src/Pure/library.ML
author haftmann
Thu Oct 22 13:48:06 2009 +0200 (2009-10-22)
changeset 33063 4d462963a7db
parent 33050 fe166e8b9f07
child 33073 2f6ce3b9ec39
child 33078 3aea60ca3900
permissions -rw-r--r--
map_range (and map_index) combinator
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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
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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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  val funpow_yield: int -> ('a -> 'b * 'a) -> 'a -> 'b list * '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 setmp_noncritical: 'a Unsynchronized.ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val setmp_CRITICAL: 'a Unsynchronized.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 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 map_range: (int -> 'a) -> int -> 'a list
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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_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 map_transpose: ('a list -> 'b) -> 'a list list -> 'b list
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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 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 match_string: string -> string -> bool
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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 union: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
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  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
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  val inter: ('a * 'b -> 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 subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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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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  val tag_list: int -> 'a list -> (int * 'a) list
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  val untag_list: (int * 'a) list -> 'a list
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  val order_list: (int * '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 divide_and_conquer': ('a -> 'b -> ('a list * ('c list * 'b -> 'c * 'b)) * 'b) ->
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    'a -> 'b -> 'c * '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 foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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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) _ = I
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  | funpow n f = f #> funpow (n - 1) f;
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fun funpow_yield (0 : int) _ x = ([], x)
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  | funpow_yield n f x = x |> f ||>> funpow_yield (n - 1) f |>> op ::;
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(* errors *)
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exception SYS_ERROR of string;
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fun sys_error msg = raise SYS_ERROR msg;
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exception ERROR of string;
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fun error msg = raise ERROR msg;
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fun cat_error "" msg = error msg
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  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
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fun assert_all pred list msg =
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  let
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    fun ass [] = ()
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      | ass (x :: xs) = if pred x then ass xs else error (msg x);
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  in ass list end;
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(* pairs *)
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fun pair x y = (x, y);
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fun rpair x y = (y, x);
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fun fst (x, y) = x;
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fun snd (x, y) = y;
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fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
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fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
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fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
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fun swap (x, y) = (y, x);
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fun apfst f (x, y) = (f x, y);
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fun apsnd f (x, y) = (x, f y);
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   292
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   293
wenzelm@233
   294
wenzelm@21395
   295
(* booleans *)
wenzelm@233
   296
wenzelm@21395
   297
(*polymorphic equality*)
wenzelm@233
   298
fun equal x y = x = y;
wenzelm@233
   299
fun not_equal x y = x <> y;
wenzelm@233
   300
wenzelm@21395
   301
(*combining predicates*)
wenzelm@16721
   302
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   303
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   304
wenzelm@25752
   305
val exists = List.exists;
wenzelm@25752
   306
val forall = List.all;
clasohm@0
   307
wenzelm@19644
   308
wenzelm@380
   309
(* flags *)
wenzelm@380
   310
wenzelm@18712
   311
(*temporarily set flag during execution*)
wenzelm@23932
   312
fun setmp_noncritical flag value f x =
wenzelm@26079
   313
  uninterruptible (fn restore_attributes => fn () =>
wenzelm@26079
   314
    let
wenzelm@26079
   315
      val orig_value = ! flag;
wenzelm@26079
   316
      val _ = flag := value;
wenzelm@26079
   317
      val result = Exn.capture (restore_attributes f) x;
wenzelm@26079
   318
      val _ = flag := orig_value;
wenzelm@26079
   319
    in Exn.release result end) ();
wenzelm@2958
   320
wenzelm@32966
   321
fun setmp_CRITICAL flag value f x =
wenzelm@26079
   322
  NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
wenzelm@23932
   323
wenzelm@25797
   324
fun setmp_thread_data tag orig_data data f x =
wenzelm@26079
   325
  uninterruptible (fn restore_attributes => fn () =>
wenzelm@26079
   326
    let
wenzelm@28122
   327
      val _ = Thread.setLocal (tag, data);
wenzelm@26079
   328
      val result = Exn.capture (restore_attributes f) x;
wenzelm@28122
   329
      val _ = Thread.setLocal (tag, orig_data);
wenzelm@26079
   330
    in Exn.release result end) ();
wenzelm@25797
   331
wenzelm@19644
   332
wenzelm@21395
   333
wenzelm@233
   334
(** lists **)
wenzelm@233
   335
skalberg@15570
   336
exception UnequalLengths;
wenzelm@233
   337
wenzelm@5285
   338
fun single x = [x];
wenzelm@233
   339
wenzelm@20882
   340
fun the_single [x] = x
wenzelm@20882
   341
  | the_single _ = raise Empty;
wenzelm@20882
   342
wenzelm@20882
   343
fun singleton f x = the_single (f [x]);
wenzelm@19273
   344
haftmann@25061
   345
fun yield_singleton f x = f [x] #>> the_single;
haftmann@25061
   346
wenzelm@5904
   347
fun apply [] x = x
wenzelm@5904
   348
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   349
wenzelm@25058
   350
fun perhaps_apply funs arg =
wenzelm@25058
   351
  let
wenzelm@25058
   352
    fun app [] res = res
wenzelm@25058
   353
      | app (f :: fs) (changed, x) =
wenzelm@25058
   354
          (case f x of
wenzelm@25058
   355
            NONE => app fs (changed, x)
wenzelm@25058
   356
          | SOME x' => app fs (true, x'));
wenzelm@25058
   357
  in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   358
wenzelm@25058
   359
fun perhaps_loop f arg =
wenzelm@25058
   360
  let
wenzelm@25058
   361
    fun loop (changed, x) =
wenzelm@25058
   362
      (case f x of
wenzelm@25058
   363
        NONE => (changed, x)
wenzelm@25058
   364
      | SOME x' => loop (true, x'));
wenzelm@25058
   365
  in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end;
wenzelm@25058
   366
wenzelm@233
   367
wenzelm@21395
   368
(* fold -- old versions *)
haftmann@16691
   369
wenzelm@233
   370
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   371
wenzelm@233
   372
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   373
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   374
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   375
  let fun itl (e, [])  = e
wenzelm@233
   376
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   377
  in  itl end;
wenzelm@233
   378
wenzelm@233
   379
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   380
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   381
fun foldr f (l, e) =
wenzelm@233
   382
  let fun itr [] = e
wenzelm@233
   383
        | itr (a::l) = f(a, itr l)
wenzelm@233
   384
  in  itr l  end;
wenzelm@233
   385
berghofe@25681
   386
(*  (op @) [x1, ..., xn]  ===>  ((x1 @ x2) @ x3) ... @ xn
berghofe@25681
   387
    for operators that associate to the left (TAIL RECURSIVE)*)
berghofe@25681
   388
fun foldl1 f [] = raise Empty
berghofe@25681
   389
  | foldl1 f (x :: xs) = foldl f (x, xs);
berghofe@25681
   390
wenzelm@233
   391
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   392
    for n > 0, operators that associate to the right (not tail recursive)*)
paulson@20443
   393
fun foldr1 f [] = raise Empty
wenzelm@20510
   394
  | foldr1 f l =
paulson@20443
   395
      let fun itr [x] = x
wenzelm@20510
   396
            | itr (x::l) = f(x, itr l)
paulson@20443
   397
      in  itr l  end;
wenzelm@233
   398
wenzelm@16705
   399
fun foldl_map f =
wenzelm@16705
   400
  let
wenzelm@16705
   401
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   402
      | fold_aux (x, y :: ys) =
wenzelm@16705
   403
          let
wenzelm@16705
   404
            val (x', y') = f (x, y);
wenzelm@16705
   405
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   406
          in (x'', y' :: ys') end;
wenzelm@16705
   407
  in fold_aux end;
wenzelm@16705
   408
wenzelm@233
   409
wenzelm@233
   410
(* basic list functions *)
wenzelm@233
   411
wenzelm@20510
   412
fun eq_list eq (list1, list2) =
haftmann@20348
   413
  let
wenzelm@20510
   414
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   415
      | eq_lst _ = true;
wenzelm@20510
   416
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   417
wenzelm@19483
   418
fun maps f [] = []
wenzelm@19483
   419
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   420
haftmann@25538
   421
val filter = List.filter;
haftmann@25538
   422
fun filter_out f = filter (not o f);
haftmann@25538
   423
val map_filter = List.mapPartial;
haftmann@25538
   424
wenzelm@24593
   425
fun chop (0: int) xs = ([], xs)
wenzelm@23220
   426
  | chop _ [] = ([], [])
wenzelm@23220
   427
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   428
wenzelm@233
   429
(*take the first n elements from a list*)
wenzelm@24593
   430
fun take (n: int, []) = []
wenzelm@233
   431
  | take (n, x :: xs) =
wenzelm@233
   432
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   433
wenzelm@233
   434
(*drop the first n elements from a list*)
wenzelm@24593
   435
fun drop (n: int, []) = []
wenzelm@233
   436
  | drop (n, x :: xs) =
wenzelm@233
   437
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   438
nipkow@4713
   439
fun dropwhile P [] = []
nipkow@4713
   440
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   441
wenzelm@233
   442
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   443
  raise Subscript if list too short*)
haftmann@18011
   444
fun nth xs i = List.nth (xs, i);
wenzelm@233
   445
wenzelm@18461
   446
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   447
haftmann@18011
   448
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   449
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
wenzelm@24593
   450
  | nth_map (_: int) _ [] = raise Subscript;
wenzelm@11773
   451
haftmann@24846
   452
fun nth_drop n xs =
haftmann@24846
   453
  List.take (xs, n) @ List.drop (xs, n + 1);
haftmann@24846
   454
haftmann@18514
   455
fun map_index f =
haftmann@18514
   456
  let
wenzelm@24593
   457
    fun mapp (_: int) [] = []
wenzelm@24593
   458
      | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs
haftmann@18514
   459
  in mapp 0 end;
haftmann@18514
   460
haftmann@21118
   461
fun fold_index f =
haftmann@21118
   462
  let
wenzelm@24593
   463
    fun fold_aux (_: int) [] y = y
wenzelm@24593
   464
      | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y);
haftmann@21118
   465
  in fold_aux 0 end;
haftmann@21118
   466
haftmann@33063
   467
fun map_range f i =
haftmann@33063
   468
  let
haftmann@33063
   469
    fun mapp k =
haftmann@33063
   470
      if k < i then f k :: mapp (k + 1) else [];
haftmann@33063
   471
  in mapp 0 end;
haftmann@33063
   472
skalberg@15570
   473
val last_elem = List.last;
wenzelm@233
   474
wenzelm@3762
   475
(*rear decomposition*)
skalberg@15570
   476
fun split_last [] = raise Empty
wenzelm@3762
   477
  | split_last [x] = ([], x)
wenzelm@3762
   478
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   479
ballarin@29209
   480
(*find position of first element satisfying a predicate*)
wenzelm@4212
   481
fun find_index pred =
wenzelm@24593
   482
  let fun find (_: int) [] = ~1
wenzelm@4212
   483
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   484
  in find 0 end;
wenzelm@3762
   485
wenzelm@4212
   486
(*find first element satisfying predicate*)
paulson@22593
   487
val find_first = List.find;
wenzelm@233
   488
wenzelm@4916
   489
(*get first element by lookup function*)
skalberg@15531
   490
fun get_first _ [] = NONE
wenzelm@4916
   491
  | get_first f (x :: xs) =
wenzelm@4916
   492
      (case f x of
skalberg@15531
   493
        NONE => get_first f xs
wenzelm@4916
   494
      | some => some);
wenzelm@4916
   495
haftmann@19233
   496
fun get_index f =
haftmann@19233
   497
  let
wenzelm@24593
   498
    fun get (_: int) [] = NONE
wenzelm@19461
   499
      | get i (x :: xs) =
haftmann@19233
   500
          case f x
wenzelm@19461
   501
           of NONE => get (i + 1) xs
haftmann@19233
   502
            | SOME y => SOME (i, y)
haftmann@19233
   503
  in get 0 end;
haftmann@19233
   504
skalberg@15531
   505
val flat = List.concat;
wenzelm@233
   506
wenzelm@12136
   507
fun unflat (xs :: xss) ys =
wenzelm@19424
   508
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   509
      in ps :: unflat xss qs end
wenzelm@12136
   510
  | unflat [] [] = []
skalberg@15570
   511
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   512
wenzelm@21479
   513
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   514
wenzelm@24864
   515
fun burrow_options f os = map (try hd) (burrow f (map the_list os));
wenzelm@24864
   516
haftmann@18549
   517
fun fold_burrow f xss s =
haftmann@18549
   518
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   519
wenzelm@233
   520
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   521
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   522
  | separate _ xs = xs;
wenzelm@233
   523
wenzelm@25980
   524
fun surround s (x :: xs) = s :: x :: surround s xs
wenzelm@25980
   525
  | surround s [] = [s];
wenzelm@25980
   526
wenzelm@233
   527
(*make the list [x, x, ..., x] of length n*)
wenzelm@24593
   528
fun replicate (n: int) x =
wenzelm@233
   529
  let fun rep (0, xs) = xs
wenzelm@233
   530
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   531
  in
skalberg@15570
   532
    if n < 0 then raise Subscript
wenzelm@233
   533
    else rep (n, [])
wenzelm@233
   534
  end;
wenzelm@233
   535
wenzelm@4248
   536
wenzelm@25549
   537
(* direct product *)
wenzelm@25549
   538
haftmann@25538
   539
fun map_product f _ [] = []
haftmann@25538
   540
  | map_product f [] _ = []
haftmann@25538
   541
  | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys;
wenzelm@233
   542
haftmann@25538
   543
fun fold_product f _ [] z = z
haftmann@25538
   544
  | fold_product f [] _ z = z
haftmann@25538
   545
  | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys;
wenzelm@233
   546
wenzelm@25549
   547
wenzelm@25549
   548
(* lists of pairs *)
wenzelm@233
   549
skalberg@15570
   550
exception UnequalLengths;
skalberg@15570
   551
haftmann@18330
   552
fun map2 _ [] [] = []
haftmann@18330
   553
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   554
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   555
wenzelm@23220
   556
fun fold2 f [] [] z = z
wenzelm@23220
   557
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@23220
   558
  | fold2 f _ _ _ = raise UnequalLengths;
wenzelm@380
   559
haftmann@25943
   560
fun map_split f [] = ([], [])
haftmann@25943
   561
  | map_split f (x :: xs) =
haftmann@25943
   562
      let
haftmann@25943
   563
        val (y, w) = f x;
haftmann@25943
   564
        val (ys, ws) = map_split f xs;
haftmann@25943
   565
      in (y :: ys, w :: ws) end;
haftmann@25943
   566
wenzelm@19799
   567
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   568
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   569
  | zip_options _ [] = []
wenzelm@19799
   570
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   571
wenzelm@233
   572
(*combine two lists forming a list of pairs:
wenzelm@233
   573
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   574
fun [] ~~ [] = []
wenzelm@233
   575
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   576
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   577
wenzelm@233
   578
(*inverse of ~~; the old 'split':
wenzelm@233
   579
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   580
val split_list = ListPair.unzip;
wenzelm@233
   581
haftmann@28347
   582
fun burrow_fst f xs = split_list xs |>> f |> op ~~;
haftmann@28347
   583
wenzelm@233
   584
wenzelm@233
   585
(* prefixes, suffixes *)
wenzelm@233
   586
haftmann@18441
   587
fun is_prefix _ [] _ = true
haftmann@18441
   588
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   589
  | is_prefix eq _ _ = false;
wenzelm@233
   590
wenzelm@233
   591
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   592
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   593
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   594
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   595
        | take (rxs, x :: xs) =
wenzelm@255
   596
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   597
  in  take([], xs)  end;
wenzelm@233
   598
haftmann@20108
   599
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   600
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   601
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   602
      if eq (x, y) then
haftmann@20108
   603
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   604
        in (x :: ps', xys'') end
haftmann@20108
   605
      else ([], (xs, ys));
haftmann@20108
   606
wenzelm@233
   607
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   608
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   609
fun take_suffix _ [] = ([], [])
wenzelm@233
   610
  | take_suffix pred (x :: xs) =
wenzelm@233
   611
      (case take_suffix pred xs of
wenzelm@233
   612
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   613
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   614
wenzelm@12249
   615
fun prefixes1 [] = []
wenzelm@12249
   616
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   617
wenzelm@19011
   618
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   619
wenzelm@12249
   620
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   621
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   622
wenzelm@23220
   623
wenzelm@23220
   624
wenzelm@233
   625
(** integers **)
wenzelm@233
   626
wenzelm@233
   627
(* lists of integers *)
wenzelm@233
   628
wenzelm@233
   629
(*make the list [from, from + 1, ..., to]*)
wenzelm@24593
   630
fun ((i: int) upto j) =
wenzelm@21859
   631
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   632
wenzelm@233
   633
(*make the list [from, from - 1, ..., to]*)
wenzelm@24593
   634
fun ((i: int) downto j) =
wenzelm@21859
   635
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   636
wenzelm@233
   637
wenzelm@233
   638
(* convert integers to strings *)
wenzelm@233
   639
wenzelm@233
   640
(*expand the number in the given base;
wenzelm@233
   641
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   642
fun radixpand (base, num) : int list =
wenzelm@233
   643
  let
wenzelm@233
   644
    fun radix (n, tail) =
wenzelm@233
   645
      if n < base then n :: tail
wenzelm@233
   646
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   647
  in radix (num, []) end;
wenzelm@233
   648
wenzelm@233
   649
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   650
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   651
fun radixstring (base, zerochar, num) =
wenzelm@233
   652
  let val offset = ord zerochar;
wenzelm@233
   653
      fun chrof n = chr (offset + n)
wenzelm@233
   654
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   655
wenzelm@233
   656
paulson@3407
   657
val string_of_int = Int.toString;
wenzelm@233
   658
wenzelm@21942
   659
fun signed_string_of_int i =
wenzelm@21942
   660
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   661
wenzelm@23220
   662
fun string_of_indexname (a, 0) = a
wenzelm@23220
   663
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   664
wenzelm@233
   665
wenzelm@14826
   666
(* read integers *)
wenzelm@14826
   667
wenzelm@24630
   668
fun read_radix_int radix cs =
wenzelm@20095
   669
  let
wenzelm@20095
   670
    val zero = ord "0";
wenzelm@20095
   671
    val limit = zero + radix;
wenzelm@20095
   672
    fun scan (num, []) = (num, [])
wenzelm@20095
   673
      | scan (num, c :: cs) =
wenzelm@20095
   674
        if zero <= ord c andalso ord c < limit then
wenzelm@24630
   675
          scan (radix * num + (ord c - zero), cs)
wenzelm@20095
   676
        else (num, c :: cs);
wenzelm@24630
   677
  in scan (0, cs) end;
wenzelm@14826
   678
wenzelm@24630
   679
val read_int = read_radix_int 10;
wenzelm@14826
   680
wenzelm@24630
   681
fun oct_char s = chr (#1 (read_radix_int 8 (explode s)));
wenzelm@14826
   682
wenzelm@14826
   683
wenzelm@14826
   684
wenzelm@233
   685
(** strings **)
wenzelm@233
   686
wenzelm@16188
   687
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   688
haftmann@18011
   689
fun nth_string str i =
wenzelm@6959
   690
  (case try String.substring (str, i, 1) of
skalberg@15531
   691
    SOME s => s
skalberg@15570
   692
  | NONE => raise Subscript);
wenzelm@6312
   693
wenzelm@16188
   694
fun fold_string f str x0 =
wenzelm@6282
   695
  let
wenzelm@6282
   696
    val n = size str;
wenzelm@16188
   697
    fun iter (x, i) =
wenzelm@16188
   698
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   699
  in iter (x0, 0) end;
wenzelm@6282
   700
wenzelm@14968
   701
fun exists_string pred str =
wenzelm@14968
   702
  let
wenzelm@14968
   703
    val n = size str;
wenzelm@14968
   704
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   705
  in ex 0 end;
wenzelm@6312
   706
wenzelm@16188
   707
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   708
wenzelm@28025
   709
fun first_field sep str =
wenzelm@28022
   710
  let
wenzelm@28025
   711
    val n = size sep;
wenzelm@28022
   712
    val len = size str;
wenzelm@28022
   713
    fun find i =
wenzelm@28022
   714
      if i + n > len then NONE
wenzelm@28025
   715
      else if String.substring (str, i, n) = sep then SOME i
wenzelm@28022
   716
      else find (i + 1);
wenzelm@28025
   717
  in
wenzelm@28025
   718
    (case find 0 of
wenzelm@28025
   719
      NONE => NONE
wenzelm@28025
   720
    | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE)))
wenzelm@28025
   721
  end;
wenzelm@28022
   722
lcp@512
   723
(*enclose in brackets*)
lcp@512
   724
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   725
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   726
wenzelm@233
   727
(*simple quoting (does not escape special chars)*)
lcp@512
   728
val quote = enclose "\"" "\"";
wenzelm@233
   729
wenzelm@4212
   730
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   731
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   732
wenzelm@255
   733
val commas = space_implode ", ";
wenzelm@380
   734
val commas_quote = commas o map quote;
wenzelm@255
   735
wenzelm@233
   736
(*concatenate messages, one per line, into a string*)
wenzelm@255
   737
val cat_lines = space_implode "\n";
wenzelm@233
   738
wenzelm@4212
   739
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   740
fun space_explode _ "" = []
paulson@21899
   741
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   742
wenzelm@3832
   743
val split_lines = space_explode "\n";
wenzelm@3832
   744
wenzelm@14826
   745
fun prefix_lines "" txt = txt
wenzelm@14826
   746
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   747
wenzelm@18681
   748
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   749
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   750
wenzelm@18681
   751
fun unprefix prfx s =
wenzelm@18681
   752
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   753
  else raise Fail "unprefix";
wenzelm@18681
   754
wenzelm@16188
   755
fun unsuffix sffx s =
wenzelm@17061
   756
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   757
  else raise Fail "unsuffix";
wenzelm@5285
   758
wenzelm@24593
   759
fun replicate_string (0: int) _ = ""
wenzelm@10951
   760
  | replicate_string 1 a = a
wenzelm@10951
   761
  | replicate_string k a =
wenzelm@10951
   762
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   763
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   764
haftmann@31250
   765
fun translate_string f = String.translate (f o String.str);
haftmann@31250
   766
kleing@29882
   767
(*crude matching of str against simple glob pat*)
kleing@29882
   768
fun match_string pat str =
kleing@29882
   769
  let
kleing@29882
   770
    fun match [] _ = true
kleing@29882
   771
      | match (p :: ps) s =
kleing@29882
   772
          size p <= size s andalso
kleing@29882
   773
            (case try (unprefix p) s of
kleing@29882
   774
              SOME s' => match ps s'
kleing@29882
   775
            | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
kleing@29882
   776
  in match (space_explode "*" pat) str end;
wenzelm@23220
   777
wenzelm@16492
   778
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   779
wenzelm@26439
   780
(* canonical operations *)
wenzelm@26439
   781
wenzelm@18923
   782
fun member eq list x =
wenzelm@18923
   783
  let
wenzelm@18923
   784
    fun memb [] = false
wenzelm@18923
   785
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   786
  in memb list end;
berghofe@1576
   787
wenzelm@18923
   788
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   789
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@24049
   790
fun update eq x xs = cons x (remove eq x xs);
wenzelm@233
   791
haftmann@33049
   792
fun inter eq xs = filter (member eq xs);
haftmann@33049
   793
haftmann@33042
   794
fun union eq = fold (insert eq);
wenzelm@19301
   795
fun subtract eq = fold (remove eq);
wenzelm@19301
   796
wenzelm@30572
   797
fun merge eq (xs, ys) =
wenzelm@30572
   798
  if pointer_eq (xs, ys) then xs
wenzelm@30572
   799
  else if null xs then ys
wenzelm@30572
   800
  else fold_rev (insert eq) ys xs;
clasohm@0
   801
wenzelm@26439
   802
wenzelm@26439
   803
(* old-style infixes *)
wenzelm@26439
   804
wenzelm@18923
   805
fun x mem xs = member (op =) xs x;
wenzelm@18923
   806
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   807
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   808
wenzelm@233
   809
haftmann@33050
   810
(* subset and set equality *)
haftmann@33050
   811
haftmann@33038
   812
fun subset eq (xs, ys) = forall (member eq ys) xs;
berghofe@1576
   813
haftmann@33038
   814
fun eq_set eq (xs, ys) =
haftmann@20348
   815
  eq_list eq (xs, ys) orelse
haftmann@33038
   816
    (subset eq (xs, ys) andalso subset (eq o swap) (ys, xs));
wenzelm@19301
   817
wenzelm@265
   818
wenzelm@233
   819
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   820
  first of equal elements*)
wenzelm@19046
   821
fun distinct eq lst =
wenzelm@233
   822
  let
wenzelm@233
   823
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   824
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   825
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   826
          else dist (x :: rev_seen, xs);
wenzelm@19046
   827
  in dist ([], lst) end;
wenzelm@233
   828
wenzelm@255
   829
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   830
  order, takes first of equal elements*)
wenzelm@18966
   831
fun duplicates eq lst =
wenzelm@255
   832
  let
wenzelm@255
   833
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   834
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   835
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   836
            dups (rev_dups, xs)
wenzelm@255
   837
          else dups (x :: rev_dups, xs);
wenzelm@18966
   838
  in dups ([], lst) end;
wenzelm@255
   839
wenzelm@16878
   840
fun has_duplicates eq =
wenzelm@16878
   841
  let
wenzelm@16878
   842
    fun dups [] = false
wenzelm@16878
   843
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   844
  in dups end;
wenzelm@16878
   845
wenzelm@255
   846
haftmann@32352
   847
(* matrices *)
haftmann@32352
   848
haftmann@32352
   849
fun map_transpose f xss =
haftmann@32352
   850
  let
haftmann@32352
   851
    val n = case distinct (op =) (map length xss)
haftmann@32352
   852
     of [] => 0
haftmann@32352
   853
      | [n] => n
haftmann@32352
   854
      | _ => raise UnequalLengths;
haftmann@32352
   855
  in map (fn m => f (map (fn xs => nth xs m) xss)) (0 upto n - 1) end;
haftmann@32352
   856
haftmann@32352
   857
wenzelm@23220
   858
nipkow@22142
   859
(** lists as multisets **)
nipkow@22142
   860
nipkow@22142
   861
fun remove1 _ _ [] = raise Empty
wenzelm@23220
   862
  | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
nipkow@22142
   863
wenzelm@23220
   864
fun submultiset _ ([], _)  = true
wenzelm@23220
   865
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
wenzelm@233
   866
clasohm@0
   867
clasohm@0
   868
wenzelm@2506
   869
(** orders **)
wenzelm@2506
   870
wenzelm@18966
   871
fun is_equal EQUAL = true
wenzelm@18966
   872
  | is_equal _ = false;
wenzelm@18966
   873
wenzelm@4445
   874
fun rev_order LESS = GREATER
wenzelm@4445
   875
  | rev_order EQUAL = EQUAL
wenzelm@4445
   876
  | rev_order GREATER = LESS;
wenzelm@4445
   877
wenzelm@4479
   878
(*assume rel is a linear strict order*)
wenzelm@4445
   879
fun make_ord rel (x, y) =
wenzelm@4445
   880
  if rel (x, y) then LESS
wenzelm@4445
   881
  else if rel (y, x) then GREATER
wenzelm@4445
   882
  else EQUAL;
wenzelm@4445
   883
wenzelm@25224
   884
fun bool_ord (false, true) = LESS
wenzelm@25224
   885
  | bool_ord (true, false) = GREATER
wenzelm@25224
   886
  | bool_ord _ = EQUAL;
wenzelm@25224
   887
wenzelm@15051
   888
val int_ord = Int.compare;
wenzelm@15051
   889
val string_ord = String.compare;
wenzelm@2506
   890
wenzelm@16676
   891
fun fast_string_ord (s1, s2) =
wenzelm@16676
   892
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   893
wenzelm@16492
   894
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   895
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   896
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   897
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   898
wenzelm@4343
   899
(*lexicographic product*)
wenzelm@4343
   900
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   901
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   902
wenzelm@4343
   903
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   904
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   905
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   906
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   907
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   908
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   909
wenzelm@4343
   910
(*lexicographic product of lists*)
wenzelm@4343
   911
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   912
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   913
wenzelm@2506
   914
wenzelm@4621
   915
(* sorting *)
wenzelm@4621
   916
wenzelm@18427
   917
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
   918
fun quicksort unique ord =
wenzelm@4621
   919
  let
wenzelm@16878
   920
    fun qsort [] = []
wenzelm@16878
   921
      | qsort (xs as [_]) = xs
wenzelm@18427
   922
      | qsort (xs as [x, y]) =
wenzelm@18427
   923
          (case ord (x, y) of
wenzelm@18427
   924
            LESS => xs
wenzelm@18427
   925
          | EQUAL => if unique then [x] else xs
wenzelm@18427
   926
          | GREATER => [y, x])
wenzelm@16878
   927
      | qsort xs =
haftmann@18011
   928
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
   929
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
   930
    and part _ [] = ([], [], [])
wenzelm@4621
   931
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
   932
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
   933
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
   934
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
   935
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
   936
  in qsort end;
wenzelm@4621
   937
wenzelm@18427
   938
fun sort ord = quicksort false ord;
wenzelm@18427
   939
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
   940
wenzelm@4621
   941
val sort_strings = sort string_ord;
wenzelm@4621
   942
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
   943
wenzelm@4621
   944
wenzelm@30558
   945
(* items tagged by integer index *)
wenzelm@30558
   946
wenzelm@30558
   947
(*insert tags*)
wenzelm@30558
   948
fun tag_list k [] = []
haftmann@30570
   949
  | tag_list k (x :: xs) = (k:int, x) :: tag_list (k + 1) xs;
wenzelm@30558
   950
wenzelm@30558
   951
(*remove tags and suppress duplicates -- list is assumed sorted!*)
wenzelm@30558
   952
fun untag_list [] = []
wenzelm@30558
   953
  | untag_list [(k: int, x)] = [x]
wenzelm@30558
   954
  | untag_list ((k, x) :: (rest as (k', x') :: _)) =
wenzelm@30558
   955
      if k = k' then untag_list rest
wenzelm@30558
   956
      else x :: untag_list rest;
wenzelm@30558
   957
wenzelm@30558
   958
(*return list elements in original order*)
wenzelm@30558
   959
fun order_list list = untag_list (sort (int_ord o pairself fst) list);
wenzelm@30558
   960
wenzelm@30558
   961
wenzelm@2506
   962
berghofe@14106
   963
(** random numbers **)
berghofe@14106
   964
berghofe@14106
   965
exception RANDOM;
berghofe@14106
   966
berghofe@14618
   967
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
   968
berghofe@14106
   969
local
berghofe@14106
   970
  val a = 16807.0;
berghofe@14106
   971
  val m = 2147483647.0;
wenzelm@32737
   972
  val random_seed = Unsynchronized.ref 1.0;
berghofe@14106
   973
in
berghofe@14106
   974
wenzelm@23922
   975
fun random () = CRITICAL (fn () =>
wenzelm@23922
   976
  let val r = rmod (a * ! random_seed) m
wenzelm@23922
   977
  in (random_seed := r; r) end);
berghofe@14106
   978
berghofe@14106
   979
end;
berghofe@14106
   980
berghofe@14106
   981
fun random_range l h =
berghofe@14106
   982
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
   983
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
   984
haftmann@18011
   985
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
   986
berghofe@14106
   987
fun frequency xs =
berghofe@14106
   988
  let
berghofe@14106
   989
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
   990
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
   991
      if n <= k then x else pick (n - k) xs
berghofe@14106
   992
  in pick (random_range 1 sum) xs end;
berghofe@14106
   993
berghofe@14106
   994
wenzelm@23220
   995
wenzelm@4621
   996
(** misc **)
wenzelm@233
   997
wenzelm@19644
   998
fun divide_and_conquer decomp x =
wenzelm@19644
   999
  let val (ys, recomb) = decomp x
wenzelm@19644
  1000
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1001
wenzelm@32978
  1002
fun divide_and_conquer' decomp x s =
wenzelm@32978
  1003
  let val ((ys, recomb), s') = decomp x s
wenzelm@32978
  1004
  in recomb (fold_map (divide_and_conquer' decomp) ys s') end;
wenzelm@32978
  1005
clasohm@0
  1006
wenzelm@233
  1007
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1008
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1009
fun partition_list p i j =
wenzelm@233
  1010
  let fun part k xs =
wenzelm@233
  1011
            if k>j then
clasohm@0
  1012
              (case xs of [] => []
skalberg@15570
  1013
                         | _ => raise Fail "partition_list")
clasohm@0
  1014
            else
wenzelm@19691
  1015
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1016
            in  ns :: part(k+1)rest  end
wenzelm@24593
  1017
  in  part (i: int) end;
clasohm@0
  1018
wenzelm@19691
  1019
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1020
  let
wenzelm@19691
  1021
    fun part [] = []
wenzelm@19691
  1022
      | part (x :: ys) =
wenzelm@19691
  1023
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1024
          in (x::xs)::(part xs') end
wenzelm@19691
  1025
  in part end;
wenzelm@19691
  1026
wenzelm@19691
  1027
clasohm@0
  1028
wenzelm@233
  1029
(* generating identifiers *)
clasohm@0
  1030
paulson@4063
  1031
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
wenzelm@22369
  1032
local
wenzelm@22369
  1033
(*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
wenzelm@22582
  1034
fun gensym_char i =
paulson@22368
  1035
  if i<26 then chr (ord "A" + i)
paulson@22368
  1036
  else if i<52 then chr (ord "a" + i - 26)
wenzelm@22369
  1037
  else chr (ord "0" + i - 52);
paulson@4063
  1038
wenzelm@22369
  1039
val char_vec = Vector.tabulate (62, gensym_char);
wenzelm@22369
  1040
fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
wenzelm@4284
  1041
wenzelm@32737
  1042
val gensym_seed = Unsynchronized.ref (0: int);
paulson@2003
  1043
wenzelm@22369
  1044
in
wenzelm@32737
  1045
  fun gensym pre =
wenzelm@32737
  1046
    pre ^ newid (NAMED_CRITICAL "gensym" (fn () => Unsynchronized.inc gensym_seed));
wenzelm@22369
  1047
end;
paulson@4063
  1048
paulson@4063
  1049
wenzelm@16439
  1050
(* stamps and serial numbers *)
wenzelm@16439
  1051
wenzelm@32737
  1052
type stamp = unit Unsynchronized.ref;
wenzelm@32737
  1053
val stamp: unit -> stamp = Unsynchronized.ref;
wenzelm@16439
  1054
wenzelm@16439
  1055
type serial = int;
wenzelm@25702
  1056
val serial = Multithreading.serial;
wenzelm@19512
  1057
val serial_string = string_of_int o serial;
wenzelm@19512
  1058
wenzelm@16535
  1059
wenzelm@16535
  1060
(* generic objects *)
wenzelm@16535
  1061
wenzelm@16535
  1062
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1063
  constructors at any time*)
wenzelm@16535
  1064
structure Object = struct type T = exn end;
wenzelm@16535
  1065
clasohm@1364
  1066
end;
clasohm@1364
  1067
wenzelm@32188
  1068
structure Basic_Library: BASIC_LIBRARY = Library;
wenzelm@32188
  1069
open Basic_Library;