src/Pure/library.ML
author wenzelm
Thu Nov 16 01:07:25 2006 +0100 (2006-11-16 ago)
changeset 21395 f34ac19659ae
parent 21335 6b9d4a19a3a8
child 21479 63e7eb863ae6
permissions -rw-r--r--
moved some fundamental concepts to General/basics.ML;
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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, balanced trees, 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 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 ? : ('a -> 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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  (*exceptions*)
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  exception EXCEPTION of exn * string
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  val do_transform_failure: bool ref
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  val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
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  datatype 'a result = Result of 'a | Exn of exn
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  val capture: ('a -> 'b) -> 'a -> 'b result
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  val release: 'a result -> 'a
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  val get_result: 'a result -> 'a option
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  val get_exn: 'a result -> exn option
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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: bool -> string -> unit
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  val deny: bool -> string -> unit
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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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  val string_of_pair: ('a -> string) -> ('b -> string) -> 'a * 'b -> string
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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: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val conditional: bool -> (unit -> unit) -> unit
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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 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_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 gcd: IntInf.int * IntInf.int -> IntInf.int
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  val lcm: IntInf.int * IntInf.int -> IntInf.int
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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 downto0: int list * int -> bool
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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 string_of_indexname: string * int -> string
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  val read_intinf: int -> string list -> IntInf.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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  val string_of_list: ('a -> string) -> 'a list -> string
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  val string_of_option: ('a -> string) -> 'a option -> 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 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 tables -- see also Pure/General/alist.ML*)
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  val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
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  val merge_lists: ''a list -> ''a list -> ''a list
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  val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
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  (*balanced trees*)
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  exception Balance
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  val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
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  val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
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  val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
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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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  (*current directory*)
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  val cd: string -> unit
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  val pwd: unit -> string
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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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  val scanwords: (string -> bool) -> string list -> string list
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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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  val seq: ('a -> unit) -> 'a list -> unit
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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 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 x 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 n f x =
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  let fun rep (0, x) = x
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        | rep (n, x) = rep (n - 1, f x)
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  in rep (n, x) end;
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(* exceptions *)
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val do_transform_failure = ref true;
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   295
fun transform_failure exn f x =
wenzelm@18681
   296
  if ! do_transform_failure then
wenzelm@18681
   297
    f x handle Interrupt => raise Interrupt | e => raise exn e
wenzelm@18681
   298
  else f x;
wenzelm@18681
   299
wenzelm@17341
   300
exception EXCEPTION of exn * string;
wenzelm@6959
   301
wenzelm@14868
   302
datatype 'a result =
wenzelm@14868
   303
  Result of 'a |
wenzelm@14868
   304
  Exn of exn;
wenzelm@14868
   305
wenzelm@14868
   306
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   307
wenzelm@14868
   308
fun release (Result y) = y
wenzelm@14868
   309
  | release (Exn e) = raise e;
wenzelm@14868
   310
skalberg@15531
   311
fun get_result (Result x) = SOME x
skalberg@15531
   312
  | get_result _ = NONE;
wenzelm@14868
   313
skalberg@15531
   314
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   315
  | get_exn _ = NONE;
wenzelm@14868
   316
wenzelm@14868
   317
wenzelm@18681
   318
(* errors *)
wenzelm@18681
   319
wenzelm@19542
   320
exception SYS_ERROR of string;
wenzelm@19542
   321
fun sys_error msg = raise SYS_ERROR msg;
wenzelm@19542
   322
wenzelm@18681
   323
exception ERROR of string;
wenzelm@18681
   324
fun error msg = raise ERROR msg;
wenzelm@18681
   325
wenzelm@18681
   326
fun cat_error "" msg = error msg
wenzelm@18681
   327
  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
wenzelm@18681
   328
wenzelm@18681
   329
fun assert p msg = if p then () else error msg;
wenzelm@18681
   330
fun deny p msg = if p then error msg else ();
wenzelm@18681
   331
wenzelm@18681
   332
fun assert_all pred list msg =
wenzelm@18681
   333
  let
wenzelm@18681
   334
    fun ass [] = ()
wenzelm@18681
   335
      | ass (x :: xs) = if pred x then ass xs else error (msg x);
wenzelm@18681
   336
  in ass list end;
wenzelm@18681
   337
wenzelm@18681
   338
wenzelm@21395
   339
(* pairs *)
wenzelm@233
   340
wenzelm@233
   341
fun pair x y = (x, y);
wenzelm@233
   342
fun rpair x y = (y, x);
wenzelm@233
   343
wenzelm@233
   344
fun fst (x, y) = x;
wenzelm@233
   345
fun snd (x, y) = y;
wenzelm@233
   346
haftmann@17498
   347
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   348
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   349
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   350
wenzelm@233
   351
fun swap (x, y) = (y, x);
wenzelm@233
   352
wenzelm@4212
   353
(*apply function to components*)
wenzelm@233
   354
fun apfst f (x, y) = (f x, y);
wenzelm@233
   355
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   356
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   357
webertj@19567
   358
fun string_of_pair f1 f2 (x, y) = "(" ^ f1 x ^ ", " ^ f2 y ^ ")";
wenzelm@233
   359
wenzelm@233
   360
wenzelm@21395
   361
(* booleans *)
wenzelm@233
   362
wenzelm@21395
   363
(*polymorphic equality*)
wenzelm@233
   364
fun equal x y = x = y;
wenzelm@233
   365
fun not_equal x y = x <> y;
wenzelm@233
   366
wenzelm@21395
   367
(*combining predicates*)
wenzelm@16721
   368
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   369
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   370
wenzelm@233
   371
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   372
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   373
  let fun boolf [] = false
wenzelm@233
   374
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   375
  in boolf end;
wenzelm@233
   376
wenzelm@233
   377
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   378
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   379
  let fun boolf [] = true
wenzelm@233
   380
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   381
  in boolf end;
clasohm@0
   382
wenzelm@19644
   383
wenzelm@380
   384
(* flags *)
wenzelm@380
   385
wenzelm@380
   386
fun set flag = (flag := true; true);
wenzelm@380
   387
fun reset flag = (flag := false; false);
wenzelm@380
   388
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   389
wenzelm@9118
   390
fun change r f = r := f (! r);
wenzelm@9118
   391
wenzelm@18712
   392
(*temporarily set flag during execution*)
wenzelm@2978
   393
fun setmp flag value f x =
wenzelm@2958
   394
  let
wenzelm@2958
   395
    val orig_value = ! flag;
wenzelm@18712
   396
    val _ = flag := value;
wenzelm@18712
   397
    val result = capture f x;
wenzelm@18712
   398
    val _ = flag := orig_value;
wenzelm@18712
   399
  in release result end;
wenzelm@2958
   400
wenzelm@19644
   401
wenzelm@11853
   402
(* conditional execution *)
wenzelm@11853
   403
wenzelm@11853
   404
fun conditional b f = if b then f () else ();
wenzelm@11853
   405
wenzelm@233
   406
wenzelm@21395
   407
wenzelm@233
   408
(** lists **)
wenzelm@233
   409
skalberg@15570
   410
exception UnequalLengths;
wenzelm@233
   411
wenzelm@5285
   412
fun single x = [x];
wenzelm@233
   413
wenzelm@20882
   414
fun the_single [x] = x
wenzelm@20882
   415
  | the_single _ = raise Empty;
wenzelm@20882
   416
wenzelm@20882
   417
fun singleton f x = the_single (f [x]);
wenzelm@19273
   418
wenzelm@5904
   419
fun apply [] x = x
wenzelm@5904
   420
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   421
wenzelm@233
   422
wenzelm@21395
   423
(* fold -- old versions *)
haftmann@16691
   424
wenzelm@233
   425
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   426
wenzelm@233
   427
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   428
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   429
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   430
  let fun itl (e, [])  = e
wenzelm@233
   431
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   432
  in  itl end;
wenzelm@233
   433
wenzelm@233
   434
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   435
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   436
fun foldr f (l, e) =
wenzelm@233
   437
  let fun itr [] = e
wenzelm@233
   438
        | itr (a::l) = f(a, itr l)
wenzelm@233
   439
  in  itr l  end;
wenzelm@233
   440
wenzelm@233
   441
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   442
    for n > 0, operators that associate to the right (not tail recursive)*)
paulson@20443
   443
fun foldr1 f [] = raise Empty
wenzelm@20510
   444
  | foldr1 f l =
paulson@20443
   445
      let fun itr [x] = x
wenzelm@20510
   446
            | itr (x::l) = f(x, itr l)
paulson@20443
   447
      in  itr l  end;
wenzelm@233
   448
wenzelm@16705
   449
fun foldl_map f =
wenzelm@16705
   450
  let
wenzelm@16705
   451
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   452
      | fold_aux (x, y :: ys) =
wenzelm@16705
   453
          let
wenzelm@16705
   454
            val (x', y') = f (x, y);
wenzelm@16705
   455
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   456
          in (x'', y' :: ys') end;
wenzelm@16705
   457
  in fold_aux end;
wenzelm@16705
   458
wenzelm@233
   459
wenzelm@233
   460
(* basic list functions *)
wenzelm@233
   461
wenzelm@20510
   462
fun eq_list eq (list1, list2) =
haftmann@20348
   463
  let
wenzelm@20510
   464
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   465
      | eq_lst _ = true;
wenzelm@20510
   466
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   467
wenzelm@19483
   468
fun maps f [] = []
wenzelm@19483
   469
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   470
wenzelm@21395
   471
fun chop n xs = unfold_rev n dest xs;
wenzelm@19011
   472
wenzelm@233
   473
(*take the first n elements from a list*)
wenzelm@233
   474
fun take (n, []) = []
wenzelm@233
   475
  | take (n, x :: xs) =
wenzelm@233
   476
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   477
wenzelm@233
   478
(*drop the first n elements from a list*)
wenzelm@233
   479
fun drop (n, []) = []
wenzelm@233
   480
  | drop (n, x :: xs) =
wenzelm@233
   481
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   482
nipkow@4713
   483
fun dropwhile P [] = []
nipkow@4713
   484
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   485
wenzelm@233
   486
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   487
  raise Subscript if list too short*)
haftmann@18011
   488
fun nth xs i = List.nth (xs, i);
wenzelm@233
   489
wenzelm@18461
   490
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   491
haftmann@18011
   492
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   493
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   494
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   495
haftmann@18514
   496
fun map_index f =
haftmann@18514
   497
  let
haftmann@18514
   498
    fun mapp _ [] = []
haftmann@18514
   499
      | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
haftmann@18514
   500
  in mapp 0 end;
haftmann@18514
   501
haftmann@21118
   502
fun fold_index f =
haftmann@21118
   503
  let
haftmann@21118
   504
    fun fold_aux _ [] y = y
haftmann@21118
   505
      | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
haftmann@21118
   506
  in fold_aux 0 end;
haftmann@21118
   507
skalberg@15570
   508
val last_elem = List.last;
wenzelm@233
   509
wenzelm@3762
   510
(*rear decomposition*)
skalberg@15570
   511
fun split_last [] = raise Empty
wenzelm@3762
   512
  | split_last [x] = ([], x)
wenzelm@3762
   513
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   514
wenzelm@4212
   515
(*find the position of an element in a list*)
wenzelm@4212
   516
fun find_index pred =
wenzelm@4212
   517
  let fun find _ [] = ~1
wenzelm@4212
   518
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   519
  in find 0 end;
wenzelm@3762
   520
wenzelm@4224
   521
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   522
wenzelm@4212
   523
(*find first element satisfying predicate*)
skalberg@15531
   524
fun find_first _ [] = NONE
wenzelm@4212
   525
  | find_first pred (x :: xs) =
skalberg@15531
   526
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   527
wenzelm@4916
   528
(*get first element by lookup function*)
skalberg@15531
   529
fun get_first _ [] = NONE
wenzelm@4916
   530
  | get_first f (x :: xs) =
wenzelm@4916
   531
      (case f x of
skalberg@15531
   532
        NONE => get_first f xs
wenzelm@4916
   533
      | some => some);
wenzelm@4916
   534
haftmann@19233
   535
fun get_index f =
haftmann@19233
   536
  let
haftmann@19233
   537
    fun get _ [] = NONE
wenzelm@19461
   538
      | get i (x :: xs) =
haftmann@19233
   539
          case f x
wenzelm@19461
   540
           of NONE => get (i + 1) xs
haftmann@19233
   541
            | SOME y => SOME (i, y)
haftmann@19233
   542
  in get 0 end;
haftmann@19233
   543
skalberg@15531
   544
val flat = List.concat;
wenzelm@233
   545
wenzelm@12136
   546
fun unflat (xs :: xss) ys =
wenzelm@19424
   547
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   548
      in ps :: unflat xss qs end
wenzelm@12136
   549
  | unflat [] [] = []
skalberg@15570
   550
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   551
haftmann@18441
   552
fun burrow f xss =
haftmann@18359
   553
  unflat xss ((f o flat) xss);
haftmann@18359
   554
haftmann@18549
   555
fun fold_burrow f xss s =
haftmann@18549
   556
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   557
wenzelm@233
   558
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   559
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   560
val seq = List.app;
wenzelm@233
   561
wenzelm@233
   562
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   563
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   564
  | separate _ xs = xs;
wenzelm@233
   565
wenzelm@233
   566
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   567
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   568
  let fun rep (0, xs) = xs
wenzelm@233
   569
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   570
  in
skalberg@15570
   571
    if n < 0 then raise Subscript
wenzelm@233
   572
    else rep (n, [])
wenzelm@233
   573
  end;
wenzelm@233
   574
wenzelm@14926
   575
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   576
wenzelm@4248
   577
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   578
fun multiply [] _ = []
wenzelm@18148
   579
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   580
wenzelm@14792
   581
(*direct product*)
wenzelm@14792
   582
fun product _ [] = []
wenzelm@14792
   583
  | product [] _ = []
wenzelm@14792
   584
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   585
wenzelm@233
   586
wenzelm@233
   587
(* filter *)
wenzelm@233
   588
wenzelm@233
   589
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   590
val filter = List.filter;
clasohm@0
   591
fun filter_out f = filter (not o f);
wenzelm@19483
   592
val map_filter = List.mapPartial;
wenzelm@233
   593
wenzelm@233
   594
wenzelm@233
   595
(* lists of pairs *)
wenzelm@233
   596
skalberg@15570
   597
exception UnequalLengths;
skalberg@15570
   598
haftmann@18330
   599
fun map2 _ [] [] = []
haftmann@18330
   600
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   601
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   602
haftmann@18330
   603
fun fold2 f =
haftmann@18330
   604
  let
haftmann@18330
   605
    fun fold_aux [] [] z = z
haftmann@18330
   606
      | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
haftmann@18330
   607
      | fold_aux _ _ _ = raise UnequalLengths;
haftmann@18330
   608
  in fold_aux end;
wenzelm@380
   609
wenzelm@19799
   610
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   611
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   612
  | zip_options _ [] = []
wenzelm@19799
   613
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   614
wenzelm@233
   615
(*combine two lists forming a list of pairs:
wenzelm@233
   616
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   617
fun [] ~~ [] = []
wenzelm@233
   618
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   619
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   620
wenzelm@233
   621
(*inverse of ~~; the old 'split':
wenzelm@233
   622
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   623
val split_list = ListPair.unzip;
wenzelm@233
   624
wenzelm@233
   625
wenzelm@233
   626
(* prefixes, suffixes *)
wenzelm@233
   627
haftmann@18441
   628
fun is_prefix _ [] _ = true
haftmann@18441
   629
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   630
  | is_prefix eq _ _ = false;
wenzelm@233
   631
wenzelm@233
   632
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   633
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   634
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   635
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   636
        | take (rxs, x :: xs) =
wenzelm@255
   637
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   638
  in  take([], xs)  end;
wenzelm@233
   639
haftmann@20108
   640
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   641
  | chop_prefix eq (xs, []) = ([], (xs, []))
haftmann@20108
   642
  | chop_prefix eq (xs as x::xs', ys as y::ys') =
haftmann@20108
   643
      if eq (x, y) then
haftmann@20108
   644
        let val (ps', xys'') = chop_prefix eq (xs', ys')
haftmann@20108
   645
        in (x::ps', xys'') end
haftmann@20108
   646
      else ([], (xs, ys));
haftmann@20108
   647
wenzelm@233
   648
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   649
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   650
fun take_suffix _ [] = ([], [])
wenzelm@233
   651
  | take_suffix pred (x :: xs) =
wenzelm@233
   652
      (case take_suffix pred xs of
wenzelm@233
   653
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   654
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   655
wenzelm@12249
   656
fun prefixes1 [] = []
wenzelm@12249
   657
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   658
wenzelm@19011
   659
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   660
wenzelm@12249
   661
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   662
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   663
wenzelm@233
   664
wenzelm@233
   665
(** integers **)
wenzelm@233
   666
wenzelm@16439
   667
fun gcd (x, y) =
paulson@15965
   668
  let fun gxd x y : IntInf.int =
nipkow@10692
   669
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   670
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   671
wenzelm@16439
   672
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   673
wenzelm@2958
   674
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   675
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   676
wenzelm@233
   677
wenzelm@233
   678
(* lists of integers *)
wenzelm@233
   679
wenzelm@233
   680
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   681
fun (from upto to) =
wenzelm@233
   682
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   683
wenzelm@233
   684
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   685
fun (from downto to) =
wenzelm@233
   686
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   687
wenzelm@233
   688
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   689
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   690
  | downto0 ([], n) = n = ~1;
wenzelm@233
   691
wenzelm@233
   692
wenzelm@233
   693
(* convert integers to strings *)
wenzelm@233
   694
wenzelm@233
   695
(*expand the number in the given base;
wenzelm@233
   696
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   697
fun radixpand (base, num) : int list =
wenzelm@233
   698
  let
wenzelm@233
   699
    fun radix (n, tail) =
wenzelm@233
   700
      if n < base then n :: tail
wenzelm@233
   701
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   702
  in radix (num, []) end;
wenzelm@233
   703
wenzelm@233
   704
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   705
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   706
fun radixstring (base, zerochar, num) =
wenzelm@233
   707
  let val offset = ord zerochar;
wenzelm@233
   708
      fun chrof n = chr (offset + n)
wenzelm@233
   709
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   710
wenzelm@233
   711
paulson@3407
   712
val string_of_int = Int.toString;
wenzelm@233
   713
paulson@3407
   714
fun string_of_indexname (a,0) = a
paulson@3407
   715
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   716
wenzelm@233
   717
wenzelm@14826
   718
(* read integers *)
wenzelm@14826
   719
wenzelm@20095
   720
fun read_intinf radix cs =
wenzelm@20095
   721
  let
wenzelm@20095
   722
    val zero = ord "0";
wenzelm@20095
   723
    val limit = zero + radix;
wenzelm@20095
   724
    fun scan (num, []) = (num, [])
wenzelm@20095
   725
      | scan (num, c :: cs) =
wenzelm@20095
   726
        if zero <= ord c andalso ord c < limit then
wenzelm@20095
   727
          scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
wenzelm@20095
   728
        else (num, c :: cs);
wenzelm@20095
   729
  in scan (0, cs) end;
wenzelm@14826
   730
wenzelm@20095
   731
fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
wenzelm@14826
   732
wenzelm@20095
   733
fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
wenzelm@14826
   734
wenzelm@14826
   735
wenzelm@14826
   736
wenzelm@233
   737
(** strings **)
wenzelm@233
   738
wenzelm@16188
   739
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   740
haftmann@18011
   741
fun nth_string str i =
wenzelm@6959
   742
  (case try String.substring (str, i, 1) of
skalberg@15531
   743
    SOME s => s
skalberg@15570
   744
  | NONE => raise Subscript);
wenzelm@6312
   745
wenzelm@16188
   746
fun fold_string f str x0 =
wenzelm@6282
   747
  let
wenzelm@6282
   748
    val n = size str;
wenzelm@16188
   749
    fun iter (x, i) =
wenzelm@16188
   750
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   751
  in iter (x0, 0) end;
wenzelm@6282
   752
wenzelm@14968
   753
fun exists_string pred str =
wenzelm@14968
   754
  let
wenzelm@14968
   755
    val n = size str;
wenzelm@14968
   756
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   757
  in ex 0 end;
wenzelm@6312
   758
wenzelm@16188
   759
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   760
lcp@512
   761
(*enclose in brackets*)
lcp@512
   762
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   763
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   764
wenzelm@233
   765
(*simple quoting (does not escape special chars)*)
lcp@512
   766
val quote = enclose "\"" "\"";
wenzelm@233
   767
wenzelm@4212
   768
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   769
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   770
wenzelm@255
   771
val commas = space_implode ", ";
wenzelm@380
   772
val commas_quote = commas o map quote;
wenzelm@255
   773
wenzelm@233
   774
(*concatenate messages, one per line, into a string*)
wenzelm@255
   775
val cat_lines = space_implode "\n";
wenzelm@233
   776
wenzelm@4212
   777
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   778
fun space_explode _ "" = []
wenzelm@3832
   779
  | space_explode sep str =
wenzelm@3832
   780
      let
wenzelm@3832
   781
        fun expl chs =
wenzelm@19301
   782
          (case take_prefix (fn s => s <> sep) chs of
wenzelm@3832
   783
            (cs, []) => [implode cs]
wenzelm@3832
   784
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   785
      in expl (explode str) end;
wenzelm@3832
   786
wenzelm@3832
   787
val split_lines = space_explode "\n";
wenzelm@3832
   788
wenzelm@14826
   789
fun prefix_lines "" txt = txt
wenzelm@14826
   790
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   791
wenzelm@7712
   792
fun untabify chs =
wenzelm@7712
   793
  let
wenzelm@7712
   794
    val tab_width = 8;
wenzelm@7712
   795
wenzelm@7712
   796
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   797
      | untab (pos, "\t") =
wenzelm@9118
   798
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   799
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   800
  in
wenzelm@19301
   801
    if not (exists (fn c => c = "\t") chs) then chs
wenzelm@7712
   802
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   803
  end;
wenzelm@7712
   804
wenzelm@18681
   805
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   806
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   807
wenzelm@18681
   808
fun unprefix prfx s =
wenzelm@18681
   809
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   810
  else raise Fail "unprefix";
wenzelm@18681
   811
wenzelm@16188
   812
fun unsuffix sffx s =
wenzelm@17061
   813
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   814
  else raise Fail "unsuffix";
wenzelm@5285
   815
wenzelm@10951
   816
fun replicate_string 0 _ = ""
wenzelm@10951
   817
  | replicate_string 1 a = a
wenzelm@10951
   818
  | replicate_string k a =
wenzelm@10951
   819
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   820
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   821
wenzelm@19644
   822
fun string_of_list f = enclose "[" "]" o commas o map f;
wenzelm@19644
   823
wenzelm@19644
   824
fun string_of_option f NONE = "NONE"
wenzelm@19644
   825
  | string_of_option f (SOME x) = "SOME (" ^ f x ^ ")";
wenzelm@19644
   826
wenzelm@3832
   827
wenzelm@233
   828
wenzelm@16492
   829
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   830
wenzelm@18923
   831
(*canonical member, insert, remove*)
wenzelm@18923
   832
fun member eq list x =
wenzelm@18923
   833
  let
wenzelm@18923
   834
    fun memb [] = false
wenzelm@18923
   835
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   836
  in memb list end;
berghofe@1576
   837
wenzelm@18923
   838
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   839
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   840
wenzelm@19301
   841
fun subtract eq = fold (remove eq);
wenzelm@19301
   842
wenzelm@18923
   843
fun merge _ ([], ys) = ys
wenzelm@18923
   844
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   845
wenzelm@18923
   846
(*old-style infixes*)
wenzelm@18923
   847
fun x mem xs = member (op =) xs x;
wenzelm@18923
   848
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   849
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   850
wenzelm@233
   851
wenzelm@233
   852
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   853
fun xs union [] = xs
wenzelm@233
   854
  | [] union ys = ys
haftmann@20854
   855
  | (x :: xs) union ys = xs union (insert (op =) x ys);
clasohm@0
   856
paulson@2175
   857
(*union of sets, optimized version for ints*)
berghofe@1576
   858
fun (xs:int list) union_int [] = xs
berghofe@1576
   859
  | [] union_int ys = ys
haftmann@20854
   860
  | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
berghofe@1576
   861
paulson@2175
   862
(*union of sets, optimized version for strings*)
berghofe@1576
   863
fun (xs:string list) union_string [] = xs
berghofe@1576
   864
  | [] union_string ys = ys
haftmann@20854
   865
  | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
berghofe@1576
   866
clasohm@0
   867
(*generalized union*)
wenzelm@233
   868
fun gen_union eq (xs, []) = xs
wenzelm@233
   869
  | gen_union eq ([], ys) = ys
wenzelm@18923
   870
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   871
wenzelm@233
   872
wenzelm@233
   873
(*intersection*)
wenzelm@233
   874
fun [] inter ys = []
wenzelm@233
   875
  | (x :: xs) inter ys =
wenzelm@233
   876
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   877
paulson@2175
   878
(*intersection, optimized version for ints*)
berghofe@1576
   879
fun ([]:int list) inter_int ys = []
berghofe@1576
   880
  | (x :: xs) inter_int ys =
berghofe@1576
   881
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   882
paulson@2175
   883
(*intersection, optimized version for strings *)
berghofe@1576
   884
fun ([]:string list) inter_string ys = []
berghofe@1576
   885
  | (x :: xs) inter_string ys =
berghofe@1576
   886
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   887
paulson@7090
   888
(*generalized intersection*)
paulson@7090
   889
fun gen_inter eq ([], ys) = []
wenzelm@12284
   890
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
   891
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
   892
      else gen_inter eq (xs, ys);
paulson@7090
   893
wenzelm@233
   894
wenzelm@233
   895
(*subset*)
wenzelm@233
   896
fun [] subset ys = true
wenzelm@233
   897
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   898
paulson@2175
   899
(*subset, optimized version for ints*)
wenzelm@16439
   900
fun ([]: int list) subset_int ys = true
berghofe@1576
   901
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   902
paulson@2175
   903
(*subset, optimized version for strings*)
wenzelm@16439
   904
fun ([]: string list) subset_string ys = true
berghofe@1576
   905
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   906
wenzelm@4363
   907
(*set equality*)
wenzelm@4363
   908
fun eq_set (xs, ys) =
wenzelm@4363
   909
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   910
paulson@2182
   911
(*set equality for strings*)
wenzelm@16439
   912
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   913
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   914
wenzelm@18923
   915
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
   916
wenzelm@19301
   917
fun gen_eq_set eq (xs, ys) =
haftmann@20348
   918
  eq_list eq (xs, ys) orelse
wenzelm@19301
   919
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
   920
wenzelm@265
   921
wenzelm@233
   922
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   923
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   924
  | [] \ x = [];
paulson@2243
   925
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   926
wenzelm@233
   927
wenzelm@233
   928
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   929
  first of equal elements*)
wenzelm@19046
   930
fun distinct eq lst =
wenzelm@233
   931
  let
wenzelm@233
   932
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   933
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   934
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   935
          else dist (x :: rev_seen, xs);
wenzelm@19046
   936
  in dist ([], lst) end;
wenzelm@233
   937
wenzelm@255
   938
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   939
  order, takes first of equal elements*)
wenzelm@18966
   940
fun duplicates eq lst =
wenzelm@255
   941
  let
wenzelm@255
   942
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   943
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   944
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   945
            dups (rev_dups, xs)
wenzelm@255
   946
          else dups (x :: rev_dups, xs);
wenzelm@18966
   947
  in dups ([], lst) end;
wenzelm@255
   948
wenzelm@16878
   949
fun has_duplicates eq =
wenzelm@16878
   950
  let
wenzelm@16878
   951
    fun dups [] = false
wenzelm@16878
   952
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   953
  in dups end;
wenzelm@16878
   954
wenzelm@255
   955
haftmann@19119
   956
(** association lists -- legacy operations **)
wenzelm@233
   957
wenzelm@12284
   958
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
   959
  | gen_merge_lists _ [] ys = ys
haftmann@20951
   960
  | gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys;
clasohm@0
   961
wenzelm@12284
   962
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
haftmann@20951
   963
fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs;
clasohm@0
   964
clasohm@0
   965
wenzelm@233
   966
(** balanced trees **)
wenzelm@233
   967
wenzelm@233
   968
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   969
wenzelm@233
   970
(*balanced folding; avoids deep nesting*)
wenzelm@233
   971
fun fold_bal f [x] = x
wenzelm@233
   972
  | fold_bal f [] = raise Balance
wenzelm@233
   973
  | fold_bal f xs =
wenzelm@19474
   974
      let val (ps, qs) = chop (length xs div 2) xs
nipkow@13629
   975
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
   976
wenzelm@233
   977
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   978
fun access_bal (f, g, x) n i =
wenzelm@233
   979
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   980
          if n=1 then x else
wenzelm@233
   981
          let val n2 = n div 2
wenzelm@233
   982
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   983
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   984
          end
wenzelm@233
   985
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   986
wenzelm@233
   987
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   988
fun accesses_bal (f, g, x) n =
wenzelm@233
   989
  let fun acc n =
wenzelm@233
   990
          if n=1 then [x] else
wenzelm@233
   991
          let val n2 = n div 2
wenzelm@233
   992
              val acc2 = acc n2
wenzelm@233
   993
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   994
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   995
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   996
wenzelm@233
   997
wenzelm@233
   998
wenzelm@2506
   999
(** orders **)
wenzelm@2506
  1000
wenzelm@18966
  1001
fun is_equal EQUAL = true
wenzelm@18966
  1002
  | is_equal _ = false;
wenzelm@18966
  1003
wenzelm@4445
  1004
fun rev_order LESS = GREATER
wenzelm@4445
  1005
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1006
  | rev_order GREATER = LESS;
wenzelm@4445
  1007
wenzelm@4479
  1008
(*assume rel is a linear strict order*)
wenzelm@4445
  1009
fun make_ord rel (x, y) =
wenzelm@4445
  1010
  if rel (x, y) then LESS
wenzelm@4445
  1011
  else if rel (y, x) then GREATER
wenzelm@4445
  1012
  else EQUAL;
wenzelm@4445
  1013
wenzelm@15051
  1014
val int_ord = Int.compare;
wenzelm@15051
  1015
val string_ord = String.compare;
wenzelm@2506
  1016
wenzelm@16676
  1017
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1018
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1019
wenzelm@16492
  1020
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1021
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1022
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1023
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1024
wenzelm@4343
  1025
(*lexicographic product*)
wenzelm@4343
  1026
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1027
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1028
wenzelm@4343
  1029
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1030
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1031
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1032
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1033
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1034
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1035
wenzelm@4343
  1036
(*lexicographic product of lists*)
wenzelm@4343
  1037
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1038
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1039
wenzelm@2506
  1040
wenzelm@4621
  1041
(* sorting *)
wenzelm@4621
  1042
wenzelm@18427
  1043
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
  1044
fun quicksort unique ord =
wenzelm@4621
  1045
  let
wenzelm@16878
  1046
    fun qsort [] = []
wenzelm@16878
  1047
      | qsort (xs as [_]) = xs
wenzelm@18427
  1048
      | qsort (xs as [x, y]) =
wenzelm@18427
  1049
          (case ord (x, y) of
wenzelm@18427
  1050
            LESS => xs
wenzelm@18427
  1051
          | EQUAL => if unique then [x] else xs
wenzelm@18427
  1052
          | GREATER => [y, x])
wenzelm@16878
  1053
      | qsort xs =
haftmann@18011
  1054
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
  1055
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1056
    and part _ [] = ([], [], [])
wenzelm@4621
  1057
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1058
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
  1059
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
  1060
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
  1061
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1062
  in qsort end;
wenzelm@4621
  1063
wenzelm@18427
  1064
fun sort ord = quicksort false ord;
wenzelm@18427
  1065
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
  1066
wenzelm@4621
  1067
val sort_strings = sort string_ord;
wenzelm@4621
  1068
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1069
wenzelm@4621
  1070
wenzelm@2506
  1071
berghofe@14106
  1072
(** random numbers **)
berghofe@14106
  1073
berghofe@14106
  1074
exception RANDOM;
berghofe@14106
  1075
berghofe@14618
  1076
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1077
berghofe@14106
  1078
local
berghofe@14106
  1079
  val a = 16807.0;
berghofe@14106
  1080
  val m = 2147483647.0;
berghofe@14106
  1081
  val random_seed = ref 1.0;
berghofe@14106
  1082
in
berghofe@14106
  1083
berghofe@14106
  1084
fun random () =
berghofe@14106
  1085
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1086
  in (random_seed := r; r) end;
berghofe@14106
  1087
berghofe@14106
  1088
end;
berghofe@14106
  1089
berghofe@14106
  1090
fun random_range l h =
berghofe@14106
  1091
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1092
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1093
haftmann@18011
  1094
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1095
berghofe@14106
  1096
fun frequency xs =
berghofe@14106
  1097
  let
berghofe@14106
  1098
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1099
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1100
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1101
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1102
berghofe@14106
  1103
wenzelm@14826
  1104
(** current directory **)
wenzelm@233
  1105
paulson@2243
  1106
val cd = OS.FileSys.chDir;
wenzelm@2317
  1107
val pwd = OS.FileSys.getDir;
paulson@2243
  1108
berghofe@3606
  1109
wenzelm@19644
  1110
wenzelm@4621
  1111
(** misc **)
wenzelm@233
  1112
wenzelm@19644
  1113
fun divide_and_conquer decomp x =
wenzelm@19644
  1114
  let val (ys, recomb) = decomp x
wenzelm@19644
  1115
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1116
clasohm@0
  1117
wenzelm@233
  1118
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1119
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1120
fun partition_list p i j =
wenzelm@233
  1121
  let fun part k xs =
wenzelm@233
  1122
            if k>j then
clasohm@0
  1123
              (case xs of [] => []
skalberg@15570
  1124
                         | _ => raise Fail "partition_list")
clasohm@0
  1125
            else
wenzelm@19691
  1126
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1127
            in  ns :: part(k+1)rest  end
clasohm@0
  1128
  in  part i end;
clasohm@0
  1129
wenzelm@19691
  1130
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1131
  let
wenzelm@19691
  1132
    fun part [] = []
wenzelm@19691
  1133
      | part (x :: ys) =
wenzelm@19691
  1134
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1135
          in (x::xs)::(part xs') end
wenzelm@19691
  1136
  in part end;
wenzelm@19691
  1137
wenzelm@19691
  1138
clasohm@0
  1139
wenzelm@233
  1140
(* generating identifiers *)
clasohm@0
  1141
paulson@4063
  1142
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1143
local
paulson@4063
  1144
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1145
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1146
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1147
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1148
             else if i=62 then "_"
wenzelm@5904
  1149
             else  (*i=63*)    "'";
paulson@4063
  1150
paulson@4063
  1151
val charVec = Vector.tabulate (64, char);
paulson@4063
  1152
wenzelm@5904
  1153
fun newid n =
wenzelm@5904
  1154
  let
wenzelm@4284
  1155
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1156
wenzelm@4284
  1157
val seedr = ref 0;
clasohm@0
  1158
paulson@4063
  1159
in
wenzelm@4284
  1160
wenzelm@12346
  1161
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1162
paulson@4063
  1163
end;
paulson@4063
  1164
paulson@4063
  1165
wenzelm@233
  1166
(* lexical scanning *)
clasohm@0
  1167
wenzelm@233
  1168
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1169
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1170
fun scanwords is_let cs =
clasohm@0
  1171
  let fun scan1 [] = []
wenzelm@233
  1172
        | scan1 cs =
wenzelm@233
  1173
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1174
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1175
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1176
wenzelm@4212
  1177
wenzelm@16439
  1178
(* stamps and serial numbers *)
wenzelm@16439
  1179
wenzelm@16439
  1180
type stamp = unit ref;
wenzelm@16439
  1181
val stamp: unit -> stamp = ref;
wenzelm@16439
  1182
wenzelm@16439
  1183
type serial = int;
wenzelm@16439
  1184
local val count = ref 0
wenzelm@16439
  1185
in fun serial () = inc count end;
wenzelm@16439
  1186
wenzelm@19512
  1187
val serial_string = string_of_int o serial;
wenzelm@19512
  1188
wenzelm@16535
  1189
wenzelm@16535
  1190
(* generic objects *)
wenzelm@16535
  1191
wenzelm@16535
  1192
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1193
  constructors at any time*)
wenzelm@16535
  1194
structure Object = struct type T = exn end;
wenzelm@16535
  1195
clasohm@1364
  1196
end;
clasohm@1364
  1197
wenzelm@15745
  1198
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1199
open BasicLibrary;