src/Pure/library.ML
author ballarin
Thu Dec 11 17:55:51 2008 +0100 (2008-12-11)
changeset 29209 c2a750c8a37b
parent 28732 99492b224b7b
child 29882 29154e67731d
permissions -rw-r--r--
Clarified comment.
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(*  Title:      Pure/library.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Markus Wenzel, TU Muenchen
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Basic library: functions, pairs, booleans, lists, integers,
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strings, lists as sets, orders, current directory, misc.
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See also General/basics.ML for the most fundamental concepts.
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*)
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infix 2 ?
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infix 3 o oo ooo oooo
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infix 4 ~~ upto downto
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infix orf andf \ \\ mem mem_int mem_string union union_int
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  union_string inter inter_int inter_string subset subset_int subset_string
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signature BASIC_LIBRARY =
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sig
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  (*functions*)
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  val undefined: 'a -> 'b
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  val I: 'a -> 'a
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  val K: 'a -> 'b -> 'a
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  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
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  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
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  val ? : bool * ('a -> 'a) -> 'a -> 'a
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  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
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  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
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  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
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  val funpow: int -> ('a -> 'a) -> 'a -> 'a
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  (*errors*)
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  exception SYS_ERROR of string
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  val sys_error: string -> 'a
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  exception ERROR of string
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  val error: string -> 'a
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  val cat_error: string -> string -> 'a
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  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
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  (*pairs*)
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  val pair: 'a -> 'b -> 'a * 'b
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  val rpair: 'a -> 'b -> 'b * 'a
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  val fst: 'a * 'b -> 'a
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  val snd: 'a * 'b -> 'b
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  val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val swap: 'a * 'b -> 'b * 'a
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  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
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  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
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  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
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  (*booleans*)
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  val equal: ''a -> ''a -> bool
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  val not_equal: ''a -> ''a -> bool
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  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val exists: ('a -> bool) -> 'a list -> bool
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  val forall: ('a -> bool) -> 'a list -> bool
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  val set: bool ref -> bool
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  val reset: bool ref -> bool
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  val toggle: bool ref -> bool
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  val change: 'a ref -> ('a -> 'a) -> unit
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  val change_result: 'a ref -> ('a -> 'b * 'a) -> 'b
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  val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val setmp_thread_data: 'a Universal.tag -> 'a -> 'a -> ('b -> 'c) -> 'b -> 'c
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  (*lists*)
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  exception UnequalLengths
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  val single: 'a -> 'a list
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  val the_single: 'a list -> 'a
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  val singleton: ('a list -> 'b list) -> 'a -> 'b
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  val yield_singleton: ('a list -> 'c -> 'b list * 'c) -> 'a -> 'c -> 'b * 'c
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  val apply: ('a -> 'a) list -> 'a -> 'a
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  val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option
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  val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option
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  val foldl1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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  val flat: 'a list list -> 'a list
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  val unflat: 'a list list -> 'b list -> 'b list list
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  val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
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  val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list
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  val burrow_fst: ('a list -> 'b list) -> ('a * 'c) list -> ('b * 'c) list
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  val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
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  val maps: ('a -> 'b list) -> 'a list -> 'b list
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  val filter: ('a -> bool) -> 'a list -> 'a list
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  val filter_out: ('a -> bool) -> 'a list -> 'a list
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  val map_filter: ('a -> 'b option) -> 'a list -> 'b list
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  val chop: int -> 'a list -> 'a list * 'a list
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  val dropwhile: ('a -> bool) -> 'a list -> 'a list
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  val nth: 'a list -> int -> 'a
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  val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
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  val nth_drop: int -> 'a list -> 'a list
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  val nth_list: 'a list list -> int -> 'a list
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  val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
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  val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val split_last: 'a list -> 'a list * 'a
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  val find_index: ('a -> bool) -> 'a list -> int
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  val find_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 map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list
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  val split_list: ('a * 'b) list -> 'a list * 'b list
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  val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
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  val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
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  val separate: 'a -> 'a list -> 'a list
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  val surround: 'a -> 'a list -> 'a list
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  val replicate: int -> 'a -> 'a list
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  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
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  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
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  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val prefixes1: 'a list -> 'a list list
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  val prefixes: 'a list -> 'a list list
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  val suffixes1: 'a list -> 'a list list
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  val suffixes: 'a list -> 'a list list
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  (*integers*)
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  val inc: int ref -> int
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  val dec: int ref -> int
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  val upto: int * int -> int list
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  val downto: int * int -> int list
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  val radixpand: int * int -> int list
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  val radixstring: int * string * int -> string
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  val string_of_int: int -> string
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  val signed_string_of_int: int -> string
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  val string_of_indexname: string * int -> string
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  val read_radix_int: int -> string list -> int * string list
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  val read_int: string list -> int * string list
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  val oct_char: string -> string
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  (*strings*)
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  val nth_string: string -> int -> string
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  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
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  val exists_string: (string -> bool) -> string -> bool
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  val forall_string: (string -> bool) -> string -> bool
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  val first_field: string -> string -> (string * string) option
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  val enclose: string -> string -> string -> string
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  val unenclose: string -> string
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  val quote: string -> string
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  val space_implode: string -> string list -> string
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  val commas: string list -> string
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  val commas_quote: string list -> string
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  val cat_lines: string list -> string
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  val space_explode: string -> string -> string list
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  val split_lines: string -> string list
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  val prefix_lines: string -> string -> string
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  val prefix: string -> string -> string
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  val suffix: string -> string -> string
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  val unprefix: string -> string -> string
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  val unsuffix: string -> string -> string
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  val replicate_string: int -> string -> string
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  val translate_string: (string -> string) -> string -> string
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  val multiply: 'a list -> 'a list list -> 'a list list
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  (*lists as sets -- see also Pure/General/ord_list.ML*)
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  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
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  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
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  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
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  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
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  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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  val mem: ''a * ''a list -> bool
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  val mem_int: int * int list -> bool
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  val mem_string: string * string list -> bool
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  val union: ''a list * ''a list -> ''a list
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  val union_int: int list * int list -> int list
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  val union_string: string list * string list -> string list
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  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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  val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
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  val inter: ''a list * ''a list -> ''a list
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  val inter_int: int list * int list -> int list
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  val inter_string: string list * string list -> string list
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  val subset: ''a list * ''a list -> bool
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  val subset_int: int list * int list -> bool
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  val subset_string: string list * string list -> bool
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  val eq_set: ''a list * ''a list -> bool
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  val eq_set_string: string list * string list -> bool
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  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val \ : ''a list * ''a -> ''a list
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  val \\ : ''a list * ''a list -> ''a list
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  val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
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  val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
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  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
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  (*lists as multisets*)
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  val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  (*orders*)
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  val is_equal: order -> bool
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  val rev_order: order -> order
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  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
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  val bool_ord: bool * bool -> order
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  val int_ord: int * int -> order
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  val string_ord: string * string -> order
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  val fast_string_ord: string * string -> order
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  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
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  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
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  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val sort: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_strings: string list -> string list
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  val sort_wrt: ('a -> string) -> 'a list -> 'a list
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  (*random numbers*)
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  exception RANDOM
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  val random: unit -> real
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  val random_range: int -> int -> int
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  val one_of: 'a list -> 'a
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  val frequency: (int * 'a) list -> 'a
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  (*misc*)
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  val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
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  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
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  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
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  val gensym: string -> string
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  type stamp
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  val stamp: unit -> stamp
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  type serial
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  val serial: unit -> serial
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  val serial_string: unit -> string
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  structure Object: sig type T end
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end;
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signature LIBRARY =
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sig
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  include BASIC_LIBRARY
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  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
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  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
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  val take: int * 'a list -> 'a list
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  val drop: int * 'a list -> 'a list
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  val last_elem: 'a list -> 'a
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end;
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structure Library: LIBRARY =
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struct
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(* functions *)
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fun undefined _ = raise Match;
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fun I x = x;
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fun K x = fn _ => x;
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fun curry f x y = f (x, y);
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fun uncurry f (x, y) = f x y;
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(*conditional application*)
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fun b ? f = fn x => if b then f x else x;
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(*composition with multiple args*)
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fun (f oo g) x y = f (g x y);
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fun (f ooo g) x y z = f (g x y z);
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fun (f oooo g) x y z w = f (g x y z w);
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(*function exponentiation: f(...(f x)...) with n applications of f*)
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fun funpow (0: int) _ x = x
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  | funpow n f x = funpow (n - 1) f (f x);
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(* errors *)
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exception SYS_ERROR of string;
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fun sys_error msg = raise SYS_ERROR msg;
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exception ERROR of string;
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fun error msg = raise ERROR msg;
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fun cat_error "" msg = error msg
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  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
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fun assert_all pred list msg =
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  let
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    fun ass [] = ()
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      | ass (x :: xs) = if pred x then ass xs else error (msg x);
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  in ass list end;
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(* pairs *)
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fun pair x y = (x, y);
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fun rpair x y = (y, x);
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fun fst (x, y) = x;
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fun snd (x, y) = y;
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   296
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   297
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   298
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   299
wenzelm@233
   300
fun swap (x, y) = (y, x);
wenzelm@233
   301
wenzelm@233
   302
fun apfst f (x, y) = (f x, y);
wenzelm@233
   303
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   304
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   305
wenzelm@233
   306
wenzelm@21395
   307
(* booleans *)
wenzelm@233
   308
wenzelm@21395
   309
(*polymorphic equality*)
wenzelm@233
   310
fun equal x y = x = y;
wenzelm@233
   311
fun not_equal x y = x <> y;
wenzelm@233
   312
wenzelm@21395
   313
(*combining predicates*)
wenzelm@16721
   314
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   315
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   316
wenzelm@25752
   317
val exists = List.exists;
wenzelm@25752
   318
val forall = List.all;
clasohm@0
   319
wenzelm@19644
   320
wenzelm@380
   321
(* flags *)
wenzelm@380
   322
wenzelm@380
   323
fun set flag = (flag := true; true);
wenzelm@380
   324
fun reset flag = (flag := false; false);
wenzelm@380
   325
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   326
wenzelm@9118
   327
fun change r f = r := f (! r);
wenzelm@28157
   328
fun change_result r f = let val (x, y) = f (! r) in r := y; x end;
wenzelm@9118
   329
wenzelm@18712
   330
(*temporarily set flag during execution*)
wenzelm@23932
   331
fun setmp_noncritical flag value f x =
wenzelm@26079
   332
  uninterruptible (fn restore_attributes => fn () =>
wenzelm@26079
   333
    let
wenzelm@26079
   334
      val orig_value = ! flag;
wenzelm@26079
   335
      val _ = flag := value;
wenzelm@26079
   336
      val result = Exn.capture (restore_attributes f) x;
wenzelm@26079
   337
      val _ = flag := orig_value;
wenzelm@26079
   338
    in Exn.release result end) ();
wenzelm@2958
   339
wenzelm@26079
   340
fun setmp flag value f x =
wenzelm@26079
   341
  NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
wenzelm@23932
   342
wenzelm@25797
   343
fun setmp_thread_data tag orig_data data f x =
wenzelm@26079
   344
  uninterruptible (fn restore_attributes => fn () =>
wenzelm@26079
   345
    let
wenzelm@28122
   346
      val _ = Thread.setLocal (tag, data);
wenzelm@26079
   347
      val result = Exn.capture (restore_attributes f) x;
wenzelm@28122
   348
      val _ = Thread.setLocal (tag, orig_data);
wenzelm@26079
   349
    in Exn.release result end) ();
wenzelm@25797
   350
wenzelm@19644
   351
wenzelm@21395
   352
wenzelm@233
   353
(** lists **)
wenzelm@233
   354
skalberg@15570
   355
exception UnequalLengths;
wenzelm@233
   356
wenzelm@5285
   357
fun single x = [x];
wenzelm@233
   358
wenzelm@20882
   359
fun the_single [x] = x
wenzelm@20882
   360
  | the_single _ = raise Empty;
wenzelm@20882
   361
wenzelm@20882
   362
fun singleton f x = the_single (f [x]);
wenzelm@19273
   363
haftmann@25061
   364
fun yield_singleton f x = f [x] #>> the_single;
haftmann@25061
   365
wenzelm@5904
   366
fun apply [] x = x
wenzelm@5904
   367
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   368
wenzelm@25058
   369
fun perhaps_apply funs arg =
wenzelm@25058
   370
  let
wenzelm@25058
   371
    fun app [] res = res
wenzelm@25058
   372
      | app (f :: fs) (changed, x) =
wenzelm@25058
   373
          (case f x of
wenzelm@25058
   374
            NONE => app fs (changed, x)
wenzelm@25058
   375
          | SOME x' => app fs (true, x'));
wenzelm@25058
   376
  in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   377
wenzelm@25058
   378
fun perhaps_loop f arg =
wenzelm@25058
   379
  let
wenzelm@25058
   380
    fun loop (changed, x) =
wenzelm@25058
   381
      (case f x of
wenzelm@25058
   382
        NONE => (changed, x)
wenzelm@25058
   383
      | SOME x' => loop (true, x'));
wenzelm@25058
   384
  in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   385
wenzelm@233
   386
wenzelm@21395
   387
(* fold -- old versions *)
haftmann@16691
   388
wenzelm@233
   389
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   390
wenzelm@233
   391
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   392
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   393
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   394
  let fun itl (e, [])  = e
wenzelm@233
   395
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   396
  in  itl end;
wenzelm@233
   397
wenzelm@233
   398
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   399
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   400
fun foldr f (l, e) =
wenzelm@233
   401
  let fun itr [] = e
wenzelm@233
   402
        | itr (a::l) = f(a, itr l)
wenzelm@233
   403
  in  itr l  end;
wenzelm@233
   404
berghofe@25681
   405
(*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
berghofe@25681
   406
    for operators that associate to the left (TAIL RECURSIVE)*)
berghofe@25681
   407
fun foldl1 f [] = raise Empty
berghofe@25681
   408
  | foldl1 f (x :: xs) = foldl f (x, xs);
berghofe@25681
   409
wenzelm@233
   410
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   411
    for n > 0, operators that associate to the right (not tail recursive)*)
paulson@20443
   412
fun foldr1 f [] = raise Empty
wenzelm@20510
   413
  | foldr1 f l =
paulson@20443
   414
      let fun itr [x] = x
wenzelm@20510
   415
            | itr (x::l) = f(x, itr l)
paulson@20443
   416
      in  itr l  end;
wenzelm@233
   417
wenzelm@16705
   418
fun foldl_map f =
wenzelm@16705
   419
  let
wenzelm@16705
   420
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   421
      | fold_aux (x, y :: ys) =
wenzelm@16705
   422
          let
wenzelm@16705
   423
            val (x', y') = f (x, y);
wenzelm@16705
   424
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   425
          in (x'', y' :: ys') end;
wenzelm@16705
   426
  in fold_aux end;
wenzelm@16705
   427
wenzelm@233
   428
wenzelm@233
   429
(* basic list functions *)
wenzelm@233
   430
wenzelm@20510
   431
fun eq_list eq (list1, list2) =
haftmann@20348
   432
  let
wenzelm@20510
   433
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   434
      | eq_lst _ = true;
wenzelm@20510
   435
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   436
wenzelm@19483
   437
fun maps f [] = []
wenzelm@19483
   438
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   439
haftmann@25538
   440
val filter = List.filter;
haftmann@25538
   441
fun filter_out f = filter (not o f);
haftmann@25538
   442
val map_filter = List.mapPartial;
haftmann@25538
   443
wenzelm@24593
   444
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   445
  | chop _ [] = ([], [])
wenzelm@23220
   446
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   447
wenzelm@233
   448
(*take the first n elements from a list*)
wenzelm@24593
   449
fun take (n: int, []) = []
wenzelm@233
   450
  | take (n, x :: xs) =
wenzelm@233
   451
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   452
wenzelm@233
   453
(*drop the first n elements from a list*)
wenzelm@24593
   454
fun drop (n: int, []) = []
wenzelm@233
   455
  | drop (n, x :: xs) =
wenzelm@233
   456
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   457
nipkow@4713
   458
fun dropwhile P [] = []
nipkow@4713
   459
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   460
wenzelm@233
   461
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   462
  raise Subscript if list too short*)
haftmann@18011
   463
fun nth xs i = List.nth (xs, i);
wenzelm@233
   464
wenzelm@18461
   465
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   466
haftmann@18011
   467
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   468
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
wenzelm@24593
   469
  | nth_map (_: int) _ [] = raise Subscript;
wenzelm@11773
   470
haftmann@24846
   471
fun nth_drop n xs =
haftmann@24846
   472
  List.take (xs, n) @ List.drop (xs, n + 1);
haftmann@24846
   473
haftmann@18514
   474
fun map_index f =
haftmann@18514
   475
  let
wenzelm@24593
   476
    fun mapp (_: int) [] = []
wenzelm@24593
   477
      | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
haftmann@18514
   478
  in mapp 0 end;
haftmann@18514
   479
haftmann@21118
   480
fun fold_index f =
haftmann@21118
   481
  let
wenzelm@24593
   482
    fun fold_aux (_: int) [] y = y
wenzelm@24593
   483
      | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
haftmann@21118
   484
  in fold_aux 0 end;
haftmann@21118
   485
skalberg@15570
   486
val last_elem = List.last;
wenzelm@233
   487
wenzelm@3762
   488
(*rear decomposition*)
skalberg@15570
   489
fun split_last [] = raise Empty
wenzelm@3762
   490
  | split_last [x] = ([], x)
wenzelm@3762
   491
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   492
ballarin@29209
   493
(*find position of first element satisfying a predicate*)
wenzelm@4212
   494
fun find_index pred =
wenzelm@24593
   495
  let fun find (_: int) [] = ~1
wenzelm@4212
   496
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   497
  in find 0 end;
wenzelm@3762
   498
wenzelm@4224
   499
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   500
wenzelm@4212
   501
(*find first element satisfying predicate*)
paulson@22593
   502
val find_first = List.find;
wenzelm@233
   503
wenzelm@4916
   504
(*get first element by lookup function*)
skalberg@15531
   505
fun get_first _ [] = NONE
wenzelm@4916
   506
  | get_first f (x :: xs) =
wenzelm@4916
   507
      (case f x of
skalberg@15531
   508
        NONE => get_first f xs
wenzelm@4916
   509
      | some => some);
wenzelm@4916
   510
haftmann@19233
   511
fun get_index f =
haftmann@19233
   512
  let
wenzelm@24593
   513
    fun get (_: int) [] = NONE
wenzelm@19461
   514
      | get i (x :: xs) =
haftmann@19233
   515
          case f x
wenzelm@19461
   516
           of NONE => get (i + 1) xs
haftmann@19233
   517
            | SOME y => SOME (i, y)
haftmann@19233
   518
  in get 0 end;
haftmann@19233
   519
skalberg@15531
   520
val flat = List.concat;
wenzelm@233
   521
wenzelm@12136
   522
fun unflat (xs :: xss) ys =
wenzelm@19424
   523
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   524
      in ps :: unflat xss qs end
wenzelm@12136
   525
  | unflat [] [] = []
skalberg@15570
   526
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   527
wenzelm@21479
   528
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   529
wenzelm@24864
   530
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   531
haftmann@18549
   532
fun fold_burrow f xss s =
haftmann@18549
   533
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   534
wenzelm@233
   535
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   536
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   537
  | separate _ xs = xs;
wenzelm@233
   538
wenzelm@25980
   539
fun surround s (x :: xs) = s :: x :: surround s xs
wenzelm@25980
   540
  | surround s [] = [s];
wenzelm@25980
   541
wenzelm@233
   542
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   543
fun replicate (n: int) x =
wenzelm@233
   544
  let fun rep (0, xs) = xs
wenzelm@233
   545
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   546
  in
skalberg@15570
   547
    if n < 0 then raise Subscript
wenzelm@233
   548
    else rep (n, [])
wenzelm@233
   549
  end;
wenzelm@233
   550
wenzelm@14926
   551
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   552
wenzelm@4248
   553
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   554
fun multiply [] _ = []
wenzelm@18148
   555
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   556
wenzelm@25549
   557
wenzelm@25549
   558
(* direct product *)
wenzelm@25549
   559
haftmann@25538
   560
fun map_product f _ [] = []
haftmann@25538
   561
  | map_product f [] _ = []
haftmann@25538
   562
  | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
wenzelm@233
   563
haftmann@25538
   564
fun fold_product f _ [] z = z
haftmann@25538
   565
  | fold_product f [] _ z = z
haftmann@25538
   566
  | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
wenzelm@233
   567
wenzelm@25549
   568
wenzelm@25549
   569
(* lists of pairs *)
wenzelm@233
   570
skalberg@15570
   571
exception UnequalLengths;
skalberg@15570
   572
haftmann@18330
   573
fun map2 _ [] [] = []
haftmann@18330
   574
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   575
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   576
wenzelm@23220
   577
fun fold2 f [] [] z = z
wenzelm@23220
   578
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@23220
   579
  | fold2 f _ _ _ = raise UnequalLengths;
wenzelm@380
   580
haftmann@25943
   581
fun map_split f [] = ([], [])
haftmann@25943
   582
  | map_split f (x :: xs) =
haftmann@25943
   583
      let
haftmann@25943
   584
        val (y, w) = f x;
haftmann@25943
   585
        val (ys, ws) = map_split f xs;
haftmann@25943
   586
      in (y :: ys, w :: ws) end;
haftmann@25943
   587
wenzelm@19799
   588
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   589
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   590
  | zip_options _ [] = []
wenzelm@19799
   591
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   592
wenzelm@233
   593
(*combine two lists forming a list of pairs:
wenzelm@233
   594
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   595
fun [] ~~ [] = []
wenzelm@233
   596
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   597
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   598
wenzelm@233
   599
(*inverse of ~~; the old 'split':
wenzelm@233
   600
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   601
val split_list = ListPair.unzip;
wenzelm@233
   602
haftmann@28347
   603
fun burrow_fst f xs = split_list xs |>> f |> op ~~;
haftmann@28347
   604
wenzelm@233
   605
wenzelm@233
   606
(* prefixes, suffixes *)
wenzelm@233
   607
haftmann@18441
   608
fun is_prefix _ [] _ = true
haftmann@18441
   609
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   610
  | is_prefix eq _ _ = false;
wenzelm@233
   611
wenzelm@233
   612
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   613
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   614
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   615
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   616
        | take (rxs, x :: xs) =
wenzelm@255
   617
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   618
  in  take([], xs)  end;
wenzelm@233
   619
haftmann@20108
   620
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   621
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   622
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   623
      if eq (x, y) then
haftmann@20108
   624
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   625
        in (x :: ps', xys'') end
haftmann@20108
   626
      else ([], (xs, ys));
haftmann@20108
   627
wenzelm@233
   628
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   629
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   630
fun take_suffix _ [] = ([], [])
wenzelm@233
   631
  | take_suffix pred (x :: xs) =
wenzelm@233
   632
      (case take_suffix pred xs of
wenzelm@233
   633
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   634
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   635
wenzelm@12249
   636
fun prefixes1 [] = []
wenzelm@12249
   637
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   638
wenzelm@19011
   639
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   640
wenzelm@12249
   641
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   642
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   643
wenzelm@23220
   644
wenzelm@23220
   645
wenzelm@233
   646
(** integers **)
wenzelm@233
   647
wenzelm@24593
   648
fun inc i = (i := ! i + (1: int); ! i);
wenzelm@24593
   649
fun dec i = (i := ! i - (1: int); ! i);
wenzelm@233
   650
wenzelm@233
   651
wenzelm@233
   652
(* lists of integers *)
wenzelm@233
   653
wenzelm@233
   654
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   655
fun ((i: int) upto j) =
wenzelm@21859
   656
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   657
wenzelm@233
   658
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   659
fun ((i: int) downto j) =
wenzelm@21859
   660
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   661
wenzelm@233
   662
wenzelm@233
   663
(* convert integers to strings *)
wenzelm@233
   664
wenzelm@233
   665
(*expand the number in the given base;
wenzelm@233
   666
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   667
fun radixpand (base, num) : int list =
wenzelm@233
   668
  let
wenzelm@233
   669
    fun radix (n, tail) =
wenzelm@233
   670
      if n < base then n :: tail
wenzelm@233
   671
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   672
  in radix (num, []) end;
wenzelm@233
   673
wenzelm@233
   674
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   675
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   676
fun radixstring (base, zerochar, num) =
wenzelm@233
   677
  let val offset = ord zerochar;
wenzelm@233
   678
      fun chrof n = chr (offset + n)
wenzelm@233
   679
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   680
wenzelm@233
   681
paulson@3407
   682
val string_of_int = Int.toString;
wenzelm@233
   683
wenzelm@21942
   684
fun signed_string_of_int i =
wenzelm@21942
   685
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   686
wenzelm@23220
   687
fun string_of_indexname (a, 0) = a
wenzelm@23220
   688
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   689
wenzelm@233
   690
wenzelm@14826
   691
(* read integers *)
wenzelm@14826
   692
wenzelm@24630
   693
fun read_radix_int radix cs =
wenzelm@20095
   694
  let
wenzelm@20095
   695
    val zero = ord "0";
wenzelm@20095
   696
    val limit = zero + radix;
wenzelm@20095
   697
    fun scan (num, []) = (num, [])
wenzelm@20095
   698
      | scan (num, c :: cs) =
wenzelm@20095
   699
        if zero <= ord c andalso ord c < limit then
wenzelm@24630
   700
          scan (radix * num + (ord c - zero), cs)
wenzelm@20095
   701
        else (num, c :: cs);
wenzelm@24630
   702
  in scan (0, cs) end;
wenzelm@14826
   703
wenzelm@24630
   704
val read_int = read_radix_int 10;
wenzelm@14826
   705
wenzelm@24630
   706
fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
wenzelm@14826
   707
wenzelm@14826
   708
wenzelm@14826
   709
wenzelm@233
   710
(** strings **)
wenzelm@233
   711
wenzelm@16188
   712
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   713
haftmann@18011
   714
fun nth_string str i =
wenzelm@6959
   715
  (case try String.substring (str, i, 1) of
skalberg@15531
   716
    SOME s => s
skalberg@15570
   717
  | NONE => raise Subscript);
wenzelm@6312
   718
wenzelm@16188
   719
fun fold_string f str x0 =
wenzelm@6282
   720
  let
wenzelm@6282
   721
    val n = size str;
wenzelm@16188
   722
    fun iter (x, i) =
wenzelm@16188
   723
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   724
  in iter (x0, 0) end;
wenzelm@6282
   725
wenzelm@14968
   726
fun exists_string pred str =
wenzelm@14968
   727
  let
wenzelm@14968
   728
    val n = size str;
wenzelm@14968
   729
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   730
  in ex 0 end;
wenzelm@6312
   731
wenzelm@16188
   732
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   733
wenzelm@28025
   734
fun first_field sep str =
wenzelm@28022
   735
  let
wenzelm@28025
   736
    val n = size sep;
wenzelm@28022
   737
    val len = size str;
wenzelm@28022
   738
    fun find i =
wenzelm@28022
   739
      if i + n > len then NONE
wenzelm@28025
   740
      else if String.substring (str, i, n) = sep then SOME i
wenzelm@28022
   741
      else find (i + 1);
wenzelm@28025
   742
  in
wenzelm@28025
   743
    (case find 0 of
wenzelm@28025
   744
      NONE => NONE
wenzelm@28025
   745
    | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
wenzelm@28025
   746
  end;
wenzelm@28022
   747
lcp@512
   748
(*enclose in brackets*)
lcp@512
   749
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   750
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   751
wenzelm@233
   752
(*simple quoting (does not escape special chars)*)
lcp@512
   753
val quote = enclose "\"" "\"";
wenzelm@233
   754
wenzelm@4212
   755
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   756
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   757
wenzelm@255
   758
val commas = space_implode ", ";
wenzelm@380
   759
val commas_quote = commas o map quote;
wenzelm@255
   760
wenzelm@233
   761
(*concatenate messages, one per line, into a string*)
wenzelm@255
   762
val cat_lines = space_implode "\n";
wenzelm@233
   763
wenzelm@4212
   764
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   765
fun space_explode _ "" = []
paulson@21899
   766
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   767
wenzelm@3832
   768
val split_lines = space_explode "\n";
wenzelm@3832
   769
wenzelm@14826
   770
fun prefix_lines "" txt = txt
wenzelm@14826
   771
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   772
wenzelm@18681
   773
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   774
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   775
wenzelm@18681
   776
fun unprefix prfx s =
wenzelm@18681
   777
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   778
  else raise Fail "unprefix";
wenzelm@18681
   779
wenzelm@16188
   780
fun unsuffix sffx s =
wenzelm@17061
   781
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   782
  else raise Fail "unsuffix";
wenzelm@5285
   783
wenzelm@24593
   784
fun replicate_string (0: int) _ = ""
wenzelm@10951
   785
  | replicate_string 1 a = a
wenzelm@10951
   786
  | replicate_string k a =
wenzelm@10951
   787
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   788
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   789
wenzelm@233
   790
wenzelm@23220
   791
wenzelm@16492
   792
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   793
wenzelm@26439
   794
(* canonical operations *)
wenzelm@26439
   795
wenzelm@18923
   796
fun member eq list x =
wenzelm@18923
   797
  let
wenzelm@18923
   798
    fun memb [] = false
wenzelm@18923
   799
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   800
  in memb list end;
berghofe@1576
   801
wenzelm@18923
   802
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   803
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   804
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   805
wenzelm@19301
   806
fun subtract eq = fold (remove eq);
wenzelm@19301
   807
wenzelm@18923
   808
fun merge _ ([], ys) = ys
wenzelm@18923
   809
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   810
wenzelm@26439
   811
wenzelm@26439
   812
(* old-style infixes *)
wenzelm@26439
   813
wenzelm@18923
   814
fun x mem xs = member (op =) xs x;
wenzelm@18923
   815
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   816
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   817
wenzelm@233
   818
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   819
fun xs union [] = xs
wenzelm@233
   820
  | [] union ys = ys
haftmann@20854
   821
  | (x :: xs) union ys = xs union (insert (op =) x ys);
clasohm@0
   822
paulson@2175
   823
(*union of sets, optimized version for ints*)
berghofe@1576
   824
fun (xs:int list) union_int [] = xs
berghofe@1576
   825
  | [] union_int ys = ys
haftmann@20854
   826
  | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
berghofe@1576
   827
paulson@2175
   828
(*union of sets, optimized version for strings*)
berghofe@1576
   829
fun (xs:string list) union_string [] = xs
berghofe@1576
   830
  | [] union_string ys = ys
haftmann@20854
   831
  | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
berghofe@1576
   832
clasohm@0
   833
(*generalized union*)
wenzelm@233
   834
fun gen_union eq (xs, []) = xs
wenzelm@233
   835
  | gen_union eq ([], ys) = ys
wenzelm@18923
   836
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   837
wenzelm@233
   838
wenzelm@233
   839
(*intersection*)
wenzelm@233
   840
fun [] inter ys = []
wenzelm@233
   841
  | (x :: xs) inter ys =
wenzelm@233
   842
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   843
paulson@2175
   844
(*intersection, optimized version for ints*)
berghofe@1576
   845
fun ([]:int list) inter_int ys = []
berghofe@1576
   846
  | (x :: xs) inter_int ys =
berghofe@1576
   847
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   848
paulson@2175
   849
(*intersection, optimized version for strings *)
berghofe@1576
   850
fun ([]:string list) inter_string ys = []
berghofe@1576
   851
  | (x :: xs) inter_string ys =
berghofe@1576
   852
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   853
paulson@7090
   854
(*generalized intersection*)
paulson@7090
   855
fun gen_inter eq ([], ys) = []
wenzelm@12284
   856
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
   857
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
   858
      else gen_inter eq (xs, ys);
paulson@7090
   859
wenzelm@233
   860
wenzelm@233
   861
(*subset*)
wenzelm@233
   862
fun [] subset ys = true
wenzelm@233
   863
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   864
paulson@2175
   865
(*subset, optimized version for ints*)
wenzelm@16439
   866
fun ([]: int list) subset_int ys = true
berghofe@1576
   867
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   868
paulson@2175
   869
(*subset, optimized version for strings*)
wenzelm@16439
   870
fun ([]: string list) subset_string ys = true
berghofe@1576
   871
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   872
wenzelm@4363
   873
(*set equality*)
wenzelm@4363
   874
fun eq_set (xs, ys) =
wenzelm@4363
   875
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   876
paulson@2182
   877
(*set equality for strings*)
wenzelm@16439
   878
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   879
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   880
wenzelm@18923
   881
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
   882
wenzelm@19301
   883
fun gen_eq_set eq (xs, ys) =
haftmann@20348
   884
  eq_list eq (xs, ys) orelse
wenzelm@19301
   885
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
   886
wenzelm@265
   887
wenzelm@233
   888
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   889
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   890
  | [] \ x = [];
paulson@2243
   891
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   892
wenzelm@233
   893
wenzelm@233
   894
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   895
  first of equal elements*)
wenzelm@19046
   896
fun distinct eq lst =
wenzelm@233
   897
  let
wenzelm@233
   898
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   899
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   900
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   901
          else dist (x :: rev_seen, xs);
wenzelm@19046
   902
  in dist ([], lst) end;
wenzelm@233
   903
wenzelm@255
   904
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   905
  order, takes first of equal elements*)
wenzelm@18966
   906
fun duplicates eq lst =
wenzelm@255
   907
  let
wenzelm@255
   908
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   909
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   910
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   911
            dups (rev_dups, xs)
wenzelm@255
   912
          else dups (x :: rev_dups, xs);
wenzelm@18966
   913
  in dups ([], lst) end;
wenzelm@255
   914
wenzelm@16878
   915
fun has_duplicates eq =
wenzelm@16878
   916
  let
wenzelm@16878
   917
    fun dups [] = false
wenzelm@16878
   918
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   919
  in dups end;
wenzelm@16878
   920
wenzelm@255
   921
wenzelm@23220
   922
nipkow@22142
   923
(** lists as multisets **)
nipkow@22142
   924
nipkow@22142
   925
fun remove1 _ _ [] = raise Empty
wenzelm@23220
   926
  | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
nipkow@22142
   927
wenzelm@23220
   928
fun submultiset _ ([], _)  = true
wenzelm@23220
   929
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
wenzelm@233
   930
clasohm@0
   931
clasohm@0
   932
wenzelm@2506
   933
(** orders **)
wenzelm@2506
   934
wenzelm@18966
   935
fun is_equal EQUAL = true
wenzelm@18966
   936
  | is_equal _ = false;
wenzelm@18966
   937
wenzelm@4445
   938
fun rev_order LESS = GREATER
wenzelm@4445
   939
  | rev_order EQUAL = EQUAL
wenzelm@4445
   940
  | rev_order GREATER = LESS;
wenzelm@4445
   941
wenzelm@4479
   942
(*assume rel is a linear strict order*)
wenzelm@4445
   943
fun make_ord rel (x, y) =
wenzelm@4445
   944
  if rel (x, y) then LESS
wenzelm@4445
   945
  else if rel (y, x) then GREATER
wenzelm@4445
   946
  else EQUAL;
wenzelm@4445
   947
wenzelm@25224
   948
fun bool_ord (false, true) = LESS
wenzelm@25224
   949
  | bool_ord (true, false) = GREATER
wenzelm@25224
   950
  | bool_ord _ = EQUAL;
wenzelm@25224
   951
wenzelm@15051
   952
val int_ord = Int.compare;
wenzelm@15051
   953
val string_ord = String.compare;
wenzelm@2506
   954
wenzelm@16676
   955
fun fast_string_ord (s1, s2) =
wenzelm@16676
   956
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   957
wenzelm@16492
   958
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   959
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   960
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   961
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   962
wenzelm@4343
   963
(*lexicographic product*)
wenzelm@4343
   964
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   965
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   966
wenzelm@4343
   967
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   968
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   969
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   970
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   971
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   972
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   973
wenzelm@4343
   974
(*lexicographic product of lists*)
wenzelm@4343
   975
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   976
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   977
wenzelm@2506
   978
wenzelm@4621
   979
(* sorting *)
wenzelm@4621
   980
wenzelm@18427
   981
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
   982
fun quicksort unique ord =
wenzelm@4621
   983
  let
wenzelm@16878
   984
    fun qsort [] = []
wenzelm@16878
   985
      | qsort (xs as [_]) = xs
wenzelm@18427
   986
      | qsort (xs as [x, y]) =
wenzelm@18427
   987
          (case ord (x, y) of
wenzelm@18427
   988
            LESS => xs
wenzelm@18427
   989
          | EQUAL => if unique then [x] else xs
wenzelm@18427
   990
          | GREATER => [y, x])
wenzelm@16878
   991
      | qsort xs =
haftmann@18011
   992
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
   993
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
   994
    and part _ [] = ([], [], [])
wenzelm@4621
   995
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
   996
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
   997
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
   998
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
   999
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1000
  in qsort end;
wenzelm@4621
  1001
wenzelm@18427
  1002
fun sort ord = quicksort false ord;
wenzelm@18427
  1003
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
  1004
wenzelm@4621
  1005
val sort_strings = sort string_ord;
wenzelm@4621
  1006
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1007
wenzelm@4621
  1008
wenzelm@2506
  1009
berghofe@14106
  1010
(** random numbers **)
berghofe@14106
  1011
berghofe@14106
  1012
exception RANDOM;
berghofe@14106
  1013
berghofe@14618
  1014
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1015
berghofe@14106
  1016
local
berghofe@14106
  1017
  val a = 16807.0;
berghofe@14106
  1018
  val m = 2147483647.0;
berghofe@14106
  1019
  val random_seed = ref 1.0;
berghofe@14106
  1020
in
berghofe@14106
  1021
wenzelm@23922
  1022
fun random () = CRITICAL (fn () =>
wenzelm@23922
  1023
  let val r = rmod (a * ! random_seed) m
wenzelm@23922
  1024
  in (random_seed := r; r) end);
berghofe@14106
  1025
berghofe@14106
  1026
end;
berghofe@14106
  1027
berghofe@14106
  1028
fun random_range l h =
berghofe@14106
  1029
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1030
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1031
haftmann@18011
  1032
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1033
berghofe@14106
  1034
fun frequency xs =
berghofe@14106
  1035
  let
berghofe@14106
  1036
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1037
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1038
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1039
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1040
berghofe@14106
  1041
wenzelm@23220
  1042
wenzelm@4621
  1043
(** misc **)
wenzelm@233
  1044
wenzelm@19644
  1045
fun divide_and_conquer decomp x =
wenzelm@19644
  1046
  let val (ys, recomb) = decomp x
wenzelm@19644
  1047
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1048
clasohm@0
  1049
wenzelm@233
  1050
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1051
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1052
fun partition_list p i j =
wenzelm@233
  1053
  let fun part k xs =
wenzelm@233
  1054
            if k>j then
clasohm@0
  1055
              (case xs of [] => []
skalberg@15570
  1056
                         | _ => raise Fail "partition_list")
clasohm@0
  1057
            else
wenzelm@19691
  1058
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1059
            in  ns :: part(k+1)rest  end
wenzelm@24593
  1060
  in  part (i: int) end;
clasohm@0
  1061
wenzelm@19691
  1062
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1063
  let
wenzelm@19691
  1064
    fun part [] = []
wenzelm@19691
  1065
      | part (x :: ys) =
wenzelm@19691
  1066
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1067
          in (x::xs)::(part xs') end
wenzelm@19691
  1068
  in part end;
wenzelm@19691
  1069
wenzelm@19691
  1070
clasohm@0
  1071
wenzelm@233
  1072
(* generating identifiers *)
clasohm@0
  1073
paulson@4063
  1074
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
wenzelm@22369
  1075
local
wenzelm@22369
  1076
(*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
wenzelm@22582
  1077
fun gensym_char i =
paulson@22368
  1078
  if i<26 then chr (ord "A" + i)
paulson@22368
  1079
  else if i<52 then chr (ord "a" + i - 26)
wenzelm@22369
  1080
  else chr (ord "0" + i - 52);
paulson@4063
  1081
wenzelm@22369
  1082
val char_vec = Vector.tabulate (62, gensym_char);
wenzelm@22369
  1083
fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
wenzelm@4284
  1084
wenzelm@24593
  1085
val gensym_seed = ref (0: int);
paulson@2003
  1086
wenzelm@22369
  1087
in
wenzelm@24148
  1088
  fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed));
wenzelm@22369
  1089
end;
paulson@4063
  1090
paulson@4063
  1091
wenzelm@16439
  1092
(* stamps and serial numbers *)
wenzelm@16439
  1093
wenzelm@16439
  1094
type stamp = unit ref;
wenzelm@16439
  1095
val stamp: unit -> stamp = ref;
wenzelm@16439
  1096
wenzelm@16439
  1097
type serial = int;
wenzelm@25702
  1098
val serial = Multithreading.serial;
wenzelm@19512
  1099
val serial_string = string_of_int o serial;
wenzelm@19512
  1100
wenzelm@16535
  1101
wenzelm@16535
  1102
(* generic objects *)
wenzelm@16535
  1103
wenzelm@16535
  1104
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1105
  constructors at any time*)
wenzelm@16535
  1106
structure Object = struct type T = exn end;
wenzelm@16535
  1107
clasohm@1364
  1108
end;
clasohm@1364
  1109
wenzelm@15745
  1110
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1111
open BasicLibrary;