src/Pure/library.ML
author webertj
Sat Jul 15 18:17:47 2006 +0200 (2006-07-15)
changeset 20133 9ee091573fa0
parent 20108 289050bdfff5
child 20137 6c04453ac1bd
permissions -rw-r--r--
function butlast added
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(*  Title:      Pure/library.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Markus Wenzel, TU Muenchen
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Basic library: functions, options, pairs, booleans, lists, integers,
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strings, lists as sets, balanced trees, orders, current directory, misc.
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*)
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infix 1 |> |-> ||> ||>> |>> |>>> #> #->;
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infix 2 ?;
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infix 3 o oo ooo oooo;
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infix 4 ~~ upto downto;
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infix orf andf \ \\ ins ins_string ins_int mem mem_int mem_string union union_int
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  union_string inter inter_int inter_string subset subset_int subset_string;
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signature BASIC_LIBRARY =
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sig
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  (*functions*)
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  val I: 'a -> 'a
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  val K: 'a -> 'b -> 'a
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  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
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  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
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  val |> : 'a * ('a -> 'b) -> 'b
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  val |-> : ('c * 'a) * ('c -> 'a -> 'b) -> 'b
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  val ||> : ('c * 'a) * ('a -> 'b) -> 'c * 'b
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  val ||>> : ('c * 'a) * ('a -> 'd * 'b) -> ('c * 'd) * 'b
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  val |>> : ('a * 'c) * ('a -> 'b) -> 'b * 'c
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  val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
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  val #> : ('a -> 'b) * ('b -> 'c) -> 'a -> 'c
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  val #-> : ('a -> 'c * 'b) * ('c -> 'b -> 'd) -> 'a -> 'd
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  val ? : ('a -> bool) * ('a -> 'a) -> 'a -> 'a
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  val ` : ('b -> 'a) -> 'b -> 'a * 'b
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  val tap: ('b -> 'a) -> 'b -> 'b
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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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  (*options*)
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  val the: 'a option -> 'a
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  val these: 'a list option -> 'a list
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  val the_default: 'a -> 'a option -> 'a
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  val the_list: 'a option -> 'a list
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  val is_some: 'a option -> bool
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  val is_none: 'a option -> bool
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  val perhaps: ('a -> 'a option) -> 'a -> 'a
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  val merge_opt: ('a * 'a -> bool) -> 'a option * 'a option -> 'a option
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  (*exceptions*)
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  val try: ('a -> 'b) -> 'a -> 'b option
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  val can: ('a -> 'b) -> 'a -> bool
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  exception EXCEPTION of exn * string
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  val do_transform_failure: bool ref
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  val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
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  datatype 'a result = Result of 'a | Exn of exn
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  val capture: ('a -> 'b) -> 'a -> 'b result
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  val release: 'a result -> 'a
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  val get_result: 'a result -> 'a option
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  val get_exn: 'a result -> exn option
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  (*errors*)
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  exception SYS_ERROR of string
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  val sys_error: string -> 'a
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  exception ERROR of string
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  val error: string -> 'a
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  val cat_error: string -> string -> 'a
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  val assert: bool -> string -> unit
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  val deny: bool -> string -> unit
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  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
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  (*pairs*)
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  val pair: 'a -> 'b -> 'a * 'b
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  val rpair: 'a -> 'b -> 'b * 'a
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  val fst: 'a * 'b -> 'a
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  val snd: 'a * 'b -> 'b
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  val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val swap: 'a * 'b -> 'b * 'a
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  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
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  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
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  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
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  val string_of_pair: ('a -> string) -> ('b -> string) -> 'a * 'b -> string
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  (*booleans*)
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  val equal: ''a -> ''a -> bool
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  val not_equal: ''a -> ''a -> bool
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  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val exists: ('a -> bool) -> 'a list -> bool
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  val forall: ('a -> bool) -> 'a list -> bool
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  val set: bool ref -> bool
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  val reset: bool ref -> bool
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  val toggle: bool ref -> bool
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  val change: 'a ref -> ('a -> 'a) -> unit
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  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val conditional: bool -> (unit -> unit) -> unit
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  (*lists*)
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  exception UnequalLengths
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  val cons: 'a -> 'a list -> 'a list
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  val single: 'a -> 'a list
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  val singleton: ('a list -> 'b list) -> 'a -> 'b
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  val butlast: 'a list -> 'a list
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  val append: 'a list -> 'a list -> 'a list
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  val apply: ('a -> 'a) list -> 'a -> 'a
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  val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val fold_map: ('a -> 'b -> 'c * 'b) -> 'a list -> 'b -> 'c list * 'b
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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 maps: ('a -> 'b list) -> 'a list -> 'b list
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  val unflat: 'a list list -> 'b list -> 'b list list
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  val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
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  val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
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  val 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_update: int * 'a -> 'a list -> 'a list
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  val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
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  val nth_list: 'a list list -> int -> 'a list
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  val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
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  val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val split_last: 'a list -> 'a list * 'a
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  val find_index: ('a -> bool) -> 'a list -> int
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  val find_index_eq: ''a -> ''a list -> int
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  val find_first: ('a -> bool) -> 'a list -> 'a option
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  val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
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  val get_first: ('a -> 'b option) -> 'a list -> 'b option
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  val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
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  val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
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  val zip_options: 'a list -> 'b option list -> ('a * 'b) list
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  val ~~ : 'a list * 'b list -> ('a * 'b) list
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  val split_list: ('a * 'b) list -> 'a list * 'b list
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  val separate: 'a -> 'a list -> 'a list
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  val replicate: int -> 'a -> 'a list
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  val multiply: 'a list -> 'a list list -> 'a list list
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  val product: 'a list -> 'b list -> ('a * 'b) list
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  val filter: ('a -> bool) -> 'a list -> 'a list
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  val filter_out: ('a -> bool) -> 'a list -> 'a list
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  val map_filter: ('a -> 'b option) -> 'a list -> 'b list
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  val equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
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  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list)
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  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val prefixes1: 'a list -> 'a list list
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  val prefixes: 'a list -> 'a list list
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  val suffixes1: 'a list -> 'a list list
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  val suffixes: 'a list -> 'a list list
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  (*integers*)
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  val gcd: IntInf.int * IntInf.int -> IntInf.int
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  val lcm: IntInf.int * IntInf.int -> IntInf.int
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  val inc: int ref -> int
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  val dec: int ref -> int
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  val upto: int * int -> int list
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  val downto: int * int -> int list
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  val downto0: int list * int -> bool
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  val radixpand: int * int -> int list
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  val radixstring: int * string * int -> string
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  val string_of_int: int -> string
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  val string_of_indexname: string * int -> string
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  val read_intinf: int -> string list -> IntInf.int * string list
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  val read_int: string list -> int * string list
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  val oct_char: string -> string
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  (*strings*)
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  val nth_string: string -> int -> string
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  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
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  val exists_string: (string -> bool) -> string -> bool
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  val forall_string: (string -> bool) -> string -> bool
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  val enclose: string -> string -> string -> string
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  val unenclose: string -> string
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  val quote: string -> string
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  val space_implode: string -> string list -> string
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  val commas: string list -> string
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  val commas_quote: string list -> string
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  val cat_lines: string list -> string
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  val space_explode: string -> string -> string list
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  val split_lines: string -> string list
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  val prefix_lines: string -> string -> string
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  val untabify: string list -> string list
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  val prefix: string -> string -> string
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  val suffix: string -> string -> string
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  val unprefix: string -> string -> string
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  val unsuffix: string -> string -> string
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  val replicate_string: int -> string -> string
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  val translate_string: (string -> string) -> string -> string
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  val string_of_list: ('a -> string) -> 'a list -> string
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  val string_of_option: ('a -> string) -> 'a option -> string
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  (*lists as sets -- see also Pure/General/ord_list.ML*)
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  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
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  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
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  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
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  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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  val mem: ''a * ''a list -> bool
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  val mem_int: int * int list -> bool
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  val mem_string: string * string list -> bool
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  val ins: ''a * ''a list -> ''a list
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  val ins_int: int * int list -> int list
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  val ins_string: string * string list -> string list
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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 gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list
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  val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
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  val findrep: ''a list -> ''a list
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  val distinct: ('a * 'a -> bool) -> 'a list -> 'a list
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  val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
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  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
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  (*lists as tables -- see also Pure/General/alist.ML*)
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  val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list
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  val merge_lists: ''a list -> ''a list -> ''a list
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  val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
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  (*balanced trees*)
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  exception Balance
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  val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
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  val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
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  val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
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  (*orders*)
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  val is_equal: order -> bool
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  val rev_order: order -> order
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  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
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  val int_ord: int * int -> order
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  val string_ord: string * string -> order
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  val fast_string_ord: string * string -> order
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  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
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  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
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  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val sort: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_strings: string list -> string list
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  val sort_wrt: ('a -> string) -> 'a list -> 'a list
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  (*random numbers*)
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  exception RANDOM
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  val random: unit -> real
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  val random_range: int -> int -> int
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  val one_of: 'a list -> 'a
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  val frequency: (int * 'a) list -> 'a
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  (*current directory*)
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  val cd: string -> unit
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  val pwd: unit -> string
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  (*misc*)
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  val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
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  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
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  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
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  val gensym: string -> string
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  val scanwords: (string -> bool) -> string list -> string list
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  type stamp
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  val stamp: unit -> stamp
wenzelm@16439
   279
  type serial
wenzelm@16439
   280
  val serial: unit -> serial
wenzelm@19512
   281
  val serial_string: unit -> string
wenzelm@16535
   282
  structure Object: sig type T end
wenzelm@4621
   283
end;
wenzelm@4621
   284
wenzelm@15745
   285
signature LIBRARY =
skalberg@15570
   286
sig
wenzelm@15745
   287
  include BASIC_LIBRARY
skalberg@15570
   288
  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
skalberg@15570
   289
  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
skalberg@15570
   290
  val take: int * 'a list -> 'a list
skalberg@15570
   291
  val drop: int * 'a list -> 'a list
skalberg@15570
   292
  val last_elem: 'a list -> 'a
skalberg@15570
   293
  val seq: ('a -> unit) -> 'a list -> unit
skalberg@15570
   294
end;
skalberg@15570
   295
wenzelm@15745
   296
structure Library: LIBRARY =
clasohm@1364
   297
struct
clasohm@0
   298
wenzelm@4995
   299
wenzelm@233
   300
(** functions **)
clasohm@0
   301
wenzelm@16842
   302
fun I x = x;
wenzelm@16842
   303
fun K x = fn _ => x;
wenzelm@233
   304
fun curry f x y = f (x, y);
wenzelm@233
   305
fun uncurry f (x, y) = f x y;
clasohm@0
   306
wenzelm@16705
   307
(*reverse application and structured results*)
wenzelm@16705
   308
fun x |> f = f x;
wenzelm@16705
   309
fun (x, y) |-> f = f x y;
wenzelm@16705
   310
fun (x, y) |>> f = (f x, y);
wenzelm@16705
   311
fun (x, y) ||> f = (x, f y);
wenzelm@16705
   312
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16705
   313
fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
wenzelm@16842
   314
wenzelm@16842
   315
(*reverse composition*)
haftmann@16780
   316
fun f #> g = g o f;
wenzelm@16842
   317
fun f #-> g = uncurry g o f;
wenzelm@16842
   318
haftmann@17141
   319
(*conditional application*)
wenzelm@17545
   320
fun b ? f = fn x => if b x then f x else x;
haftmann@17141
   321
wenzelm@16842
   322
(*view results*)
wenzelm@16842
   323
fun `f = fn x => (f x, x);
wenzelm@17545
   324
fun tap f = fn x => (f x; x);
wenzelm@380
   325
wenzelm@16721
   326
(*composition with multiple args*)
wenzelm@16721
   327
fun (f oo g) x y = f (g x y);
wenzelm@16721
   328
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   329
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   330
wenzelm@233
   331
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   332
fun funpow n f x =
wenzelm@233
   333
  let fun rep (0, x) = x
wenzelm@233
   334
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   335
  in rep (n, x) end;
wenzelm@160
   336
wenzelm@160
   337
wenzelm@233
   338
(** options **)
clasohm@0
   339
wenzelm@15970
   340
val the = Option.valOf;
wenzelm@17341
   341
haftmann@17153
   342
fun these (SOME x) = x
haftmann@17313
   343
  | these _ = [];
wenzelm@17341
   344
haftmann@17313
   345
fun the_default x (SOME y) = y
haftmann@17313
   346
  | the_default x _ = x;
wenzelm@17341
   347
haftmann@17313
   348
fun the_list (SOME x) = [x]
haftmann@17313
   349
  | the_list _ = []
wenzelm@15970
   350
wenzelm@15970
   351
fun is_some (SOME _) = true
wenzelm@15970
   352
  | is_some NONE = false;
wenzelm@15970
   353
wenzelm@15970
   354
fun is_none (SOME _) = false
wenzelm@15970
   355
  | is_none NONE = true;
wenzelm@15970
   356
wenzelm@18376
   357
fun perhaps f x = the_default x (f x);
wenzelm@18376
   358
haftmann@19454
   359
fun merge_opt _ (NONE, y) = y
haftmann@19454
   360
  | merge_opt _ (x, NONE) = x
haftmann@19454
   361
  | merge_opt eq (SOME x, SOME y) = if eq (x, y) then SOME y else raise Option;
wenzelm@6959
   362
wenzelm@19474
   363
wenzelm@17341
   364
(* exceptions *)
wenzelm@17341
   365
wenzelm@18681
   366
val do_transform_failure = ref true;
wenzelm@18681
   367
wenzelm@18681
   368
fun transform_failure exn f x =
wenzelm@18681
   369
  if ! do_transform_failure then
wenzelm@18681
   370
    f x handle Interrupt => raise Interrupt | e => raise exn e
wenzelm@18681
   371
  else f x;
wenzelm@18681
   372
wenzelm@17341
   373
exception EXCEPTION of exn * string;
wenzelm@6959
   374
wenzelm@6959
   375
skalberg@15531
   376
fun try f x = SOME (f x)
wenzelm@18681
   377
  handle Interrupt => raise Interrupt | _ => NONE;
wenzelm@6959
   378
wenzelm@6959
   379
fun can f x = is_some (try f x);
wenzelm@4139
   380
wenzelm@4139
   381
wenzelm@14868
   382
datatype 'a result =
wenzelm@14868
   383
  Result of 'a |
wenzelm@14868
   384
  Exn of exn;
wenzelm@14868
   385
wenzelm@14868
   386
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   387
wenzelm@14868
   388
fun release (Result y) = y
wenzelm@14868
   389
  | release (Exn e) = raise e;
wenzelm@14868
   390
skalberg@15531
   391
fun get_result (Result x) = SOME x
skalberg@15531
   392
  | get_result _ = NONE;
wenzelm@14868
   393
skalberg@15531
   394
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   395
  | get_exn _ = NONE;
wenzelm@14868
   396
wenzelm@14868
   397
wenzelm@18681
   398
(* errors *)
wenzelm@18681
   399
wenzelm@19542
   400
exception SYS_ERROR of string;
wenzelm@19542
   401
fun sys_error msg = raise SYS_ERROR msg;
wenzelm@19542
   402
wenzelm@18681
   403
exception ERROR of string;
wenzelm@18681
   404
fun error msg = raise ERROR msg;
wenzelm@18681
   405
wenzelm@18681
   406
fun cat_error "" msg = error msg
wenzelm@18681
   407
  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
wenzelm@18681
   408
wenzelm@18681
   409
fun assert p msg = if p then () else error msg;
wenzelm@18681
   410
fun deny p msg = if p then error msg else ();
wenzelm@18681
   411
wenzelm@18681
   412
fun assert_all pred list msg =
wenzelm@18681
   413
  let
wenzelm@18681
   414
    fun ass [] = ()
wenzelm@18681
   415
      | ass (x :: xs) = if pred x then ass xs else error (msg x);
wenzelm@18681
   416
  in ass list end;
wenzelm@18681
   417
wenzelm@18681
   418
wenzelm@233
   419
(** pairs **)
wenzelm@233
   420
wenzelm@233
   421
fun pair x y = (x, y);
wenzelm@233
   422
fun rpair x y = (y, x);
wenzelm@233
   423
wenzelm@233
   424
fun fst (x, y) = x;
wenzelm@233
   425
fun snd (x, y) = y;
wenzelm@233
   426
haftmann@17498
   427
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   428
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   429
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   430
wenzelm@233
   431
fun swap (x, y) = (y, x);
wenzelm@233
   432
wenzelm@4212
   433
(*apply function to components*)
wenzelm@233
   434
fun apfst f (x, y) = (f x, y);
wenzelm@233
   435
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   436
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   437
webertj@19567
   438
fun string_of_pair f1 f2 (x, y) = "(" ^ f1 x ^ ", " ^ f2 y ^ ")";
wenzelm@233
   439
wenzelm@233
   440
wenzelm@233
   441
(** booleans **)
wenzelm@233
   442
wenzelm@233
   443
(* equality *)
wenzelm@233
   444
wenzelm@233
   445
fun equal x y = x = y;
wenzelm@233
   446
fun not_equal x y = x <> y;
wenzelm@233
   447
wenzelm@233
   448
(* operators for combining predicates *)
wenzelm@233
   449
wenzelm@16721
   450
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   451
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   452
wenzelm@233
   453
(* predicates on lists *)
wenzelm@233
   454
wenzelm@233
   455
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   456
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   457
  let fun boolf [] = false
wenzelm@233
   458
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   459
  in boolf end;
wenzelm@233
   460
wenzelm@233
   461
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   462
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   463
  let fun boolf [] = true
wenzelm@233
   464
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   465
  in boolf end;
clasohm@0
   466
wenzelm@19644
   467
wenzelm@380
   468
(* flags *)
wenzelm@380
   469
wenzelm@380
   470
fun set flag = (flag := true; true);
wenzelm@380
   471
fun reset flag = (flag := false; false);
wenzelm@380
   472
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   473
wenzelm@9118
   474
fun change r f = r := f (! r);
wenzelm@9118
   475
wenzelm@18712
   476
(*temporarily set flag during execution*)
wenzelm@2978
   477
fun setmp flag value f x =
wenzelm@2958
   478
  let
wenzelm@2958
   479
    val orig_value = ! flag;
wenzelm@18712
   480
    val _ = flag := value;
wenzelm@18712
   481
    val result = capture f x;
wenzelm@18712
   482
    val _ = flag := orig_value;
wenzelm@18712
   483
  in release result end;
wenzelm@2958
   484
wenzelm@19644
   485
wenzelm@11853
   486
(* conditional execution *)
wenzelm@11853
   487
wenzelm@11853
   488
fun conditional b f = if b then f () else ();
wenzelm@11853
   489
wenzelm@233
   490
wenzelm@233
   491
(** lists **)
wenzelm@233
   492
skalberg@15570
   493
exception UnequalLengths;
wenzelm@233
   494
wenzelm@233
   495
fun cons x xs = x :: xs;
wenzelm@5285
   496
fun single x = [x];
wenzelm@233
   497
wenzelm@19273
   498
fun singleton f x = (case f [x] of [y] => y | _ => raise Empty);
wenzelm@19273
   499
webertj@20133
   500
fun butlast []        = raise Empty
webertj@20133
   501
  | butlast (x :: []) = []
webertj@20133
   502
  | butlast (x :: xs) = x :: butlast xs;
webertj@20133
   503
wenzelm@4629
   504
fun append xs ys = xs @ ys;
wenzelm@4629
   505
wenzelm@5904
   506
fun apply [] x = x
wenzelm@5904
   507
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   508
wenzelm@233
   509
wenzelm@233
   510
(* fold *)
wenzelm@233
   511
wenzelm@16654
   512
fun fold f =
wenzelm@16654
   513
  let
wenzelm@16654
   514
    fun fold_aux [] y = y
wenzelm@16654
   515
      | fold_aux (x :: xs) y = fold_aux xs (f x y);
wenzelm@16654
   516
  in fold_aux end;
wenzelm@15760
   517
wenzelm@16654
   518
fun fold_rev f =
wenzelm@16654
   519
  let
wenzelm@16654
   520
    fun fold_aux [] y = y
wenzelm@16654
   521
      | fold_aux (x :: xs) y = f x (fold_aux xs y);
wenzelm@16654
   522
  in fold_aux end;
wenzelm@16654
   523
haftmann@16869
   524
fun fold_map f =
haftmann@16691
   525
  let
haftmann@16691
   526
    fun fold_aux [] y = ([], y)
haftmann@16691
   527
      | fold_aux (x :: xs) y =
haftmann@16691
   528
          let
wenzelm@16705
   529
            val (x', y') = f x y;
wenzelm@16705
   530
            val (xs', y'') = fold_aux xs y';
haftmann@16691
   531
          in (x' :: xs', y'') end;
haftmann@16691
   532
  in fold_aux end;
haftmann@16691
   533
wenzelm@233
   534
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   535
wenzelm@233
   536
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   537
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   538
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   539
  let fun itl (e, [])  = e
wenzelm@233
   540
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   541
  in  itl end;
wenzelm@233
   542
wenzelm@233
   543
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   544
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   545
fun foldr f (l, e) =
wenzelm@233
   546
  let fun itr [] = e
wenzelm@233
   547
        | itr (a::l) = f(a, itr l)
wenzelm@233
   548
  in  itr l  end;
wenzelm@233
   549
wenzelm@233
   550
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   551
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   552
fun foldr1 f l =
wenzelm@4181
   553
  let fun itr [x] = x
wenzelm@233
   554
        | itr (x::l) = f(x, itr l)
wenzelm@233
   555
  in  itr l  end;
wenzelm@233
   556
haftmann@18050
   557
fun fold_index f =
haftmann@18050
   558
  let
haftmann@18514
   559
    fun fold_aux _ [] y = y
haftmann@18050
   560
      | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
haftmann@18050
   561
  in fold_aux 0 end;
wenzelm@14792
   562
wenzelm@16705
   563
fun foldl_map f =
wenzelm@16705
   564
  let
wenzelm@16705
   565
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   566
      | fold_aux (x, y :: ys) =
wenzelm@16705
   567
          let
wenzelm@16705
   568
            val (x', y') = f (x, y);
wenzelm@16705
   569
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   570
          in (x'', y' :: ys') end;
wenzelm@16705
   571
  in fold_aux end;
wenzelm@16705
   572
wenzelm@233
   573
wenzelm@233
   574
(* basic list functions *)
wenzelm@233
   575
wenzelm@19483
   576
fun maps f [] = []
wenzelm@19483
   577
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   578
wenzelm@19011
   579
fun chop 0 xs = ([], xs)
wenzelm@19011
   580
  | chop _ [] = ([], [])
wenzelm@19011
   581
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   582
wenzelm@233
   583
(*take the first n elements from a list*)
wenzelm@233
   584
fun take (n, []) = []
wenzelm@233
   585
  | take (n, x :: xs) =
wenzelm@233
   586
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   587
wenzelm@233
   588
(*drop the first n elements from a list*)
wenzelm@233
   589
fun drop (n, []) = []
wenzelm@233
   590
  | drop (n, x :: xs) =
wenzelm@233
   591
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   592
nipkow@4713
   593
fun dropwhile P [] = []
nipkow@4713
   594
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   595
wenzelm@233
   596
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   597
  raise Subscript if list too short*)
haftmann@18011
   598
fun nth xs i = List.nth (xs, i);
wenzelm@233
   599
wenzelm@18461
   600
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   601
haftmann@18011
   602
(*update nth element*)
haftmann@18011
   603
fun nth_update (n, x) xs =
wenzelm@19474
   604
  (case chop n xs of
wenzelm@19474
   605
    (_, []) => raise Subscript
wenzelm@19474
   606
  | (prfx, _ :: sffx') => prfx @ (x :: sffx'));
haftmann@18011
   607
haftmann@18011
   608
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   609
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   610
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   611
haftmann@18514
   612
fun map_index f =
haftmann@18514
   613
  let
haftmann@18514
   614
    fun mapp _ [] = []
haftmann@18514
   615
      | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
haftmann@18514
   616
  in mapp 0 end;
haftmann@18514
   617
skalberg@15570
   618
val last_elem = List.last;
wenzelm@233
   619
wenzelm@3762
   620
(*rear decomposition*)
skalberg@15570
   621
fun split_last [] = raise Empty
wenzelm@3762
   622
  | split_last [x] = ([], x)
wenzelm@3762
   623
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   624
wenzelm@4212
   625
(*find the position of an element in a list*)
wenzelm@4212
   626
fun find_index pred =
wenzelm@4212
   627
  let fun find _ [] = ~1
wenzelm@4212
   628
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   629
  in find 0 end;
wenzelm@3762
   630
wenzelm@4224
   631
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   632
wenzelm@4212
   633
(*find first element satisfying predicate*)
skalberg@15531
   634
fun find_first _ [] = NONE
wenzelm@4212
   635
  | find_first pred (x :: xs) =
skalberg@15531
   636
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   637
wenzelm@4916
   638
(*get first element by lookup function*)
skalberg@15531
   639
fun get_first _ [] = NONE
wenzelm@4916
   640
  | get_first f (x :: xs) =
wenzelm@4916
   641
      (case f x of
skalberg@15531
   642
        NONE => get_first f xs
wenzelm@4916
   643
      | some => some);
wenzelm@4916
   644
haftmann@19233
   645
fun get_index f =
haftmann@19233
   646
  let
haftmann@19233
   647
    fun get _ [] = NONE
wenzelm@19461
   648
      | get i (x :: xs) =
haftmann@19233
   649
          case f x
wenzelm@19461
   650
           of NONE => get (i + 1) xs
haftmann@19233
   651
            | SOME y => SOME (i, y)
haftmann@19233
   652
  in get 0 end;
haftmann@19233
   653
haftmann@19454
   654
fun eq_list _ ([], []) = true
wenzelm@19461
   655
  | eq_list eq (x :: xs, y :: ys) = eq (x, y) andalso eq_list eq (xs, ys)
haftmann@19454
   656
  | eq_list _ _ = false;
haftmann@19454
   657
skalberg@15531
   658
val flat = List.concat;
wenzelm@233
   659
wenzelm@12136
   660
fun unflat (xs :: xss) ys =
wenzelm@19424
   661
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   662
      in ps :: unflat xss qs end
wenzelm@12136
   663
  | unflat [] [] = []
skalberg@15570
   664
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   665
haftmann@18441
   666
fun burrow f xss =
haftmann@18359
   667
  unflat xss ((f o flat) xss);
haftmann@18359
   668
haftmann@18549
   669
fun fold_burrow f xss s =
haftmann@18549
   670
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   671
wenzelm@233
   672
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   673
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   674
val seq = List.app;
wenzelm@233
   675
wenzelm@233
   676
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   677
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   678
  | separate _ xs = xs;
wenzelm@233
   679
wenzelm@233
   680
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   681
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   682
  let fun rep (0, xs) = xs
wenzelm@233
   683
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   684
  in
skalberg@15570
   685
    if n < 0 then raise Subscript
wenzelm@233
   686
    else rep (n, [])
wenzelm@233
   687
  end;
wenzelm@233
   688
wenzelm@14926
   689
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   690
wenzelm@4248
   691
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   692
fun multiply [] _ = []
wenzelm@18148
   693
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   694
wenzelm@14792
   695
(*direct product*)
wenzelm@14792
   696
fun product _ [] = []
wenzelm@14792
   697
  | product [] _ = []
wenzelm@14792
   698
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   699
wenzelm@233
   700
wenzelm@233
   701
(* filter *)
wenzelm@233
   702
wenzelm@233
   703
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   704
val filter = List.filter;
clasohm@0
   705
fun filter_out f = filter (not o f);
wenzelm@19483
   706
val map_filter = List.mapPartial;
wenzelm@233
   707
wenzelm@233
   708
wenzelm@233
   709
(* lists of pairs *)
wenzelm@233
   710
skalberg@15570
   711
exception UnequalLengths;
skalberg@15570
   712
haftmann@18330
   713
fun map2 _ [] [] = []
haftmann@18330
   714
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   715
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   716
haftmann@18330
   717
fun fold2 f =
haftmann@18330
   718
  let
haftmann@18330
   719
    fun fold_aux [] [] z = z
haftmann@18330
   720
      | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
haftmann@18330
   721
      | fold_aux _ _ _ = raise UnequalLengths;
haftmann@18330
   722
  in fold_aux end;
wenzelm@380
   723
wenzelm@19799
   724
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   725
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   726
  | zip_options _ [] = []
wenzelm@19799
   727
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   728
wenzelm@233
   729
(*combine two lists forming a list of pairs:
wenzelm@233
   730
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   731
fun [] ~~ [] = []
wenzelm@233
   732
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   733
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   734
wenzelm@233
   735
(*inverse of ~~; the old 'split':
wenzelm@233
   736
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   737
val split_list = ListPair.unzip;
wenzelm@233
   738
haftmann@18330
   739
fun equal_lists eq (xs, ys) =
haftmann@18330
   740
  let
haftmann@18330
   741
    fun eq' [] [] = true
haftmann@18330
   742
      | eq' (x :: xs) (y :: ys) = eq (x, y) andalso eq' xs ys
haftmann@18330
   743
  in length xs = length ys andalso eq' xs ys end;
wenzelm@7468
   744
wenzelm@233
   745
wenzelm@233
   746
(* prefixes, suffixes *)
wenzelm@233
   747
haftmann@18441
   748
fun is_prefix _ [] _ = true
haftmann@18441
   749
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   750
  | is_prefix eq _ _ = false;
wenzelm@233
   751
wenzelm@233
   752
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   753
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   754
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   755
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   756
        | take (rxs, x :: xs) =
wenzelm@255
   757
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   758
  in  take([], xs)  end;
wenzelm@233
   759
haftmann@20108
   760
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   761
  | chop_prefix eq (xs, []) = ([], (xs, []))
haftmann@20108
   762
  | chop_prefix eq (xs as x::xs', ys as y::ys') =
haftmann@20108
   763
      if eq (x, y) then
haftmann@20108
   764
        let val (ps', xys'') = chop_prefix eq (xs', ys')
haftmann@20108
   765
        in (x::ps', xys'') end
haftmann@20108
   766
      else ([], (xs, ys));
haftmann@20108
   767
wenzelm@233
   768
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   769
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   770
fun take_suffix _ [] = ([], [])
wenzelm@233
   771
  | take_suffix pred (x :: xs) =
wenzelm@233
   772
      (case take_suffix pred xs of
wenzelm@233
   773
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   774
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   775
wenzelm@12249
   776
fun prefixes1 [] = []
wenzelm@12249
   777
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   778
wenzelm@19011
   779
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   780
wenzelm@12249
   781
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   782
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   783
wenzelm@233
   784
wenzelm@233
   785
(** integers **)
wenzelm@233
   786
wenzelm@16439
   787
fun gcd (x, y) =
paulson@15965
   788
  let fun gxd x y : IntInf.int =
nipkow@10692
   789
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   790
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   791
wenzelm@16439
   792
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   793
wenzelm@2958
   794
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   795
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   796
wenzelm@233
   797
wenzelm@233
   798
(* lists of integers *)
wenzelm@233
   799
wenzelm@233
   800
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   801
fun (from upto to) =
wenzelm@233
   802
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   803
wenzelm@233
   804
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   805
fun (from downto to) =
wenzelm@233
   806
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   807
wenzelm@233
   808
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   809
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   810
  | downto0 ([], n) = n = ~1;
wenzelm@233
   811
wenzelm@233
   812
wenzelm@233
   813
(* convert integers to strings *)
wenzelm@233
   814
wenzelm@233
   815
(*expand the number in the given base;
wenzelm@233
   816
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   817
fun radixpand (base, num) : int list =
wenzelm@233
   818
  let
wenzelm@233
   819
    fun radix (n, tail) =
wenzelm@233
   820
      if n < base then n :: tail
wenzelm@233
   821
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   822
  in radix (num, []) end;
wenzelm@233
   823
wenzelm@233
   824
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   825
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   826
fun radixstring (base, zerochar, num) =
wenzelm@233
   827
  let val offset = ord zerochar;
wenzelm@233
   828
      fun chrof n = chr (offset + n)
wenzelm@233
   829
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   830
wenzelm@233
   831
paulson@3407
   832
val string_of_int = Int.toString;
wenzelm@233
   833
paulson@3407
   834
fun string_of_indexname (a,0) = a
paulson@3407
   835
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   836
wenzelm@233
   837
wenzelm@14826
   838
(* read integers *)
wenzelm@14826
   839
wenzelm@20095
   840
fun read_intinf radix cs =
wenzelm@20095
   841
  let
wenzelm@20095
   842
    val zero = ord "0";
wenzelm@20095
   843
    val limit = zero + radix;
wenzelm@20095
   844
    fun scan (num, []) = (num, [])
wenzelm@20095
   845
      | scan (num, c :: cs) =
wenzelm@20095
   846
        if zero <= ord c andalso ord c < limit then
wenzelm@20095
   847
          scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
wenzelm@20095
   848
        else (num, c :: cs);
wenzelm@20095
   849
  in scan (0, cs) end;
wenzelm@14826
   850
wenzelm@20095
   851
fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
wenzelm@14826
   852
wenzelm@20095
   853
fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
wenzelm@14826
   854
wenzelm@14826
   855
wenzelm@14826
   856
wenzelm@233
   857
(** strings **)
wenzelm@233
   858
wenzelm@16188
   859
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   860
haftmann@18011
   861
fun nth_string str i =
wenzelm@6959
   862
  (case try String.substring (str, i, 1) of
skalberg@15531
   863
    SOME s => s
skalberg@15570
   864
  | NONE => raise Subscript);
wenzelm@6312
   865
wenzelm@16188
   866
fun fold_string f str x0 =
wenzelm@6282
   867
  let
wenzelm@6282
   868
    val n = size str;
wenzelm@16188
   869
    fun iter (x, i) =
wenzelm@16188
   870
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   871
  in iter (x0, 0) end;
wenzelm@6282
   872
wenzelm@14968
   873
fun exists_string pred str =
wenzelm@14968
   874
  let
wenzelm@14968
   875
    val n = size str;
wenzelm@14968
   876
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   877
  in ex 0 end;
wenzelm@6312
   878
wenzelm@16188
   879
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   880
lcp@512
   881
(*enclose in brackets*)
lcp@512
   882
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   883
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   884
wenzelm@233
   885
(*simple quoting (does not escape special chars)*)
lcp@512
   886
val quote = enclose "\"" "\"";
wenzelm@233
   887
wenzelm@4212
   888
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   889
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   890
wenzelm@255
   891
val commas = space_implode ", ";
wenzelm@380
   892
val commas_quote = commas o map quote;
wenzelm@255
   893
wenzelm@233
   894
(*concatenate messages, one per line, into a string*)
wenzelm@255
   895
val cat_lines = space_implode "\n";
wenzelm@233
   896
wenzelm@4212
   897
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   898
fun space_explode _ "" = []
wenzelm@3832
   899
  | space_explode sep str =
wenzelm@3832
   900
      let
wenzelm@3832
   901
        fun expl chs =
wenzelm@19301
   902
          (case take_prefix (fn s => s <> sep) chs of
wenzelm@3832
   903
            (cs, []) => [implode cs]
wenzelm@3832
   904
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   905
      in expl (explode str) end;
wenzelm@3832
   906
wenzelm@3832
   907
val split_lines = space_explode "\n";
wenzelm@3832
   908
wenzelm@14826
   909
fun prefix_lines "" txt = txt
wenzelm@14826
   910
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   911
wenzelm@7712
   912
fun untabify chs =
wenzelm@7712
   913
  let
wenzelm@7712
   914
    val tab_width = 8;
wenzelm@7712
   915
wenzelm@7712
   916
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   917
      | untab (pos, "\t") =
wenzelm@9118
   918
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   919
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   920
  in
wenzelm@19301
   921
    if not (exists (fn c => c = "\t") chs) then chs
wenzelm@7712
   922
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   923
  end;
wenzelm@7712
   924
wenzelm@18681
   925
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   926
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   927
wenzelm@18681
   928
fun unprefix prfx s =
wenzelm@18681
   929
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   930
  else raise Fail "unprefix";
wenzelm@18681
   931
wenzelm@16188
   932
fun unsuffix sffx s =
wenzelm@17061
   933
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   934
  else raise Fail "unsuffix";
wenzelm@5285
   935
wenzelm@10951
   936
fun replicate_string 0 _ = ""
wenzelm@10951
   937
  | replicate_string 1 a = a
wenzelm@10951
   938
  | replicate_string k a =
wenzelm@10951
   939
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   940
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   941
wenzelm@19644
   942
fun string_of_list f = enclose "[" "]" o commas o map f;
wenzelm@19644
   943
wenzelm@19644
   944
fun string_of_option f NONE = "NONE"
wenzelm@19644
   945
  | string_of_option f (SOME x) = "SOME (" ^ f x ^ ")";
wenzelm@19644
   946
wenzelm@3832
   947
wenzelm@233
   948
wenzelm@16492
   949
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   950
wenzelm@18923
   951
(*canonical member, insert, remove*)
wenzelm@18923
   952
fun member eq list x =
wenzelm@18923
   953
  let
wenzelm@18923
   954
    fun memb [] = false
wenzelm@18923
   955
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   956
  in memb list end;
berghofe@1576
   957
wenzelm@18923
   958
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   959
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   960
wenzelm@19301
   961
fun subtract eq = fold (remove eq);
wenzelm@19301
   962
wenzelm@18923
   963
fun merge _ ([], ys) = ys
wenzelm@18923
   964
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   965
wenzelm@18923
   966
(*old-style infixes*)
wenzelm@18923
   967
fun x mem xs = member (op =) xs x;
wenzelm@18923
   968
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   969
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   970
wenzelm@18923
   971
fun x ins xs = insert (op =) x xs;
wenzelm@18989
   972
fun (x: int) ins_int xs = insert (op =) x xs;
wenzelm@18989
   973
fun (x: string) ins_string xs = insert (op =) x xs;
wenzelm@18989
   974
wenzelm@233
   975
wenzelm@233
   976
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   977
fun xs union [] = xs
wenzelm@233
   978
  | [] union ys = ys
wenzelm@233
   979
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   980
paulson@2175
   981
(*union of sets, optimized version for ints*)
berghofe@1576
   982
fun (xs:int list) union_int [] = xs
berghofe@1576
   983
  | [] union_int ys = ys
berghofe@1576
   984
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   985
paulson@2175
   986
(*union of sets, optimized version for strings*)
berghofe@1576
   987
fun (xs:string list) union_string [] = xs
berghofe@1576
   988
  | [] union_string ys = ys
berghofe@1576
   989
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   990
clasohm@0
   991
(*generalized union*)
wenzelm@233
   992
fun gen_union eq (xs, []) = xs
wenzelm@233
   993
  | gen_union eq ([], ys) = ys
wenzelm@18923
   994
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   995
wenzelm@233
   996
wenzelm@233
   997
(*intersection*)
wenzelm@233
   998
fun [] inter ys = []
wenzelm@233
   999
  | (x :: xs) inter ys =
wenzelm@233
  1000
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
  1001
paulson@2175
  1002
(*intersection, optimized version for ints*)
berghofe@1576
  1003
fun ([]:int list) inter_int ys = []
berghofe@1576
  1004
  | (x :: xs) inter_int ys =
berghofe@1576
  1005
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
  1006
paulson@2175
  1007
(*intersection, optimized version for strings *)
berghofe@1576
  1008
fun ([]:string list) inter_string ys = []
berghofe@1576
  1009
  | (x :: xs) inter_string ys =
berghofe@1576
  1010
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
  1011
paulson@7090
  1012
(*generalized intersection*)
paulson@7090
  1013
fun gen_inter eq ([], ys) = []
wenzelm@12284
  1014
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
  1015
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
  1016
      else gen_inter eq (xs, ys);
paulson@7090
  1017
wenzelm@233
  1018
wenzelm@233
  1019
(*subset*)
wenzelm@233
  1020
fun [] subset ys = true
wenzelm@233
  1021
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
  1022
paulson@2175
  1023
(*subset, optimized version for ints*)
wenzelm@16439
  1024
fun ([]: int list) subset_int ys = true
berghofe@1576
  1025
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
  1026
paulson@2175
  1027
(*subset, optimized version for strings*)
wenzelm@16439
  1028
fun ([]: string list) subset_string ys = true
berghofe@1576
  1029
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
  1030
wenzelm@4363
  1031
(*set equality*)
wenzelm@4363
  1032
fun eq_set (xs, ys) =
wenzelm@4363
  1033
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
  1034
paulson@2182
  1035
(*set equality for strings*)
wenzelm@16439
  1036
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
  1037
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
  1038
wenzelm@18923
  1039
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
  1040
wenzelm@19301
  1041
fun gen_eq_set eq (xs, ys) =
wenzelm@19301
  1042
  equal_lists eq (xs, ys) orelse
wenzelm@19301
  1043
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
  1044
wenzelm@265
  1045
wenzelm@233
  1046
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
  1047
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
  1048
  | [] \ x = [];
wenzelm@233
  1049
paulson@2243
  1050
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
  1051
wenzelm@233
  1052
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
  1053
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@18923
  1054
fun gen_rems eq (xs, ys) = filter_out (member eq ys) xs;
wenzelm@233
  1055
wenzelm@19046
  1056
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@19046
  1057
fun findrep [] = []
wenzelm@19046
  1058
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@19046
  1059
wenzelm@19046
  1060
wenzelm@233
  1061
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
  1062
  first of equal elements*)
wenzelm@19046
  1063
fun distinct eq lst =
wenzelm@233
  1064
  let
wenzelm@233
  1065
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
  1066
      | dist (rev_seen, x :: xs) =
wenzelm@18923
  1067
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
  1068
          else dist (x :: rev_seen, xs);
wenzelm@19046
  1069
  in dist ([], lst) end;
wenzelm@233
  1070
wenzelm@255
  1071
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
  1072
  order, takes first of equal elements*)
wenzelm@18966
  1073
fun duplicates eq lst =
wenzelm@255
  1074
  let
wenzelm@255
  1075
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
  1076
      | dups (rev_dups, x :: xs) =
wenzelm@18923
  1077
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
  1078
            dups (rev_dups, xs)
wenzelm@255
  1079
          else dups (x :: rev_dups, xs);
wenzelm@18966
  1080
  in dups ([], lst) end;
wenzelm@255
  1081
wenzelm@16878
  1082
fun has_duplicates eq =
wenzelm@16878
  1083
  let
wenzelm@16878
  1084
    fun dups [] = false
wenzelm@16878
  1085
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
  1086
  in dups end;
wenzelm@16878
  1087
wenzelm@255
  1088
haftmann@19119
  1089
(** association lists -- legacy operations **)
wenzelm@233
  1090
wenzelm@12284
  1091
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1092
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1093
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1094
wenzelm@12284
  1095
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
haftmann@17498
  1096
fun merge_alists al = gen_merge_lists (eq_fst (op =)) al;
clasohm@0
  1097
clasohm@0
  1098
wenzelm@233
  1099
(** balanced trees **)
wenzelm@233
  1100
wenzelm@233
  1101
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1102
wenzelm@233
  1103
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1104
fun fold_bal f [x] = x
wenzelm@233
  1105
  | fold_bal f [] = raise Balance
wenzelm@233
  1106
  | fold_bal f xs =
wenzelm@19474
  1107
      let val (ps, qs) = chop (length xs div 2) xs
nipkow@13629
  1108
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1109
wenzelm@233
  1110
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1111
fun access_bal (f, g, x) n i =
wenzelm@233
  1112
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1113
          if n=1 then x else
wenzelm@233
  1114
          let val n2 = n div 2
wenzelm@233
  1115
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1116
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1117
          end
wenzelm@233
  1118
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1119
wenzelm@233
  1120
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1121
fun accesses_bal (f, g, x) n =
wenzelm@233
  1122
  let fun acc n =
wenzelm@233
  1123
          if n=1 then [x] else
wenzelm@233
  1124
          let val n2 = n div 2
wenzelm@233
  1125
              val acc2 = acc n2
wenzelm@233
  1126
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1127
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1128
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1129
wenzelm@233
  1130
wenzelm@233
  1131
wenzelm@2506
  1132
(** orders **)
wenzelm@2506
  1133
wenzelm@18966
  1134
fun is_equal EQUAL = true
wenzelm@18966
  1135
  | is_equal _ = false;
wenzelm@18966
  1136
wenzelm@4445
  1137
fun rev_order LESS = GREATER
wenzelm@4445
  1138
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1139
  | rev_order GREATER = LESS;
wenzelm@4445
  1140
wenzelm@4479
  1141
(*assume rel is a linear strict order*)
wenzelm@4445
  1142
fun make_ord rel (x, y) =
wenzelm@4445
  1143
  if rel (x, y) then LESS
wenzelm@4445
  1144
  else if rel (y, x) then GREATER
wenzelm@4445
  1145
  else EQUAL;
wenzelm@4445
  1146
wenzelm@15051
  1147
val int_ord = Int.compare;
wenzelm@15051
  1148
val string_ord = String.compare;
wenzelm@2506
  1149
wenzelm@16676
  1150
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1151
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1152
wenzelm@16492
  1153
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1154
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1155
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1156
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1157
wenzelm@4343
  1158
(*lexicographic product*)
wenzelm@4343
  1159
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1160
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1161
wenzelm@4343
  1162
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1163
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1164
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1165
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1166
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1167
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1168
wenzelm@4343
  1169
(*lexicographic product of lists*)
wenzelm@4343
  1170
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1171
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1172
wenzelm@2506
  1173
wenzelm@4621
  1174
(* sorting *)
wenzelm@4621
  1175
wenzelm@18427
  1176
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
  1177
fun quicksort unique ord =
wenzelm@4621
  1178
  let
wenzelm@16878
  1179
    fun qsort [] = []
wenzelm@16878
  1180
      | qsort (xs as [_]) = xs
wenzelm@18427
  1181
      | qsort (xs as [x, y]) =
wenzelm@18427
  1182
          (case ord (x, y) of
wenzelm@18427
  1183
            LESS => xs
wenzelm@18427
  1184
          | EQUAL => if unique then [x] else xs
wenzelm@18427
  1185
          | GREATER => [y, x])
wenzelm@16878
  1186
      | qsort xs =
haftmann@18011
  1187
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
  1188
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1189
    and part _ [] = ([], [], [])
wenzelm@4621
  1190
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1191
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
  1192
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
  1193
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
  1194
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1195
  in qsort end;
wenzelm@4621
  1196
wenzelm@18427
  1197
fun sort ord = quicksort false ord;
wenzelm@18427
  1198
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
  1199
wenzelm@4621
  1200
val sort_strings = sort string_ord;
wenzelm@4621
  1201
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1202
wenzelm@4621
  1203
wenzelm@2506
  1204
berghofe@14106
  1205
(** random numbers **)
berghofe@14106
  1206
berghofe@14106
  1207
exception RANDOM;
berghofe@14106
  1208
berghofe@14618
  1209
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1210
berghofe@14106
  1211
local
berghofe@14106
  1212
  val a = 16807.0;
berghofe@14106
  1213
  val m = 2147483647.0;
berghofe@14106
  1214
  val random_seed = ref 1.0;
berghofe@14106
  1215
in
berghofe@14106
  1216
berghofe@14106
  1217
fun random () =
berghofe@14106
  1218
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1219
  in (random_seed := r; r) end;
berghofe@14106
  1220
berghofe@14106
  1221
end;
berghofe@14106
  1222
berghofe@14106
  1223
fun random_range l h =
berghofe@14106
  1224
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1225
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1226
haftmann@18011
  1227
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1228
berghofe@14106
  1229
fun frequency xs =
berghofe@14106
  1230
  let
berghofe@14106
  1231
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1232
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1233
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1234
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1235
berghofe@14106
  1236
wenzelm@14826
  1237
(** current directory **)
wenzelm@233
  1238
paulson@2243
  1239
val cd = OS.FileSys.chDir;
wenzelm@2317
  1240
val pwd = OS.FileSys.getDir;
paulson@2243
  1241
berghofe@3606
  1242
wenzelm@19644
  1243
wenzelm@4621
  1244
(** misc **)
wenzelm@233
  1245
wenzelm@19644
  1246
fun divide_and_conquer decomp x =
wenzelm@19644
  1247
  let val (ys, recomb) = decomp x
wenzelm@19644
  1248
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
  1249
clasohm@0
  1250
wenzelm@233
  1251
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1252
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1253
fun partition_list p i j =
wenzelm@233
  1254
  let fun part k xs =
wenzelm@233
  1255
            if k>j then
clasohm@0
  1256
              (case xs of [] => []
skalberg@15570
  1257
                         | _ => raise Fail "partition_list")
clasohm@0
  1258
            else
wenzelm@19691
  1259
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1260
            in  ns :: part(k+1)rest  end
clasohm@0
  1261
  in  part i end;
clasohm@0
  1262
wenzelm@19691
  1263
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1264
  let
wenzelm@19691
  1265
    fun part [] = []
wenzelm@19691
  1266
      | part (x :: ys) =
wenzelm@19691
  1267
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1268
          in (x::xs)::(part xs') end
wenzelm@19691
  1269
  in part end;
wenzelm@19691
  1270
wenzelm@19691
  1271
clasohm@0
  1272
wenzelm@233
  1273
(* generating identifiers *)
clasohm@0
  1274
paulson@4063
  1275
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1276
local
paulson@4063
  1277
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1278
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1279
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1280
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1281
             else if i=62 then "_"
wenzelm@5904
  1282
             else  (*i=63*)    "'";
paulson@4063
  1283
paulson@4063
  1284
val charVec = Vector.tabulate (64, char);
paulson@4063
  1285
wenzelm@5904
  1286
fun newid n =
wenzelm@5904
  1287
  let
wenzelm@4284
  1288
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1289
wenzelm@4284
  1290
val seedr = ref 0;
clasohm@0
  1291
paulson@4063
  1292
in
wenzelm@4284
  1293
wenzelm@12346
  1294
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1295
paulson@4063
  1296
end;
paulson@4063
  1297
paulson@4063
  1298
wenzelm@233
  1299
(* lexical scanning *)
clasohm@0
  1300
wenzelm@233
  1301
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1302
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1303
fun scanwords is_let cs =
clasohm@0
  1304
  let fun scan1 [] = []
wenzelm@233
  1305
        | scan1 cs =
wenzelm@233
  1306
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1307
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1308
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1309
wenzelm@4212
  1310
wenzelm@16439
  1311
(* stamps and serial numbers *)
wenzelm@16439
  1312
wenzelm@16439
  1313
type stamp = unit ref;
wenzelm@16439
  1314
val stamp: unit -> stamp = ref;
wenzelm@16439
  1315
wenzelm@16439
  1316
type serial = int;
wenzelm@16439
  1317
local val count = ref 0
wenzelm@16439
  1318
in fun serial () = inc count end;
wenzelm@16439
  1319
wenzelm@19512
  1320
val serial_string = string_of_int o serial;
wenzelm@19512
  1321
wenzelm@16535
  1322
wenzelm@16535
  1323
(* generic objects *)
wenzelm@16535
  1324
wenzelm@16535
  1325
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1326
  constructors at any time*)
wenzelm@16535
  1327
structure Object = struct type T = exn end;
wenzelm@16535
  1328
clasohm@1364
  1329
end;
clasohm@1364
  1330
wenzelm@15745
  1331
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1332
open BasicLibrary;