src/Pure/library.ML
author wenzelm
Thu Oct 11 19:10:21 2007 +0200 (2007-10-11)
changeset 24979 783bf93c8f92
parent 24864 f33ff5fc1f7e
child 25058 d8d8bac48031
permissions -rw-r--r--
removed obsolete flip;
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(*  Title:      Pure/library.ML
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    ID:         $Id$
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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, options, 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 1 |>>>
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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 |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
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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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  (*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 set: bool ref -> bool
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  val reset: bool ref -> bool
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  val toggle: bool ref -> bool
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  val change: 'a ref -> ('a -> 'a) -> unit
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  val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val setmp: 'a ref -> '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 apply: ('a -> 'a) list -> 'a -> 'a
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  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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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 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 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_index_eq: ''a -> ''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 split_list: ('a * 'b) list -> 'a list * 'b list
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  val separate: 'a -> 'a list -> 'a list
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  val replicate: int -> 'a -> 'a list
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  val multiply: 'a list -> 'a list list -> 'a list list
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  val product: 'a list -> 'b list -> ('a * '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 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 inc: int ref -> int
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  val dec: int ref -> int
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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 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 untabify: string list -> string list
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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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  (*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 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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  (*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 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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(*application and structured results -- old version*)
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fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
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(*conditional application*)
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fun b ? f = fn x => if b then f x else x;
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(*composition with multiple args*)
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fun (f oo g) x y = f (g x y);
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fun (f ooo g) x y z = f (g x y z);
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fun (f oooo g) x y z w = f (g x y z w);
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(*function exponentiation: f(...(f x)...) with n applications of f*)
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fun funpow (0: int) _ x = x
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  | funpow n f x = funpow (n - 1) f (f x);
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(* 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;
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fun snd (x, y) = y;
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fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
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fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
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fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
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fun swap (x, y) = (y, x);
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fun apfst f (x, y) = (f x, y);
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fun apsnd f (x, y) = (x, f y);
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fun pairself f (x, y) = (f x, f y);
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wenzelm@21395
   302
(* booleans *)
wenzelm@233
   303
wenzelm@21395
   304
(*polymorphic equality*)
wenzelm@233
   305
fun equal x y = x = y;
wenzelm@233
   306
fun not_equal x y = x <> y;
wenzelm@233
   307
wenzelm@21395
   308
(*combining predicates*)
wenzelm@16721
   309
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   310
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   311
wenzelm@233
   312
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   313
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   314
  let fun boolf [] = false
wenzelm@233
   315
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   316
  in boolf end;
wenzelm@233
   317
wenzelm@233
   318
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   319
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   320
  let fun boolf [] = true
wenzelm@233
   321
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   322
  in boolf end;
clasohm@0
   323
wenzelm@19644
   324
wenzelm@380
   325
(* flags *)
wenzelm@380
   326
wenzelm@380
   327
fun set flag = (flag := true; true);
wenzelm@380
   328
fun reset flag = (flag := false; false);
wenzelm@380
   329
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   330
wenzelm@9118
   331
fun change r f = r := f (! r);
wenzelm@9118
   332
wenzelm@18712
   333
(*temporarily set flag during execution*)
wenzelm@23932
   334
fun setmp_noncritical flag value f x =
wenzelm@2958
   335
  let
wenzelm@2958
   336
    val orig_value = ! flag;
wenzelm@18712
   337
    val _ = flag := value;
wenzelm@23963
   338
    val result = Exn.capture f x;
wenzelm@18712
   339
    val _ = flag := orig_value;
wenzelm@23963
   340
  in Exn.release result end;
wenzelm@2958
   341
wenzelm@24023
   342
fun setmp flag value f x = NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
wenzelm@23932
   343
wenzelm@19644
   344
wenzelm@21395
   345
wenzelm@233
   346
(** lists **)
wenzelm@233
   347
skalberg@15570
   348
exception UnequalLengths;
wenzelm@233
   349
wenzelm@5285
   350
fun single x = [x];
wenzelm@233
   351
wenzelm@20882
   352
fun the_single [x] = x
wenzelm@20882
   353
  | the_single _ = raise Empty;
wenzelm@20882
   354
wenzelm@20882
   355
fun singleton f x = the_single (f [x]);
wenzelm@19273
   356
wenzelm@5904
   357
fun apply [] x = x
wenzelm@5904
   358
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   359
wenzelm@233
   360
wenzelm@21395
   361
(* fold -- old versions *)
haftmann@16691
   362
wenzelm@233
   363
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   364
wenzelm@233
   365
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   366
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   367
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   368
  let fun itl (e, [])  = e
wenzelm@233
   369
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   370
  in  itl end;
wenzelm@233
   371
wenzelm@233
   372
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   373
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   374
fun foldr f (l, e) =
wenzelm@233
   375
  let fun itr [] = e
wenzelm@233
   376
        | itr (a::l) = f(a, itr l)
wenzelm@233
   377
  in  itr l  end;
wenzelm@233
   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)*)
paulson@20443
   381
fun foldr1 f [] = raise 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@16705
   387
fun foldl_map f =
wenzelm@16705
   388
  let
wenzelm@16705
   389
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   390
      | fold_aux (x, y :: ys) =
wenzelm@16705
   391
          let
wenzelm@16705
   392
            val (x', y') = f (x, y);
wenzelm@16705
   393
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   394
          in (x'', y' :: ys') end;
wenzelm@16705
   395
  in fold_aux end;
wenzelm@16705
   396
wenzelm@233
   397
wenzelm@233
   398
(* basic list functions *)
wenzelm@233
   399
wenzelm@20510
   400
fun eq_list eq (list1, list2) =
haftmann@20348
   401
  let
wenzelm@20510
   402
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   403
      | eq_lst _ = true;
wenzelm@20510
   404
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   405
wenzelm@19483
   406
fun maps f [] = []
wenzelm@19483
   407
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   408
wenzelm@24593
   409
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   410
  | chop _ [] = ([], [])
wenzelm@23220
   411
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   412
wenzelm@233
   413
(*take the first n elements from a list*)
wenzelm@24593
   414
fun take (n: int, []) = []
wenzelm@233
   415
  | take (n, x :: xs) =
wenzelm@233
   416
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   417
wenzelm@233
   418
(*drop the first n elements from a list*)
wenzelm@24593
   419
fun drop (n: int, []) = []
wenzelm@233
   420
  | drop (n, x :: xs) =
wenzelm@233
   421
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   422
nipkow@4713
   423
fun dropwhile P [] = []
nipkow@4713
   424
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   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@18461
   430
fun nth_list xss i = nth xss i handle 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
skalberg@15570
   451
val last_elem = List.last;
wenzelm@233
   452
wenzelm@3762
   453
(*rear decomposition*)
skalberg@15570
   454
fun split_last [] = raise Empty
wenzelm@3762
   455
  | split_last [x] = ([], x)
wenzelm@3762
   456
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   457
wenzelm@4212
   458
(*find the position of an element in a list*)
wenzelm@4212
   459
fun find_index pred =
wenzelm@24593
   460
  let fun find (_: int) [] = ~1
wenzelm@4212
   461
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   462
  in find 0 end;
wenzelm@3762
   463
wenzelm@4224
   464
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   465
wenzelm@4212
   466
(*find first element satisfying predicate*)
paulson@22593
   467
val find_first = List.find;
wenzelm@233
   468
wenzelm@4916
   469
(*get first element by lookup function*)
skalberg@15531
   470
fun get_first _ [] = NONE
wenzelm@4916
   471
  | get_first f (x :: xs) =
wenzelm@4916
   472
      (case f x of
skalberg@15531
   473
        NONE => get_first f xs
wenzelm@4916
   474
      | some => some);
wenzelm@4916
   475
haftmann@19233
   476
fun get_index f =
haftmann@19233
   477
  let
wenzelm@24593
   478
    fun get (_: int) [] = NONE
wenzelm@19461
   479
      | get i (x :: xs) =
haftmann@19233
   480
          case f x
wenzelm@19461
   481
           of NONE => get (i + 1) xs
haftmann@19233
   482
            | SOME y => SOME (i, y)
haftmann@19233
   483
  in get 0 end;
haftmann@19233
   484
skalberg@15531
   485
val flat = List.concat;
wenzelm@233
   486
wenzelm@12136
   487
fun unflat (xs :: xss) ys =
wenzelm@19424
   488
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   489
      in ps :: unflat xss qs end
wenzelm@12136
   490
  | unflat [] [] = []
skalberg@15570
   491
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   492
wenzelm@21479
   493
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   494
wenzelm@24864
   495
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   496
haftmann@18549
   497
fun fold_burrow f xss s =
haftmann@18549
   498
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   499
wenzelm@233
   500
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   501
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   502
  | separate _ xs = xs;
wenzelm@233
   503
wenzelm@233
   504
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   505
fun replicate (n: int) x =
wenzelm@233
   506
  let fun rep (0, xs) = xs
wenzelm@233
   507
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   508
  in
skalberg@15570
   509
    if n < 0 then raise Subscript
wenzelm@233
   510
    else rep (n, [])
wenzelm@233
   511
  end;
wenzelm@233
   512
wenzelm@14926
   513
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   514
wenzelm@4248
   515
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   516
fun multiply [] _ = []
wenzelm@18148
   517
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   518
wenzelm@14792
   519
(*direct product*)
wenzelm@14792
   520
fun product _ [] = []
wenzelm@14792
   521
  | product [] _ = []
wenzelm@14792
   522
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   523
wenzelm@233
   524
wenzelm@233
   525
(* filter *)
wenzelm@233
   526
wenzelm@233
   527
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   528
val filter = List.filter;
clasohm@0
   529
fun filter_out f = filter (not o f);
wenzelm@19483
   530
val map_filter = List.mapPartial;
wenzelm@233
   531
wenzelm@233
   532
wenzelm@233
   533
(* lists of pairs *)
wenzelm@233
   534
skalberg@15570
   535
exception UnequalLengths;
skalberg@15570
   536
haftmann@18330
   537
fun map2 _ [] [] = []
haftmann@18330
   538
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   539
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   540
wenzelm@23220
   541
fun fold2 f [] [] z = z
wenzelm@23220
   542
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@23220
   543
  | fold2 f _ _ _ = raise UnequalLengths;
wenzelm@380
   544
wenzelm@19799
   545
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   546
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   547
  | zip_options _ [] = []
wenzelm@19799
   548
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   549
wenzelm@233
   550
(*combine two lists forming a list of pairs:
wenzelm@233
   551
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   552
fun [] ~~ [] = []
wenzelm@233
   553
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   554
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   555
wenzelm@233
   556
(*inverse of ~~; the old 'split':
wenzelm@233
   557
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   558
val split_list = ListPair.unzip;
wenzelm@233
   559
wenzelm@233
   560
wenzelm@233
   561
(* prefixes, suffixes *)
wenzelm@233
   562
haftmann@18441
   563
fun is_prefix _ [] _ = true
haftmann@18441
   564
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   565
  | is_prefix eq _ _ = false;
wenzelm@233
   566
wenzelm@233
   567
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   568
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   569
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   570
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   571
        | take (rxs, x :: xs) =
wenzelm@255
   572
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   573
  in  take([], xs)  end;
wenzelm@233
   574
haftmann@20108
   575
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   576
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   577
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   578
      if eq (x, y) then
haftmann@20108
   579
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   580
        in (x :: ps', xys'') end
haftmann@20108
   581
      else ([], (xs, ys));
haftmann@20108
   582
wenzelm@233
   583
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   584
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   585
fun take_suffix _ [] = ([], [])
wenzelm@233
   586
  | take_suffix pred (x :: xs) =
wenzelm@233
   587
      (case take_suffix pred xs of
wenzelm@233
   588
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   589
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   590
wenzelm@12249
   591
fun prefixes1 [] = []
wenzelm@12249
   592
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   593
wenzelm@19011
   594
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   595
wenzelm@12249
   596
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   597
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   598
wenzelm@23220
   599
wenzelm@23220
   600
wenzelm@233
   601
(** integers **)
wenzelm@233
   602
wenzelm@24593
   603
fun inc i = (i := ! i + (1: int); ! i);
wenzelm@24593
   604
fun dec i = (i := ! i - (1: int); ! i);
wenzelm@233
   605
wenzelm@233
   606
wenzelm@233
   607
(* lists of integers *)
wenzelm@233
   608
wenzelm@233
   609
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   610
fun ((i: int) upto j) =
wenzelm@21859
   611
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   612
wenzelm@233
   613
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   614
fun ((i: int) downto j) =
wenzelm@21859
   615
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   616
wenzelm@233
   617
wenzelm@233
   618
(* convert integers to strings *)
wenzelm@233
   619
wenzelm@233
   620
(*expand the number in the given base;
wenzelm@233
   621
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   622
fun radixpand (base, num) : int list =
wenzelm@233
   623
  let
wenzelm@233
   624
    fun radix (n, tail) =
wenzelm@233
   625
      if n < base then n :: tail
wenzelm@233
   626
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   627
  in radix (num, []) end;
wenzelm@233
   628
wenzelm@233
   629
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   630
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   631
fun radixstring (base, zerochar, num) =
wenzelm@233
   632
  let val offset = ord zerochar;
wenzelm@233
   633
      fun chrof n = chr (offset + n)
wenzelm@233
   634
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   635
wenzelm@233
   636
paulson@3407
   637
val string_of_int = Int.toString;
wenzelm@233
   638
wenzelm@21942
   639
fun signed_string_of_int i =
wenzelm@21942
   640
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   641
wenzelm@23220
   642
fun string_of_indexname (a, 0) = a
wenzelm@23220
   643
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   644
wenzelm@233
   645
wenzelm@14826
   646
(* read integers *)
wenzelm@14826
   647
wenzelm@24630
   648
fun read_radix_int radix cs =
wenzelm@20095
   649
  let
wenzelm@20095
   650
    val zero = ord "0";
wenzelm@20095
   651
    val limit = zero + radix;
wenzelm@20095
   652
    fun scan (num, []) = (num, [])
wenzelm@20095
   653
      | scan (num, c :: cs) =
wenzelm@20095
   654
        if zero <= ord c andalso ord c < limit then
wenzelm@24630
   655
          scan (radix * num + (ord c - zero), cs)
wenzelm@20095
   656
        else (num, c :: cs);
wenzelm@24630
   657
  in scan (0, cs) end;
wenzelm@14826
   658
wenzelm@24630
   659
val read_int = read_radix_int 10;
wenzelm@14826
   660
wenzelm@24630
   661
fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
wenzelm@14826
   662
wenzelm@14826
   663
wenzelm@14826
   664
wenzelm@233
   665
(** strings **)
wenzelm@233
   666
wenzelm@16188
   667
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   668
haftmann@18011
   669
fun nth_string str i =
wenzelm@6959
   670
  (case try String.substring (str, i, 1) of
skalberg@15531
   671
    SOME s => s
skalberg@15570
   672
  | NONE => raise Subscript);
wenzelm@6312
   673
wenzelm@16188
   674
fun fold_string f str x0 =
wenzelm@6282
   675
  let
wenzelm@6282
   676
    val n = size str;
wenzelm@16188
   677
    fun iter (x, i) =
wenzelm@16188
   678
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   679
  in iter (x0, 0) end;
wenzelm@6282
   680
wenzelm@14968
   681
fun exists_string pred str =
wenzelm@14968
   682
  let
wenzelm@14968
   683
    val n = size str;
wenzelm@14968
   684
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   685
  in ex 0 end;
wenzelm@6312
   686
wenzelm@16188
   687
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   688
lcp@512
   689
(*enclose in brackets*)
lcp@512
   690
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   691
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   692
wenzelm@233
   693
(*simple quoting (does not escape special chars)*)
lcp@512
   694
val quote = enclose "\"" "\"";
wenzelm@233
   695
wenzelm@4212
   696
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   697
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   698
wenzelm@255
   699
val commas = space_implode ", ";
wenzelm@380
   700
val commas_quote = commas o map quote;
wenzelm@255
   701
wenzelm@233
   702
(*concatenate messages, one per line, into a string*)
wenzelm@255
   703
val cat_lines = space_implode "\n";
wenzelm@233
   704
wenzelm@4212
   705
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   706
fun space_explode _ "" = []
paulson@21899
   707
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   708
wenzelm@3832
   709
val split_lines = space_explode "\n";
wenzelm@3832
   710
wenzelm@14826
   711
fun prefix_lines "" txt = txt
wenzelm@14826
   712
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   713
wenzelm@7712
   714
fun untabify chs =
wenzelm@7712
   715
  let
wenzelm@7712
   716
    val tab_width = 8;
wenzelm@7712
   717
wenzelm@22582
   718
    fun untab pos [] ys = rev ys
berghofe@22256
   719
      | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
berghofe@22256
   720
      | untab pos ("\t" :: xs) ys =
wenzelm@22582
   721
          let val d = tab_width - (pos mod tab_width)
wenzelm@23718
   722
          in untab (pos + d) xs (funpow d (cons " ") ys) end
berghofe@22256
   723
      | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
wenzelm@7712
   724
  in
wenzelm@19301
   725
    if not (exists (fn c => c = "\t") chs) then chs
berghofe@22256
   726
    else untab 0 chs []
wenzelm@7712
   727
  end;
wenzelm@7712
   728
wenzelm@18681
   729
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   730
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   731
wenzelm@18681
   732
fun unprefix prfx s =
wenzelm@18681
   733
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   734
  else raise Fail "unprefix";
wenzelm@18681
   735
wenzelm@16188
   736
fun unsuffix sffx s =
wenzelm@17061
   737
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   738
  else raise Fail "unsuffix";
wenzelm@5285
   739
wenzelm@24593
   740
fun replicate_string (0: int) _ = ""
wenzelm@10951
   741
  | replicate_string 1 a = a
wenzelm@10951
   742
  | replicate_string k a =
wenzelm@10951
   743
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   744
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   745
wenzelm@233
   746
wenzelm@23220
   747
wenzelm@16492
   748
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   749
wenzelm@18923
   750
(*canonical member, insert, remove*)
wenzelm@18923
   751
fun member eq list x =
wenzelm@18923
   752
  let
wenzelm@18923
   753
    fun memb [] = false
wenzelm@18923
   754
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   755
  in memb list end;
berghofe@1576
   756
wenzelm@18923
   757
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   758
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   759
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   760
wenzelm@19301
   761
fun subtract eq = fold (remove eq);
wenzelm@19301
   762
wenzelm@18923
   763
fun merge _ ([], ys) = ys
wenzelm@18923
   764
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   765
wenzelm@18923
   766
(*old-style infixes*)
wenzelm@18923
   767
fun x mem xs = member (op =) xs x;
wenzelm@18923
   768
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   769
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   770
wenzelm@233
   771
wenzelm@233
   772
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   773
fun xs union [] = xs
wenzelm@233
   774
  | [] union ys = ys
haftmann@20854
   775
  | (x :: xs) union ys = xs union (insert (op =) x ys);
clasohm@0
   776
paulson@2175
   777
(*union of sets, optimized version for ints*)
berghofe@1576
   778
fun (xs:int list) union_int [] = xs
berghofe@1576
   779
  | [] union_int ys = ys
haftmann@20854
   780
  | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
berghofe@1576
   781
paulson@2175
   782
(*union of sets, optimized version for strings*)
berghofe@1576
   783
fun (xs:string list) union_string [] = xs
berghofe@1576
   784
  | [] union_string ys = ys
haftmann@20854
   785
  | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
berghofe@1576
   786
clasohm@0
   787
(*generalized union*)
wenzelm@233
   788
fun gen_union eq (xs, []) = xs
wenzelm@233
   789
  | gen_union eq ([], ys) = ys
wenzelm@18923
   790
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   791
wenzelm@233
   792
wenzelm@233
   793
(*intersection*)
wenzelm@233
   794
fun [] inter ys = []
wenzelm@233
   795
  | (x :: xs) inter ys =
wenzelm@233
   796
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   797
paulson@2175
   798
(*intersection, optimized version for ints*)
berghofe@1576
   799
fun ([]:int list) inter_int ys = []
berghofe@1576
   800
  | (x :: xs) inter_int ys =
berghofe@1576
   801
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   802
paulson@2175
   803
(*intersection, optimized version for strings *)
berghofe@1576
   804
fun ([]:string list) inter_string ys = []
berghofe@1576
   805
  | (x :: xs) inter_string ys =
berghofe@1576
   806
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   807
paulson@7090
   808
(*generalized intersection*)
paulson@7090
   809
fun gen_inter eq ([], ys) = []
wenzelm@12284
   810
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
   811
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
   812
      else gen_inter eq (xs, ys);
paulson@7090
   813
wenzelm@233
   814
wenzelm@233
   815
(*subset*)
wenzelm@233
   816
fun [] subset ys = true
wenzelm@233
   817
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   818
paulson@2175
   819
(*subset, optimized version for ints*)
wenzelm@16439
   820
fun ([]: int list) subset_int ys = true
berghofe@1576
   821
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   822
paulson@2175
   823
(*subset, optimized version for strings*)
wenzelm@16439
   824
fun ([]: string list) subset_string ys = true
berghofe@1576
   825
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   826
wenzelm@4363
   827
(*set equality*)
wenzelm@4363
   828
fun eq_set (xs, ys) =
wenzelm@4363
   829
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   830
paulson@2182
   831
(*set equality for strings*)
wenzelm@16439
   832
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   833
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   834
wenzelm@18923
   835
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
   836
wenzelm@19301
   837
fun gen_eq_set eq (xs, ys) =
haftmann@20348
   838
  eq_list eq (xs, ys) orelse
wenzelm@19301
   839
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
   840
wenzelm@265
   841
wenzelm@233
   842
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   843
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   844
  | [] \ x = [];
paulson@2243
   845
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   846
wenzelm@233
   847
wenzelm@233
   848
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   849
  first of equal elements*)
wenzelm@19046
   850
fun distinct eq lst =
wenzelm@233
   851
  let
wenzelm@233
   852
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   853
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   854
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   855
          else dist (x :: rev_seen, xs);
wenzelm@19046
   856
  in dist ([], lst) end;
wenzelm@233
   857
wenzelm@255
   858
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   859
  order, takes first of equal elements*)
wenzelm@18966
   860
fun duplicates eq lst =
wenzelm@255
   861
  let
wenzelm@255
   862
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   863
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   864
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   865
            dups (rev_dups, xs)
wenzelm@255
   866
          else dups (x :: rev_dups, xs);
wenzelm@18966
   867
  in dups ([], lst) end;
wenzelm@255
   868
wenzelm@16878
   869
fun has_duplicates eq =
wenzelm@16878
   870
  let
wenzelm@16878
   871
    fun dups [] = false
wenzelm@16878
   872
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   873
  in dups end;
wenzelm@16878
   874
wenzelm@255
   875
wenzelm@23220
   876
nipkow@22142
   877
(** lists as multisets **)
nipkow@22142
   878
nipkow@22142
   879
fun remove1 _ _ [] = raise Empty
wenzelm@23220
   880
  | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
nipkow@22142
   881
wenzelm@23220
   882
fun submultiset _ ([], _)  = true
wenzelm@23220
   883
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
wenzelm@233
   884
clasohm@0
   885
clasohm@0
   886
wenzelm@2506
   887
(** orders **)
wenzelm@2506
   888
wenzelm@18966
   889
fun is_equal EQUAL = true
wenzelm@18966
   890
  | is_equal _ = false;
wenzelm@18966
   891
wenzelm@4445
   892
fun rev_order LESS = GREATER
wenzelm@4445
   893
  | rev_order EQUAL = EQUAL
wenzelm@4445
   894
  | rev_order GREATER = LESS;
wenzelm@4445
   895
wenzelm@4479
   896
(*assume rel is a linear strict order*)
wenzelm@4445
   897
fun make_ord rel (x, y) =
wenzelm@4445
   898
  if rel (x, y) then LESS
wenzelm@4445
   899
  else if rel (y, x) then GREATER
wenzelm@4445
   900
  else EQUAL;
wenzelm@4445
   901
wenzelm@15051
   902
val int_ord = Int.compare;
wenzelm@15051
   903
val string_ord = String.compare;
wenzelm@2506
   904
wenzelm@16676
   905
fun fast_string_ord (s1, s2) =
wenzelm@16676
   906
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   907
wenzelm@16492
   908
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   909
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   910
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   911
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   912
wenzelm@4343
   913
(*lexicographic product*)
wenzelm@4343
   914
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   915
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   916
wenzelm@4343
   917
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   918
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   919
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   920
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   921
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   922
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   923
wenzelm@4343
   924
(*lexicographic product of lists*)
wenzelm@4343
   925
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   926
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   927
wenzelm@2506
   928
wenzelm@4621
   929
(* sorting *)
wenzelm@4621
   930
wenzelm@18427
   931
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
   932
fun quicksort unique ord =
wenzelm@4621
   933
  let
wenzelm@16878
   934
    fun qsort [] = []
wenzelm@16878
   935
      | qsort (xs as [_]) = xs
wenzelm@18427
   936
      | qsort (xs as [x, y]) =
wenzelm@18427
   937
          (case ord (x, y) of
wenzelm@18427
   938
            LESS => xs
wenzelm@18427
   939
          | EQUAL => if unique then [x] else xs
wenzelm@18427
   940
          | GREATER => [y, x])
wenzelm@16878
   941
      | qsort xs =
haftmann@18011
   942
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
   943
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
   944
    and part _ [] = ([], [], [])
wenzelm@4621
   945
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
   946
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
   947
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
   948
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
   949
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
   950
  in qsort end;
wenzelm@4621
   951
wenzelm@18427
   952
fun sort ord = quicksort false ord;
wenzelm@18427
   953
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
   954
wenzelm@4621
   955
val sort_strings = sort string_ord;
wenzelm@4621
   956
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
   957
wenzelm@4621
   958
wenzelm@2506
   959
berghofe@14106
   960
(** random numbers **)
berghofe@14106
   961
berghofe@14106
   962
exception RANDOM;
berghofe@14106
   963
berghofe@14618
   964
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
   965
berghofe@14106
   966
local
berghofe@14106
   967
  val a = 16807.0;
berghofe@14106
   968
  val m = 2147483647.0;
berghofe@14106
   969
  val random_seed = ref 1.0;
berghofe@14106
   970
in
berghofe@14106
   971
wenzelm@23922
   972
fun random () = CRITICAL (fn () =>
wenzelm@23922
   973
  let val r = rmod (a * ! random_seed) m
wenzelm@23922
   974
  in (random_seed := r; r) end);
berghofe@14106
   975
berghofe@14106
   976
end;
berghofe@14106
   977
berghofe@14106
   978
fun random_range l h =
berghofe@14106
   979
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
   980
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
   981
haftmann@18011
   982
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
   983
berghofe@14106
   984
fun frequency xs =
berghofe@14106
   985
  let
berghofe@14106
   986
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
   987
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
   988
      if n <= k then x else pick (n - k) xs
berghofe@14106
   989
  in pick (random_range 1 sum) xs end;
berghofe@14106
   990
berghofe@14106
   991
wenzelm@23220
   992
wenzelm@4621
   993
(** misc **)
wenzelm@233
   994
wenzelm@19644
   995
fun divide_and_conquer decomp x =
wenzelm@19644
   996
  let val (ys, recomb) = decomp x
wenzelm@19644
   997
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
   998
clasohm@0
   999
wenzelm@233
  1000
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1001
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1002
fun partition_list p i j =
wenzelm@233
  1003
  let fun part k xs =
wenzelm@233
  1004
            if k>j then
clasohm@0
  1005
              (case xs of [] => []
skalberg@15570
  1006
                         | _ => raise Fail "partition_list")
clasohm@0
  1007
            else
wenzelm@19691
  1008
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1009
            in  ns :: part(k+1)rest  end
wenzelm@24593
  1010
  in  part (i: int) end;
clasohm@0
  1011
wenzelm@19691
  1012
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1013
  let
wenzelm@19691
  1014
    fun part [] = []
wenzelm@19691
  1015
      | part (x :: ys) =
wenzelm@19691
  1016
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1017
          in (x::xs)::(part xs') end
wenzelm@19691
  1018
  in part end;
wenzelm@19691
  1019
wenzelm@19691
  1020
clasohm@0
  1021
wenzelm@233
  1022
(* generating identifiers *)
clasohm@0
  1023
paulson@4063
  1024
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
wenzelm@22369
  1025
local
wenzelm@22369
  1026
(*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
wenzelm@22582
  1027
fun gensym_char i =
paulson@22368
  1028
  if i<26 then chr (ord "A" + i)
paulson@22368
  1029
  else if i<52 then chr (ord "a" + i - 26)
wenzelm@22369
  1030
  else chr (ord "0" + i - 52);
paulson@4063
  1031
wenzelm@22369
  1032
val char_vec = Vector.tabulate (62, gensym_char);
wenzelm@22369
  1033
fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
wenzelm@4284
  1034
wenzelm@24593
  1035
val gensym_seed = ref (0: int);
paulson@2003
  1036
wenzelm@22369
  1037
in
wenzelm@24148
  1038
  fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
wenzelm@22369
  1039
end;
paulson@4063
  1040
paulson@4063
  1041
wenzelm@16439
  1042
(* stamps and serial numbers *)
wenzelm@16439
  1043
wenzelm@16439
  1044
type stamp = unit ref;
wenzelm@16439
  1045
val stamp: unit -> stamp = ref;
wenzelm@16439
  1046
wenzelm@16439
  1047
type serial = int;
wenzelm@24593
  1048
local val count = ref (0: int)
wenzelm@24148
  1049
in fun serial () = NAMED_CRITICAL "serial" (fn () => inc count) end;
wenzelm@16439
  1050
wenzelm@19512
  1051
val serial_string = string_of_int o serial;
wenzelm@19512
  1052
wenzelm@16535
  1053
wenzelm@16535
  1054
(* generic objects *)
wenzelm@16535
  1055
wenzelm@16535
  1056
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1057
  constructors at any time*)
wenzelm@16535
  1058
structure Object = struct type T = exn end;
wenzelm@16535
  1059
clasohm@1364
  1060
end;
clasohm@1364
  1061
wenzelm@15745
  1062
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1063
open BasicLibrary;