adb01
child 70586 57df8a85317a
permissions -rw-r--r--
support for (fully reconstructed) proof terms in Scala;
proper cache_typs;
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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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infixr 0 <<<
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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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  (*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 apply2: ('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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  (*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 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 take_prefix: ('a -> bool) -> 'a list -> 'a list
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  val drop_prefix: ('a -> bool) -> 'a list -> 'a list
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  val chop_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val take_suffix: ('a -> bool) -> 'a list -> 'a list
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  val drop_suffix: ('a -> bool) -> 'a list -> 'a list
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  val chop_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
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  val chop_common_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b 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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  val trim: ('a -> bool) -> 'a list -> 'a 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 hex_digit: int -> string
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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 plain_words: string -> string
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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 trim_split_lines: string -> string list
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  val normalize_lines: 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 encode_lines: string -> string
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  val decode_lines: string -> string
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  val align_right: string -> int -> 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 is_less: order -> bool
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  val is_less_equal: order -> bool
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  val is_greater: order -> bool
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  val is_greater_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 <<< : ('a -> order) * ('a -> order) -> 'a -> 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_by: ('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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  (*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 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) _ x = x
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  | funpow n f x = funpow (n - 1) f (f x);
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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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(* 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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fun apsnd f (x, y) = (x, f y);
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fun apply2 f (x, y) = (f x, f y);
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(* booleans *)
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(*polymorphic equality*)
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fun equal x y = x = y;
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fun not_equal x y = x <> y;
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(*combining predicates*)
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fun p orf q = fn x => p x orelse q x;
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fun p andf q = fn x => p x andalso q x;
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wenzelm@25752
   292
val exists = List.exists;
wenzelm@25752
   293
val forall = List.all;
clasohm@0
   294
wenzelm@19644
   295
wenzelm@21395
   296
wenzelm@233
   297
(** lists **)
wenzelm@233
   298
wenzelm@5285
   299
fun single x = [x];
wenzelm@233
   300
wenzelm@20882
   301
fun the_single [x] = x
wenzelm@47060
   302
  | the_single _ = raise List.Empty;
wenzelm@20882
   303
wenzelm@20882
   304
fun singleton f x = the_single (f [x]);
wenzelm@19273
   305
haftmann@25061
   306
fun yield_singleton f x = f [x] #>> the_single;
haftmann@25061
   307
wenzelm@25058
   308
fun perhaps_apply funs arg =
wenzelm@25058
   309
  let
wenzelm@25058
   310
    fun app [] res = res
wenzelm@25058
   311
      | app (f :: fs) (changed, x) =
wenzelm@25058
   312
          (case f x of
wenzelm@25058
   313
            NONE => app fs (changed, x)
wenzelm@25058
   314
          | SOME x' => app fs (true, x'));
wenzelm@25058
   315
  in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   316
wenzelm@25058
   317
fun perhaps_loop f arg =
wenzelm@25058
   318
  let
wenzelm@25058
   319
    fun loop (changed, x) =
wenzelm@25058
   320
      (case f x of
wenzelm@25058
   321
        NONE => (changed, x)
wenzelm@25058
   322
      | SOME x' => loop (true, x'));
wenzelm@25058
   323
  in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   324
wenzelm@233
   325
wenzelm@21395
   326
(* fold -- old versions *)
haftmann@16691
   327
wenzelm@233
   328
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   329
wenzelm@233
   330
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   331
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   332
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   333
  let fun itl (e, [])  = e
wenzelm@233
   334
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   335
  in  itl end;
wenzelm@233
   336
wenzelm@233
   337
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   338
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   339
fun foldr f (l, e) =
wenzelm@233
   340
  let fun itr [] = e
wenzelm@233
   341
        | itr (a::l) = f(a, itr l)
wenzelm@233
   342
  in  itr l  end;
wenzelm@233
   343
berghofe@25681
   344
(*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
berghofe@25681
   345
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@47060
   346
fun foldl1 f [] = raise List.Empty
berghofe@25681
   347
  | foldl1 f (x :: xs) = foldl f (x, xs);
berghofe@25681
   348
wenzelm@233
   349
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   350
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@47060
   351
fun foldr1 f [] = raise List.Empty
wenzelm@20510
   352
  | foldr1 f l =
paulson@20443
   353
      let fun itr [x] = x
wenzelm@20510
   354
            | itr (x::l) = f(x, itr l)
paulson@20443
   355
      in  itr l  end;
wenzelm@233
   356
wenzelm@233
   357
wenzelm@233
   358
(* basic list functions *)
wenzelm@233
   359
wenzelm@20510
   360
fun eq_list eq (list1, list2) =
wenzelm@42403
   361
  pointer_eq (list1, list2) orelse
wenzelm@42403
   362
    let
wenzelm@42403
   363
      fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@42403
   364
        | eq_lst _ = true;
wenzelm@42403
   365
    in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   366
wenzelm@19483
   367
fun maps f [] = []
wenzelm@19483
   368
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   369
haftmann@25538
   370
val filter = List.filter;
haftmann@25538
   371
fun filter_out f = filter (not o f);
haftmann@25538
   372
val map_filter = List.mapPartial;
haftmann@25538
   373
haftmann@33955
   374
fun take (0: int) xs = []
haftmann@33955
   375
  | take _ [] = []
haftmann@34059
   376
  | take n (x :: xs) = x :: take (n - 1) xs;
haftmann@33955
   377
haftmann@33955
   378
fun drop (0: int) xs = xs
haftmann@33955
   379
  | drop _ [] = []
haftmann@34059
   380
  | drop n (x :: xs) = drop (n - 1) xs;
haftmann@33955
   381
wenzelm@24593
   382
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   383
  | chop _ [] = ([], [])
wenzelm@23220
   384
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   385
wenzelm@46891
   386
fun chop_groups n list =
wenzelm@46891
   387
  (case chop (Int.max (n, 1)) list of
wenzelm@46891
   388
    ([], _) => []
wenzelm@46891
   389
  | (g, rest) => g :: chop_groups n rest);
wenzelm@46891
   390
wenzelm@46891
   391
wenzelm@233
   392
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   393
  raise Subscript if list too short*)
haftmann@18011
   394
fun nth xs i = List.nth (xs, i);
wenzelm@233
   395
wenzelm@43278
   396
fun nth_list xss i = nth xss i handle General.Subscript => [];
wenzelm@18461
   397
haftmann@18011
   398
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   399
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
wenzelm@24593
   400
  | nth_map (_: int) _ [] = raise Subscript;
wenzelm@11773
   401
haftmann@24846
   402
fun nth_drop n xs =
haftmann@24846
   403
  List.take (xs, n) @ List.drop (xs, n + 1);
haftmann@24846
   404
haftmann@18514
   405
fun map_index f =
haftmann@18514
   406
  let
haftmann@52271
   407
    fun map_aux (_: int) [] = []
haftmann@52271
   408
      | map_aux i (x :: xs) = f (i, x) :: map_aux (i + 1) xs
haftmann@52271
   409
  in map_aux 0 end;
haftmann@18514
   410
haftmann@21118
   411
fun fold_index f =
haftmann@21118
   412
  let
wenzelm@24593
   413
    fun fold_aux (_: int) [] y = y
haftmann@52271
   414
      | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y)
haftmann@21118
   415
  in fold_aux 0 end;
haftmann@21118
   416
haftmann@33063
   417
fun map_range f i =
haftmann@33063
   418
  let
haftmann@52271
   419
    fun map_aux (k: int) =
haftmann@52271
   420
      if k < i then f k :: map_aux (k + 1) else []
haftmann@52271
   421
  in map_aux 0 end;
haftmann@52271
   422
haftmann@52271
   423
fun fold_range f i =
haftmann@52271
   424
  let
haftmann@52271
   425
    fun fold_aux (k: int) y =
haftmann@52271
   426
      if k < i then fold_aux (k + 1) (f k y) else y
haftmann@52271
   427
  in fold_aux 0 end;
haftmann@52271
   428
haftmann@33063
   429
wenzelm@3762
   430
(*rear decomposition*)
wenzelm@47060
   431
fun split_last [] = raise List.Empty
wenzelm@3762
   432
  | split_last [x] = ([], x)
wenzelm@3762
   433
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   434
wenzelm@46891
   435
(*find first element satisfying predicate*)
wenzelm@46891
   436
val find_first = List.find;
wenzelm@46891
   437
ballarin@29209
   438
(*find position of first element satisfying a predicate*)
wenzelm@4212
   439
fun find_index pred =
wenzelm@24593
   440
  let fun find (_: int) [] = ~1
wenzelm@4212
   441
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   442
  in find 0 end;
wenzelm@3762
   443
wenzelm@4916
   444
(*get first element by lookup function*)
skalberg@15531
   445
fun get_first _ [] = NONE
wenzelm@4916
   446
  | get_first f (x :: xs) =
wenzelm@4916
   447
      (case f x of
skalberg@15531
   448
        NONE => get_first f xs
wenzelm@4916
   449
      | some => some);
wenzelm@4916
   450
haftmann@19233
   451
fun get_index f =
haftmann@19233
   452
  let
wenzelm@69237
   453
    fun get_aux (_: int) [] = NONE
wenzelm@69237
   454
      | get_aux i (x :: xs) =
wenzelm@46838
   455
          (case f x of
wenzelm@69237
   456
            NONE => get_aux (i + 1) xs
wenzelm@46838
   457
          | SOME y => SOME (i, y))
wenzelm@69237
   458
  in get_aux 0 end;
haftmann@19233
   459
skalberg@15531
   460
val flat = List.concat;
wenzelm@233
   461
wenzelm@12136
   462
fun unflat (xs :: xss) ys =
wenzelm@19424
   463
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   464
      in ps :: unflat xss qs end
wenzelm@12136
   465
  | unflat [] [] = []
wenzelm@40722
   466
  | unflat _ _ = raise ListPair.UnequalLengths;
wenzelm@12136
   467
wenzelm@46891
   468
fun grouped n comb f = chop_groups n #> comb (map f) #> flat;
wenzelm@46891
   469
wenzelm@21479
   470
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   471
wenzelm@24864
   472
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   473
haftmann@18549
   474
fun fold_burrow f xss s =
haftmann@18549
   475
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   476
wenzelm@233
   477
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   478
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   479
  | separate _ xs = xs;
wenzelm@233
   480
wenzelm@25980
   481
fun surround s (x :: xs) = s :: x :: surround s xs
wenzelm@25980
   482
  | surround s [] = [s];
wenzelm@25980
   483
wenzelm@233
   484
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   485
fun replicate (n: int) x =
wenzelm@233
   486
  let fun rep (0, xs) = xs
wenzelm@233
   487
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   488
  in
skalberg@15570
   489
    if n < 0 then raise Subscript
wenzelm@233
   490
    else rep (n, [])
wenzelm@233
   491
  end;
wenzelm@233
   492
wenzelm@4248
   493
wenzelm@25549
   494
(* direct product *)
wenzelm@25549
   495
haftmann@25538
   496
fun map_product f _ [] = []
haftmann@25538
   497
  | map_product f [] _ = []
haftmann@25538
   498
  | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
wenzelm@233
   499
haftmann@25538
   500
fun fold_product f _ [] z = z
haftmann@25538
   501
  | fold_product f [] _ z = z
haftmann@25538
   502
  | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
wenzelm@233
   503
wenzelm@25549
   504
wenzelm@25549
   505
(* lists of pairs *)
wenzelm@233
   506
haftmann@18330
   507
fun map2 _ [] [] = []
haftmann@18330
   508
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
wenzelm@40722
   509
  | map2 _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   510
wenzelm@58633
   511
fun fold2 _ [] [] z = z
wenzelm@23220
   512
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@58633
   513
  | fold2 _ _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   514
wenzelm@58633
   515
fun map_split _ [] = ([], [])
haftmann@25943
   516
  | map_split f (x :: xs) =
haftmann@25943
   517
      let
haftmann@25943
   518
        val (y, w) = f x;
haftmann@25943
   519
        val (ys, ws) = map_split f xs;
haftmann@25943
   520
      in (y :: ys, w :: ws) end;
haftmann@25943
   521
wenzelm@19799
   522
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   523
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   524
  | zip_options _ [] = []
wenzelm@40722
   525
  | zip_options [] _ = raise ListPair.UnequalLengths;
wenzelm@4956
   526
wenzelm@233
   527
(*combine two lists forming a list of pairs:
wenzelm@233
   528
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   529
fun [] ~~ [] = []
wenzelm@233
   530
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@40722
   531
  | _ ~~ _ = raise ListPair.UnequalLengths;
wenzelm@233
   532
wenzelm@233
   533
(*inverse of ~~; the old 'split':
wenzelm@233
   534
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   535
val split_list = ListPair.unzip;
wenzelm@233
   536
haftmann@28347
   537
fun burrow_fst f xs = split_list xs |>> f |> op ~~;
haftmann@28347
   538
wenzelm@233
   539
wenzelm@67522
   540
(* take, drop, chop, trim according to predicate *)
wenzelm@67522
   541
wenzelm@67522
   542
fun take_prefix pred list =
wenzelm@67522
   543
  let
wenzelm@67522
   544
    fun take res (x :: xs) = if pred x then take (x :: res) xs else rev res
wenzelm@67522
   545
      | take res [] = rev res;
wenzelm@67522
   546
  in take [] list end;
wenzelm@67522
   547
wenzelm@67522
   548
fun drop_prefix pred list =
wenzelm@67522
   549
  let
wenzelm@67522
   550
    fun drop (x :: xs) = if pred x then drop xs else x :: xs
wenzelm@67522
   551
      | drop [] = [];
wenzelm@67522
   552
  in drop list end;
wenzelm@67522
   553
wenzelm@67522
   554
fun chop_prefix pred list =
wenzelm@67522
   555
  let
wenzelm@67522
   556
    val prfx = take_prefix pred list;
wenzelm@67522
   557
    val sffx = drop (length prfx) list;
wenzelm@67522
   558
  in (prfx, sffx) end;
wenzelm@67522
   559
wenzelm@67522
   560
fun take_suffix pred list =
wenzelm@67522
   561
  let
wenzelm@67522
   562
    fun take res (x :: xs) = if pred x then take (x :: res) xs else res
wenzelm@67522
   563
      | take res [] = res;
wenzelm@67522
   564
  in take [] (rev list) end;
wenzelm@67522
   565
wenzelm@67522
   566
fun drop_suffix pred list =
wenzelm@67522
   567
  let
wenzelm@67522
   568
    fun drop (x :: xs) = if pred x then drop xs else rev (x :: xs)
wenzelm@67522
   569
      | drop [] = [];
wenzelm@67522
   570
  in drop (rev list) end;
wenzelm@67522
   571
wenzelm@67522
   572
fun chop_suffix pred list =
wenzelm@67522
   573
  let
wenzelm@67522
   574
    val prfx = drop_suffix pred list;
wenzelm@67522
   575
    val sffx = drop (length prfx) list;
wenzelm@67522
   576
  in (prfx, sffx) end;
wenzelm@67522
   577
wenzelm@67522
   578
fun trim pred = drop_prefix pred #> drop_suffix pred;
wenzelm@67522
   579
wenzelm@67522
   580
wenzelm@233
   581
(* prefixes, suffixes *)
wenzelm@233
   582
haftmann@18441
   583
fun is_prefix _ [] _ = true
haftmann@18441
   584
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   585
  | is_prefix eq _ _ = false;
wenzelm@233
   586
wenzelm@67521
   587
fun chop_common_prefix eq ([], ys) = ([], ([], ys))
wenzelm@67521
   588
  | chop_common_prefix eq (xs, []) = ([], (xs, []))
wenzelm@67521
   589
  | chop_common_prefix eq (xs as x :: xs', ys as y :: ys') =
wenzelm@67521
   590
      if eq (x, y) then
wenzelm@67521
   591
        let val (ps', xys'') = chop_common_prefix eq (xs', ys')
wenzelm@67521
   592
        in (x :: ps', xys'') end
wenzelm@67521
   593
      else ([], (xs, ys));
wenzelm@67521
   594
wenzelm@12249
   595
fun prefixes1 [] = []
wenzelm@12249
   596
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   597
wenzelm@19011
   598
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   599
wenzelm@12249
   600
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   601
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   602
wenzelm@23220
   603
wenzelm@69468
   604
wenzelm@233
   605
(** integers **)
wenzelm@233
   606
wenzelm@233
   607
(* lists of integers *)
wenzelm@233
   608
wenzelm@233
   609
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   610
fun ((i: int) upto j) =
wenzelm@21859
   611
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   612
wenzelm@233
   613
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   614
fun ((i: int) downto j) =
wenzelm@21859
   615
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   616
wenzelm@233
   617
wenzelm@233
   618
(* convert integers to strings *)
wenzelm@233
   619
wenzelm@68087
   620
(*hexadecimal*)
wenzelm@68087
   621
fun hex_digit i =
wenzelm@68087
   622
  if i < 10 then chr (Char.ord #"0" + i) else chr (Char.ord #"a" + i - 10);
wenzelm@68087
   623
wenzelm@233
   624
(*expand the number in the given base;
wenzelm@233
   625
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   626
fun radixpand (base, num) : int list =
wenzelm@233
   627
  let
wenzelm@233
   628
    fun radix (n, tail) =
wenzelm@233
   629
      if n < base then n :: tail
wenzelm@233
   630
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   631
  in radix (num, []) end;
wenzelm@233
   632
wenzelm@233
   633
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   634
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   635
fun radixstring (base, zerochar, num) =
wenzelm@233
   636
  let val offset = ord zerochar;
wenzelm@233
   637
      fun chrof n = chr (offset + n)
wenzelm@233
   638
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   639
wenzelm@233
   640
wenzelm@41492
   641
local
wenzelm@64275
   642
  val zero = Char.ord #"0";
wenzelm@57909
   643
  val small_int = 10000: int;
wenzelm@57909
   644
  val small_int_table = Vector.tabulate (small_int, Int.toString);
wenzelm@41492
   645
in
wenzelm@41492
   646
wenzelm@41492
   647
fun string_of_int i =
wenzelm@41492
   648
  if i < 0 then Int.toString i
wenzelm@41492
   649
  else if i < 10 then chr (zero + i)
wenzelm@57909
   650
  else if i < small_int then Vector.sub (small_int_table, i)
wenzelm@41492
   651
  else Int.toString i;
wenzelm@41492
   652
wenzelm@41492
   653
end;
wenzelm@233
   654
wenzelm@21942
   655
fun signed_string_of_int i =
wenzelm@21942
   656
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   657
wenzelm@23220
   658
fun string_of_indexname (a, 0) = a
wenzelm@23220
   659
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   660
wenzelm@233
   661
wenzelm@14826
   662
(* read integers *)
wenzelm@14826
   663
wenzelm@24630
   664
fun read_radix_int radix cs =
wenzelm@20095
   665
  let
wenzelm@64275
   666
    val zero = Char.ord #"0";
wenzelm@20095
   667
    val limit = zero + radix;
wenzelm@20095
   668
    fun scan (num, []) = (num, [])
wenzelm@20095
   669
      | scan (num, c :: cs) =
wenzelm@50637
   670
          if zero <= ord c andalso ord c < limit then
wenzelm@50637
   671
            scan (radix * num + (ord c - zero), cs)
wenzelm@50637
   672
          else (num, c :: cs);
wenzelm@24630
   673
  in scan (0, cs) end;
wenzelm@14826
   674
wenzelm@24630
   675
val read_int = read_radix_int 10;
wenzelm@14826
   676
wenzelm@40627
   677
fun oct_char s = chr (#1 (read_radix_int 8 (raw_explode s)));
wenzelm@14826
   678
wenzelm@14826
   679
wenzelm@14826
   680
wenzelm@233
   681
(** strings **)
wenzelm@233
   682
wenzelm@16188
   683
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   684
haftmann@18011
   685
fun nth_string str i =
wenzelm@6959
   686
  (case try String.substring (str, i, 1) of
skalberg@15531
   687
    SOME s => s
skalberg@15570
   688
  | NONE => raise Subscript);
wenzelm@6312
   689
wenzelm@16188
   690
fun fold_string f str x0 =
wenzelm@6282
   691
  let
wenzelm@6282
   692
    val n = size str;
wenzelm@16188
   693
    fun iter (x, i) =
wenzelm@16188
   694
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   695
  in iter (x0, 0) end;
wenzelm@6282
   696
wenzelm@14968
   697
fun exists_string pred str =
wenzelm@14968
   698
  let
wenzelm@14968
   699
    val n = size str;
wenzelm@14968
   700
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   701
  in ex 0 end;
wenzelm@6312
   702
wenzelm@16188
   703
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   704
wenzelm@28025
   705
fun first_field sep str =
wenzelm@28022
   706
  let
wenzelm@28025
   707
    val n = size sep;
wenzelm@28022
   708
    val len = size str;
wenzelm@28022
   709
    fun find i =
wenzelm@28022
   710
      if i + n > len then NONE
wenzelm@28025
   711
      else if String.substring (str, i, n) = sep then SOME i
wenzelm@28022
   712
      else find (i + 1);
wenzelm@28025
   713
  in
wenzelm@28025
   714
    (case find 0 of
wenzelm@28025
   715
      NONE => NONE
wenzelm@28025
   716
    | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
wenzelm@28025
   717
  end;
wenzelm@28022
   718
lcp@512
   719
(*enclose in brackets*)
lcp@512
   720
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   721
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   722
wenzelm@233
   723
(*simple quoting (does not escape special chars)*)
lcp@512
   724
val quote = enclose "\"" "\"";
wenzelm@233
   725
wenzelm@62529
   726
val cartouche = enclose "\<open>" "\<close>";
wenzelm@55033
   727
wenzelm@59469
   728
val space_implode = String.concatWith;
wenzelm@233
   729
wenzelm@255
   730
val commas = space_implode ", ";
wenzelm@380
   731
val commas_quote = commas o map quote;
wenzelm@255
   732
wenzelm@255
   733
val cat_lines = space_implode "\n";
wenzelm@233
   734
wenzelm@4212
   735
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   736
fun space_explode _ "" = []
paulson@21899
   737
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   738
wenzelm@3832
   739
val split_lines = space_explode "\n";
wenzelm@3832
   740
wenzelm@56038
   741
fun plain_words s = space_explode "_" s |> space_implode " ";
wenzelm@56038
   742
wenzelm@14826
   743
fun prefix_lines "" txt = txt
wenzelm@14826
   744
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   745
wenzelm@18681
   746
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   747
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   748
wenzelm@18681
   749
fun unprefix prfx s =
wenzelm@18681
   750
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   751
  else raise Fail "unprefix";
wenzelm@18681
   752
wenzelm@16188
   753
fun unsuffix sffx s =
wenzelm@17061
   754
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   755
  else raise Fail "unsuffix";
wenzelm@5285
   756
wenzelm@65904
   757
fun trim_line s =
wenzelm@65904
   758
  if String.isSuffix "\r\n" s
wenzelm@65904
   759
  then String.substring (s, 0, size s - 2)
wenzelm@65904
   760
  else if String.isSuffix "\r" s orelse String.isSuffix "\n" s
wenzelm@65904
   761
  then String.substring (s, 0, size s - 1)
wenzelm@65904
   762
  else s;
wenzelm@65904
   763
wenzelm@65904
   764
val trim_split_lines = trim_line #> split_lines #> map trim_line;
wenzelm@47499
   765
wenzelm@67179
   766
fun normalize_lines str =
wenzelm@67179
   767
  if exists_string (fn s => s = "\r") str then
wenzelm@67179
   768
    split_lines str |> map trim_line |> cat_lines
wenzelm@67179
   769
  else str;
wenzelm@67179
   770
wenzelm@24593
   771
fun replicate_string (0: int) _ = ""
wenzelm@10951
   772
  | replicate_string 1 a = a
wenzelm@10951
   773
  | replicate_string k a =
wenzelm@10951
   774
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   775
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   776
haftmann@31250
   777
fun translate_string f = String.translate (f o String.str);
haftmann@31250
   778
wenzelm@65934
   779
val encode_lines = translate_string (fn "\n" => "\v" | c => c);
wenzelm@65934
   780
val decode_lines = translate_string (fn "\v" => "\n" | c => c);
wenzelm@65934
   781
haftmann@63304
   782
fun align_right c k s =
haftmann@63304
   783
  let
haftmann@63304
   784
    val _ = if size c <> 1 orelse size s > k
haftmann@63304
   785
      then raise Fail "align_right" else ()
haftmann@63304
   786
  in replicate_string (k - size s) c ^ s end;
haftmann@63304
   787
kleing@29882
   788
(*crude matching of str against simple glob pat*)
kleing@29882
   789
fun match_string pat str =
kleing@29882
   790
  let
kleing@29882
   791
    fun match [] _ = true
kleing@29882
   792
      | match (p :: ps) s =
kleing@29882
   793
          size p <= size s andalso
kleing@29882
   794
            (case try (unprefix p) s of
kleing@29882
   795
              SOME s' => match ps s'
kleing@29882
   796
            | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
kleing@29882
   797
  in match (space_explode "*" pat) str end;
wenzelm@23220
   798
wenzelm@35976
   799
wenzelm@69468
   800
wenzelm@41516
   801
(** reals **)
wenzelm@41516
   802
wenzelm@41516
   803
val string_of_real = Real.fmt (StringCvt.GEN NONE);
wenzelm@41516
   804
wenzelm@41516
   805
fun signed_string_of_real x =
wenzelm@41516
   806
  if x < 0.0 then "-" ^ string_of_real (~ x) else string_of_real x;
wenzelm@41516
   807
wenzelm@41516
   808
wenzelm@35976
   809
wenzelm@16492
   810
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   811
wenzelm@26439
   812
(* canonical operations *)
wenzelm@26439
   813
wenzelm@18923
   814
fun member eq list x =
wenzelm@18923
   815
  let
wenzelm@18923
   816
    fun memb [] = false
wenzelm@18923
   817
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   818
  in memb list end;
berghofe@1576
   819
wenzelm@18923
   820
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   821
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   822
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   823
haftmann@33049
   824
fun inter eq xs = filter (member eq xs);
haftmann@33049
   825
haftmann@33042
   826
fun union eq = fold (insert eq);
wenzelm@19301
   827
fun subtract eq = fold (remove eq);
wenzelm@19301
   828
wenzelm@30572
   829
fun merge eq (xs, ys) =
wenzelm@30572
   830
  if pointer_eq (xs, ys) then xs
wenzelm@30572
   831
  else if null xs then ys
wenzelm@30572
   832
  else fold_rev (insert eq) ys xs;
clasohm@0
   833
wenzelm@26439
   834
haftmann@33050
   835
(* subset and set equality *)
haftmann@33050
   836
haftmann@33038
   837
fun subset eq (xs, ys) = forall (member eq ys) xs;
berghofe@1576
   838
haftmann@33038
   839
fun eq_set eq (xs, ys) =
haftmann@20348
   840
  eq_list eq (xs, ys) orelse
haftmann@33038
   841
    (subset eq (xs, ys) andalso subset (eq o swap) (ys, xs));
wenzelm@19301
   842
wenzelm@265
   843
wenzelm@233
   844
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   845
  first of equal elements*)
wenzelm@19046
   846
fun distinct eq lst =
wenzelm@233
   847
  let
wenzelm@233
   848
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   849
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   850
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   851
          else dist (x :: rev_seen, xs);
wenzelm@19046
   852
  in dist ([], lst) end;
wenzelm@233
   853
wenzelm@255
   854
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   855
  order, takes first of equal elements*)
wenzelm@18966
   856
fun duplicates eq lst =
wenzelm@255
   857
  let
wenzelm@255
   858
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   859
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   860
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   861
            dups (rev_dups, xs)
wenzelm@255
   862
          else dups (x :: rev_dups, xs);
wenzelm@18966
   863
  in dups ([], lst) end;
wenzelm@255
   864
wenzelm@16878
   865
fun has_duplicates eq =
wenzelm@16878
   866
  let
wenzelm@16878
   867
    fun dups [] = false
wenzelm@16878
   868
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   869
  in dups end;
wenzelm@16878
   870
wenzelm@255
   871
haftmann@32352
   872
(* matrices *)
haftmann@32352
   873
haftmann@32352
   874
fun map_transpose f xss =
haftmann@32352
   875
  let
wenzelm@40722
   876
    val n =
wenzelm@40722
   877
      (case distinct (op =) (map length xss) of
wenzelm@40722
   878
        [] => 0
haftmann@32352
   879
      | [n] => n
wenzelm@40722
   880
      | _ => raise ListPair.UnequalLengths);
haftmann@33206
   881
  in map_range (fn m => f (map (fn xs => nth xs m) xss)) n end;
haftmann@32352
   882
haftmann@32352
   883
wenzelm@23220
   884
nipkow@22142
   885
(** lists as multisets **)
nipkow@22142
   886
haftmann@33078
   887
fun remove1 eq x [] = []
haftmann@33078
   888
  | remove1 eq x (y :: ys) = if eq (x, y) then ys else y :: remove1 eq x ys;
nipkow@22142
   889
haftmann@33078
   890
fun combine eq xs ys = fold (remove1 eq) ys xs @ ys;
wenzelm@233
   891
haftmann@33079
   892
fun submultiset _ ([], _)  = true
haftmann@33079
   893
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
haftmann@33079
   894
clasohm@0
   895
clasohm@0
   896
wenzelm@2506
   897
(** orders **)
wenzelm@2506
   898
wenzelm@67560
   899
fun is_equal ord = ord = EQUAL;
wenzelm@67560
   900
fun is_less ord = ord = LESS;
wenzelm@67560
   901
fun is_less_equal ord = ord = LESS orelse ord = EQUAL;
wenzelm@67560
   902
fun is_greater ord = ord = GREATER;
wenzelm@67560
   903
fun is_greater_equal ord = ord = GREATER orelse ord = EQUAL;
wenzelm@18966
   904
wenzelm@4445
   905
fun rev_order LESS = GREATER
wenzelm@4445
   906
  | rev_order EQUAL = EQUAL
wenzelm@4445
   907
  | rev_order GREATER = LESS;
wenzelm@4445
   908
wenzelm@70464
   909
(*compose orders*)
wenzelm@70464
   910
fun (a_ord <<< b_ord) p = (case a_ord p of EQUAL => b_ord p | ord => ord);
wenzelm@70464
   911
wenzelm@4479
   912
(*assume rel is a linear strict order*)
wenzelm@4445
   913
fun make_ord rel (x, y) =
wenzelm@4445
   914
  if rel (x, y) then LESS
wenzelm@4445
   915
  else if rel (y, x) then GREATER
wenzelm@4445
   916
  else EQUAL;
wenzelm@4445
   917
wenzelm@25224
   918
fun bool_ord (false, true) = LESS
wenzelm@25224
   919
  | bool_ord (true, false) = GREATER
wenzelm@25224
   920
  | bool_ord _ = EQUAL;
wenzelm@25224
   921
wenzelm@15051
   922
val int_ord = Int.compare;
wenzelm@15051
   923
val string_ord = String.compare;
wenzelm@2506
   924
wenzelm@16676
   925
fun fast_string_ord (s1, s2) =
wenzelm@43793
   926
  if pointer_eq (s1, s2) then EQUAL
wenzelm@43793
   927
  else (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   928
wenzelm@16492
   929
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   930
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   931
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   932
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   933
wenzelm@4343
   934
(*lexicographic product*)
wenzelm@4343
   935
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   936
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   937
wenzelm@4343
   938
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   939
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   940
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   941
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   942
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   943
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   944
wenzelm@4343
   945
(*lexicographic product of lists*)
wenzelm@4343
   946
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   947
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   948
wenzelm@2506
   949
wenzelm@4621
   950
(* sorting *)
wenzelm@4621
   951
wenzelm@48271
   952
(*stable mergesort -- preserves order of equal elements*)
wenzelm@48271
   953
fun mergesort unique ord =
wenzelm@4621
   954
  let
wenzelm@48271
   955
    fun merge (xs as x :: xs') (ys as y :: ys') =
wenzelm@48271
   956
          (case ord (x, y) of
wenzelm@48271
   957
            LESS => x :: merge xs' ys
wenzelm@48271
   958
          | EQUAL =>
wenzelm@48271
   959
              if unique then merge xs ys'
wenzelm@48271
   960
              else x :: merge xs' ys
wenzelm@48271
   961
          | GREATER => y :: merge xs ys')
wenzelm@48271
   962
      | merge [] ys = ys
wenzelm@48271
   963
      | merge xs [] = xs;
wenzelm@48271
   964
wenzelm@48271
   965
    fun merge_all [xs] = xs
wenzelm@48271
   966
      | merge_all xss = merge_all (merge_pairs xss)
wenzelm@48271
   967
    and merge_pairs (xs :: ys :: xss) = merge xs ys :: merge_pairs xss
wenzelm@48271
   968
      | merge_pairs xss = xss;
wenzelm@48271
   969
wenzelm@48271
   970
    fun runs (x :: y :: xs) =
wenzelm@18427
   971
          (case ord (x, y) of
wenzelm@48271
   972
             LESS => ascending y [x] xs
wenzelm@48271
   973
           | EQUAL =>
wenzelm@48271
   974
               if unique then runs (x :: xs)
wenzelm@48271
   975
               else ascending y [x] xs
wenzelm@48271
   976
           | GREATER => descending y [x] xs)
wenzelm@48271
   977
      | runs xs = [xs]
wenzelm@4621
   978
wenzelm@48271
   979
    and ascending x xs (zs as y :: ys) =
wenzelm@48271
   980
          (case ord (x, y) of
wenzelm@48271
   981
             LESS => ascending y (x :: xs) ys
wenzelm@48271
   982
           | EQUAL =>
wenzelm@48271
   983
               if unique then ascending x xs ys
wenzelm@48271
   984
               else ascending y (x :: xs) ys
wenzelm@48271
   985
           | GREATER => rev (x :: xs) :: runs zs)
wenzelm@48271
   986
      | ascending x xs [] = [rev (x :: xs)]
wenzelm@48271
   987
wenzelm@48271
   988
    and descending x xs (zs as y :: ys) =
wenzelm@48271
   989
          (case ord (x, y) of
wenzelm@48271
   990
             GREATER => descending y (x :: xs) ys
wenzelm@48271
   991
           | EQUAL =>
wenzelm@48271
   992
               if unique then descending x xs ys
wenzelm@48271
   993
               else (x :: xs) :: runs zs
wenzelm@48271
   994
           | LESS => (x :: xs) :: runs zs)
wenzelm@48271
   995
      | descending x xs [] = [x :: xs];
wenzelm@48271
   996
wenzelm@48271
   997
  in merge_all o runs end;
wenzelm@48271
   998
wenzelm@48271
   999
fun sort ord = mergesort false ord;
wenzelm@48271
  1000
fun sort_distinct ord = mergesort true ord;
wenzelm@18427
  1001
wenzelm@4621
  1002
val sort_strings = sort string_ord;
wenzelm@60924
  1003
fun sort_by key xs = sort (string_ord o apply2 key) xs;
wenzelm@4621
  1004
wenzelm@4621
  1005
wenzelm@30558
  1006
(* items tagged by integer index *)
wenzelm@30558
  1007
wenzelm@30558
  1008
(*insert tags*)
wenzelm@30558
  1009
fun tag_list k [] = []
haftmann@30570
  1010
  | tag_list k (x :: xs) = (k:int, x) :: tag_list (k + 1) xs;
wenzelm@30558
  1011
wenzelm@30558
  1012
(*remove tags and suppress duplicates -- list is assumed sorted!*)
wenzelm@30558
  1013
fun untag_list [] = []
wenzelm@30558
  1014
  | untag_list [(k: int, x)] = [x]
wenzelm@30558
  1015
  | untag_list ((k, x) :: (rest as (k', x') :: _)) =
wenzelm@30558
  1016
      if k = k' then untag_list rest
wenzelm@30558
  1017
      else x :: untag_list rest;
wenzelm@30558
  1018
wenzelm@30558
  1019
(*return list elements in original order*)
wenzelm@59058
  1020
fun order_list list = untag_list (sort (int_ord o apply2 fst) list);
wenzelm@30558
  1021
wenzelm@30558
  1022
wenzelm@2506
  1023
wenzelm@4621
  1024
(** misc **)
wenzelm@233
  1025
wenzelm@19644
  1026
fun divide_and_conquer decomp x =
wenzelm@19644
  1027
  let val (ys, recomb) = decomp x
wenzelm@19644
  1028
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1029
wenzelm@32978
  1030
fun divide_and_conquer' decomp x s =
wenzelm@32978
  1031
  let val ((ys, recomb), s') = decomp x s
wenzelm@32978
  1032
  in recomb (fold_map (divide_and_conquer' decomp) ys s') end;
wenzelm@32978
  1033
clasohm@0
  1034
wenzelm@233
  1035
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1036
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1037
fun partition_list p i j =
wenzelm@37851
  1038
  let
wenzelm@37851
  1039
    fun part (k: int) xs =
wenzelm@37851
  1040
      if k > j then
wenzelm@37851
  1041
        (case xs of
wenzelm@37851
  1042
          [] => []
wenzelm@37851
  1043
        | _ => raise Fail "partition_list")
wenzelm@37851
  1044
      else
wenzelm@37851
  1045
        let val (ns, rest) = List.partition (p k) xs
wenzelm@37851
  1046
        in ns :: part (k + 1) rest end;
wenzelm@37851
  1047
  in part (i: int) end;
clasohm@0
  1048
wenzelm@37851
  1049
fun partition_eq (eq: 'a * 'a -> bool) =
wenzelm@19691
  1050
  let
wenzelm@19691
  1051
    fun part [] = []
wenzelm@19691
  1052
      | part (x :: ys) =
wenzelm@19691
  1053
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@37851
  1054
          in (x :: xs) :: part xs' end;
wenzelm@19691
  1055
  in part end;
wenzelm@19691
  1056
wenzelm@19691
  1057
wenzelm@45626
  1058
(* serial numbers and abstract stamps *)
wenzelm@16439
  1059
wenzelm@16439
  1060
type serial = int;
wenzelm@62918
  1061
val serial = Counter.make ();
wenzelm@19512
  1062
val serial_string = string_of_int o serial;
wenzelm@19512
  1063
wenzelm@45626
  1064
datatype stamp = Stamp of serial;
wenzelm@45626
  1065
fun stamp () = Stamp (serial ());
wenzelm@45626
  1066
wenzelm@16535
  1067
wenzelm@51368
  1068
(* values of any type *)
wenzelm@16535
  1069
wenzelm@16535
  1070
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1071
  constructors at any time*)
wenzelm@51368
  1072
structure Any = struct type T = exn end;
wenzelm@16535
  1073
wenzelm@43603
  1074
wenzelm@43603
  1075
(* getenv *)
wenzelm@43603
  1076
wenzelm@43603
  1077
fun getenv x =
wenzelm@43603
  1078
  (case OS.Process.getEnv x of
wenzelm@43603
  1079
    NONE => ""
wenzelm@43603
  1080
  | SOME y => y);
wenzelm@43603
  1081
wenzelm@43603
  1082
fun getenv_strict x =
wenzelm@43603
  1083
  (case getenv x of
wenzelm@43603
  1084
    "" => error ("Undefined Isabelle environment variable: " ^ quote x)
wenzelm@43603
  1085
  | y => y);
wenzelm@43603
  1086
clasohm@1364
  1087
end;
clasohm@1364
  1088
wenzelm@32188
  1089
structure Basic_Library: BASIC_LIBRARY = Library;
wenzelm@32188
  1090
open Basic_Library;