src/Pure/library.ML
author paulson
Fri Dec 22 20:58:14 2006 +0100 (2006-12-22)
changeset 21899 dab16d14db60
parent 21859 03e1e75ad2e5
child 21920 f1c096441023
permissions -rw-r--r--
string primtives
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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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  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 nospaces: 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 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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fun transform_failure exn f x =
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  if ! do_transform_failure then
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    f x handle Interrupt => raise Interrupt | e => raise exn e
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  else f x;
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wenzelm@17341
   298
exception EXCEPTION of exn * string;
wenzelm@6959
   299
wenzelm@14868
   300
datatype 'a result =
wenzelm@14868
   301
  Result of 'a |
wenzelm@14868
   302
  Exn of exn;
wenzelm@14868
   303
wenzelm@14868
   304
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   305
wenzelm@14868
   306
fun release (Result y) = y
wenzelm@14868
   307
  | release (Exn e) = raise e;
wenzelm@14868
   308
skalberg@15531
   309
fun get_result (Result x) = SOME x
skalberg@15531
   310
  | get_result _ = NONE;
wenzelm@14868
   311
skalberg@15531
   312
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   313
  | get_exn _ = NONE;
wenzelm@14868
   314
wenzelm@14868
   315
wenzelm@18681
   316
(* errors *)
wenzelm@18681
   317
wenzelm@19542
   318
exception SYS_ERROR of string;
wenzelm@19542
   319
fun sys_error msg = raise SYS_ERROR msg;
wenzelm@19542
   320
wenzelm@18681
   321
exception ERROR of string;
wenzelm@18681
   322
fun error msg = raise ERROR msg;
wenzelm@18681
   323
wenzelm@18681
   324
fun cat_error "" msg = error msg
wenzelm@18681
   325
  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
wenzelm@18681
   326
wenzelm@18681
   327
fun assert p msg = if p then () else error msg;
wenzelm@18681
   328
fun deny p msg = if p then error msg else ();
wenzelm@18681
   329
wenzelm@18681
   330
fun assert_all pred list msg =
wenzelm@18681
   331
  let
wenzelm@18681
   332
    fun ass [] = ()
wenzelm@18681
   333
      | ass (x :: xs) = if pred x then ass xs else error (msg x);
wenzelm@18681
   334
  in ass list end;
wenzelm@18681
   335
wenzelm@18681
   336
wenzelm@21395
   337
(* pairs *)
wenzelm@233
   338
wenzelm@233
   339
fun pair x y = (x, y);
wenzelm@233
   340
fun rpair x y = (y, x);
wenzelm@233
   341
wenzelm@233
   342
fun fst (x, y) = x;
wenzelm@233
   343
fun snd (x, y) = y;
wenzelm@233
   344
haftmann@17498
   345
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   346
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   347
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   348
wenzelm@233
   349
fun swap (x, y) = (y, x);
wenzelm@233
   350
wenzelm@4212
   351
(*apply function to components*)
wenzelm@233
   352
fun apfst f (x, y) = (f x, y);
wenzelm@233
   353
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   354
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   355
wenzelm@233
   356
wenzelm@21395
   357
(* booleans *)
wenzelm@233
   358
wenzelm@21395
   359
(*polymorphic equality*)
wenzelm@233
   360
fun equal x y = x = y;
wenzelm@233
   361
fun not_equal x y = x <> y;
wenzelm@233
   362
wenzelm@21395
   363
(*combining predicates*)
wenzelm@16721
   364
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   365
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   366
wenzelm@233
   367
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   368
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   369
  let fun boolf [] = false
wenzelm@233
   370
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   371
  in boolf end;
wenzelm@233
   372
wenzelm@233
   373
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   374
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   375
  let fun boolf [] = true
wenzelm@233
   376
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   377
  in boolf end;
clasohm@0
   378
wenzelm@19644
   379
wenzelm@380
   380
(* flags *)
wenzelm@380
   381
wenzelm@380
   382
fun set flag = (flag := true; true);
wenzelm@380
   383
fun reset flag = (flag := false; false);
wenzelm@380
   384
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   385
wenzelm@9118
   386
fun change r f = r := f (! r);
wenzelm@9118
   387
wenzelm@18712
   388
(*temporarily set flag during execution*)
wenzelm@2978
   389
fun setmp flag value f x =
wenzelm@2958
   390
  let
wenzelm@2958
   391
    val orig_value = ! flag;
wenzelm@18712
   392
    val _ = flag := value;
wenzelm@18712
   393
    val result = capture f x;
wenzelm@18712
   394
    val _ = flag := orig_value;
wenzelm@18712
   395
  in release result end;
wenzelm@2958
   396
wenzelm@19644
   397
wenzelm@11853
   398
(* conditional execution *)
wenzelm@11853
   399
wenzelm@11853
   400
fun conditional b f = if b then f () else ();
wenzelm@11853
   401
wenzelm@233
   402
wenzelm@21395
   403
wenzelm@233
   404
(** lists **)
wenzelm@233
   405
skalberg@15570
   406
exception UnequalLengths;
wenzelm@233
   407
wenzelm@5285
   408
fun single x = [x];
wenzelm@233
   409
wenzelm@20882
   410
fun the_single [x] = x
wenzelm@20882
   411
  | the_single _ = raise Empty;
wenzelm@20882
   412
wenzelm@20882
   413
fun singleton f x = the_single (f [x]);
wenzelm@19273
   414
wenzelm@5904
   415
fun apply [] x = x
wenzelm@5904
   416
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   417
wenzelm@233
   418
wenzelm@21395
   419
(* fold -- old versions *)
haftmann@16691
   420
wenzelm@233
   421
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   422
wenzelm@233
   423
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   424
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   425
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   426
  let fun itl (e, [])  = e
wenzelm@233
   427
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   428
  in  itl end;
wenzelm@233
   429
wenzelm@233
   430
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   431
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   432
fun foldr f (l, e) =
wenzelm@233
   433
  let fun itr [] = e
wenzelm@233
   434
        | itr (a::l) = f(a, itr l)
wenzelm@233
   435
  in  itr l  end;
wenzelm@233
   436
wenzelm@233
   437
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   438
    for n > 0, operators that associate to the right (not tail recursive)*)
paulson@20443
   439
fun foldr1 f [] = raise Empty
wenzelm@20510
   440
  | foldr1 f l =
paulson@20443
   441
      let fun itr [x] = x
wenzelm@20510
   442
            | itr (x::l) = f(x, itr l)
paulson@20443
   443
      in  itr l  end;
wenzelm@233
   444
wenzelm@16705
   445
fun foldl_map f =
wenzelm@16705
   446
  let
wenzelm@16705
   447
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   448
      | fold_aux (x, y :: ys) =
wenzelm@16705
   449
          let
wenzelm@16705
   450
            val (x', y') = f (x, y);
wenzelm@16705
   451
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   452
          in (x'', y' :: ys') end;
wenzelm@16705
   453
  in fold_aux end;
wenzelm@16705
   454
wenzelm@233
   455
wenzelm@233
   456
(* basic list functions *)
wenzelm@233
   457
wenzelm@20510
   458
fun eq_list eq (list1, list2) =
haftmann@20348
   459
  let
wenzelm@20510
   460
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   461
      | eq_lst _ = true;
wenzelm@20510
   462
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   463
wenzelm@19483
   464
fun maps f [] = []
wenzelm@19483
   465
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   466
wenzelm@21395
   467
fun chop n xs = unfold_rev n dest xs;
wenzelm@19011
   468
wenzelm@233
   469
(*take the first n elements from a list*)
wenzelm@233
   470
fun take (n, []) = []
wenzelm@233
   471
  | take (n, x :: xs) =
wenzelm@233
   472
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   473
wenzelm@233
   474
(*drop the first n elements from a list*)
wenzelm@233
   475
fun drop (n, []) = []
wenzelm@233
   476
  | drop (n, x :: xs) =
wenzelm@233
   477
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   478
nipkow@4713
   479
fun dropwhile P [] = []
nipkow@4713
   480
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   481
wenzelm@233
   482
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   483
  raise Subscript if list too short*)
haftmann@18011
   484
fun nth xs i = List.nth (xs, i);
wenzelm@233
   485
wenzelm@18461
   486
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   487
haftmann@18011
   488
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   489
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   490
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   491
haftmann@18514
   492
fun map_index f =
haftmann@18514
   493
  let
haftmann@18514
   494
    fun mapp _ [] = []
haftmann@18514
   495
      | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
haftmann@18514
   496
  in mapp 0 end;
haftmann@18514
   497
haftmann@21118
   498
fun fold_index f =
haftmann@21118
   499
  let
haftmann@21118
   500
    fun fold_aux _ [] y = y
haftmann@21118
   501
      | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
haftmann@21118
   502
  in fold_aux 0 end;
haftmann@21118
   503
skalberg@15570
   504
val last_elem = List.last;
wenzelm@233
   505
wenzelm@3762
   506
(*rear decomposition*)
skalberg@15570
   507
fun split_last [] = raise Empty
wenzelm@3762
   508
  | split_last [x] = ([], x)
wenzelm@3762
   509
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   510
wenzelm@4212
   511
(*find the position of an element in a list*)
wenzelm@4212
   512
fun find_index pred =
wenzelm@4212
   513
  let fun find _ [] = ~1
wenzelm@4212
   514
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   515
  in find 0 end;
wenzelm@3762
   516
wenzelm@4224
   517
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   518
wenzelm@4212
   519
(*find first element satisfying predicate*)
skalberg@15531
   520
fun find_first _ [] = NONE
wenzelm@4212
   521
  | find_first pred (x :: xs) =
skalberg@15531
   522
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   523
wenzelm@4916
   524
(*get first element by lookup function*)
skalberg@15531
   525
fun get_first _ [] = NONE
wenzelm@4916
   526
  | get_first f (x :: xs) =
wenzelm@4916
   527
      (case f x of
skalberg@15531
   528
        NONE => get_first f xs
wenzelm@4916
   529
      | some => some);
wenzelm@4916
   530
haftmann@19233
   531
fun get_index f =
haftmann@19233
   532
  let
haftmann@19233
   533
    fun get _ [] = NONE
wenzelm@19461
   534
      | get i (x :: xs) =
haftmann@19233
   535
          case f x
wenzelm@19461
   536
           of NONE => get (i + 1) xs
haftmann@19233
   537
            | SOME y => SOME (i, y)
haftmann@19233
   538
  in get 0 end;
haftmann@19233
   539
skalberg@15531
   540
val flat = List.concat;
wenzelm@233
   541
wenzelm@12136
   542
fun unflat (xs :: xss) ys =
wenzelm@19424
   543
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   544
      in ps :: unflat xss qs end
wenzelm@12136
   545
  | unflat [] [] = []
skalberg@15570
   546
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   547
wenzelm@21479
   548
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   549
haftmann@18549
   550
fun fold_burrow f xss s =
haftmann@18549
   551
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   552
wenzelm@233
   553
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   554
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   555
val seq = List.app;
wenzelm@233
   556
wenzelm@233
   557
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   558
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   559
  | separate _ xs = xs;
wenzelm@233
   560
wenzelm@233
   561
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   562
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   563
  let fun rep (0, xs) = xs
wenzelm@233
   564
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   565
  in
skalberg@15570
   566
    if n < 0 then raise Subscript
wenzelm@233
   567
    else rep (n, [])
wenzelm@233
   568
  end;
wenzelm@233
   569
wenzelm@14926
   570
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   571
wenzelm@4248
   572
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   573
fun multiply [] _ = []
wenzelm@18148
   574
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   575
wenzelm@14792
   576
(*direct product*)
wenzelm@14792
   577
fun product _ [] = []
wenzelm@14792
   578
  | product [] _ = []
wenzelm@14792
   579
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   580
wenzelm@233
   581
wenzelm@233
   582
(* filter *)
wenzelm@233
   583
wenzelm@233
   584
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   585
val filter = List.filter;
clasohm@0
   586
fun filter_out f = filter (not o f);
wenzelm@19483
   587
val map_filter = List.mapPartial;
wenzelm@233
   588
wenzelm@233
   589
wenzelm@233
   590
(* lists of pairs *)
wenzelm@233
   591
skalberg@15570
   592
exception UnequalLengths;
skalberg@15570
   593
haftmann@18330
   594
fun map2 _ [] [] = []
haftmann@18330
   595
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   596
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   597
haftmann@18330
   598
fun fold2 f =
haftmann@18330
   599
  let
haftmann@18330
   600
    fun fold_aux [] [] z = z
haftmann@18330
   601
      | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
haftmann@18330
   602
      | fold_aux _ _ _ = raise UnequalLengths;
haftmann@18330
   603
  in fold_aux end;
wenzelm@380
   604
wenzelm@19799
   605
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   606
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   607
  | zip_options _ [] = []
wenzelm@19799
   608
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   609
wenzelm@233
   610
(*combine two lists forming a list of pairs:
wenzelm@233
   611
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   612
fun [] ~~ [] = []
wenzelm@233
   613
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   614
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   615
wenzelm@233
   616
(*inverse of ~~; the old 'split':
wenzelm@233
   617
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   618
val split_list = ListPair.unzip;
wenzelm@233
   619
wenzelm@233
   620
wenzelm@233
   621
(* prefixes, suffixes *)
wenzelm@233
   622
haftmann@18441
   623
fun is_prefix _ [] _ = true
haftmann@18441
   624
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   625
  | is_prefix eq _ _ = false;
wenzelm@233
   626
wenzelm@233
   627
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   628
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   629
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   630
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   631
        | take (rxs, x :: xs) =
wenzelm@255
   632
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   633
  in  take([], xs)  end;
wenzelm@233
   634
haftmann@20108
   635
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   636
  | chop_prefix eq (xs, []) = ([], (xs, []))
haftmann@20108
   637
  | chop_prefix eq (xs as x::xs', ys as y::ys') =
haftmann@20108
   638
      if eq (x, y) then
haftmann@20108
   639
        let val (ps', xys'') = chop_prefix eq (xs', ys')
haftmann@20108
   640
        in (x::ps', xys'') end
haftmann@20108
   641
      else ([], (xs, ys));
haftmann@20108
   642
wenzelm@233
   643
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   644
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   645
fun take_suffix _ [] = ([], [])
wenzelm@233
   646
  | take_suffix pred (x :: xs) =
wenzelm@233
   647
      (case take_suffix pred xs of
wenzelm@233
   648
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   649
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   650
wenzelm@12249
   651
fun prefixes1 [] = []
wenzelm@12249
   652
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   653
wenzelm@19011
   654
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   655
wenzelm@12249
   656
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   657
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   658
wenzelm@233
   659
wenzelm@233
   660
(** integers **)
wenzelm@233
   661
wenzelm@16439
   662
fun gcd (x, y) =
paulson@15965
   663
  let fun gxd x y : IntInf.int =
wenzelm@21859
   664
    if y = IntInf.fromInt 0 then x else gxd y (x mod y)
nipkow@10692
   665
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   666
wenzelm@16439
   667
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   668
wenzelm@2958
   669
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   670
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   671
wenzelm@233
   672
wenzelm@233
   673
(* lists of integers *)
wenzelm@233
   674
wenzelm@233
   675
(*make the list [from, from + 1, ..., to]*)
wenzelm@21859
   676
fun (i upto j) =
wenzelm@21859
   677
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   678
wenzelm@233
   679
(*make the list [from, from - 1, ..., to]*)
wenzelm@21859
   680
fun (i downto j) =
wenzelm@21859
   681
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   682
wenzelm@233
   683
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   684
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   685
  | downto0 ([], n) = n = ~1;
wenzelm@233
   686
wenzelm@233
   687
wenzelm@233
   688
(* convert integers to strings *)
wenzelm@233
   689
wenzelm@233
   690
(*expand the number in the given base;
wenzelm@233
   691
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   692
fun radixpand (base, num) : int list =
wenzelm@233
   693
  let
wenzelm@233
   694
    fun radix (n, tail) =
wenzelm@233
   695
      if n < base then n :: tail
wenzelm@233
   696
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   697
  in radix (num, []) end;
wenzelm@233
   698
wenzelm@233
   699
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   700
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   701
fun radixstring (base, zerochar, num) =
wenzelm@233
   702
  let val offset = ord zerochar;
wenzelm@233
   703
      fun chrof n = chr (offset + n)
wenzelm@233
   704
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   705
wenzelm@233
   706
paulson@3407
   707
val string_of_int = Int.toString;
wenzelm@233
   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
wenzelm@7712
   785
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   786
      | untab (pos, "\t") =
wenzelm@9118
   787
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   788
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   789
  in
wenzelm@19301
   790
    if not (exists (fn c => c = "\t") chs) then chs
wenzelm@7712
   791
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   792
  end;
wenzelm@7712
   793
wenzelm@18681
   794
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   795
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   796
wenzelm@18681
   797
fun unprefix prfx s =
wenzelm@18681
   798
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   799
  else raise Fail "unprefix";
wenzelm@18681
   800
wenzelm@16188
   801
fun unsuffix sffx s =
wenzelm@17061
   802
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   803
  else raise Fail "unsuffix";
wenzelm@5285
   804
wenzelm@10951
   805
fun replicate_string 0 _ = ""
wenzelm@10951
   806
  | replicate_string 1 a = a
wenzelm@10951
   807
  | replicate_string k a =
wenzelm@10951
   808
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   809
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   810
paulson@21899
   811
val nospaces = String.translate (fn c => if Char.isSpace c then "" else str c);
wenzelm@3832
   812
wenzelm@233
   813
wenzelm@16492
   814
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   815
wenzelm@18923
   816
(*canonical member, insert, remove*)
wenzelm@18923
   817
fun member eq list x =
wenzelm@18923
   818
  let
wenzelm@18923
   819
    fun memb [] = false
wenzelm@18923
   820
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   821
  in memb list end;
berghofe@1576
   822
wenzelm@18923
   823
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   824
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   825
wenzelm@19301
   826
fun subtract eq = fold (remove eq);
wenzelm@19301
   827
wenzelm@18923
   828
fun merge _ ([], ys) = ys
wenzelm@18923
   829
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   830
wenzelm@18923
   831
(*old-style infixes*)
wenzelm@18923
   832
fun x mem xs = member (op =) xs x;
wenzelm@18923
   833
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   834
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   835
wenzelm@233
   836
wenzelm@233
   837
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   838
fun xs union [] = xs
wenzelm@233
   839
  | [] union ys = ys
haftmann@20854
   840
  | (x :: xs) union ys = xs union (insert (op =) x ys);
clasohm@0
   841
paulson@2175
   842
(*union of sets, optimized version for ints*)
berghofe@1576
   843
fun (xs:int list) union_int [] = xs
berghofe@1576
   844
  | [] union_int ys = ys
haftmann@20854
   845
  | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
berghofe@1576
   846
paulson@2175
   847
(*union of sets, optimized version for strings*)
berghofe@1576
   848
fun (xs:string list) union_string [] = xs
berghofe@1576
   849
  | [] union_string ys = ys
haftmann@20854
   850
  | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
berghofe@1576
   851
clasohm@0
   852
(*generalized union*)
wenzelm@233
   853
fun gen_union eq (xs, []) = xs
wenzelm@233
   854
  | gen_union eq ([], ys) = ys
wenzelm@18923
   855
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   856
wenzelm@233
   857
wenzelm@233
   858
(*intersection*)
wenzelm@233
   859
fun [] inter ys = []
wenzelm@233
   860
  | (x :: xs) inter ys =
wenzelm@233
   861
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   862
paulson@2175
   863
(*intersection, optimized version for ints*)
berghofe@1576
   864
fun ([]:int list) inter_int ys = []
berghofe@1576
   865
  | (x :: xs) inter_int ys =
berghofe@1576
   866
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   867
paulson@2175
   868
(*intersection, optimized version for strings *)
berghofe@1576
   869
fun ([]:string list) inter_string ys = []
berghofe@1576
   870
  | (x :: xs) inter_string ys =
berghofe@1576
   871
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   872
paulson@7090
   873
(*generalized intersection*)
paulson@7090
   874
fun gen_inter eq ([], ys) = []
wenzelm@12284
   875
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
   876
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
   877
      else gen_inter eq (xs, ys);
paulson@7090
   878
wenzelm@233
   879
wenzelm@233
   880
(*subset*)
wenzelm@233
   881
fun [] subset ys = true
wenzelm@233
   882
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   883
paulson@2175
   884
(*subset, optimized version for ints*)
wenzelm@16439
   885
fun ([]: int list) subset_int ys = true
berghofe@1576
   886
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   887
paulson@2175
   888
(*subset, optimized version for strings*)
wenzelm@16439
   889
fun ([]: string list) subset_string ys = true
berghofe@1576
   890
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   891
wenzelm@4363
   892
(*set equality*)
wenzelm@4363
   893
fun eq_set (xs, ys) =
wenzelm@4363
   894
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   895
paulson@2182
   896
(*set equality for strings*)
wenzelm@16439
   897
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   898
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   899
wenzelm@18923
   900
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
   901
wenzelm@19301
   902
fun gen_eq_set eq (xs, ys) =
haftmann@20348
   903
  eq_list eq (xs, ys) orelse
wenzelm@19301
   904
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
   905
wenzelm@265
   906
wenzelm@233
   907
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   908
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   909
  | [] \ x = [];
paulson@2243
   910
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   911
wenzelm@233
   912
wenzelm@233
   913
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   914
  first of equal elements*)
wenzelm@19046
   915
fun distinct eq lst =
wenzelm@233
   916
  let
wenzelm@233
   917
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   918
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   919
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   920
          else dist (x :: rev_seen, xs);
wenzelm@19046
   921
  in dist ([], lst) end;
wenzelm@233
   922
wenzelm@255
   923
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   924
  order, takes first of equal elements*)
wenzelm@18966
   925
fun duplicates eq lst =
wenzelm@255
   926
  let
wenzelm@255
   927
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   928
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   929
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   930
            dups (rev_dups, xs)
wenzelm@255
   931
          else dups (x :: rev_dups, xs);
wenzelm@18966
   932
  in dups ([], lst) end;
wenzelm@255
   933
wenzelm@16878
   934
fun has_duplicates eq =
wenzelm@16878
   935
  let
wenzelm@16878
   936
    fun dups [] = false
wenzelm@16878
   937
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   938
  in dups end;
wenzelm@16878
   939
wenzelm@255
   940
haftmann@19119
   941
(** association lists -- legacy operations **)
wenzelm@233
   942
wenzelm@12284
   943
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
   944
  | gen_merge_lists _ [] ys = ys
haftmann@20951
   945
  | gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys;
clasohm@0
   946
wenzelm@12284
   947
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
haftmann@20951
   948
fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs;
clasohm@0
   949
clasohm@0
   950
wenzelm@233
   951
(** balanced trees **)
wenzelm@233
   952
wenzelm@233
   953
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   954
wenzelm@233
   955
(*balanced folding; avoids deep nesting*)
wenzelm@233
   956
fun fold_bal f [x] = x
wenzelm@233
   957
  | fold_bal f [] = raise Balance
wenzelm@233
   958
  | fold_bal f xs =
wenzelm@19474
   959
      let val (ps, qs) = chop (length xs div 2) xs
nipkow@13629
   960
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
   961
wenzelm@233
   962
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   963
fun access_bal (f, g, x) n i =
wenzelm@233
   964
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   965
          if n=1 then x else
wenzelm@233
   966
          let val n2 = n div 2
wenzelm@233
   967
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   968
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   969
          end
wenzelm@233
   970
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   971
wenzelm@233
   972
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   973
fun accesses_bal (f, g, x) n =
wenzelm@233
   974
  let fun acc n =
wenzelm@233
   975
          if n=1 then [x] else
wenzelm@233
   976
          let val n2 = n div 2
wenzelm@233
   977
              val acc2 = acc n2
wenzelm@233
   978
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   979
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   980
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   981
wenzelm@233
   982
wenzelm@233
   983
wenzelm@2506
   984
(** orders **)
wenzelm@2506
   985
wenzelm@18966
   986
fun is_equal EQUAL = true
wenzelm@18966
   987
  | is_equal _ = false;
wenzelm@18966
   988
wenzelm@4445
   989
fun rev_order LESS = GREATER
wenzelm@4445
   990
  | rev_order EQUAL = EQUAL
wenzelm@4445
   991
  | rev_order GREATER = LESS;
wenzelm@4445
   992
wenzelm@4479
   993
(*assume rel is a linear strict order*)
wenzelm@4445
   994
fun make_ord rel (x, y) =
wenzelm@4445
   995
  if rel (x, y) then LESS
wenzelm@4445
   996
  else if rel (y, x) then GREATER
wenzelm@4445
   997
  else EQUAL;
wenzelm@4445
   998
wenzelm@15051
   999
val int_ord = Int.compare;
wenzelm@15051
  1000
val string_ord = String.compare;
wenzelm@2506
  1001
wenzelm@16676
  1002
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1003
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1004
wenzelm@16492
  1005
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1006
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1007
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1008
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1009
wenzelm@4343
  1010
(*lexicographic product*)
wenzelm@4343
  1011
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1012
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1013
wenzelm@4343
  1014
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1015
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1016
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1017
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1018
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1019
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1020
wenzelm@4343
  1021
(*lexicographic product of lists*)
wenzelm@4343
  1022
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1023
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1024
wenzelm@2506
  1025
wenzelm@4621
  1026
(* sorting *)
wenzelm@4621
  1027
wenzelm@18427
  1028
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
  1029
fun quicksort unique ord =
wenzelm@4621
  1030
  let
wenzelm@16878
  1031
    fun qsort [] = []
wenzelm@16878
  1032
      | qsort (xs as [_]) = xs
wenzelm@18427
  1033
      | qsort (xs as [x, y]) =
wenzelm@18427
  1034
          (case ord (x, y) of
wenzelm@18427
  1035
            LESS => xs
wenzelm@18427
  1036
          | EQUAL => if unique then [x] else xs
wenzelm@18427
  1037
          | GREATER => [y, x])
wenzelm@16878
  1038
      | qsort xs =
haftmann@18011
  1039
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
  1040
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1041
    and part _ [] = ([], [], [])
wenzelm@4621
  1042
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1043
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
  1044
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
  1045
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
  1046
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1047
  in qsort end;
wenzelm@4621
  1048
wenzelm@18427
  1049
fun sort ord = quicksort false ord;
wenzelm@18427
  1050
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
  1051
wenzelm@4621
  1052
val sort_strings = sort string_ord;
wenzelm@4621
  1053
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1054
wenzelm@4621
  1055
wenzelm@2506
  1056
berghofe@14106
  1057
(** random numbers **)
berghofe@14106
  1058
berghofe@14106
  1059
exception RANDOM;
berghofe@14106
  1060
berghofe@14618
  1061
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1062
berghofe@14106
  1063
local
berghofe@14106
  1064
  val a = 16807.0;
berghofe@14106
  1065
  val m = 2147483647.0;
berghofe@14106
  1066
  val random_seed = ref 1.0;
berghofe@14106
  1067
in
berghofe@14106
  1068
berghofe@14106
  1069
fun random () =
berghofe@14106
  1070
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1071
  in (random_seed := r; r) end;
berghofe@14106
  1072
berghofe@14106
  1073
end;
berghofe@14106
  1074
berghofe@14106
  1075
fun random_range l h =
berghofe@14106
  1076
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1077
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1078
haftmann@18011
  1079
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1080
berghofe@14106
  1081
fun frequency xs =
berghofe@14106
  1082
  let
berghofe@14106
  1083
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1084
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1085
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1086
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1087
berghofe@14106
  1088
wenzelm@14826
  1089
(** current directory **)
wenzelm@233
  1090
paulson@2243
  1091
val cd = OS.FileSys.chDir;
wenzelm@2317
  1092
val pwd = OS.FileSys.getDir;
paulson@2243
  1093
berghofe@3606
  1094
wenzelm@19644
  1095
wenzelm@4621
  1096
(** misc **)
wenzelm@233
  1097
wenzelm@19644
  1098
fun divide_and_conquer decomp x =
wenzelm@19644
  1099
  let val (ys, recomb) = decomp x
wenzelm@19644
  1100
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1101
clasohm@0
  1102
wenzelm@233
  1103
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1104
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1105
fun partition_list p i j =
wenzelm@233
  1106
  let fun part k xs =
wenzelm@233
  1107
            if k>j then
clasohm@0
  1108
              (case xs of [] => []
skalberg@15570
  1109
                         | _ => raise Fail "partition_list")
clasohm@0
  1110
            else
wenzelm@19691
  1111
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1112
            in  ns :: part(k+1)rest  end
clasohm@0
  1113
  in  part i end;
clasohm@0
  1114
wenzelm@19691
  1115
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1116
  let
wenzelm@19691
  1117
    fun part [] = []
wenzelm@19691
  1118
      | part (x :: ys) =
wenzelm@19691
  1119
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1120
          in (x::xs)::(part xs') end
wenzelm@19691
  1121
  in part end;
wenzelm@19691
  1122
wenzelm@19691
  1123
clasohm@0
  1124
wenzelm@233
  1125
(* generating identifiers *)
clasohm@0
  1126
paulson@4063
  1127
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1128
local
paulson@4063
  1129
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1130
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1131
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1132
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1133
             else if i=62 then "_"
wenzelm@5904
  1134
             else  (*i=63*)    "'";
paulson@4063
  1135
paulson@4063
  1136
val charVec = Vector.tabulate (64, char);
paulson@4063
  1137
wenzelm@5904
  1138
fun newid n =
wenzelm@5904
  1139
  let
wenzelm@4284
  1140
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1141
wenzelm@4284
  1142
val seedr = ref 0;
clasohm@0
  1143
paulson@4063
  1144
in
wenzelm@4284
  1145
wenzelm@12346
  1146
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1147
paulson@4063
  1148
end;
paulson@4063
  1149
paulson@4063
  1150
wenzelm@233
  1151
(* lexical scanning *)
clasohm@0
  1152
wenzelm@233
  1153
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1154
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1155
fun scanwords is_let cs =
clasohm@0
  1156
  let fun scan1 [] = []
wenzelm@233
  1157
        | scan1 cs =
wenzelm@233
  1158
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1159
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1160
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1161
wenzelm@4212
  1162
wenzelm@16439
  1163
(* stamps and serial numbers *)
wenzelm@16439
  1164
wenzelm@16439
  1165
type stamp = unit ref;
wenzelm@16439
  1166
val stamp: unit -> stamp = ref;
wenzelm@16439
  1167
wenzelm@16439
  1168
type serial = int;
wenzelm@16439
  1169
local val count = ref 0
wenzelm@16439
  1170
in fun serial () = inc count end;
wenzelm@16439
  1171
wenzelm@19512
  1172
val serial_string = string_of_int o serial;
wenzelm@19512
  1173
wenzelm@16535
  1174
wenzelm@16535
  1175
(* generic objects *)
wenzelm@16535
  1176
wenzelm@16535
  1177
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1178
  constructors at any time*)
wenzelm@16535
  1179
structure Object = struct type T = exn end;
wenzelm@16535
  1180
clasohm@1364
  1181
end;
clasohm@1364
  1182
wenzelm@15745
  1183
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1184
open BasicLibrary;