src/Pure/library.ML
author wenzelm
Mon Jul 16 15:57:21 2012 +0200 (2012-07-16 ago)
changeset 48271 b28defd0b5a5
parent 47499 4b0daca2bf88
child 48902 44a6967240b7
permissions -rw-r--r--
replaced quicksort by mergesort, which might be a bit more efficient for key operations like Ord_List.make, Sorts.minimize_sort;
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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_while: ('a -> bool) -> '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 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 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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  val smart_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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  val one_of: 'a list -> 'a
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  val frequency: (int * 'a) list -> 'a
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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 Object: 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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   291
fun swap (x, y) = (y, x);
wenzelm@233
   292
wenzelm@233
   293
fun apfst f (x, y) = (f x, y);
wenzelm@233
   294
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   295
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   296
wenzelm@233
   297
wenzelm@21395
   298
(* booleans *)
wenzelm@233
   299
wenzelm@21395
   300
(*polymorphic equality*)
wenzelm@233
   301
fun equal x y = x = y;
wenzelm@233
   302
fun not_equal x y = x <> y;
wenzelm@233
   303
wenzelm@21395
   304
(*combining predicates*)
wenzelm@16721
   305
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   306
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   307
wenzelm@25752
   308
val exists = List.exists;
wenzelm@25752
   309
val forall = List.all;
clasohm@0
   310
wenzelm@19644
   311
wenzelm@380
   312
(* flags *)
wenzelm@380
   313
wenzelm@32966
   314
fun setmp_CRITICAL flag value f x =
wenzelm@39616
   315
  NAMED_CRITICAL "setmp" (fn () => Unsynchronized.setmp flag value f x);
wenzelm@23932
   316
wenzelm@25797
   317
fun setmp_thread_data tag orig_data data f x =
wenzelm@26079
   318
  uninterruptible (fn restore_attributes => fn () =>
wenzelm@26079
   319
    let
wenzelm@28122
   320
      val _ = Thread.setLocal (tag, data);
wenzelm@26079
   321
      val result = Exn.capture (restore_attributes f) x;
wenzelm@28122
   322
      val _ = Thread.setLocal (tag, orig_data);
wenzelm@26079
   323
    in Exn.release result end) ();
wenzelm@25797
   324
wenzelm@19644
   325
wenzelm@21395
   326
wenzelm@233
   327
(** lists **)
wenzelm@233
   328
wenzelm@5285
   329
fun single x = [x];
wenzelm@233
   330
wenzelm@20882
   331
fun the_single [x] = x
wenzelm@47060
   332
  | the_single _ = raise List.Empty;
wenzelm@20882
   333
wenzelm@20882
   334
fun singleton f x = the_single (f [x]);
wenzelm@19273
   335
haftmann@25061
   336
fun yield_singleton f x = f [x] #>> the_single;
haftmann@25061
   337
wenzelm@25058
   338
fun perhaps_apply funs arg =
wenzelm@25058
   339
  let
wenzelm@25058
   340
    fun app [] res = res
wenzelm@25058
   341
      | app (f :: fs) (changed, x) =
wenzelm@25058
   342
          (case f x of
wenzelm@25058
   343
            NONE => app fs (changed, x)
wenzelm@25058
   344
          | SOME x' => app fs (true, x'));
wenzelm@25058
   345
  in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   346
wenzelm@25058
   347
fun perhaps_loop f arg =
wenzelm@25058
   348
  let
wenzelm@25058
   349
    fun loop (changed, x) =
wenzelm@25058
   350
      (case f x of
wenzelm@25058
   351
        NONE => (changed, x)
wenzelm@25058
   352
      | SOME x' => loop (true, x'));
wenzelm@25058
   353
  in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   354
wenzelm@233
   355
wenzelm@21395
   356
(* fold -- old versions *)
haftmann@16691
   357
wenzelm@233
   358
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   359
wenzelm@233
   360
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   361
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   362
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   363
  let fun itl (e, [])  = e
wenzelm@233
   364
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   365
  in  itl end;
wenzelm@233
   366
wenzelm@233
   367
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   368
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   369
fun foldr f (l, e) =
wenzelm@233
   370
  let fun itr [] = e
wenzelm@233
   371
        | itr (a::l) = f(a, itr l)
wenzelm@233
   372
  in  itr l  end;
wenzelm@233
   373
berghofe@25681
   374
(*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
berghofe@25681
   375
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@47060
   376
fun foldl1 f [] = raise List.Empty
berghofe@25681
   377
  | foldl1 f (x :: xs) = foldl f (x, xs);
berghofe@25681
   378
wenzelm@233
   379
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   380
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@47060
   381
fun foldr1 f [] = raise List.Empty
wenzelm@20510
   382
  | foldr1 f l =
paulson@20443
   383
      let fun itr [x] = x
wenzelm@20510
   384
            | itr (x::l) = f(x, itr l)
paulson@20443
   385
      in  itr l  end;
wenzelm@233
   386
wenzelm@233
   387
wenzelm@233
   388
(* basic list functions *)
wenzelm@233
   389
wenzelm@20510
   390
fun eq_list eq (list1, list2) =
wenzelm@42403
   391
  pointer_eq (list1, list2) orelse
wenzelm@42403
   392
    let
wenzelm@42403
   393
      fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@42403
   394
        | eq_lst _ = true;
wenzelm@42403
   395
    in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   396
wenzelm@19483
   397
fun maps f [] = []
wenzelm@19483
   398
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   399
haftmann@25538
   400
val filter = List.filter;
haftmann@25538
   401
fun filter_out f = filter (not o f);
haftmann@25538
   402
val map_filter = List.mapPartial;
haftmann@25538
   403
haftmann@33955
   404
fun take (0: int) xs = []
haftmann@33955
   405
  | take _ [] = []
haftmann@34059
   406
  | take n (x :: xs) = x :: take (n - 1) xs;
haftmann@33955
   407
haftmann@33955
   408
fun drop (0: int) xs = xs
haftmann@33955
   409
  | drop _ [] = []
haftmann@34059
   410
  | drop n (x :: xs) = drop (n - 1) xs;
haftmann@33955
   411
wenzelm@24593
   412
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   413
  | chop _ [] = ([], [])
wenzelm@23220
   414
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   415
haftmann@39811
   416
fun chop_while P [] = ([], [])
haftmann@39811
   417
  | chop_while P (ys as x :: xs) =
haftmann@39811
   418
      if P x then chop_while P xs |>> cons x else ([], ys);
nipkow@4713
   419
wenzelm@46891
   420
fun chop_groups n list =
wenzelm@46891
   421
  (case chop (Int.max (n, 1)) list of
wenzelm@46891
   422
    ([], _) => []
wenzelm@46891
   423
  | (g, rest) => g :: chop_groups n rest);
wenzelm@46891
   424
wenzelm@46891
   425
wenzelm@233
   426
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   427
  raise Subscript if list too short*)
haftmann@18011
   428
fun nth xs i = List.nth (xs, i);
wenzelm@233
   429
wenzelm@43278
   430
fun nth_list xss i = nth xss i handle General.Subscript => [];
wenzelm@18461
   431
haftmann@18011
   432
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   433
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
wenzelm@24593
   434
  | nth_map (_: int) _ [] = raise Subscript;
wenzelm@11773
   435
haftmann@24846
   436
fun nth_drop n xs =
haftmann@24846
   437
  List.take (xs, n) @ List.drop (xs, n + 1);
haftmann@24846
   438
haftmann@18514
   439
fun map_index f =
haftmann@18514
   440
  let
wenzelm@24593
   441
    fun mapp (_: int) [] = []
wenzelm@24593
   442
      | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
haftmann@18514
   443
  in mapp 0 end;
haftmann@18514
   444
haftmann@21118
   445
fun fold_index f =
haftmann@21118
   446
  let
wenzelm@24593
   447
    fun fold_aux (_: int) [] y = y
wenzelm@24593
   448
      | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
haftmann@21118
   449
  in fold_aux 0 end;
haftmann@21118
   450
haftmann@33063
   451
fun map_range f i =
haftmann@33063
   452
  let
wenzelm@33073
   453
    fun mapp (k: int) =
haftmann@33063
   454
      if k < i then f k :: mapp (k + 1) else [];
haftmann@33063
   455
  in mapp 0 end;
haftmann@33063
   456
wenzelm@3762
   457
(*rear decomposition*)
wenzelm@47060
   458
fun split_last [] = raise List.Empty
wenzelm@3762
   459
  | split_last [x] = ([], x)
wenzelm@3762
   460
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   461
wenzelm@46891
   462
(*find first element satisfying predicate*)
wenzelm@46891
   463
val find_first = List.find;
wenzelm@46891
   464
ballarin@29209
   465
(*find position of first element satisfying a predicate*)
wenzelm@4212
   466
fun find_index pred =
wenzelm@24593
   467
  let fun find (_: int) [] = ~1
wenzelm@4212
   468
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   469
  in find 0 end;
wenzelm@3762
   470
wenzelm@4916
   471
(*get first element by lookup function*)
skalberg@15531
   472
fun get_first _ [] = NONE
wenzelm@4916
   473
  | get_first f (x :: xs) =
wenzelm@4916
   474
      (case f x of
skalberg@15531
   475
        NONE => get_first f xs
wenzelm@4916
   476
      | some => some);
wenzelm@4916
   477
haftmann@19233
   478
fun get_index f =
haftmann@19233
   479
  let
wenzelm@24593
   480
    fun get (_: int) [] = NONE
wenzelm@19461
   481
      | get i (x :: xs) =
wenzelm@46838
   482
          (case f x of
wenzelm@46838
   483
            NONE => get (i + 1) xs
wenzelm@46838
   484
          | SOME y => SOME (i, y))
haftmann@19233
   485
  in get 0 end;
haftmann@19233
   486
skalberg@15531
   487
val flat = List.concat;
wenzelm@233
   488
wenzelm@12136
   489
fun unflat (xs :: xss) ys =
wenzelm@19424
   490
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   491
      in ps :: unflat xss qs end
wenzelm@12136
   492
  | unflat [] [] = []
wenzelm@40722
   493
  | unflat _ _ = raise ListPair.UnequalLengths;
wenzelm@12136
   494
wenzelm@46891
   495
fun grouped n comb f = chop_groups n #> comb (map f) #> flat;
wenzelm@46891
   496
wenzelm@21479
   497
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   498
wenzelm@24864
   499
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   500
haftmann@18549
   501
fun fold_burrow f xss s =
haftmann@18549
   502
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   503
wenzelm@233
   504
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   505
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   506
  | separate _ xs = xs;
wenzelm@233
   507
wenzelm@25980
   508
fun surround s (x :: xs) = s :: x :: surround s xs
wenzelm@25980
   509
  | surround s [] = [s];
wenzelm@25980
   510
wenzelm@233
   511
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   512
fun replicate (n: int) x =
wenzelm@233
   513
  let fun rep (0, xs) = xs
wenzelm@233
   514
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   515
  in
skalberg@15570
   516
    if n < 0 then raise Subscript
wenzelm@233
   517
    else rep (n, [])
wenzelm@233
   518
  end;
wenzelm@233
   519
wenzelm@4248
   520
wenzelm@25549
   521
(* direct product *)
wenzelm@25549
   522
haftmann@25538
   523
fun map_product f _ [] = []
haftmann@25538
   524
  | map_product f [] _ = []
haftmann@25538
   525
  | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
wenzelm@233
   526
haftmann@25538
   527
fun fold_product f _ [] z = z
haftmann@25538
   528
  | fold_product f [] _ z = z
haftmann@25538
   529
  | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
wenzelm@233
   530
wenzelm@25549
   531
wenzelm@25549
   532
(* lists of pairs *)
wenzelm@233
   533
haftmann@18330
   534
fun map2 _ [] [] = []
haftmann@18330
   535
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
wenzelm@40722
   536
  | map2 _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   537
wenzelm@23220
   538
fun fold2 f [] [] z = z
wenzelm@23220
   539
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@40722
   540
  | fold2 f _ _ _ = raise ListPair.UnequalLengths;
wenzelm@380
   541
wenzelm@40721
   542
fun fold_rev2 f [] [] z = z
wenzelm@40721
   543
  | fold_rev2 f (x :: xs) (y :: ys) z = f x y (fold_rev2 f xs ys z)
wenzelm@40722
   544
  | fold_rev2 f _ _ _ = raise ListPair.UnequalLengths;
wenzelm@40721
   545
haftmann@40564
   546
fun forall2 P [] [] = true
haftmann@40564
   547
  | forall2 P (x :: xs) (y :: ys) = P x y andalso forall2 P xs ys
wenzelm@40733
   548
  | forall2 P _ _ = raise ListPair.UnequalLengths;
haftmann@40564
   549
haftmann@25943
   550
fun map_split f [] = ([], [])
haftmann@25943
   551
  | map_split f (x :: xs) =
haftmann@25943
   552
      let
haftmann@25943
   553
        val (y, w) = f x;
haftmann@25943
   554
        val (ys, ws) = map_split f xs;
haftmann@25943
   555
      in (y :: ys, w :: ws) end;
haftmann@25943
   556
wenzelm@19799
   557
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   558
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   559
  | zip_options _ [] = []
wenzelm@40722
   560
  | zip_options [] _ = raise ListPair.UnequalLengths;
wenzelm@4956
   561
wenzelm@233
   562
(*combine two lists forming a list of pairs:
wenzelm@233
   563
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   564
fun [] ~~ [] = []
wenzelm@233
   565
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@40722
   566
  | _ ~~ _ = raise ListPair.UnequalLengths;
wenzelm@233
   567
wenzelm@233
   568
(*inverse of ~~; the old 'split':
wenzelm@233
   569
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   570
val split_list = ListPair.unzip;
wenzelm@233
   571
haftmann@28347
   572
fun burrow_fst f xs = split_list xs |>> f |> op ~~;
haftmann@28347
   573
wenzelm@233
   574
wenzelm@233
   575
(* prefixes, suffixes *)
wenzelm@233
   576
haftmann@18441
   577
fun is_prefix _ [] _ = true
haftmann@18441
   578
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   579
  | is_prefix eq _ _ = false;
wenzelm@233
   580
wenzelm@233
   581
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   582
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   583
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   584
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   585
        | take (rxs, x :: xs) =
wenzelm@255
   586
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   587
  in  take([], xs)  end;
wenzelm@233
   588
haftmann@20108
   589
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   590
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   591
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   592
      if eq (x, y) then
haftmann@20108
   593
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   594
        in (x :: ps', xys'') end
haftmann@20108
   595
      else ([], (xs, ys));
haftmann@20108
   596
wenzelm@233
   597
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   598
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   599
fun take_suffix _ [] = ([], [])
wenzelm@233
   600
  | take_suffix pred (x :: xs) =
wenzelm@233
   601
      (case take_suffix pred xs of
wenzelm@233
   602
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   603
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   604
wenzelm@12249
   605
fun prefixes1 [] = []
wenzelm@12249
   606
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   607
wenzelm@19011
   608
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   609
wenzelm@12249
   610
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   611
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   612
wenzelm@23220
   613
wenzelm@23220
   614
wenzelm@233
   615
(** integers **)
wenzelm@233
   616
wenzelm@233
   617
(* lists of integers *)
wenzelm@233
   618
wenzelm@233
   619
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   620
fun ((i: int) upto j) =
wenzelm@21859
   621
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   622
wenzelm@233
   623
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   624
fun ((i: int) downto j) =
wenzelm@21859
   625
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   626
wenzelm@233
   627
wenzelm@233
   628
(* convert integers to strings *)
wenzelm@233
   629
wenzelm@233
   630
(*expand the number in the given base;
wenzelm@233
   631
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   632
fun radixpand (base, num) : int list =
wenzelm@233
   633
  let
wenzelm@233
   634
    fun radix (n, tail) =
wenzelm@233
   635
      if n < base then n :: tail
wenzelm@233
   636
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   637
  in radix (num, []) end;
wenzelm@233
   638
wenzelm@233
   639
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   640
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   641
fun radixstring (base, zerochar, num) =
wenzelm@233
   642
  let val offset = ord zerochar;
wenzelm@233
   643
      fun chrof n = chr (offset + n)
wenzelm@233
   644
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   645
wenzelm@233
   646
wenzelm@41492
   647
local
wenzelm@41492
   648
  val zero = ord "0";
wenzelm@41494
   649
  val small = 10000: int;
wenzelm@41492
   650
  val small_table = Vector.tabulate (small, Int.toString);
wenzelm@41492
   651
in
wenzelm@41492
   652
wenzelm@41492
   653
fun string_of_int i =
wenzelm@41492
   654
  if i < 0 then Int.toString i
wenzelm@41492
   655
  else if i < 10 then chr (zero + i)
wenzelm@41492
   656
  else if i < small then Vector.sub (small_table, i)
wenzelm@41492
   657
  else Int.toString i;
wenzelm@41492
   658
wenzelm@41492
   659
end;
wenzelm@233
   660
wenzelm@21942
   661
fun signed_string_of_int i =
wenzelm@21942
   662
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   663
wenzelm@23220
   664
fun string_of_indexname (a, 0) = a
wenzelm@23220
   665
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   666
wenzelm@233
   667
wenzelm@14826
   668
(* read integers *)
wenzelm@14826
   669
wenzelm@24630
   670
fun read_radix_int radix cs =
wenzelm@20095
   671
  let
wenzelm@20095
   672
    val zero = ord "0";
wenzelm@20095
   673
    val limit = zero + radix;
wenzelm@20095
   674
    fun scan (num, []) = (num, [])
wenzelm@20095
   675
      | scan (num, c :: cs) =
wenzelm@20095
   676
        if zero <= ord c andalso ord c < limit then
wenzelm@24630
   677
          scan (radix * num + (ord c - zero), cs)
wenzelm@20095
   678
        else (num, c :: cs);
wenzelm@24630
   679
  in scan (0, cs) end;
wenzelm@14826
   680
wenzelm@24630
   681
val read_int = read_radix_int 10;
wenzelm@14826
   682
wenzelm@40627
   683
fun oct_char s = chr (#1 (read_radix_int 8 (raw_explode s)));
wenzelm@14826
   684
wenzelm@14826
   685
wenzelm@14826
   686
wenzelm@233
   687
(** strings **)
wenzelm@233
   688
wenzelm@16188
   689
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   690
haftmann@18011
   691
fun nth_string str i =
wenzelm@6959
   692
  (case try String.substring (str, i, 1) of
skalberg@15531
   693
    SOME s => s
skalberg@15570
   694
  | NONE => raise Subscript);
wenzelm@6312
   695
wenzelm@16188
   696
fun fold_string f str x0 =
wenzelm@6282
   697
  let
wenzelm@6282
   698
    val n = size str;
wenzelm@16188
   699
    fun iter (x, i) =
wenzelm@16188
   700
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   701
  in iter (x0, 0) end;
wenzelm@6282
   702
wenzelm@14968
   703
fun exists_string pred str =
wenzelm@14968
   704
  let
wenzelm@14968
   705
    val n = size str;
wenzelm@14968
   706
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   707
  in ex 0 end;
wenzelm@6312
   708
wenzelm@16188
   709
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   710
wenzelm@28025
   711
fun first_field sep str =
wenzelm@28022
   712
  let
wenzelm@28025
   713
    val n = size sep;
wenzelm@28022
   714
    val len = size str;
wenzelm@28022
   715
    fun find i =
wenzelm@28022
   716
      if i + n > len then NONE
wenzelm@28025
   717
      else if String.substring (str, i, n) = sep then SOME i
wenzelm@28022
   718
      else find (i + 1);
wenzelm@28025
   719
  in
wenzelm@28025
   720
    (case find 0 of
wenzelm@28025
   721
      NONE => NONE
wenzelm@28025
   722
    | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
wenzelm@28025
   723
  end;
wenzelm@28022
   724
lcp@512
   725
(*enclose in brackets*)
lcp@512
   726
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   727
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   728
wenzelm@233
   729
(*simple quoting (does not escape special chars)*)
lcp@512
   730
val quote = enclose "\"" "\"";
wenzelm@233
   731
wenzelm@233
   732
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   733
wenzelm@255
   734
val commas = space_implode ", ";
wenzelm@380
   735
val commas_quote = commas o map quote;
wenzelm@255
   736
wenzelm@255
   737
val cat_lines = space_implode "\n";
wenzelm@233
   738
wenzelm@4212
   739
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   740
fun space_explode _ "" = []
paulson@21899
   741
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   742
wenzelm@3832
   743
val split_lines = space_explode "\n";
wenzelm@3832
   744
wenzelm@14826
   745
fun prefix_lines "" txt = txt
wenzelm@14826
   746
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   747
wenzelm@18681
   748
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   749
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   750
wenzelm@18681
   751
fun unprefix prfx s =
wenzelm@18681
   752
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   753
  else raise Fail "unprefix";
wenzelm@18681
   754
wenzelm@16188
   755
fun unsuffix sffx s =
wenzelm@17061
   756
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   757
  else raise Fail "unsuffix";
wenzelm@5285
   758
wenzelm@47499
   759
val trim_line = perhaps (try (unsuffix "\n"));
wenzelm@47499
   760
wenzelm@24593
   761
fun replicate_string (0: int) _ = ""
wenzelm@10951
   762
  | replicate_string 1 a = a
wenzelm@10951
   763
  | replicate_string k a =
wenzelm@10951
   764
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   765
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   766
haftmann@31250
   767
fun translate_string f = String.translate (f o String.str);
haftmann@31250
   768
kleing@29882
   769
(*crude matching of str against simple glob pat*)
kleing@29882
   770
fun match_string pat str =
kleing@29882
   771
  let
kleing@29882
   772
    fun match [] _ = true
kleing@29882
   773
      | match (p :: ps) s =
kleing@29882
   774
          size p <= size s andalso
kleing@29882
   775
            (case try (unprefix p) s of
kleing@29882
   776
              SOME s' => match ps s'
kleing@29882
   777
            | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
kleing@29882
   778
  in match (space_explode "*" pat) str end;
wenzelm@23220
   779
wenzelm@35976
   780
wenzelm@41516
   781
(** reals **)
wenzelm@41516
   782
wenzelm@41516
   783
val string_of_real = Real.fmt (StringCvt.GEN NONE);
wenzelm@41516
   784
wenzelm@41516
   785
fun signed_string_of_real x =
wenzelm@41516
   786
  if x < 0.0 then "-" ^ string_of_real (~ x) else string_of_real x;
wenzelm@41516
   787
wenzelm@41516
   788
fun smart_string_of_real x =
wenzelm@41516
   789
  let
wenzelm@41516
   790
    val s = signed_string_of_real x;
wenzelm@41516
   791
  in
wenzelm@41516
   792
    (case space_explode "." s of
wenzelm@41516
   793
      [a, b] => if forall_string (fn c => c = "0") b then a else s
wenzelm@41516
   794
    | _ => s)
wenzelm@41516
   795
  end;
wenzelm@41516
   796
wenzelm@41516
   797
wenzelm@35976
   798
wenzelm@16492
   799
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   800
wenzelm@26439
   801
(* canonical operations *)
wenzelm@26439
   802
wenzelm@18923
   803
fun member eq list x =
wenzelm@18923
   804
  let
wenzelm@18923
   805
    fun memb [] = false
wenzelm@18923
   806
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   807
  in memb list end;
berghofe@1576
   808
wenzelm@18923
   809
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   810
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   811
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   812
haftmann@33049
   813
fun inter eq xs = filter (member eq xs);
haftmann@33049
   814
haftmann@33042
   815
fun union eq = fold (insert eq);
wenzelm@19301
   816
fun subtract eq = fold (remove eq);
wenzelm@19301
   817
wenzelm@30572
   818
fun merge eq (xs, ys) =
wenzelm@30572
   819
  if pointer_eq (xs, ys) then xs
wenzelm@30572
   820
  else if null xs then ys
wenzelm@30572
   821
  else fold_rev (insert eq) ys xs;
clasohm@0
   822
wenzelm@26439
   823
haftmann@33050
   824
(* subset and set equality *)
haftmann@33050
   825
haftmann@33038
   826
fun subset eq (xs, ys) = forall (member eq ys) xs;
berghofe@1576
   827
haftmann@33038
   828
fun eq_set eq (xs, ys) =
haftmann@20348
   829
  eq_list eq (xs, ys) orelse
haftmann@33038
   830
    (subset eq (xs, ys) andalso subset (eq o swap) (ys, xs));
wenzelm@19301
   831
wenzelm@265
   832
wenzelm@233
   833
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   834
  first of equal elements*)
wenzelm@19046
   835
fun distinct eq lst =
wenzelm@233
   836
  let
wenzelm@233
   837
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   838
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   839
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   840
          else dist (x :: rev_seen, xs);
wenzelm@19046
   841
  in dist ([], lst) end;
wenzelm@233
   842
wenzelm@255
   843
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   844
  order, takes first of equal elements*)
wenzelm@18966
   845
fun duplicates eq lst =
wenzelm@255
   846
  let
wenzelm@255
   847
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   848
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   849
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   850
            dups (rev_dups, xs)
wenzelm@255
   851
          else dups (x :: rev_dups, xs);
wenzelm@18966
   852
  in dups ([], lst) end;
wenzelm@255
   853
wenzelm@16878
   854
fun has_duplicates eq =
wenzelm@16878
   855
  let
wenzelm@16878
   856
    fun dups [] = false
wenzelm@16878
   857
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   858
  in dups end;
wenzelm@16878
   859
wenzelm@255
   860
haftmann@32352
   861
(* matrices *)
haftmann@32352
   862
haftmann@32352
   863
fun map_transpose f xss =
haftmann@32352
   864
  let
wenzelm@40722
   865
    val n =
wenzelm@40722
   866
      (case distinct (op =) (map length xss) of
wenzelm@40722
   867
        [] => 0
haftmann@32352
   868
      | [n] => n
wenzelm@40722
   869
      | _ => raise ListPair.UnequalLengths);
haftmann@33206
   870
  in map_range (fn m => f (map (fn xs => nth xs m) xss)) n end;
haftmann@32352
   871
haftmann@32352
   872
wenzelm@23220
   873
nipkow@22142
   874
(** lists as multisets **)
nipkow@22142
   875
haftmann@33078
   876
fun remove1 eq x [] = []
haftmann@33078
   877
  | remove1 eq x (y :: ys) = if eq (x, y) then ys else y :: remove1 eq x ys;
nipkow@22142
   878
haftmann@33078
   879
fun combine eq xs ys = fold (remove1 eq) ys xs @ ys;
wenzelm@233
   880
haftmann@33079
   881
fun submultiset _ ([], _)  = true
haftmann@33079
   882
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
haftmann@33079
   883
clasohm@0
   884
clasohm@0
   885
wenzelm@2506
   886
(** orders **)
wenzelm@2506
   887
wenzelm@18966
   888
fun is_equal EQUAL = true
wenzelm@18966
   889
  | is_equal _ = false;
wenzelm@18966
   890
wenzelm@4445
   891
fun rev_order LESS = GREATER
wenzelm@4445
   892
  | rev_order EQUAL = EQUAL
wenzelm@4445
   893
  | rev_order GREATER = LESS;
wenzelm@4445
   894
wenzelm@4479
   895
(*assume rel is a linear strict order*)
wenzelm@4445
   896
fun make_ord rel (x, y) =
wenzelm@4445
   897
  if rel (x, y) then LESS
wenzelm@4445
   898
  else if rel (y, x) then GREATER
wenzelm@4445
   899
  else EQUAL;
wenzelm@4445
   900
wenzelm@25224
   901
fun bool_ord (false, true) = LESS
wenzelm@25224
   902
  | bool_ord (true, false) = GREATER
wenzelm@25224
   903
  | bool_ord _ = EQUAL;
wenzelm@25224
   904
wenzelm@15051
   905
val int_ord = Int.compare;
wenzelm@15051
   906
val string_ord = String.compare;
wenzelm@2506
   907
wenzelm@16676
   908
fun fast_string_ord (s1, s2) =
wenzelm@43793
   909
  if pointer_eq (s1, s2) then EQUAL
wenzelm@43793
   910
  else (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   911
wenzelm@16492
   912
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   913
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   914
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   915
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   916
wenzelm@4343
   917
(*lexicographic product*)
wenzelm@4343
   918
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   919
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   920
wenzelm@4343
   921
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   922
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   923
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   924
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   925
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   926
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   927
wenzelm@4343
   928
(*lexicographic product of lists*)
wenzelm@4343
   929
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   930
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   931
wenzelm@2506
   932
wenzelm@4621
   933
(* sorting *)
wenzelm@4621
   934
wenzelm@48271
   935
(*stable mergesort -- preserves order of equal elements*)
wenzelm@48271
   936
fun mergesort unique ord =
wenzelm@4621
   937
  let
wenzelm@48271
   938
    fun merge (xs as x :: xs') (ys as y :: ys') =
wenzelm@48271
   939
          (case ord (x, y) of
wenzelm@48271
   940
            LESS => x :: merge xs' ys
wenzelm@48271
   941
          | EQUAL =>
wenzelm@48271
   942
              if unique then merge xs ys'
wenzelm@48271
   943
              else x :: merge xs' ys
wenzelm@48271
   944
          | GREATER => y :: merge xs ys')
wenzelm@48271
   945
      | merge [] ys = ys
wenzelm@48271
   946
      | merge xs [] = xs;
wenzelm@48271
   947
wenzelm@48271
   948
    fun merge_all [xs] = xs
wenzelm@48271
   949
      | merge_all xss = merge_all (merge_pairs xss)
wenzelm@48271
   950
    and merge_pairs (xs :: ys :: xss) = merge xs ys :: merge_pairs xss
wenzelm@48271
   951
      | merge_pairs xss = xss;
wenzelm@48271
   952
wenzelm@48271
   953
    fun runs (x :: y :: xs) =
wenzelm@18427
   954
          (case ord (x, y) of
wenzelm@48271
   955
             LESS => ascending y [x] xs
wenzelm@48271
   956
           | EQUAL =>
wenzelm@48271
   957
               if unique then runs (x :: xs)
wenzelm@48271
   958
               else ascending y [x] xs
wenzelm@48271
   959
           | GREATER => descending y [x] xs)
wenzelm@48271
   960
      | runs xs = [xs]
wenzelm@4621
   961
wenzelm@48271
   962
    and ascending x xs (zs as y :: ys) =
wenzelm@48271
   963
          (case ord (x, y) of
wenzelm@48271
   964
             LESS => ascending y (x :: xs) ys
wenzelm@48271
   965
           | EQUAL =>
wenzelm@48271
   966
               if unique then ascending x xs ys
wenzelm@48271
   967
               else ascending y (x :: xs) ys
wenzelm@48271
   968
           | GREATER => rev (x :: xs) :: runs zs)
wenzelm@48271
   969
      | ascending x xs [] = [rev (x :: xs)]
wenzelm@48271
   970
wenzelm@48271
   971
    and descending x xs (zs as y :: ys) =
wenzelm@48271
   972
          (case ord (x, y) of
wenzelm@48271
   973
             GREATER => descending y (x :: xs) ys
wenzelm@48271
   974
           | EQUAL =>
wenzelm@48271
   975
               if unique then descending x xs ys
wenzelm@48271
   976
               else (x :: xs) :: runs zs
wenzelm@48271
   977
           | LESS => (x :: xs) :: runs zs)
wenzelm@48271
   978
      | descending x xs [] = [x :: xs];
wenzelm@48271
   979
wenzelm@48271
   980
  in merge_all o runs end;
wenzelm@48271
   981
wenzelm@48271
   982
fun sort ord = mergesort false ord;
wenzelm@48271
   983
fun sort_distinct ord = mergesort true ord;
wenzelm@18427
   984
wenzelm@4621
   985
val sort_strings = sort string_ord;
wenzelm@44617
   986
fun sort_wrt key xs = sort (string_ord o pairself key) xs;
wenzelm@4621
   987
wenzelm@4621
   988
wenzelm@30558
   989
(* items tagged by integer index *)
wenzelm@30558
   990
wenzelm@30558
   991
(*insert tags*)
wenzelm@30558
   992
fun tag_list k [] = []
haftmann@30570
   993
  | tag_list k (x :: xs) = (k:int, x) :: tag_list (k + 1) xs;
wenzelm@30558
   994
wenzelm@30558
   995
(*remove tags and suppress duplicates -- list is assumed sorted!*)
wenzelm@30558
   996
fun untag_list [] = []
wenzelm@30558
   997
  | untag_list [(k: int, x)] = [x]
wenzelm@30558
   998
  | untag_list ((k, x) :: (rest as (k', x') :: _)) =
wenzelm@30558
   999
      if k = k' then untag_list rest
wenzelm@30558
  1000
      else x :: untag_list rest;
wenzelm@30558
  1001
wenzelm@30558
  1002
(*return list elements in original order*)
wenzelm@30558
  1003
fun order_list list = untag_list (sort (int_ord o pairself fst) list);
wenzelm@30558
  1004
wenzelm@30558
  1005
wenzelm@2506
  1006
berghofe@14106
  1007
(** random numbers **)
berghofe@14106
  1008
berghofe@14106
  1009
exception RANDOM;
berghofe@14106
  1010
berghofe@14618
  1011
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1012
berghofe@14106
  1013
local
berghofe@14106
  1014
  val a = 16807.0;
berghofe@14106
  1015
  val m = 2147483647.0;
wenzelm@32737
  1016
  val random_seed = Unsynchronized.ref 1.0;
berghofe@14106
  1017
in
berghofe@14106
  1018
wenzelm@23922
  1019
fun random () = CRITICAL (fn () =>
wenzelm@23922
  1020
  let val r = rmod (a * ! random_seed) m
wenzelm@23922
  1021
  in (random_seed := r; r) end);
berghofe@14106
  1022
berghofe@14106
  1023
end;
berghofe@14106
  1024
berghofe@14106
  1025
fun random_range l h =
berghofe@14106
  1026
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1027
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1028
haftmann@18011
  1029
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1030
berghofe@14106
  1031
fun frequency xs =
berghofe@14106
  1032
  let
berghofe@14106
  1033
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1034
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1035
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1036
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1037
berghofe@14106
  1038
wenzelm@23220
  1039
wenzelm@4621
  1040
(** misc **)
wenzelm@233
  1041
wenzelm@19644
  1042
fun divide_and_conquer decomp x =
wenzelm@19644
  1043
  let val (ys, recomb) = decomp x
wenzelm@19644
  1044
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1045
wenzelm@32978
  1046
fun divide_and_conquer' decomp x s =
wenzelm@32978
  1047
  let val ((ys, recomb), s') = decomp x s
wenzelm@32978
  1048
  in recomb (fold_map (divide_and_conquer' decomp) ys s') end;
wenzelm@32978
  1049
clasohm@0
  1050
wenzelm@233
  1051
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1052
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1053
fun partition_list p i j =
wenzelm@37851
  1054
  let
wenzelm@37851
  1055
    fun part (k: int) xs =
wenzelm@37851
  1056
      if k > j then
wenzelm@37851
  1057
        (case xs of
wenzelm@37851
  1058
          [] => []
wenzelm@37851
  1059
        | _ => raise Fail "partition_list")
wenzelm@37851
  1060
      else
wenzelm@37851
  1061
        let val (ns, rest) = List.partition (p k) xs
wenzelm@37851
  1062
        in ns :: part (k + 1) rest end;
wenzelm@37851
  1063
  in part (i: int) end;
clasohm@0
  1064
wenzelm@37851
  1065
fun partition_eq (eq: 'a * 'a -> bool) =
wenzelm@19691
  1066
  let
wenzelm@19691
  1067
    fun part [] = []
wenzelm@19691
  1068
      | part (x :: ys) =
wenzelm@19691
  1069
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@37851
  1070
          in (x :: xs) :: part xs' end;
wenzelm@19691
  1071
  in part end;
wenzelm@19691
  1072
wenzelm@19691
  1073
wenzelm@45626
  1074
(* serial numbers and abstract stamps *)
wenzelm@16439
  1075
wenzelm@16439
  1076
type serial = int;
wenzelm@25702
  1077
val serial = Multithreading.serial;
wenzelm@19512
  1078
val serial_string = string_of_int o serial;
wenzelm@19512
  1079
wenzelm@45626
  1080
datatype stamp = Stamp of serial;
wenzelm@45626
  1081
fun stamp () = Stamp (serial ());
wenzelm@45626
  1082
wenzelm@16535
  1083
wenzelm@16535
  1084
(* generic objects *)
wenzelm@16535
  1085
wenzelm@16535
  1086
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1087
  constructors at any time*)
wenzelm@16535
  1088
structure Object = struct type T = exn end;
wenzelm@16535
  1089
wenzelm@43603
  1090
wenzelm@43603
  1091
(* current directory *)
wenzelm@43603
  1092
wenzelm@43603
  1093
val cd = OS.FileSys.chDir;
wenzelm@43603
  1094
val pwd = OS.FileSys.getDir;
wenzelm@43603
  1095
wenzelm@43603
  1096
wenzelm@43603
  1097
(* getenv *)
wenzelm@43603
  1098
wenzelm@43603
  1099
fun getenv x =
wenzelm@43603
  1100
  (case OS.Process.getEnv x of
wenzelm@43603
  1101
    NONE => ""
wenzelm@43603
  1102
  | SOME y => y);
wenzelm@43603
  1103
wenzelm@43603
  1104
fun getenv_strict x =
wenzelm@43603
  1105
  (case getenv x of
wenzelm@43603
  1106
    "" => error ("Undefined Isabelle environment variable: " ^ quote x)
wenzelm@43603
  1107
  | y => y);
wenzelm@43603
  1108
clasohm@1364
  1109
end;
clasohm@1364
  1110
wenzelm@32188
  1111
structure Basic_Library: BASIC_LIBRARY = Library;
wenzelm@32188
  1112
open Basic_Library;
wenzelm@40722
  1113