src/Pure/library.ML
author paulson
Tue Feb 27 11:10:35 2007 +0100 (2007-02-27)
changeset 22368 0e0fe77d4768
parent 22256 23f3ca04d3b3
child 22369 a7263f330494
permissions -rw-r--r--
gensym no longer includes ' or _ in names (trailing _ is bad)
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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 ? : 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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  (*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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  (*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 signed_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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  (*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 multisets *)
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  val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val gen_submultiset: ('a * 'b -> bool) -> 'a list * 'b 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 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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   296
fun transform_failure exn f x =
wenzelm@18681
   297
  if ! do_transform_failure then
wenzelm@18681
   298
    f x handle Interrupt => raise Interrupt | e => raise exn e
wenzelm@18681
   299
  else f x;
wenzelm@18681
   300
wenzelm@17341
   301
exception EXCEPTION of exn * string;
wenzelm@6959
   302
wenzelm@14868
   303
datatype 'a result =
wenzelm@14868
   304
  Result of 'a |
wenzelm@14868
   305
  Exn of exn;
wenzelm@14868
   306
wenzelm@14868
   307
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   308
wenzelm@14868
   309
fun release (Result y) = y
wenzelm@14868
   310
  | release (Exn e) = raise e;
wenzelm@14868
   311
skalberg@15531
   312
fun get_result (Result x) = SOME x
skalberg@15531
   313
  | get_result _ = NONE;
wenzelm@14868
   314
skalberg@15531
   315
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   316
  | get_exn _ = NONE;
wenzelm@14868
   317
wenzelm@14868
   318
wenzelm@18681
   319
(* errors *)
wenzelm@18681
   320
wenzelm@19542
   321
exception SYS_ERROR of string;
wenzelm@19542
   322
fun sys_error msg = raise SYS_ERROR msg;
wenzelm@19542
   323
wenzelm@18681
   324
exception ERROR of string;
wenzelm@18681
   325
fun error msg = raise ERROR msg;
wenzelm@18681
   326
wenzelm@18681
   327
fun cat_error "" msg = error msg
wenzelm@18681
   328
  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
wenzelm@18681
   329
wenzelm@18681
   330
fun assert p msg = if p then () else error msg;
wenzelm@18681
   331
fun deny p msg = if p then error msg else ();
wenzelm@18681
   332
wenzelm@18681
   333
fun assert_all pred list msg =
wenzelm@18681
   334
  let
wenzelm@18681
   335
    fun ass [] = ()
wenzelm@18681
   336
      | ass (x :: xs) = if pred x then ass xs else error (msg x);
wenzelm@18681
   337
  in ass list end;
wenzelm@18681
   338
wenzelm@18681
   339
wenzelm@21395
   340
(* pairs *)
wenzelm@233
   341
wenzelm@233
   342
fun pair x y = (x, y);
wenzelm@233
   343
fun rpair x y = (y, x);
wenzelm@233
   344
wenzelm@233
   345
fun fst (x, y) = x;
wenzelm@233
   346
fun snd (x, y) = y;
wenzelm@233
   347
haftmann@17498
   348
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   349
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   350
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   351
wenzelm@233
   352
fun swap (x, y) = (y, x);
wenzelm@233
   353
wenzelm@4212
   354
(*apply function to components*)
wenzelm@233
   355
fun apfst f (x, y) = (f x, y);
wenzelm@233
   356
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   357
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   358
wenzelm@233
   359
wenzelm@21395
   360
(* booleans *)
wenzelm@233
   361
wenzelm@21395
   362
(*polymorphic equality*)
wenzelm@233
   363
fun equal x y = x = y;
wenzelm@233
   364
fun not_equal x y = x <> y;
wenzelm@233
   365
wenzelm@21395
   366
(*combining predicates*)
wenzelm@16721
   367
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   368
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   369
wenzelm@233
   370
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   371
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   372
  let fun boolf [] = false
wenzelm@233
   373
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   374
  in boolf end;
wenzelm@233
   375
wenzelm@233
   376
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   377
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   378
  let fun boolf [] = true
wenzelm@233
   379
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   380
  in boolf end;
clasohm@0
   381
wenzelm@19644
   382
wenzelm@380
   383
(* flags *)
wenzelm@380
   384
wenzelm@380
   385
fun set flag = (flag := true; true);
wenzelm@380
   386
fun reset flag = (flag := false; false);
wenzelm@380
   387
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   388
wenzelm@9118
   389
fun change r f = r := f (! r);
wenzelm@9118
   390
wenzelm@18712
   391
(*temporarily set flag during execution*)
wenzelm@2978
   392
fun setmp flag value f x =
wenzelm@2958
   393
  let
wenzelm@2958
   394
    val orig_value = ! flag;
wenzelm@18712
   395
    val _ = flag := value;
wenzelm@18712
   396
    val result = capture f x;
wenzelm@18712
   397
    val _ = flag := orig_value;
wenzelm@18712
   398
  in release result end;
wenzelm@2958
   399
wenzelm@19644
   400
wenzelm@21395
   401
wenzelm@233
   402
(** lists **)
wenzelm@233
   403
skalberg@15570
   404
exception UnequalLengths;
wenzelm@233
   405
wenzelm@5285
   406
fun single x = [x];
wenzelm@233
   407
wenzelm@20882
   408
fun the_single [x] = x
wenzelm@20882
   409
  | the_single _ = raise Empty;
wenzelm@20882
   410
wenzelm@20882
   411
fun singleton f x = the_single (f [x]);
wenzelm@19273
   412
wenzelm@5904
   413
fun apply [] x = x
wenzelm@5904
   414
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   415
wenzelm@233
   416
wenzelm@21395
   417
(* fold -- old versions *)
haftmann@16691
   418
wenzelm@233
   419
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   420
wenzelm@233
   421
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   422
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   423
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   424
  let fun itl (e, [])  = e
wenzelm@233
   425
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   426
  in  itl end;
wenzelm@233
   427
wenzelm@233
   428
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   429
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   430
fun foldr f (l, e) =
wenzelm@233
   431
  let fun itr [] = e
wenzelm@233
   432
        | itr (a::l) = f(a, itr l)
wenzelm@233
   433
  in  itr l  end;
wenzelm@233
   434
wenzelm@233
   435
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   436
    for n > 0, operators that associate to the right (not tail recursive)*)
paulson@20443
   437
fun foldr1 f [] = raise Empty
wenzelm@20510
   438
  | foldr1 f l =
paulson@20443
   439
      let fun itr [x] = x
wenzelm@20510
   440
            | itr (x::l) = f(x, itr l)
paulson@20443
   441
      in  itr l  end;
wenzelm@233
   442
wenzelm@16705
   443
fun foldl_map f =
wenzelm@16705
   444
  let
wenzelm@16705
   445
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   446
      | fold_aux (x, y :: ys) =
wenzelm@16705
   447
          let
wenzelm@16705
   448
            val (x', y') = f (x, y);
wenzelm@16705
   449
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   450
          in (x'', y' :: ys') end;
wenzelm@16705
   451
  in fold_aux end;
wenzelm@16705
   452
wenzelm@233
   453
wenzelm@233
   454
(* basic list functions *)
wenzelm@233
   455
wenzelm@20510
   456
fun eq_list eq (list1, list2) =
haftmann@20348
   457
  let
wenzelm@20510
   458
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   459
      | eq_lst _ = true;
wenzelm@20510
   460
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   461
wenzelm@19483
   462
fun maps f [] = []
wenzelm@19483
   463
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   464
wenzelm@21395
   465
fun chop n xs = unfold_rev n dest xs;
wenzelm@19011
   466
wenzelm@233
   467
(*take the first n elements from a list*)
wenzelm@233
   468
fun take (n, []) = []
wenzelm@233
   469
  | take (n, x :: xs) =
wenzelm@233
   470
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   471
wenzelm@233
   472
(*drop the first n elements from a list*)
wenzelm@233
   473
fun drop (n, []) = []
wenzelm@233
   474
  | drop (n, x :: xs) =
wenzelm@233
   475
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   476
nipkow@4713
   477
fun dropwhile P [] = []
nipkow@4713
   478
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   479
wenzelm@233
   480
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   481
  raise Subscript if list too short*)
haftmann@18011
   482
fun nth xs i = List.nth (xs, i);
wenzelm@233
   483
wenzelm@18461
   484
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   485
haftmann@18011
   486
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   487
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   488
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   489
haftmann@18514
   490
fun map_index f =
haftmann@18514
   491
  let
haftmann@18514
   492
    fun mapp _ [] = []
haftmann@18514
   493
      | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
haftmann@18514
   494
  in mapp 0 end;
haftmann@18514
   495
haftmann@21118
   496
fun fold_index f =
haftmann@21118
   497
  let
haftmann@21118
   498
    fun fold_aux _ [] y = y
haftmann@21118
   499
      | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
haftmann@21118
   500
  in fold_aux 0 end;
haftmann@21118
   501
skalberg@15570
   502
val last_elem = List.last;
wenzelm@233
   503
wenzelm@3762
   504
(*rear decomposition*)
skalberg@15570
   505
fun split_last [] = raise Empty
wenzelm@3762
   506
  | split_last [x] = ([], x)
wenzelm@3762
   507
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   508
wenzelm@4212
   509
(*find the position of an element in a list*)
wenzelm@4212
   510
fun find_index pred =
wenzelm@4212
   511
  let fun find _ [] = ~1
wenzelm@4212
   512
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   513
  in find 0 end;
wenzelm@3762
   514
wenzelm@4224
   515
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   516
wenzelm@4212
   517
(*find first element satisfying predicate*)
skalberg@15531
   518
fun find_first _ [] = NONE
wenzelm@4212
   519
  | find_first pred (x :: xs) =
skalberg@15531
   520
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   521
wenzelm@4916
   522
(*get first element by lookup function*)
skalberg@15531
   523
fun get_first _ [] = NONE
wenzelm@4916
   524
  | get_first f (x :: xs) =
wenzelm@4916
   525
      (case f x of
skalberg@15531
   526
        NONE => get_first f xs
wenzelm@4916
   527
      | some => some);
wenzelm@4916
   528
haftmann@19233
   529
fun get_index f =
haftmann@19233
   530
  let
haftmann@19233
   531
    fun get _ [] = NONE
wenzelm@19461
   532
      | get i (x :: xs) =
haftmann@19233
   533
          case f x
wenzelm@19461
   534
           of NONE => get (i + 1) xs
haftmann@19233
   535
            | SOME y => SOME (i, y)
haftmann@19233
   536
  in get 0 end;
haftmann@19233
   537
skalberg@15531
   538
val flat = List.concat;
wenzelm@233
   539
wenzelm@12136
   540
fun unflat (xs :: xss) ys =
wenzelm@19424
   541
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   542
      in ps :: unflat xss qs end
wenzelm@12136
   543
  | unflat [] [] = []
skalberg@15570
   544
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   545
wenzelm@21479
   546
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   547
haftmann@18549
   548
fun fold_burrow f xss s =
haftmann@18549
   549
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   550
wenzelm@233
   551
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   552
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   553
val seq = List.app;
wenzelm@233
   554
wenzelm@233
   555
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   556
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   557
  | separate _ xs = xs;
wenzelm@233
   558
wenzelm@233
   559
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   560
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   561
  let fun rep (0, xs) = xs
wenzelm@233
   562
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   563
  in
skalberg@15570
   564
    if n < 0 then raise Subscript
wenzelm@233
   565
    else rep (n, [])
wenzelm@233
   566
  end;
wenzelm@233
   567
wenzelm@14926
   568
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   569
wenzelm@4248
   570
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   571
fun multiply [] _ = []
wenzelm@18148
   572
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   573
wenzelm@14792
   574
(*direct product*)
wenzelm@14792
   575
fun product _ [] = []
wenzelm@14792
   576
  | product [] _ = []
wenzelm@14792
   577
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   578
wenzelm@233
   579
wenzelm@233
   580
(* filter *)
wenzelm@233
   581
wenzelm@233
   582
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   583
val filter = List.filter;
clasohm@0
   584
fun filter_out f = filter (not o f);
wenzelm@19483
   585
val map_filter = List.mapPartial;
wenzelm@233
   586
wenzelm@233
   587
wenzelm@233
   588
(* lists of pairs *)
wenzelm@233
   589
skalberg@15570
   590
exception UnequalLengths;
skalberg@15570
   591
haftmann@18330
   592
fun map2 _ [] [] = []
haftmann@18330
   593
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   594
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   595
haftmann@18330
   596
fun fold2 f =
haftmann@18330
   597
  let
haftmann@18330
   598
    fun fold_aux [] [] z = z
haftmann@18330
   599
      | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
haftmann@18330
   600
      | fold_aux _ _ _ = raise UnequalLengths;
haftmann@18330
   601
  in fold_aux end;
wenzelm@380
   602
wenzelm@19799
   603
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   604
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   605
  | zip_options _ [] = []
wenzelm@19799
   606
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   607
wenzelm@233
   608
(*combine two lists forming a list of pairs:
wenzelm@233
   609
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   610
fun [] ~~ [] = []
wenzelm@233
   611
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   612
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   613
wenzelm@233
   614
(*inverse of ~~; the old 'split':
wenzelm@233
   615
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   616
val split_list = ListPair.unzip;
wenzelm@233
   617
wenzelm@233
   618
wenzelm@233
   619
(* prefixes, suffixes *)
wenzelm@233
   620
haftmann@18441
   621
fun is_prefix _ [] _ = true
haftmann@18441
   622
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   623
  | is_prefix eq _ _ = false;
wenzelm@233
   624
wenzelm@233
   625
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   626
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   627
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   628
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   629
        | take (rxs, x :: xs) =
wenzelm@255
   630
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   631
  in  take([], xs)  end;
wenzelm@233
   632
haftmann@20108
   633
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   634
  | chop_prefix eq (xs, []) = ([], (xs, []))
haftmann@20108
   635
  | chop_prefix eq (xs as x::xs', ys as y::ys') =
haftmann@20108
   636
      if eq (x, y) then
haftmann@20108
   637
        let val (ps', xys'') = chop_prefix eq (xs', ys')
haftmann@20108
   638
        in (x::ps', xys'') end
haftmann@20108
   639
      else ([], (xs, ys));
haftmann@20108
   640
wenzelm@233
   641
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   642
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   643
fun take_suffix _ [] = ([], [])
wenzelm@233
   644
  | take_suffix pred (x :: xs) =
wenzelm@233
   645
      (case take_suffix pred xs of
wenzelm@233
   646
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   647
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   648
wenzelm@12249
   649
fun prefixes1 [] = []
wenzelm@12249
   650
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   651
wenzelm@19011
   652
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   653
wenzelm@12249
   654
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   655
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   656
wenzelm@233
   657
(** integers **)
wenzelm@233
   658
wenzelm@16439
   659
fun gcd (x, y) =
paulson@15965
   660
  let fun gxd x y : IntInf.int =
wenzelm@21859
   661
    if y = IntInf.fromInt 0 then x else gxd y (x mod y)
nipkow@10692
   662
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   663
wenzelm@16439
   664
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   665
wenzelm@2958
   666
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   667
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   668
wenzelm@233
   669
wenzelm@233
   670
(* lists of integers *)
wenzelm@233
   671
wenzelm@233
   672
(*make the list [from, from + 1, ..., to]*)
wenzelm@21859
   673
fun (i upto j) =
wenzelm@21859
   674
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   675
wenzelm@233
   676
(*make the list [from, from - 1, ..., to]*)
wenzelm@21859
   677
fun (i downto j) =
wenzelm@21859
   678
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   679
wenzelm@233
   680
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   681
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   682
  | downto0 ([], n) = n = ~1;
wenzelm@233
   683
wenzelm@233
   684
wenzelm@233
   685
(* convert integers to strings *)
wenzelm@233
   686
wenzelm@233
   687
(*expand the number in the given base;
wenzelm@233
   688
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   689
fun radixpand (base, num) : int list =
wenzelm@233
   690
  let
wenzelm@233
   691
    fun radix (n, tail) =
wenzelm@233
   692
      if n < base then n :: tail
wenzelm@233
   693
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   694
  in radix (num, []) end;
wenzelm@233
   695
wenzelm@233
   696
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   697
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   698
fun radixstring (base, zerochar, num) =
wenzelm@233
   699
  let val offset = ord zerochar;
wenzelm@233
   700
      fun chrof n = chr (offset + n)
wenzelm@233
   701
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   702
wenzelm@233
   703
paulson@3407
   704
val string_of_int = Int.toString;
wenzelm@233
   705
wenzelm@21942
   706
fun signed_string_of_int i =
wenzelm@21942
   707
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   708
paulson@3407
   709
fun string_of_indexname (a,0) = a
paulson@3407
   710
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   711
wenzelm@233
   712
wenzelm@14826
   713
(* read integers *)
wenzelm@14826
   714
wenzelm@20095
   715
fun read_intinf radix cs =
wenzelm@20095
   716
  let
wenzelm@20095
   717
    val zero = ord "0";
wenzelm@20095
   718
    val limit = zero + radix;
wenzelm@20095
   719
    fun scan (num, []) = (num, [])
wenzelm@20095
   720
      | scan (num, c :: cs) =
wenzelm@20095
   721
        if zero <= ord c andalso ord c < limit then
wenzelm@20095
   722
          scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
wenzelm@20095
   723
        else (num, c :: cs);
wenzelm@21859
   724
  in scan (IntInf.fromInt 0, cs) end;
wenzelm@14826
   725
wenzelm@20095
   726
fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
wenzelm@14826
   727
wenzelm@20095
   728
fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
wenzelm@14826
   729
wenzelm@14826
   730
wenzelm@14826
   731
wenzelm@233
   732
(** strings **)
wenzelm@233
   733
wenzelm@16188
   734
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   735
haftmann@18011
   736
fun nth_string str i =
wenzelm@6959
   737
  (case try String.substring (str, i, 1) of
skalberg@15531
   738
    SOME s => s
skalberg@15570
   739
  | NONE => raise Subscript);
wenzelm@6312
   740
wenzelm@16188
   741
fun fold_string f str x0 =
wenzelm@6282
   742
  let
wenzelm@6282
   743
    val n = size str;
wenzelm@16188
   744
    fun iter (x, i) =
wenzelm@16188
   745
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   746
  in iter (x0, 0) end;
wenzelm@6282
   747
wenzelm@14968
   748
fun exists_string pred str =
wenzelm@14968
   749
  let
wenzelm@14968
   750
    val n = size str;
wenzelm@14968
   751
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   752
  in ex 0 end;
wenzelm@6312
   753
wenzelm@16188
   754
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   755
lcp@512
   756
(*enclose in brackets*)
lcp@512
   757
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   758
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   759
wenzelm@233
   760
(*simple quoting (does not escape special chars)*)
lcp@512
   761
val quote = enclose "\"" "\"";
wenzelm@233
   762
wenzelm@4212
   763
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   764
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   765
wenzelm@255
   766
val commas = space_implode ", ";
wenzelm@380
   767
val commas_quote = commas o map quote;
wenzelm@255
   768
wenzelm@233
   769
(*concatenate messages, one per line, into a string*)
wenzelm@255
   770
val cat_lines = space_implode "\n";
wenzelm@233
   771
wenzelm@4212
   772
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   773
fun space_explode _ "" = []
paulson@21899
   774
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   775
wenzelm@3832
   776
val split_lines = space_explode "\n";
wenzelm@3832
   777
wenzelm@14826
   778
fun prefix_lines "" txt = txt
wenzelm@14826
   779
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   780
wenzelm@7712
   781
fun untabify chs =
wenzelm@7712
   782
  let
wenzelm@7712
   783
    val tab_width = 8;
wenzelm@7712
   784
berghofe@22256
   785
    fun untab pos [] ys = rev ys 
berghofe@22256
   786
      | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
berghofe@22256
   787
      | untab pos ("\t" :: xs) ys =
berghofe@22256
   788
          let val d = tab_width - (pos mod tab_width) in untab (pos + d) xs (replicate d " " @ ys) end
berghofe@22256
   789
      | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
wenzelm@7712
   790
  in
wenzelm@19301
   791
    if not (exists (fn c => c = "\t") chs) then chs
berghofe@22256
   792
    else untab 0 chs []
wenzelm@7712
   793
  end;
wenzelm@7712
   794
wenzelm@18681
   795
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   796
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   797
wenzelm@18681
   798
fun unprefix prfx s =
wenzelm@18681
   799
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   800
  else raise Fail "unprefix";
wenzelm@18681
   801
wenzelm@16188
   802
fun unsuffix sffx s =
wenzelm@17061
   803
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   804
  else raise Fail "unsuffix";
wenzelm@5285
   805
wenzelm@10951
   806
fun replicate_string 0 _ = ""
wenzelm@10951
   807
  | replicate_string 1 a = a
wenzelm@10951
   808
  | replicate_string k a =
wenzelm@10951
   809
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   810
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   811
wenzelm@233
   812
wenzelm@16492
   813
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   814
wenzelm@18923
   815
(*canonical member, insert, remove*)
wenzelm@18923
   816
fun member eq list x =
wenzelm@18923
   817
  let
wenzelm@18923
   818
    fun memb [] = false
wenzelm@18923
   819
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   820
  in memb list end;
berghofe@1576
   821
wenzelm@18923
   822
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   823
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   824
wenzelm@19301
   825
fun subtract eq = fold (remove eq);
wenzelm@19301
   826
wenzelm@18923
   827
fun merge _ ([], ys) = ys
wenzelm@18923
   828
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   829
wenzelm@18923
   830
(*old-style infixes*)
wenzelm@18923
   831
fun x mem xs = member (op =) xs x;
wenzelm@18923
   832
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   833
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   834
wenzelm@233
   835
wenzelm@233
   836
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   837
fun xs union [] = xs
wenzelm@233
   838
  | [] union ys = ys
haftmann@20854
   839
  | (x :: xs) union ys = xs union (insert (op =) x ys);
clasohm@0
   840
paulson@2175
   841
(*union of sets, optimized version for ints*)
berghofe@1576
   842
fun (xs:int list) union_int [] = xs
berghofe@1576
   843
  | [] union_int ys = ys
haftmann@20854
   844
  | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
berghofe@1576
   845
paulson@2175
   846
(*union of sets, optimized version for strings*)
berghofe@1576
   847
fun (xs:string list) union_string [] = xs
berghofe@1576
   848
  | [] union_string ys = ys
haftmann@20854
   849
  | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
berghofe@1576
   850
clasohm@0
   851
(*generalized union*)
wenzelm@233
   852
fun gen_union eq (xs, []) = xs
wenzelm@233
   853
  | gen_union eq ([], ys) = ys
wenzelm@18923
   854
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   855
wenzelm@233
   856
wenzelm@233
   857
(*intersection*)
wenzelm@233
   858
fun [] inter ys = []
wenzelm@233
   859
  | (x :: xs) inter ys =
wenzelm@233
   860
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   861
paulson@2175
   862
(*intersection, optimized version for ints*)
berghofe@1576
   863
fun ([]:int list) inter_int ys = []
berghofe@1576
   864
  | (x :: xs) inter_int ys =
berghofe@1576
   865
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   866
paulson@2175
   867
(*intersection, optimized version for strings *)
berghofe@1576
   868
fun ([]:string list) inter_string ys = []
berghofe@1576
   869
  | (x :: xs) inter_string ys =
berghofe@1576
   870
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   871
paulson@7090
   872
(*generalized intersection*)
paulson@7090
   873
fun gen_inter eq ([], ys) = []
wenzelm@12284
   874
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
   875
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
   876
      else gen_inter eq (xs, ys);
paulson@7090
   877
wenzelm@233
   878
wenzelm@233
   879
(*subset*)
wenzelm@233
   880
fun [] subset ys = true
wenzelm@233
   881
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   882
paulson@2175
   883
(*subset, optimized version for ints*)
wenzelm@16439
   884
fun ([]: int list) subset_int ys = true
berghofe@1576
   885
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   886
paulson@2175
   887
(*subset, optimized version for strings*)
wenzelm@16439
   888
fun ([]: string list) subset_string ys = true
berghofe@1576
   889
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   890
wenzelm@4363
   891
(*set equality*)
wenzelm@4363
   892
fun eq_set (xs, ys) =
wenzelm@4363
   893
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   894
paulson@2182
   895
(*set equality for strings*)
wenzelm@16439
   896
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   897
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   898
wenzelm@18923
   899
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
   900
wenzelm@19301
   901
fun gen_eq_set eq (xs, ys) =
haftmann@20348
   902
  eq_list eq (xs, ys) orelse
wenzelm@19301
   903
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
   904
wenzelm@265
   905
wenzelm@233
   906
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   907
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   908
  | [] \ x = [];
paulson@2243
   909
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   910
wenzelm@233
   911
wenzelm@233
   912
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   913
  first of equal elements*)
wenzelm@19046
   914
fun distinct eq lst =
wenzelm@233
   915
  let
wenzelm@233
   916
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   917
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   918
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   919
          else dist (x :: rev_seen, xs);
wenzelm@19046
   920
  in dist ([], lst) end;
wenzelm@233
   921
wenzelm@255
   922
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   923
  order, takes first of equal elements*)
wenzelm@18966
   924
fun duplicates eq lst =
wenzelm@255
   925
  let
wenzelm@255
   926
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   927
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   928
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   929
            dups (rev_dups, xs)
wenzelm@255
   930
          else dups (x :: rev_dups, xs);
wenzelm@18966
   931
  in dups ([], lst) end;
wenzelm@255
   932
wenzelm@16878
   933
fun has_duplicates eq =
wenzelm@16878
   934
  let
wenzelm@16878
   935
    fun dups [] = false
wenzelm@16878
   936
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   937
  in dups end;
wenzelm@16878
   938
wenzelm@255
   939
nipkow@22142
   940
(** lists as multisets **)
nipkow@22142
   941
nipkow@22142
   942
fun remove1 _ _ [] = raise Empty
nipkow@22142
   943
  | remove1 eq y (x::xs) = if eq(y,x) then xs else x :: remove1 eq y xs;
nipkow@22142
   944
nipkow@22142
   945
fun gen_submultiset _  ([],    _)  = true
nipkow@22142
   946
  | gen_submultiset eq (x::xs, ys) =
nipkow@22142
   947
      member eq ys x  andalso  gen_submultiset eq (xs, remove1 eq x ys);
nipkow@22142
   948
nipkow@22142
   949
haftmann@19119
   950
(** association lists -- legacy operations **)
wenzelm@233
   951
wenzelm@12284
   952
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
   953
  | gen_merge_lists _ [] ys = ys
haftmann@20951
   954
  | gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys;
clasohm@0
   955
wenzelm@12284
   956
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
haftmann@20951
   957
fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs;
clasohm@0
   958
clasohm@0
   959
wenzelm@233
   960
(** balanced trees **)
wenzelm@233
   961
wenzelm@233
   962
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   963
wenzelm@233
   964
(*balanced folding; avoids deep nesting*)
wenzelm@233
   965
fun fold_bal f [x] = x
wenzelm@233
   966
  | fold_bal f [] = raise Balance
wenzelm@233
   967
  | fold_bal f xs =
wenzelm@19474
   968
      let val (ps, qs) = chop (length xs div 2) xs
nipkow@13629
   969
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
   970
wenzelm@233
   971
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   972
fun access_bal (f, g, x) n i =
wenzelm@233
   973
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   974
          if n=1 then x else
wenzelm@233
   975
          let val n2 = n div 2
wenzelm@233
   976
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   977
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   978
          end
wenzelm@233
   979
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   980
wenzelm@233
   981
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   982
fun accesses_bal (f, g, x) n =
wenzelm@233
   983
  let fun acc n =
wenzelm@233
   984
          if n=1 then [x] else
wenzelm@233
   985
          let val n2 = n div 2
wenzelm@233
   986
              val acc2 = acc n2
wenzelm@233
   987
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   988
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   989
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   990
wenzelm@233
   991
wenzelm@233
   992
wenzelm@2506
   993
(** orders **)
wenzelm@2506
   994
wenzelm@18966
   995
fun is_equal EQUAL = true
wenzelm@18966
   996
  | is_equal _ = false;
wenzelm@18966
   997
wenzelm@4445
   998
fun rev_order LESS = GREATER
wenzelm@4445
   999
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1000
  | rev_order GREATER = LESS;
wenzelm@4445
  1001
wenzelm@4479
  1002
(*assume rel is a linear strict order*)
wenzelm@4445
  1003
fun make_ord rel (x, y) =
wenzelm@4445
  1004
  if rel (x, y) then LESS
wenzelm@4445
  1005
  else if rel (y, x) then GREATER
wenzelm@4445
  1006
  else EQUAL;
wenzelm@4445
  1007
wenzelm@15051
  1008
val int_ord = Int.compare;
wenzelm@15051
  1009
val string_ord = String.compare;
wenzelm@2506
  1010
wenzelm@16676
  1011
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1012
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1013
wenzelm@16492
  1014
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1015
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1016
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1017
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1018
wenzelm@4343
  1019
(*lexicographic product*)
wenzelm@4343
  1020
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1021
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1022
wenzelm@4343
  1023
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1024
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1025
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1026
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1027
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1028
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1029
wenzelm@4343
  1030
(*lexicographic product of lists*)
wenzelm@4343
  1031
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1032
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1033
wenzelm@2506
  1034
wenzelm@4621
  1035
(* sorting *)
wenzelm@4621
  1036
wenzelm@18427
  1037
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
  1038
fun quicksort unique ord =
wenzelm@4621
  1039
  let
wenzelm@16878
  1040
    fun qsort [] = []
wenzelm@16878
  1041
      | qsort (xs as [_]) = xs
wenzelm@18427
  1042
      | qsort (xs as [x, y]) =
wenzelm@18427
  1043
          (case ord (x, y) of
wenzelm@18427
  1044
            LESS => xs
wenzelm@18427
  1045
          | EQUAL => if unique then [x] else xs
wenzelm@18427
  1046
          | GREATER => [y, x])
wenzelm@16878
  1047
      | qsort xs =
haftmann@18011
  1048
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
  1049
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1050
    and part _ [] = ([], [], [])
wenzelm@4621
  1051
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1052
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
  1053
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
  1054
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
  1055
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1056
  in qsort end;
wenzelm@4621
  1057
wenzelm@18427
  1058
fun sort ord = quicksort false ord;
wenzelm@18427
  1059
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
  1060
wenzelm@4621
  1061
val sort_strings = sort string_ord;
wenzelm@4621
  1062
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1063
wenzelm@4621
  1064
wenzelm@2506
  1065
berghofe@14106
  1066
(** random numbers **)
berghofe@14106
  1067
berghofe@14106
  1068
exception RANDOM;
berghofe@14106
  1069
berghofe@14618
  1070
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1071
berghofe@14106
  1072
local
berghofe@14106
  1073
  val a = 16807.0;
berghofe@14106
  1074
  val m = 2147483647.0;
berghofe@14106
  1075
  val random_seed = ref 1.0;
berghofe@14106
  1076
in
berghofe@14106
  1077
berghofe@14106
  1078
fun random () =
berghofe@14106
  1079
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1080
  in (random_seed := r; r) end;
berghofe@14106
  1081
berghofe@14106
  1082
end;
berghofe@14106
  1083
berghofe@14106
  1084
fun random_range l h =
berghofe@14106
  1085
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1086
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1087
haftmann@18011
  1088
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1089
berghofe@14106
  1090
fun frequency xs =
berghofe@14106
  1091
  let
berghofe@14106
  1092
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1093
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1094
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1095
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1096
berghofe@14106
  1097
wenzelm@14826
  1098
(** current directory **)
wenzelm@233
  1099
paulson@2243
  1100
val cd = OS.FileSys.chDir;
wenzelm@2317
  1101
val pwd = OS.FileSys.getDir;
paulson@2243
  1102
berghofe@3606
  1103
wenzelm@19644
  1104
wenzelm@4621
  1105
(** misc **)
wenzelm@233
  1106
wenzelm@19644
  1107
fun divide_and_conquer decomp x =
wenzelm@19644
  1108
  let val (ys, recomb) = decomp x
wenzelm@19644
  1109
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1110
clasohm@0
  1111
wenzelm@233
  1112
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1113
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1114
fun partition_list p i j =
wenzelm@233
  1115
  let fun part k xs =
wenzelm@233
  1116
            if k>j then
clasohm@0
  1117
              (case xs of [] => []
skalberg@15570
  1118
                         | _ => raise Fail "partition_list")
clasohm@0
  1119
            else
wenzelm@19691
  1120
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1121
            in  ns :: part(k+1)rest  end
clasohm@0
  1122
  in  part i end;
clasohm@0
  1123
wenzelm@19691
  1124
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1125
  let
wenzelm@19691
  1126
    fun part [] = []
wenzelm@19691
  1127
      | part (x :: ys) =
wenzelm@19691
  1128
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1129
          in (x::xs)::(part xs') end
wenzelm@19691
  1130
  in part end;
wenzelm@19691
  1131
wenzelm@19691
  1132
clasohm@0
  1133
wenzelm@233
  1134
(* generating identifiers *)
clasohm@0
  1135
paulson@4063
  1136
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
paulson@4063
  1137
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@22368
  1138
fun gensym_char i = 
paulson@22368
  1139
  if i<26 then chr (ord "A" + i)
paulson@22368
  1140
  else if i<52 then chr (ord "a" + i - 26)
paulson@22368
  1141
  else if i<62 then chr (ord"0" + i - 52)
paulson@22368
  1142
  else if i=62 then "_"
paulson@22368
  1143
  else  (*i=63*)    "'";
paulson@4063
  1144
paulson@22368
  1145
val charVec = Vector.tabulate (64, gensym_char);
clasohm@0
  1146
paulson@22368
  1147
(*Not 64, as _ and ' could cause problems (especially _).*)
paulson@22368
  1148
fun newid n = implode (map (fn i => Vector.sub(charVec,i)) (radixpand (62,n)));
wenzelm@4284
  1149
paulson@22368
  1150
val gensym_seed = ref 0;
paulson@2003
  1151
paulson@22368
  1152
fun gensym pre = pre ^ newid (inc gensym_seed);
paulson@4063
  1153
paulson@4063
  1154
wenzelm@233
  1155
(* lexical scanning *)
clasohm@0
  1156
wenzelm@233
  1157
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1158
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1159
fun scanwords is_let cs =
clasohm@0
  1160
  let fun scan1 [] = []
wenzelm@233
  1161
        | scan1 cs =
wenzelm@233
  1162
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1163
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1164
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1165
wenzelm@4212
  1166
wenzelm@16439
  1167
(* stamps and serial numbers *)
wenzelm@16439
  1168
wenzelm@16439
  1169
type stamp = unit ref;
wenzelm@16439
  1170
val stamp: unit -> stamp = ref;
wenzelm@16439
  1171
wenzelm@16439
  1172
type serial = int;
wenzelm@16439
  1173
local val count = ref 0
wenzelm@16439
  1174
in fun serial () = inc count end;
wenzelm@16439
  1175
wenzelm@19512
  1176
val serial_string = string_of_int o serial;
wenzelm@19512
  1177
wenzelm@16535
  1178
wenzelm@16535
  1179
(* generic objects *)
wenzelm@16535
  1180
wenzelm@16535
  1181
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1182
  constructors at any time*)
wenzelm@16535
  1183
structure Object = struct type T = exn end;
wenzelm@16535
  1184
clasohm@1364
  1185
end;
clasohm@1364
  1186
wenzelm@15745
  1187
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1188
open BasicLibrary;