src/Pure/library.ML
author wenzelm
Thu Oct 01 23:27:05 2009 +0200 (2009-10-01)
changeset 32843 c8f5a7c8353f
parent 32737 76fa673eee8b
child 32966 5b21661fe618
permissions -rw-r--r--
moved cache_conv to src/Pure/conv.ML, use Thm.cterm_cache;
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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 \ \\ mem mem_int mem_string union union_int
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  union_string inter inter_int inter_string subset subset_int subset_string
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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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  (*errors*)
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  exception SYS_ERROR of string
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  val sys_error: string -> 'a
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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_noncritical: 'a Unsynchronized.ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val setmp: '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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  exception UnequalLengths
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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 apply: ('a -> 'a) list -> 'a -> 'a
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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 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 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 burrow_fst: ('a list -> 'b list) -> ('a * 'c) list -> ('b * 'c) 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 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 chop: int -> 'a list -> 'a list * 'a list
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  val dropwhile: ('a -> bool) -> 'a list -> 'a list
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  val nth: 'a list -> int -> 'a
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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 nth_list: 'a list list -> int -> '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 split_last: 'a list -> 'a list * 'a
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  val find_index: ('a -> bool) -> 'a list -> int
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  val find_first: ('a -> bool) -> 'a list -> 'a option
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  val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
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  val get_first: ('a -> 'b option) -> 'a list -> 'b option
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  val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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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 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 map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list
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  val split_list: ('a * 'b) list -> 'a list * 'b 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 map_transpose: ('a list -> 'b) -> 'a list list -> 'b list
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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 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 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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  (*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 subtract: ('b * 'a -> 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 mem: ''a * ''a list -> bool
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  val mem_int: int * int list -> bool
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  val mem_string: string * string list -> bool
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  val union: ''a list * ''a list -> ''a list
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  val union_int: int list * int list -> int list
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  val union_string: string list * string list -> string list
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  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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  val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
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  val inter: ''a list * ''a list -> ''a list
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  val inter_int: int list * int list -> int list
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  val inter_string: string list * string list -> string list
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  val subset: ''a list * ''a list -> bool
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  val subset_int: int list * int list -> bool
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  val subset_string: string list * string list -> bool
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  val eq_set: ''a list * ''a list -> bool
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  val eq_set_string: string list * string list -> bool
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  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val \ : ''a list * ''a -> ''a list
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  val \\ : ''a list * ''a list -> ''a list
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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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  (*lists as multisets*)
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  val remove1: ('b * 'a -> bool) -> 'b -> '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 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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  val gensym: string -> string
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  type stamp
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  val stamp: unit -> stamp
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  type serial
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  val serial: unit -> serial
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  val serial_string: unit -> string
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  structure Object: sig type T end
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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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  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c 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 last_elem: 'a list -> 'a
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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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(* errors *)
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exception SYS_ERROR of string;
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fun sys_error msg = raise SYS_ERROR msg;
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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;
wenzelm@233
   293
fun snd (x, y) = y;
wenzelm@233
   294
haftmann@17498
   295
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   296
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   297
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   298
wenzelm@233
   299
fun swap (x, y) = (y, x);
wenzelm@233
   300
wenzelm@233
   301
fun apfst f (x, y) = (f x, y);
wenzelm@233
   302
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   303
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   304
wenzelm@233
   305
wenzelm@21395
   306
(* booleans *)
wenzelm@233
   307
wenzelm@21395
   308
(*polymorphic equality*)
wenzelm@233
   309
fun equal x y = x = y;
wenzelm@233
   310
fun not_equal x y = x <> y;
wenzelm@233
   311
wenzelm@21395
   312
(*combining predicates*)
wenzelm@16721
   313
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   314
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   315
wenzelm@25752
   316
val exists = List.exists;
wenzelm@25752
   317
val forall = List.all;
clasohm@0
   318
wenzelm@19644
   319
wenzelm@380
   320
(* flags *)
wenzelm@380
   321
wenzelm@18712
   322
(*temporarily set flag during execution*)
wenzelm@23932
   323
fun setmp_noncritical flag value f x =
wenzelm@26079
   324
  uninterruptible (fn restore_attributes => fn () =>
wenzelm@26079
   325
    let
wenzelm@26079
   326
      val orig_value = ! flag;
wenzelm@26079
   327
      val _ = flag := value;
wenzelm@26079
   328
      val result = Exn.capture (restore_attributes f) x;
wenzelm@26079
   329
      val _ = flag := orig_value;
wenzelm@26079
   330
    in Exn.release result end) ();
wenzelm@2958
   331
wenzelm@26079
   332
fun setmp flag value f x =
wenzelm@26079
   333
  NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
wenzelm@23932
   334
wenzelm@25797
   335
fun setmp_thread_data tag orig_data data f x =
wenzelm@26079
   336
  uninterruptible (fn restore_attributes => fn () =>
wenzelm@26079
   337
    let
wenzelm@28122
   338
      val _ = Thread.setLocal (tag, data);
wenzelm@26079
   339
      val result = Exn.capture (restore_attributes f) x;
wenzelm@28122
   340
      val _ = Thread.setLocal (tag, orig_data);
wenzelm@26079
   341
    in Exn.release result end) ();
wenzelm@25797
   342
wenzelm@19644
   343
wenzelm@21395
   344
wenzelm@233
   345
(** lists **)
wenzelm@233
   346
skalberg@15570
   347
exception UnequalLengths;
wenzelm@233
   348
wenzelm@5285
   349
fun single x = [x];
wenzelm@233
   350
wenzelm@20882
   351
fun the_single [x] = x
wenzelm@20882
   352
  | the_single _ = raise Empty;
wenzelm@20882
   353
wenzelm@20882
   354
fun singleton f x = the_single (f [x]);
wenzelm@19273
   355
haftmann@25061
   356
fun yield_singleton f x = f [x] #>> the_single;
haftmann@25061
   357
wenzelm@5904
   358
fun apply [] x = x
wenzelm@5904
   359
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   360
wenzelm@25058
   361
fun perhaps_apply funs arg =
wenzelm@25058
   362
  let
wenzelm@25058
   363
    fun app [] res = res
wenzelm@25058
   364
      | app (f :: fs) (changed, x) =
wenzelm@25058
   365
          (case f x of
wenzelm@25058
   366
            NONE => app fs (changed, x)
wenzelm@25058
   367
          | SOME x' => app fs (true, x'));
wenzelm@25058
   368
  in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   369
wenzelm@25058
   370
fun perhaps_loop f arg =
wenzelm@25058
   371
  let
wenzelm@25058
   372
    fun loop (changed, x) =
wenzelm@25058
   373
      (case f x of
wenzelm@25058
   374
        NONE => (changed, x)
wenzelm@25058
   375
      | SOME x' => loop (true, x'));
wenzelm@25058
   376
  in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   377
wenzelm@233
   378
wenzelm@21395
   379
(* fold -- old versions *)
haftmann@16691
   380
wenzelm@233
   381
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   382
wenzelm@233
   383
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   384
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   385
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   386
  let fun itl (e, [])  = e
wenzelm@233
   387
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   388
  in  itl end;
wenzelm@233
   389
wenzelm@233
   390
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   391
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   392
fun foldr f (l, e) =
wenzelm@233
   393
  let fun itr [] = e
wenzelm@233
   394
        | itr (a::l) = f(a, itr l)
wenzelm@233
   395
  in  itr l  end;
wenzelm@233
   396
berghofe@25681
   397
(*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
berghofe@25681
   398
    for operators that associate to the left (TAIL RECURSIVE)*)
berghofe@25681
   399
fun foldl1 f [] = raise Empty
berghofe@25681
   400
  | foldl1 f (x :: xs) = foldl f (x, xs);
berghofe@25681
   401
wenzelm@233
   402
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   403
    for n > 0, operators that associate to the right (not tail recursive)*)
paulson@20443
   404
fun foldr1 f [] = raise Empty
wenzelm@20510
   405
  | foldr1 f l =
paulson@20443
   406
      let fun itr [x] = x
wenzelm@20510
   407
            | itr (x::l) = f(x, itr l)
paulson@20443
   408
      in  itr l  end;
wenzelm@233
   409
wenzelm@16705
   410
fun foldl_map f =
wenzelm@16705
   411
  let
wenzelm@16705
   412
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   413
      | fold_aux (x, y :: ys) =
wenzelm@16705
   414
          let
wenzelm@16705
   415
            val (x', y') = f (x, y);
wenzelm@16705
   416
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   417
          in (x'', y' :: ys') end;
wenzelm@16705
   418
  in fold_aux end;
wenzelm@16705
   419
wenzelm@233
   420
wenzelm@233
   421
(* basic list functions *)
wenzelm@233
   422
wenzelm@20510
   423
fun eq_list eq (list1, list2) =
haftmann@20348
   424
  let
wenzelm@20510
   425
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   426
      | eq_lst _ = true;
wenzelm@20510
   427
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   428
wenzelm@19483
   429
fun maps f [] = []
wenzelm@19483
   430
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   431
haftmann@25538
   432
val filter = List.filter;
haftmann@25538
   433
fun filter_out f = filter (not o f);
haftmann@25538
   434
val map_filter = List.mapPartial;
haftmann@25538
   435
wenzelm@24593
   436
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   437
  | chop _ [] = ([], [])
wenzelm@23220
   438
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   439
wenzelm@233
   440
(*take the first n elements from a list*)
wenzelm@24593
   441
fun take (n: int, []) = []
wenzelm@233
   442
  | take (n, x :: xs) =
wenzelm@233
   443
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   444
wenzelm@233
   445
(*drop the first n elements from a list*)
wenzelm@24593
   446
fun drop (n: int, []) = []
wenzelm@233
   447
  | drop (n, x :: xs) =
wenzelm@233
   448
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   449
nipkow@4713
   450
fun dropwhile P [] = []
nipkow@4713
   451
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   452
wenzelm@233
   453
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   454
  raise Subscript if list too short*)
haftmann@18011
   455
fun nth xs i = List.nth (xs, i);
wenzelm@233
   456
wenzelm@18461
   457
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   458
haftmann@18011
   459
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   460
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
wenzelm@24593
   461
  | nth_map (_: int) _ [] = raise Subscript;
wenzelm@11773
   462
haftmann@24846
   463
fun nth_drop n xs =
haftmann@24846
   464
  List.take (xs, n) @ List.drop (xs, n + 1);
haftmann@24846
   465
haftmann@18514
   466
fun map_index f =
haftmann@18514
   467
  let
wenzelm@24593
   468
    fun mapp (_: int) [] = []
wenzelm@24593
   469
      | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
haftmann@18514
   470
  in mapp 0 end;
haftmann@18514
   471
haftmann@21118
   472
fun fold_index f =
haftmann@21118
   473
  let
wenzelm@24593
   474
    fun fold_aux (_: int) [] y = y
wenzelm@24593
   475
      | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
haftmann@21118
   476
  in fold_aux 0 end;
haftmann@21118
   477
skalberg@15570
   478
val last_elem = List.last;
wenzelm@233
   479
wenzelm@3762
   480
(*rear decomposition*)
skalberg@15570
   481
fun split_last [] = raise Empty
wenzelm@3762
   482
  | split_last [x] = ([], x)
wenzelm@3762
   483
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   484
ballarin@29209
   485
(*find position of first element satisfying a predicate*)
wenzelm@4212
   486
fun find_index pred =
wenzelm@24593
   487
  let fun find (_: int) [] = ~1
wenzelm@4212
   488
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   489
  in find 0 end;
wenzelm@3762
   490
wenzelm@4212
   491
(*find first element satisfying predicate*)
paulson@22593
   492
val find_first = List.find;
wenzelm@233
   493
wenzelm@4916
   494
(*get first element by lookup function*)
skalberg@15531
   495
fun get_first _ [] = NONE
wenzelm@4916
   496
  | get_first f (x :: xs) =
wenzelm@4916
   497
      (case f x of
skalberg@15531
   498
        NONE => get_first f xs
wenzelm@4916
   499
      | some => some);
wenzelm@4916
   500
haftmann@19233
   501
fun get_index f =
haftmann@19233
   502
  let
wenzelm@24593
   503
    fun get (_: int) [] = NONE
wenzelm@19461
   504
      | get i (x :: xs) =
haftmann@19233
   505
          case f x
wenzelm@19461
   506
           of NONE => get (i + 1) xs
haftmann@19233
   507
            | SOME y => SOME (i, y)
haftmann@19233
   508
  in get 0 end;
haftmann@19233
   509
skalberg@15531
   510
val flat = List.concat;
wenzelm@233
   511
wenzelm@12136
   512
fun unflat (xs :: xss) ys =
wenzelm@19424
   513
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   514
      in ps :: unflat xss qs end
wenzelm@12136
   515
  | unflat [] [] = []
skalberg@15570
   516
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   517
wenzelm@21479
   518
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   519
wenzelm@24864
   520
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   521
haftmann@18549
   522
fun fold_burrow f xss s =
haftmann@18549
   523
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   524
wenzelm@233
   525
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   526
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   527
  | separate _ xs = xs;
wenzelm@233
   528
wenzelm@25980
   529
fun surround s (x :: xs) = s :: x :: surround s xs
wenzelm@25980
   530
  | surround s [] = [s];
wenzelm@25980
   531
wenzelm@233
   532
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   533
fun replicate (n: int) x =
wenzelm@233
   534
  let fun rep (0, xs) = xs
wenzelm@233
   535
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   536
  in
skalberg@15570
   537
    if n < 0 then raise Subscript
wenzelm@233
   538
    else rep (n, [])
wenzelm@233
   539
  end;
wenzelm@233
   540
wenzelm@4248
   541
wenzelm@25549
   542
(* direct product *)
wenzelm@25549
   543
haftmann@25538
   544
fun map_product f _ [] = []
haftmann@25538
   545
  | map_product f [] _ = []
haftmann@25538
   546
  | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
wenzelm@233
   547
haftmann@25538
   548
fun fold_product f _ [] z = z
haftmann@25538
   549
  | fold_product f [] _ z = z
haftmann@25538
   550
  | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
wenzelm@233
   551
wenzelm@25549
   552
wenzelm@25549
   553
(* lists of pairs *)
wenzelm@233
   554
skalberg@15570
   555
exception UnequalLengths;
skalberg@15570
   556
haftmann@18330
   557
fun map2 _ [] [] = []
haftmann@18330
   558
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   559
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   560
wenzelm@23220
   561
fun fold2 f [] [] z = z
wenzelm@23220
   562
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@23220
   563
  | fold2 f _ _ _ = raise UnequalLengths;
wenzelm@380
   564
haftmann@25943
   565
fun map_split f [] = ([], [])
haftmann@25943
   566
  | map_split f (x :: xs) =
haftmann@25943
   567
      let
haftmann@25943
   568
        val (y, w) = f x;
haftmann@25943
   569
        val (ys, ws) = map_split f xs;
haftmann@25943
   570
      in (y :: ys, w :: ws) end;
haftmann@25943
   571
wenzelm@19799
   572
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   573
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   574
  | zip_options _ [] = []
wenzelm@19799
   575
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   576
wenzelm@233
   577
(*combine two lists forming a list of pairs:
wenzelm@233
   578
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   579
fun [] ~~ [] = []
wenzelm@233
   580
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   581
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   582
wenzelm@233
   583
(*inverse of ~~; the old 'split':
wenzelm@233
   584
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   585
val split_list = ListPair.unzip;
wenzelm@233
   586
haftmann@28347
   587
fun burrow_fst f xs = split_list xs |>> f |> op ~~;
haftmann@28347
   588
wenzelm@233
   589
wenzelm@233
   590
(* prefixes, suffixes *)
wenzelm@233
   591
haftmann@18441
   592
fun is_prefix _ [] _ = true
haftmann@18441
   593
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   594
  | is_prefix eq _ _ = false;
wenzelm@233
   595
wenzelm@233
   596
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   597
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   598
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   599
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   600
        | take (rxs, x :: xs) =
wenzelm@255
   601
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   602
  in  take([], xs)  end;
wenzelm@233
   603
haftmann@20108
   604
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   605
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   606
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   607
      if eq (x, y) then
haftmann@20108
   608
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   609
        in (x :: ps', xys'') end
haftmann@20108
   610
      else ([], (xs, ys));
haftmann@20108
   611
wenzelm@233
   612
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   613
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   614
fun take_suffix _ [] = ([], [])
wenzelm@233
   615
  | take_suffix pred (x :: xs) =
wenzelm@233
   616
      (case take_suffix pred xs of
wenzelm@233
   617
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   618
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   619
wenzelm@12249
   620
fun prefixes1 [] = []
wenzelm@12249
   621
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   622
wenzelm@19011
   623
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   624
wenzelm@12249
   625
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   626
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   627
wenzelm@23220
   628
wenzelm@23220
   629
wenzelm@233
   630
(** integers **)
wenzelm@233
   631
wenzelm@233
   632
(* lists of integers *)
wenzelm@233
   633
wenzelm@233
   634
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   635
fun ((i: int) upto j) =
wenzelm@21859
   636
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   637
wenzelm@233
   638
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   639
fun ((i: int) downto j) =
wenzelm@21859
   640
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   641
wenzelm@233
   642
wenzelm@233
   643
(* convert integers to strings *)
wenzelm@233
   644
wenzelm@233
   645
(*expand the number in the given base;
wenzelm@233
   646
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   647
fun radixpand (base, num) : int list =
wenzelm@233
   648
  let
wenzelm@233
   649
    fun radix (n, tail) =
wenzelm@233
   650
      if n < base then n :: tail
wenzelm@233
   651
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   652
  in radix (num, []) end;
wenzelm@233
   653
wenzelm@233
   654
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   655
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   656
fun radixstring (base, zerochar, num) =
wenzelm@233
   657
  let val offset = ord zerochar;
wenzelm@233
   658
      fun chrof n = chr (offset + n)
wenzelm@233
   659
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   660
wenzelm@233
   661
paulson@3407
   662
val string_of_int = Int.toString;
wenzelm@233
   663
wenzelm@21942
   664
fun signed_string_of_int i =
wenzelm@21942
   665
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   666
wenzelm@23220
   667
fun string_of_indexname (a, 0) = a
wenzelm@23220
   668
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   669
wenzelm@233
   670
wenzelm@14826
   671
(* read integers *)
wenzelm@14826
   672
wenzelm@24630
   673
fun read_radix_int radix cs =
wenzelm@20095
   674
  let
wenzelm@20095
   675
    val zero = ord "0";
wenzelm@20095
   676
    val limit = zero + radix;
wenzelm@20095
   677
    fun scan (num, []) = (num, [])
wenzelm@20095
   678
      | scan (num, c :: cs) =
wenzelm@20095
   679
        if zero <= ord c andalso ord c < limit then
wenzelm@24630
   680
          scan (radix * num + (ord c - zero), cs)
wenzelm@20095
   681
        else (num, c :: cs);
wenzelm@24630
   682
  in scan (0, cs) end;
wenzelm@14826
   683
wenzelm@24630
   684
val read_int = read_radix_int 10;
wenzelm@14826
   685
wenzelm@24630
   686
fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
wenzelm@14826
   687
wenzelm@14826
   688
wenzelm@14826
   689
wenzelm@233
   690
(** strings **)
wenzelm@233
   691
wenzelm@16188
   692
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   693
haftmann@18011
   694
fun nth_string str i =
wenzelm@6959
   695
  (case try String.substring (str, i, 1) of
skalberg@15531
   696
    SOME s => s
skalberg@15570
   697
  | NONE => raise Subscript);
wenzelm@6312
   698
wenzelm@16188
   699
fun fold_string f str x0 =
wenzelm@6282
   700
  let
wenzelm@6282
   701
    val n = size str;
wenzelm@16188
   702
    fun iter (x, i) =
wenzelm@16188
   703
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   704
  in iter (x0, 0) end;
wenzelm@6282
   705
wenzelm@14968
   706
fun exists_string pred str =
wenzelm@14968
   707
  let
wenzelm@14968
   708
    val n = size str;
wenzelm@14968
   709
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   710
  in ex 0 end;
wenzelm@6312
   711
wenzelm@16188
   712
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   713
wenzelm@28025
   714
fun first_field sep str =
wenzelm@28022
   715
  let
wenzelm@28025
   716
    val n = size sep;
wenzelm@28022
   717
    val len = size str;
wenzelm@28022
   718
    fun find i =
wenzelm@28022
   719
      if i + n > len then NONE
wenzelm@28025
   720
      else if String.substring (str, i, n) = sep then SOME i
wenzelm@28022
   721
      else find (i + 1);
wenzelm@28025
   722
  in
wenzelm@28025
   723
    (case find 0 of
wenzelm@28025
   724
      NONE => NONE
wenzelm@28025
   725
    | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
wenzelm@28025
   726
  end;
wenzelm@28022
   727
lcp@512
   728
(*enclose in brackets*)
lcp@512
   729
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   730
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   731
wenzelm@233
   732
(*simple quoting (does not escape special chars)*)
lcp@512
   733
val quote = enclose "\"" "\"";
wenzelm@233
   734
wenzelm@4212
   735
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   736
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   737
wenzelm@255
   738
val commas = space_implode ", ";
wenzelm@380
   739
val commas_quote = commas o map quote;
wenzelm@255
   740
wenzelm@233
   741
(*concatenate messages, one per line, into a string*)
wenzelm@255
   742
val cat_lines = space_implode "\n";
wenzelm@233
   743
wenzelm@4212
   744
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   745
fun space_explode _ "" = []
paulson@21899
   746
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   747
wenzelm@3832
   748
val split_lines = space_explode "\n";
wenzelm@3832
   749
wenzelm@14826
   750
fun prefix_lines "" txt = txt
wenzelm@14826
   751
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   752
wenzelm@18681
   753
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   754
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   755
wenzelm@18681
   756
fun unprefix prfx s =
wenzelm@18681
   757
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   758
  else raise Fail "unprefix";
wenzelm@18681
   759
wenzelm@16188
   760
fun unsuffix sffx s =
wenzelm@17061
   761
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   762
  else raise Fail "unsuffix";
wenzelm@5285
   763
wenzelm@24593
   764
fun replicate_string (0: int) _ = ""
wenzelm@10951
   765
  | replicate_string 1 a = a
wenzelm@10951
   766
  | replicate_string k a =
wenzelm@10951
   767
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   768
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   769
haftmann@31250
   770
fun translate_string f = String.translate (f o String.str);
haftmann@31250
   771
kleing@29882
   772
(*crude matching of str against simple glob pat*)
kleing@29882
   773
fun match_string pat str =
kleing@29882
   774
  let
kleing@29882
   775
    fun match [] _ = true
kleing@29882
   776
      | match (p :: ps) s =
kleing@29882
   777
          size p <= size s andalso
kleing@29882
   778
            (case try (unprefix p) s of
kleing@29882
   779
              SOME s' => match ps s'
kleing@29882
   780
            | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
kleing@29882
   781
  in match (space_explode "*" pat) str end;
wenzelm@23220
   782
wenzelm@16492
   783
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   784
wenzelm@26439
   785
(* canonical operations *)
wenzelm@26439
   786
wenzelm@18923
   787
fun member eq list x =
wenzelm@18923
   788
  let
wenzelm@18923
   789
    fun memb [] = false
wenzelm@18923
   790
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   791
  in memb list end;
berghofe@1576
   792
wenzelm@18923
   793
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   794
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   795
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   796
wenzelm@19301
   797
fun subtract eq = fold (remove eq);
wenzelm@19301
   798
wenzelm@30572
   799
fun merge eq (xs, ys) =
wenzelm@30572
   800
  if pointer_eq (xs, ys) then xs
wenzelm@30572
   801
  else if null xs then ys
wenzelm@30572
   802
  else fold_rev (insert eq) ys xs;
clasohm@0
   803
wenzelm@26439
   804
wenzelm@26439
   805
(* old-style infixes *)
wenzelm@26439
   806
wenzelm@18923
   807
fun x mem xs = member (op =) xs x;
wenzelm@18923
   808
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   809
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   810
wenzelm@233
   811
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   812
fun xs union [] = xs
wenzelm@233
   813
  | [] union ys = ys
haftmann@20854
   814
  | (x :: xs) union ys = xs union (insert (op =) x ys);
clasohm@0
   815
paulson@2175
   816
(*union of sets, optimized version for ints*)
berghofe@1576
   817
fun (xs:int list) union_int [] = xs
berghofe@1576
   818
  | [] union_int ys = ys
haftmann@20854
   819
  | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
berghofe@1576
   820
paulson@2175
   821
(*union of sets, optimized version for strings*)
berghofe@1576
   822
fun (xs:string list) union_string [] = xs
berghofe@1576
   823
  | [] union_string ys = ys
haftmann@20854
   824
  | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
berghofe@1576
   825
clasohm@0
   826
(*generalized union*)
wenzelm@233
   827
fun gen_union eq (xs, []) = xs
wenzelm@233
   828
  | gen_union eq ([], ys) = ys
wenzelm@18923
   829
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   830
wenzelm@233
   831
wenzelm@233
   832
(*intersection*)
wenzelm@233
   833
fun [] inter ys = []
wenzelm@233
   834
  | (x :: xs) inter ys =
wenzelm@233
   835
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   836
paulson@2175
   837
(*intersection, optimized version for ints*)
berghofe@1576
   838
fun ([]:int list) inter_int ys = []
berghofe@1576
   839
  | (x :: xs) inter_int ys =
berghofe@1576
   840
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   841
paulson@2175
   842
(*intersection, optimized version for strings *)
berghofe@1576
   843
fun ([]:string list) inter_string ys = []
berghofe@1576
   844
  | (x :: xs) inter_string ys =
berghofe@1576
   845
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   846
paulson@7090
   847
(*generalized intersection*)
paulson@7090
   848
fun gen_inter eq ([], ys) = []
wenzelm@12284
   849
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
   850
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
   851
      else gen_inter eq (xs, ys);
paulson@7090
   852
wenzelm@233
   853
wenzelm@233
   854
(*subset*)
wenzelm@233
   855
fun [] subset ys = true
wenzelm@233
   856
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   857
paulson@2175
   858
(*subset, optimized version for ints*)
wenzelm@16439
   859
fun ([]: int list) subset_int ys = true
berghofe@1576
   860
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   861
paulson@2175
   862
(*subset, optimized version for strings*)
wenzelm@16439
   863
fun ([]: string list) subset_string ys = true
berghofe@1576
   864
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   865
wenzelm@4363
   866
(*set equality*)
wenzelm@4363
   867
fun eq_set (xs, ys) =
wenzelm@4363
   868
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   869
paulson@2182
   870
(*set equality for strings*)
wenzelm@16439
   871
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   872
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   873
wenzelm@18923
   874
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
   875
wenzelm@19301
   876
fun gen_eq_set eq (xs, ys) =
haftmann@20348
   877
  eq_list eq (xs, ys) orelse
wenzelm@19301
   878
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
   879
wenzelm@265
   880
wenzelm@233
   881
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   882
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   883
  | [] \ x = [];
paulson@2243
   884
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   885
wenzelm@233
   886
wenzelm@233
   887
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   888
  first of equal elements*)
wenzelm@19046
   889
fun distinct eq lst =
wenzelm@233
   890
  let
wenzelm@233
   891
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   892
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   893
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   894
          else dist (x :: rev_seen, xs);
wenzelm@19046
   895
  in dist ([], lst) end;
wenzelm@233
   896
wenzelm@255
   897
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   898
  order, takes first of equal elements*)
wenzelm@18966
   899
fun duplicates eq lst =
wenzelm@255
   900
  let
wenzelm@255
   901
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   902
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   903
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   904
            dups (rev_dups, xs)
wenzelm@255
   905
          else dups (x :: rev_dups, xs);
wenzelm@18966
   906
  in dups ([], lst) end;
wenzelm@255
   907
wenzelm@16878
   908
fun has_duplicates eq =
wenzelm@16878
   909
  let
wenzelm@16878
   910
    fun dups [] = false
wenzelm@16878
   911
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   912
  in dups end;
wenzelm@16878
   913
wenzelm@255
   914
haftmann@32352
   915
(* matrices *)
haftmann@32352
   916
haftmann@32352
   917
fun map_transpose f xss =
haftmann@32352
   918
  let
haftmann@32352
   919
    val n = case distinct (op =) (map length xss)
haftmann@32352
   920
     of [] => 0
haftmann@32352
   921
      | [n] => n
haftmann@32352
   922
      | _ => raise UnequalLengths;
haftmann@32352
   923
  in map (fn m => f (map (fn xs => nth xs m) xss)) (0 upto n - 1) end;
haftmann@32352
   924
haftmann@32352
   925
wenzelm@23220
   926
nipkow@22142
   927
(** lists as multisets **)
nipkow@22142
   928
nipkow@22142
   929
fun remove1 _ _ [] = raise Empty
wenzelm@23220
   930
  | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
nipkow@22142
   931
wenzelm@23220
   932
fun submultiset _ ([], _)  = true
wenzelm@23220
   933
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
wenzelm@233
   934
clasohm@0
   935
clasohm@0
   936
wenzelm@2506
   937
(** orders **)
wenzelm@2506
   938
wenzelm@18966
   939
fun is_equal EQUAL = true
wenzelm@18966
   940
  | is_equal _ = false;
wenzelm@18966
   941
wenzelm@4445
   942
fun rev_order LESS = GREATER
wenzelm@4445
   943
  | rev_order EQUAL = EQUAL
wenzelm@4445
   944
  | rev_order GREATER = LESS;
wenzelm@4445
   945
wenzelm@4479
   946
(*assume rel is a linear strict order*)
wenzelm@4445
   947
fun make_ord rel (x, y) =
wenzelm@4445
   948
  if rel (x, y) then LESS
wenzelm@4445
   949
  else if rel (y, x) then GREATER
wenzelm@4445
   950
  else EQUAL;
wenzelm@4445
   951
wenzelm@25224
   952
fun bool_ord (false, true) = LESS
wenzelm@25224
   953
  | bool_ord (true, false) = GREATER
wenzelm@25224
   954
  | bool_ord _ = EQUAL;
wenzelm@25224
   955
wenzelm@15051
   956
val int_ord = Int.compare;
wenzelm@15051
   957
val string_ord = String.compare;
wenzelm@2506
   958
wenzelm@16676
   959
fun fast_string_ord (s1, s2) =
wenzelm@16676
   960
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   961
wenzelm@16492
   962
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   963
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   964
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   965
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   966
wenzelm@4343
   967
(*lexicographic product*)
wenzelm@4343
   968
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   969
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   970
wenzelm@4343
   971
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   972
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   973
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   974
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   975
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   976
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   977
wenzelm@4343
   978
(*lexicographic product of lists*)
wenzelm@4343
   979
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   980
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   981
wenzelm@2506
   982
wenzelm@4621
   983
(* sorting *)
wenzelm@4621
   984
wenzelm@18427
   985
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
   986
fun quicksort unique ord =
wenzelm@4621
   987
  let
wenzelm@16878
   988
    fun qsort [] = []
wenzelm@16878
   989
      | qsort (xs as [_]) = xs
wenzelm@18427
   990
      | qsort (xs as [x, y]) =
wenzelm@18427
   991
          (case ord (x, y) of
wenzelm@18427
   992
            LESS => xs
wenzelm@18427
   993
          | EQUAL => if unique then [x] else xs
wenzelm@18427
   994
          | GREATER => [y, x])
wenzelm@16878
   995
      | qsort xs =
haftmann@18011
   996
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
   997
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
   998
    and part _ [] = ([], [], [])
wenzelm@4621
   999
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1000
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
  1001
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
  1002
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
  1003
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1004
  in qsort end;
wenzelm@4621
  1005
wenzelm@18427
  1006
fun sort ord = quicksort false ord;
wenzelm@18427
  1007
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
  1008
wenzelm@4621
  1009
val sort_strings = sort string_ord;
wenzelm@4621
  1010
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1011
wenzelm@4621
  1012
wenzelm@30558
  1013
(* items tagged by integer index *)
wenzelm@30558
  1014
wenzelm@30558
  1015
(*insert tags*)
wenzelm@30558
  1016
fun tag_list k [] = []
haftmann@30570
  1017
  | tag_list k (x :: xs) = (k:int, x) :: tag_list (k + 1) xs;
wenzelm@30558
  1018
wenzelm@30558
  1019
(*remove tags and suppress duplicates -- list is assumed sorted!*)
wenzelm@30558
  1020
fun untag_list [] = []
wenzelm@30558
  1021
  | untag_list [(k: int, x)] = [x]
wenzelm@30558
  1022
  | untag_list ((k, x) :: (rest as (k', x') :: _)) =
wenzelm@30558
  1023
      if k = k' then untag_list rest
wenzelm@30558
  1024
      else x :: untag_list rest;
wenzelm@30558
  1025
wenzelm@30558
  1026
(*return list elements in original order*)
wenzelm@30558
  1027
fun order_list list = untag_list (sort (int_ord o pairself fst) list);
wenzelm@30558
  1028
wenzelm@30558
  1029
wenzelm@2506
  1030
berghofe@14106
  1031
(** random numbers **)
berghofe@14106
  1032
berghofe@14106
  1033
exception RANDOM;
berghofe@14106
  1034
berghofe@14618
  1035
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1036
berghofe@14106
  1037
local
berghofe@14106
  1038
  val a = 16807.0;
berghofe@14106
  1039
  val m = 2147483647.0;
wenzelm@32737
  1040
  val random_seed = Unsynchronized.ref 1.0;
berghofe@14106
  1041
in
berghofe@14106
  1042
wenzelm@23922
  1043
fun random () = CRITICAL (fn () =>
wenzelm@23922
  1044
  let val r = rmod (a * ! random_seed) m
wenzelm@23922
  1045
  in (random_seed := r; r) end);
berghofe@14106
  1046
berghofe@14106
  1047
end;
berghofe@14106
  1048
berghofe@14106
  1049
fun random_range l h =
berghofe@14106
  1050
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1051
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1052
haftmann@18011
  1053
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1054
berghofe@14106
  1055
fun frequency xs =
berghofe@14106
  1056
  let
berghofe@14106
  1057
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1058
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1059
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1060
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1061
berghofe@14106
  1062
wenzelm@23220
  1063
wenzelm@4621
  1064
(** misc **)
wenzelm@233
  1065
wenzelm@19644
  1066
fun divide_and_conquer decomp x =
wenzelm@19644
  1067
  let val (ys, recomb) = decomp x
wenzelm@19644
  1068
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1069
clasohm@0
  1070
wenzelm@233
  1071
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1072
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1073
fun partition_list p i j =
wenzelm@233
  1074
  let fun part k xs =
wenzelm@233
  1075
            if k>j then
clasohm@0
  1076
              (case xs of [] => []
skalberg@15570
  1077
                         | _ => raise Fail "partition_list")
clasohm@0
  1078
            else
wenzelm@19691
  1079
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1080
            in  ns :: part(k+1)rest  end
wenzelm@24593
  1081
  in  part (i: int) end;
clasohm@0
  1082
wenzelm@19691
  1083
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1084
  let
wenzelm@19691
  1085
    fun part [] = []
wenzelm@19691
  1086
      | part (x :: ys) =
wenzelm@19691
  1087
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1088
          in (x::xs)::(part xs') end
wenzelm@19691
  1089
  in part end;
wenzelm@19691
  1090
wenzelm@19691
  1091
clasohm@0
  1092
wenzelm@233
  1093
(* generating identifiers *)
clasohm@0
  1094
paulson@4063
  1095
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
wenzelm@22369
  1096
local
wenzelm@22369
  1097
(*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
wenzelm@22582
  1098
fun gensym_char i =
paulson@22368
  1099
  if i<26 then chr (ord "A" + i)
paulson@22368
  1100
  else if i<52 then chr (ord "a" + i - 26)
wenzelm@22369
  1101
  else chr (ord "0" + i - 52);
paulson@4063
  1102
wenzelm@22369
  1103
val char_vec = Vector.tabulate (62, gensym_char);
wenzelm@22369
  1104
fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
wenzelm@4284
  1105
wenzelm@32737
  1106
val gensym_seed = Unsynchronized.ref (0: int);
paulson@2003
  1107
wenzelm@22369
  1108
in
wenzelm@32737
  1109
  fun gensym pre =
wenzelm@32737
  1110
    pre ^ newid (NAMED_CRITICAL "gensym" (fn () => Unsynchronized.inc gensym_seed));
wenzelm@22369
  1111
end;
paulson@4063
  1112
paulson@4063
  1113
wenzelm@16439
  1114
(* stamps and serial numbers *)
wenzelm@16439
  1115
wenzelm@32737
  1116
type stamp = unit Unsynchronized.ref;
wenzelm@32737
  1117
val stamp: unit -> stamp = Unsynchronized.ref;
wenzelm@16439
  1118
wenzelm@16439
  1119
type serial = int;
wenzelm@25702
  1120
val serial = Multithreading.serial;
wenzelm@19512
  1121
val serial_string = string_of_int o serial;
wenzelm@19512
  1122
wenzelm@16535
  1123
wenzelm@16535
  1124
(* generic objects *)
wenzelm@16535
  1125
wenzelm@16535
  1126
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1127
  constructors at any time*)
wenzelm@16535
  1128
structure Object = struct type T = exn end;
wenzelm@16535
  1129
clasohm@1364
  1130
end;
clasohm@1364
  1131
wenzelm@32188
  1132
structure Basic_Library: BASIC_LIBRARY = Library;
wenzelm@32188
  1133
open Basic_Library;