src/Pure/library.ML
author webertj
Fri May 05 18:21:58 2006 +0200 (2006-05-05)
changeset 19567 48d3b4266b52
parent 19542 b5abe6cd4cbf
child 19588 846f0d5bfc83
permissions -rw-r--r--
string_of_... functions 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, association lists, generic
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tables, 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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  (*old options -- invalidated*)
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  datatype invalid = None of invalid
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  exception OPTION of invalid
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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 eq_opt: ('a * 'b -> bool) -> 'a option * 'b option -> bool
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  val merge_opt: ('a * 'a -> bool) -> 'a option * 'a option -> 'a option
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  val string_of_option: ('a -> string) -> 'a option -> string
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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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  val string_of_bool: bool -> string
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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 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 ~~ : '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 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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  val string_of_list: ('a -> string) -> 'a list -> string
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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_radixint: 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 enclose: string -> string -> string -> string
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  val unenclose: string -> string
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  val quote: string -> string
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  val space_implode: string -> string list -> string
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  val commas: string list -> string
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  val commas_quote: string list -> string
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  val cat_lines: string list -> string
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  val space_explode: string -> string -> string list
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  val split_lines: string -> string list
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  val prefix_lines: string -> string -> string
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  val untabify: string list -> string list
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  val prefix: string -> string -> string
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  val suffix: string -> string -> string
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  val unprefix: string -> string -> string
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  val unsuffix: string -> string -> string
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  val replicate_string: int -> string -> string
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  val translate_string: (string -> string) -> string -> string
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  (*lists as sets -- see also Pure/General/ord_list.ML*)
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  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
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  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
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  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
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  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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  val mem: ''a * ''a list -> bool
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  val mem_int: int * int list -> bool
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  val mem_string: string * string list -> bool
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  val 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 eq_ord: ('a -> order) -> 'a -> bool
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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 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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   280
  val scanwords: (string -> bool) -> string list -> string list
wenzelm@16439
   281
  type stamp
wenzelm@16439
   282
  val stamp: unit -> stamp
wenzelm@16439
   283
  type serial
wenzelm@16439
   284
  val serial: unit -> serial
wenzelm@19512
   285
  val serial_string: unit -> string
wenzelm@16535
   286
  structure Object: sig type T end
wenzelm@4621
   287
end;
wenzelm@4621
   288
wenzelm@15745
   289
signature LIBRARY =
skalberg@15570
   290
sig
wenzelm@15745
   291
  include BASIC_LIBRARY
skalberg@15570
   292
  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
skalberg@15570
   293
  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
skalberg@15570
   294
  val take: int * 'a list -> 'a list
skalberg@15570
   295
  val drop: int * 'a list -> 'a list
skalberg@15570
   296
  val last_elem: 'a list -> 'a
skalberg@15570
   297
  val seq: ('a -> unit) -> 'a list -> unit
skalberg@15570
   298
  val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
skalberg@15570
   299
end;
skalberg@15570
   300
wenzelm@15745
   301
structure Library: LIBRARY =
clasohm@1364
   302
struct
clasohm@0
   303
wenzelm@4995
   304
wenzelm@233
   305
(** functions **)
clasohm@0
   306
wenzelm@16842
   307
fun I x = x;
wenzelm@16842
   308
fun K x = fn _ => x;
wenzelm@233
   309
fun curry f x y = f (x, y);
wenzelm@233
   310
fun uncurry f (x, y) = f x y;
clasohm@0
   311
wenzelm@16705
   312
(*reverse application and structured results*)
wenzelm@16705
   313
fun x |> f = f x;
wenzelm@16705
   314
fun (x, y) |-> f = f x y;
wenzelm@16705
   315
fun (x, y) |>> f = (f x, y);
wenzelm@16705
   316
fun (x, y) ||> f = (x, f y);
wenzelm@16705
   317
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16705
   318
fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
wenzelm@16842
   319
wenzelm@16842
   320
(*reverse composition*)
haftmann@16780
   321
fun f #> g = g o f;
wenzelm@16842
   322
fun f #-> g = uncurry g o f;
wenzelm@16842
   323
haftmann@17141
   324
(*conditional application*)
wenzelm@17545
   325
fun b ? f = fn x => if b x then f x else x;
haftmann@17141
   326
wenzelm@16842
   327
(*view results*)
wenzelm@16842
   328
fun `f = fn x => (f x, x);
wenzelm@17545
   329
fun tap f = fn x => (f x; x);
wenzelm@380
   330
wenzelm@16721
   331
(*composition with multiple args*)
wenzelm@16721
   332
fun (f oo g) x y = f (g x y);
wenzelm@16721
   333
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   334
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   335
wenzelm@233
   336
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   337
fun funpow n f x =
wenzelm@233
   338
  let fun rep (0, x) = x
wenzelm@233
   339
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   340
  in rep (n, x) end;
wenzelm@160
   341
wenzelm@160
   342
wenzelm@233
   343
(** options **)
clasohm@0
   344
wenzelm@15670
   345
(*invalidate former constructors to prevent accidental use as match-all patterns!*)
wenzelm@15670
   346
datatype invalid = None of invalid;
wenzelm@15670
   347
exception OPTION of invalid;
clasohm@0
   348
wenzelm@15970
   349
val the = Option.valOf;
wenzelm@17341
   350
haftmann@17153
   351
fun these (SOME x) = x
haftmann@17313
   352
  | these _ = [];
wenzelm@17341
   353
haftmann@17313
   354
fun the_default x (SOME y) = y
haftmann@17313
   355
  | the_default x _ = x;
wenzelm@17341
   356
haftmann@17313
   357
fun the_list (SOME x) = [x]
haftmann@17313
   358
  | the_list _ = []
wenzelm@15970
   359
wenzelm@15970
   360
fun is_some (SOME _) = true
wenzelm@15970
   361
  | is_some NONE = false;
wenzelm@15970
   362
wenzelm@15970
   363
fun is_none (SOME _) = false
wenzelm@15970
   364
  | is_none NONE = true;
wenzelm@15970
   365
wenzelm@18376
   366
fun perhaps f x = the_default x (f x);
wenzelm@18376
   367
haftmann@19454
   368
fun eq_opt eq (NONE, NONE) = true
haftmann@19454
   369
  | eq_opt eq (SOME x, SOME y) = eq (x, y)
haftmann@19454
   370
  | eq_opt _ _ = false;
haftmann@19454
   371
haftmann@19454
   372
fun merge_opt _ (NONE, y) = y
haftmann@19454
   373
  | merge_opt _ (x, NONE) = x
haftmann@19454
   374
  | merge_opt eq (SOME x, SOME y) = if eq (x, y) then SOME y else raise Option;
wenzelm@6959
   375
webertj@19567
   376
fun string_of_option f NONE     = "NONE"
webertj@19567
   377
  | string_of_option f (SOME x) = "SOME " ^ f x;
webertj@19567
   378
wenzelm@19474
   379
wenzelm@17341
   380
(* exceptions *)
wenzelm@17341
   381
wenzelm@18681
   382
val do_transform_failure = ref true;
wenzelm@18681
   383
wenzelm@18681
   384
fun transform_failure exn f x =
wenzelm@18681
   385
  if ! do_transform_failure then
wenzelm@18681
   386
    f x handle Interrupt => raise Interrupt | e => raise exn e
wenzelm@18681
   387
  else f x;
wenzelm@18681
   388
wenzelm@17341
   389
exception EXCEPTION of exn * string;
wenzelm@6959
   390
wenzelm@6959
   391
skalberg@15531
   392
fun try f x = SOME (f x)
wenzelm@18681
   393
  handle Interrupt => raise Interrupt | _ => NONE;
wenzelm@6959
   394
wenzelm@6959
   395
fun can f x = is_some (try f x);
wenzelm@4139
   396
wenzelm@4139
   397
wenzelm@14868
   398
datatype 'a result =
wenzelm@14868
   399
  Result of 'a |
wenzelm@14868
   400
  Exn of exn;
wenzelm@14868
   401
wenzelm@14868
   402
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   403
wenzelm@14868
   404
fun release (Result y) = y
wenzelm@14868
   405
  | release (Exn e) = raise e;
wenzelm@14868
   406
skalberg@15531
   407
fun get_result (Result x) = SOME x
skalberg@15531
   408
  | get_result _ = NONE;
wenzelm@14868
   409
skalberg@15531
   410
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   411
  | get_exn _ = NONE;
wenzelm@14868
   412
wenzelm@14868
   413
wenzelm@18681
   414
(* errors *)
wenzelm@18681
   415
wenzelm@19542
   416
exception SYS_ERROR of string;
wenzelm@19542
   417
fun sys_error msg = raise SYS_ERROR msg;
wenzelm@19542
   418
wenzelm@18681
   419
exception ERROR of string;
wenzelm@18681
   420
fun error msg = raise ERROR msg;
wenzelm@18681
   421
wenzelm@18681
   422
fun cat_error "" msg = error msg
wenzelm@18681
   423
  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
wenzelm@18681
   424
wenzelm@18681
   425
fun assert p msg = if p then () else error msg;
wenzelm@18681
   426
fun deny p msg = if p then error msg else ();
wenzelm@18681
   427
wenzelm@18681
   428
fun assert_all pred list msg =
wenzelm@18681
   429
  let
wenzelm@18681
   430
    fun ass [] = ()
wenzelm@18681
   431
      | ass (x :: xs) = if pred x then ass xs else error (msg x);
wenzelm@18681
   432
  in ass list end;
wenzelm@18681
   433
wenzelm@18681
   434
wenzelm@233
   435
(** pairs **)
wenzelm@233
   436
wenzelm@233
   437
fun pair x y = (x, y);
wenzelm@233
   438
fun rpair x y = (y, x);
wenzelm@233
   439
wenzelm@233
   440
fun fst (x, y) = x;
wenzelm@233
   441
fun snd (x, y) = y;
wenzelm@233
   442
haftmann@17498
   443
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   444
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
haftmann@19454
   445
fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
wenzelm@233
   446
wenzelm@233
   447
fun swap (x, y) = (y, x);
wenzelm@233
   448
wenzelm@4212
   449
(*apply function to components*)
wenzelm@233
   450
fun apfst f (x, y) = (f x, y);
wenzelm@233
   451
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   452
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   453
webertj@19567
   454
fun string_of_pair f1 f2 (x, y) = "(" ^ f1 x ^ ", " ^ f2 y ^ ")";
wenzelm@233
   455
wenzelm@233
   456
wenzelm@233
   457
(** booleans **)
wenzelm@233
   458
wenzelm@233
   459
(* equality *)
wenzelm@233
   460
wenzelm@233
   461
fun equal x y = x = y;
wenzelm@233
   462
fun not_equal x y = x <> y;
wenzelm@233
   463
wenzelm@233
   464
(* operators for combining predicates *)
wenzelm@233
   465
wenzelm@16721
   466
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   467
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   468
wenzelm@233
   469
(* predicates on lists *)
wenzelm@233
   470
wenzelm@233
   471
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   472
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   473
  let fun boolf [] = false
wenzelm@233
   474
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   475
  in boolf end;
wenzelm@233
   476
wenzelm@233
   477
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   478
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   479
  let fun boolf [] = true
wenzelm@233
   480
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   481
  in boolf end;
clasohm@0
   482
wenzelm@380
   483
(* flags *)
wenzelm@380
   484
wenzelm@380
   485
fun set flag = (flag := true; true);
wenzelm@380
   486
fun reset flag = (flag := false; false);
wenzelm@380
   487
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   488
wenzelm@9118
   489
fun change r f = r := f (! r);
wenzelm@9118
   490
wenzelm@18712
   491
(*temporarily set flag during execution*)
wenzelm@2978
   492
fun setmp flag value f x =
wenzelm@2958
   493
  let
wenzelm@2958
   494
    val orig_value = ! flag;
wenzelm@18712
   495
    val _ = flag := value;
wenzelm@18712
   496
    val result = capture f x;
wenzelm@18712
   497
    val _ = flag := orig_value;
wenzelm@18712
   498
  in release result end;
wenzelm@2958
   499
wenzelm@11853
   500
(* conditional execution *)
wenzelm@11853
   501
wenzelm@11853
   502
fun conditional b f = if b then f () else ();
wenzelm@11853
   503
webertj@19567
   504
(* convert a bool to a string *)
webertj@19567
   505
webertj@19567
   506
fun string_of_bool b = if b then "true" else "false";
wenzelm@11853
   507
wenzelm@233
   508
wenzelm@233
   509
(** lists **)
wenzelm@233
   510
skalberg@15570
   511
exception UnequalLengths;
wenzelm@233
   512
wenzelm@233
   513
fun cons x xs = x :: xs;
wenzelm@5285
   514
fun single x = [x];
wenzelm@233
   515
wenzelm@19273
   516
fun singleton f x = (case f [x] of [y] => y | _ => raise Empty);
wenzelm@19273
   517
wenzelm@4629
   518
fun append xs ys = xs @ ys;
wenzelm@4629
   519
wenzelm@5904
   520
fun apply [] x = x
wenzelm@5904
   521
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   522
wenzelm@233
   523
wenzelm@233
   524
(* fold *)
wenzelm@233
   525
wenzelm@16654
   526
fun fold f =
wenzelm@16654
   527
  let
wenzelm@16654
   528
    fun fold_aux [] y = y
wenzelm@16654
   529
      | fold_aux (x :: xs) y = fold_aux xs (f x y);
wenzelm@16654
   530
  in fold_aux end;
wenzelm@15760
   531
wenzelm@16654
   532
fun fold_rev f =
wenzelm@16654
   533
  let
wenzelm@16654
   534
    fun fold_aux [] y = y
wenzelm@16654
   535
      | fold_aux (x :: xs) y = f x (fold_aux xs y);
wenzelm@16654
   536
  in fold_aux end;
wenzelm@16654
   537
haftmann@16869
   538
fun fold_map f =
haftmann@16691
   539
  let
haftmann@16691
   540
    fun fold_aux [] y = ([], y)
haftmann@16691
   541
      | fold_aux (x :: xs) y =
haftmann@16691
   542
          let
wenzelm@16705
   543
            val (x', y') = f x y;
wenzelm@16705
   544
            val (xs', y'') = fold_aux xs y';
haftmann@16691
   545
          in (x' :: xs', y'') end;
haftmann@16691
   546
  in fold_aux end;
haftmann@16691
   547
wenzelm@233
   548
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   549
wenzelm@233
   550
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   551
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   552
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   553
  let fun itl (e, [])  = e
wenzelm@233
   554
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   555
  in  itl end;
wenzelm@233
   556
wenzelm@233
   557
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   558
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   559
fun foldr f (l, e) =
wenzelm@233
   560
  let fun itr [] = e
wenzelm@233
   561
        | itr (a::l) = f(a, itr l)
wenzelm@233
   562
  in  itr l  end;
wenzelm@233
   563
wenzelm@233
   564
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   565
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   566
fun foldr1 f l =
wenzelm@4181
   567
  let fun itr [x] = x
wenzelm@233
   568
        | itr (x::l) = f(x, itr l)
wenzelm@233
   569
  in  itr l  end;
wenzelm@233
   570
haftmann@18050
   571
fun fold_index f =
haftmann@18050
   572
  let
haftmann@18514
   573
    fun fold_aux _ [] y = y
haftmann@18050
   574
      | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
haftmann@18050
   575
  in fold_aux 0 end;
wenzelm@14792
   576
wenzelm@16705
   577
fun foldl_map f =
wenzelm@16705
   578
  let
wenzelm@16705
   579
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   580
      | fold_aux (x, y :: ys) =
wenzelm@16705
   581
          let
wenzelm@16705
   582
            val (x', y') = f (x, y);
wenzelm@16705
   583
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   584
          in (x'', y' :: ys') end;
wenzelm@16705
   585
  in fold_aux end;
wenzelm@16705
   586
wenzelm@233
   587
wenzelm@233
   588
(* basic list functions *)
wenzelm@233
   589
wenzelm@19483
   590
fun maps f [] = []
wenzelm@19483
   591
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   592
wenzelm@19011
   593
fun chop 0 xs = ([], xs)
wenzelm@19011
   594
  | chop _ [] = ([], [])
wenzelm@19011
   595
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   596
wenzelm@233
   597
(*take the first n elements from a list*)
wenzelm@233
   598
fun take (n, []) = []
wenzelm@233
   599
  | take (n, x :: xs) =
wenzelm@233
   600
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   601
wenzelm@233
   602
(*drop the first n elements from a list*)
wenzelm@233
   603
fun drop (n, []) = []
wenzelm@233
   604
  | drop (n, x :: xs) =
wenzelm@233
   605
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   606
nipkow@4713
   607
fun dropwhile P [] = []
nipkow@4713
   608
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   609
wenzelm@233
   610
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   611
  raise Subscript if list too short*)
haftmann@18011
   612
fun nth xs i = List.nth (xs, i);
wenzelm@233
   613
wenzelm@18461
   614
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   615
haftmann@18011
   616
(*update nth element*)
haftmann@18011
   617
fun nth_update (n, x) xs =
wenzelm@19474
   618
  (case chop n xs of
wenzelm@19474
   619
    (_, []) => raise Subscript
wenzelm@19474
   620
  | (prfx, _ :: sffx') => prfx @ (x :: sffx'));
haftmann@18011
   621
haftmann@18011
   622
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   623
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   624
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   625
haftmann@18514
   626
fun map_index f =
haftmann@18514
   627
  let
haftmann@18514
   628
    fun mapp _ [] = []
haftmann@18514
   629
      | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
haftmann@18514
   630
  in mapp 0 end;
haftmann@18514
   631
skalberg@15570
   632
val last_elem = List.last;
wenzelm@233
   633
wenzelm@3762
   634
(*rear decomposition*)
skalberg@15570
   635
fun split_last [] = raise Empty
wenzelm@3762
   636
  | split_last [x] = ([], x)
wenzelm@3762
   637
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   638
wenzelm@4212
   639
(*find the position of an element in a list*)
wenzelm@4212
   640
fun find_index pred =
wenzelm@4212
   641
  let fun find _ [] = ~1
wenzelm@4212
   642
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   643
  in find 0 end;
wenzelm@3762
   644
wenzelm@4224
   645
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   646
wenzelm@4212
   647
(*find first element satisfying predicate*)
skalberg@15531
   648
fun find_first _ [] = NONE
wenzelm@4212
   649
  | find_first pred (x :: xs) =
skalberg@15531
   650
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   651
wenzelm@4916
   652
(*get first element by lookup function*)
skalberg@15531
   653
fun get_first _ [] = NONE
wenzelm@4916
   654
  | get_first f (x :: xs) =
wenzelm@4916
   655
      (case f x of
skalberg@15531
   656
        NONE => get_first f xs
wenzelm@4916
   657
      | some => some);
wenzelm@4916
   658
haftmann@19233
   659
fun get_index f =
haftmann@19233
   660
  let
haftmann@19233
   661
    fun get _ [] = NONE
wenzelm@19461
   662
      | get i (x :: xs) =
haftmann@19233
   663
          case f x
wenzelm@19461
   664
           of NONE => get (i + 1) xs
haftmann@19233
   665
            | SOME y => SOME (i, y)
haftmann@19233
   666
  in get 0 end;
haftmann@19233
   667
haftmann@19454
   668
fun eq_list _ ([], []) = true
wenzelm@19461
   669
  | eq_list eq (x :: xs, y :: ys) = eq (x, y) andalso eq_list eq (xs, ys)
haftmann@19454
   670
  | eq_list _ _ = false;
haftmann@19454
   671
skalberg@15531
   672
val flat = List.concat;
wenzelm@233
   673
wenzelm@12136
   674
fun unflat (xs :: xss) ys =
wenzelm@19424
   675
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   676
      in ps :: unflat xss qs end
wenzelm@12136
   677
  | unflat [] [] = []
skalberg@15570
   678
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   679
haftmann@18441
   680
fun burrow f xss =
haftmann@18359
   681
  unflat xss ((f o flat) xss);
haftmann@18359
   682
haftmann@18549
   683
fun fold_burrow f xss s =
haftmann@18549
   684
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   685
wenzelm@233
   686
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   687
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   688
val seq = List.app;
wenzelm@233
   689
wenzelm@233
   690
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   691
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   692
  | separate _ xs = xs;
wenzelm@233
   693
wenzelm@233
   694
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   695
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   696
  let fun rep (0, xs) = xs
wenzelm@233
   697
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   698
  in
skalberg@15570
   699
    if n < 0 then raise Subscript
wenzelm@233
   700
    else rep (n, [])
wenzelm@233
   701
  end;
wenzelm@233
   702
wenzelm@14926
   703
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   704
wenzelm@4248
   705
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   706
fun multiply [] _ = []
wenzelm@18148
   707
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   708
wenzelm@14792
   709
(*direct product*)
wenzelm@14792
   710
fun product _ [] = []
wenzelm@14792
   711
  | product [] _ = []
wenzelm@14792
   712
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   713
wenzelm@233
   714
wenzelm@233
   715
(* filter *)
wenzelm@233
   716
wenzelm@233
   717
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   718
val filter = List.filter;
clasohm@0
   719
fun filter_out f = filter (not o f);
wenzelm@19483
   720
val map_filter = List.mapPartial;
wenzelm@233
   721
wenzelm@233
   722
wenzelm@233
   723
(* lists of pairs *)
wenzelm@233
   724
skalberg@15570
   725
exception UnequalLengths;
skalberg@15570
   726
haftmann@18330
   727
fun map2 _ [] [] = []
haftmann@18330
   728
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   729
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   730
haftmann@18330
   731
fun fold2 f =
haftmann@18330
   732
  let
haftmann@18330
   733
    fun fold_aux [] [] z = z
haftmann@18330
   734
      | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
haftmann@18330
   735
      | fold_aux _ _ _ = raise UnequalLengths;
haftmann@18330
   736
  in fold_aux end;
wenzelm@380
   737
wenzelm@4956
   738
wenzelm@233
   739
(*combine two lists forming a list of pairs:
wenzelm@233
   740
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   741
fun [] ~~ [] = []
wenzelm@233
   742
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   743
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   744
wenzelm@233
   745
(*inverse of ~~; the old 'split':
wenzelm@233
   746
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   747
val split_list = ListPair.unzip;
wenzelm@233
   748
haftmann@18330
   749
fun equal_lists eq (xs, ys) =
haftmann@18330
   750
  let
haftmann@18330
   751
    fun eq' [] [] = true
haftmann@18330
   752
      | eq' (x :: xs) (y :: ys) = eq (x, y) andalso eq' xs ys
haftmann@18330
   753
  in length xs = length ys andalso eq' xs ys end;
wenzelm@7468
   754
wenzelm@233
   755
wenzelm@233
   756
(* prefixes, suffixes *)
wenzelm@233
   757
haftmann@18441
   758
fun is_prefix _ [] _ = true
haftmann@18441
   759
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   760
  | is_prefix eq _ _ = false;
wenzelm@233
   761
wenzelm@233
   762
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   763
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   764
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   765
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   766
        | take (rxs, x :: xs) =
wenzelm@255
   767
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   768
  in  take([], xs)  end;
wenzelm@233
   769
wenzelm@233
   770
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   771
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   772
fun take_suffix _ [] = ([], [])
wenzelm@233
   773
  | take_suffix pred (x :: xs) =
wenzelm@233
   774
      (case take_suffix pred xs of
wenzelm@233
   775
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   776
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   777
wenzelm@12249
   778
fun prefixes1 [] = []
wenzelm@12249
   779
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   780
wenzelm@19011
   781
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   782
wenzelm@12249
   783
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   784
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   785
wenzelm@233
   786
wenzelm@233
   787
(** integers **)
wenzelm@233
   788
wenzelm@16439
   789
fun gcd (x, y) =
paulson@15965
   790
  let fun gxd x y : IntInf.int =
nipkow@10692
   791
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   792
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   793
wenzelm@16439
   794
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   795
wenzelm@2958
   796
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   797
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   798
wenzelm@233
   799
wenzelm@233
   800
(* lists of integers *)
wenzelm@233
   801
wenzelm@233
   802
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   803
fun (from upto to) =
wenzelm@233
   804
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   805
wenzelm@233
   806
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   807
fun (from downto to) =
wenzelm@233
   808
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   809
wenzelm@233
   810
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   811
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   812
  | downto0 ([], n) = n = ~1;
wenzelm@233
   813
wenzelm@233
   814
wenzelm@233
   815
(* convert integers to strings *)
wenzelm@233
   816
wenzelm@233
   817
(*expand the number in the given base;
wenzelm@233
   818
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   819
fun radixpand (base, num) : int list =
wenzelm@233
   820
  let
wenzelm@233
   821
    fun radix (n, tail) =
wenzelm@233
   822
      if n < base then n :: tail
wenzelm@233
   823
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   824
  in radix (num, []) end;
wenzelm@233
   825
wenzelm@233
   826
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   827
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   828
fun radixstring (base, zerochar, num) =
wenzelm@233
   829
  let val offset = ord zerochar;
wenzelm@233
   830
      fun chrof n = chr (offset + n)
wenzelm@233
   831
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   832
wenzelm@233
   833
paulson@3407
   834
val string_of_int = Int.toString;
wenzelm@233
   835
paulson@3407
   836
fun string_of_indexname (a,0) = a
paulson@3407
   837
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   838
wenzelm@233
   839
wenzelm@14826
   840
(* read integers *)
wenzelm@14826
   841
wenzelm@14826
   842
fun read_radixint (radix: int, cs) : int * string list =
wenzelm@14826
   843
  let val zero = ord"0"
wenzelm@14826
   844
      val limit = zero+radix
wenzelm@14826
   845
      fun scan (num,[]) = (num,[])
wenzelm@14826
   846
        | scan (num, c::cs) =
wenzelm@14826
   847
              if  zero <= ord c  andalso  ord c < limit
wenzelm@14826
   848
              then scan(radix*num + ord c - zero, cs)
wenzelm@14826
   849
              else (num, c::cs)
wenzelm@14826
   850
  in  scan(0,cs)  end;
wenzelm@14826
   851
wenzelm@14826
   852
fun read_int cs = read_radixint (10, cs);
wenzelm@14826
   853
wenzelm@14826
   854
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
wenzelm@14826
   855
webertj@19567
   856
(* convert a list to a string *)
webertj@19567
   857
webertj@19567
   858
fun string_of_list f xs =
webertj@19567
   859
  let val fxs = separate ", " (map f xs)
webertj@19567
   860
  in  String.concat ("[" :: fxs @ ["]"])  end;
wenzelm@14826
   861
wenzelm@14826
   862
wenzelm@233
   863
(** strings **)
wenzelm@233
   864
wenzelm@16188
   865
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   866
haftmann@18011
   867
fun nth_string str i =
wenzelm@6959
   868
  (case try String.substring (str, i, 1) of
skalberg@15531
   869
    SOME s => s
skalberg@15570
   870
  | NONE => raise Subscript);
wenzelm@6312
   871
wenzelm@16188
   872
fun fold_string f str x0 =
wenzelm@6282
   873
  let
wenzelm@6282
   874
    val n = size str;
wenzelm@16188
   875
    fun iter (x, i) =
wenzelm@16188
   876
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   877
  in iter (x0, 0) end;
wenzelm@6282
   878
wenzelm@14968
   879
fun exists_string pred str =
wenzelm@14968
   880
  let
wenzelm@14968
   881
    val n = size str;
wenzelm@14968
   882
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   883
  in ex 0 end;
wenzelm@6312
   884
wenzelm@16188
   885
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   886
lcp@512
   887
(*enclose in brackets*)
lcp@512
   888
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   889
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   890
wenzelm@233
   891
(*simple quoting (does not escape special chars)*)
lcp@512
   892
val quote = enclose "\"" "\"";
wenzelm@233
   893
wenzelm@4212
   894
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   895
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   896
wenzelm@255
   897
val commas = space_implode ", ";
wenzelm@380
   898
val commas_quote = commas o map quote;
wenzelm@255
   899
wenzelm@233
   900
(*concatenate messages, one per line, into a string*)
wenzelm@255
   901
val cat_lines = space_implode "\n";
wenzelm@233
   902
wenzelm@4212
   903
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   904
fun space_explode _ "" = []
wenzelm@3832
   905
  | space_explode sep str =
wenzelm@3832
   906
      let
wenzelm@3832
   907
        fun expl chs =
wenzelm@19301
   908
          (case take_prefix (fn s => s <> sep) chs of
wenzelm@3832
   909
            (cs, []) => [implode cs]
wenzelm@3832
   910
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   911
      in expl (explode str) end;
wenzelm@3832
   912
wenzelm@3832
   913
val split_lines = space_explode "\n";
wenzelm@3832
   914
wenzelm@14826
   915
fun prefix_lines "" txt = txt
wenzelm@14826
   916
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   917
wenzelm@7712
   918
fun untabify chs =
wenzelm@7712
   919
  let
wenzelm@7712
   920
    val tab_width = 8;
wenzelm@7712
   921
wenzelm@7712
   922
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   923
      | untab (pos, "\t") =
wenzelm@9118
   924
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   925
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   926
  in
wenzelm@19301
   927
    if not (exists (fn c => c = "\t") chs) then chs
wenzelm@7712
   928
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   929
  end;
wenzelm@7712
   930
wenzelm@18681
   931
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   932
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   933
wenzelm@18681
   934
fun unprefix prfx s =
wenzelm@18681
   935
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   936
  else raise Fail "unprefix";
wenzelm@18681
   937
wenzelm@16188
   938
fun unsuffix sffx s =
wenzelm@17061
   939
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   940
  else raise Fail "unsuffix";
wenzelm@5285
   941
wenzelm@10951
   942
fun replicate_string 0 _ = ""
wenzelm@10951
   943
  | replicate_string 1 a = a
wenzelm@10951
   944
  | replicate_string k a =
wenzelm@10951
   945
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   946
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   947
wenzelm@3832
   948
wenzelm@233
   949
wenzelm@16492
   950
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   951
wenzelm@18923
   952
(*canonical member, insert, remove*)
wenzelm@18923
   953
fun member eq list x =
wenzelm@18923
   954
  let
wenzelm@18923
   955
    fun memb [] = false
wenzelm@18923
   956
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   957
  in memb list end;
berghofe@1576
   958
wenzelm@18923
   959
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   960
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   961
wenzelm@19301
   962
fun subtract eq = fold (remove eq);
wenzelm@19301
   963
wenzelm@18923
   964
fun merge _ ([], ys) = ys
wenzelm@18923
   965
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   966
wenzelm@18923
   967
(*old-style infixes*)
wenzelm@18923
   968
fun x mem xs = member (op =) xs x;
wenzelm@18923
   969
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   970
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   971
wenzelm@18923
   972
fun x ins xs = insert (op =) x xs;
wenzelm@18989
   973
fun (x: int) ins_int xs = insert (op =) x xs;
wenzelm@18989
   974
fun (x: string) ins_string xs = insert (op =) x xs;
wenzelm@18989
   975
wenzelm@233
   976
wenzelm@233
   977
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   978
fun xs union [] = xs
wenzelm@233
   979
  | [] union ys = ys
wenzelm@233
   980
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   981
paulson@2175
   982
(*union of sets, optimized version for ints*)
berghofe@1576
   983
fun (xs:int list) union_int [] = xs
berghofe@1576
   984
  | [] union_int ys = ys
berghofe@1576
   985
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   986
paulson@2175
   987
(*union of sets, optimized version for strings*)
berghofe@1576
   988
fun (xs:string list) union_string [] = xs
berghofe@1576
   989
  | [] union_string ys = ys
berghofe@1576
   990
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   991
clasohm@0
   992
(*generalized union*)
wenzelm@233
   993
fun gen_union eq (xs, []) = xs
wenzelm@233
   994
  | gen_union eq ([], ys) = ys
wenzelm@18923
   995
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   996
wenzelm@233
   997
wenzelm@233
   998
(*intersection*)
wenzelm@233
   999
fun [] inter ys = []
wenzelm@233
  1000
  | (x :: xs) inter ys =
wenzelm@233
  1001
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
  1002
paulson@2175
  1003
(*intersection, optimized version for ints*)
berghofe@1576
  1004
fun ([]:int list) inter_int ys = []
berghofe@1576
  1005
  | (x :: xs) inter_int ys =
berghofe@1576
  1006
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
  1007
paulson@2175
  1008
(*intersection, optimized version for strings *)
berghofe@1576
  1009
fun ([]:string list) inter_string ys = []
berghofe@1576
  1010
  | (x :: xs) inter_string ys =
berghofe@1576
  1011
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
  1012
paulson@7090
  1013
(*generalized intersection*)
paulson@7090
  1014
fun gen_inter eq ([], ys) = []
wenzelm@12284
  1015
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
  1016
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
  1017
      else gen_inter eq (xs, ys);
paulson@7090
  1018
wenzelm@233
  1019
wenzelm@233
  1020
(*subset*)
wenzelm@233
  1021
fun [] subset ys = true
wenzelm@233
  1022
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
  1023
paulson@2175
  1024
(*subset, optimized version for ints*)
wenzelm@16439
  1025
fun ([]: int list) subset_int ys = true
berghofe@1576
  1026
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
  1027
paulson@2175
  1028
(*subset, optimized version for strings*)
wenzelm@16439
  1029
fun ([]: string list) subset_string ys = true
berghofe@1576
  1030
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
  1031
wenzelm@4363
  1032
(*set equality*)
wenzelm@4363
  1033
fun eq_set (xs, ys) =
wenzelm@4363
  1034
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
  1035
paulson@2182
  1036
(*set equality for strings*)
wenzelm@16439
  1037
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
  1038
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
  1039
wenzelm@18923
  1040
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
  1041
wenzelm@19301
  1042
fun gen_eq_set eq (xs, ys) =
wenzelm@19301
  1043
  equal_lists eq (xs, ys) orelse
wenzelm@19301
  1044
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
  1045
wenzelm@265
  1046
wenzelm@233
  1047
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
  1048
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
  1049
  | [] \ x = [];
wenzelm@233
  1050
paulson@2243
  1051
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
  1052
wenzelm@233
  1053
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
  1054
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@18923
  1055
fun gen_rems eq (xs, ys) = filter_out (member eq ys) xs;
wenzelm@233
  1056
wenzelm@19046
  1057
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@19046
  1058
fun findrep [] = []
wenzelm@19046
  1059
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@19046
  1060
wenzelm@19046
  1061
wenzelm@233
  1062
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
  1063
  first of equal elements*)
wenzelm@19046
  1064
fun distinct eq lst =
wenzelm@233
  1065
  let
wenzelm@233
  1066
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
  1067
      | dist (rev_seen, x :: xs) =
wenzelm@18923
  1068
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
  1069
          else dist (x :: rev_seen, xs);
wenzelm@19046
  1070
  in dist ([], lst) end;
wenzelm@233
  1071
wenzelm@255
  1072
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
  1073
  order, takes first of equal elements*)
wenzelm@18966
  1074
fun duplicates eq lst =
wenzelm@255
  1075
  let
wenzelm@255
  1076
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
  1077
      | dups (rev_dups, x :: xs) =
wenzelm@18923
  1078
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
  1079
            dups (rev_dups, xs)
wenzelm@255
  1080
          else dups (x :: rev_dups, xs);
wenzelm@18966
  1081
  in dups ([], lst) end;
wenzelm@255
  1082
wenzelm@16878
  1083
fun has_duplicates eq =
wenzelm@16878
  1084
  let
wenzelm@16878
  1085
    fun dups [] = false
wenzelm@16878
  1086
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
  1087
  in dups end;
wenzelm@16878
  1088
wenzelm@255
  1089
haftmann@19119
  1090
(** association lists -- legacy operations **)
wenzelm@233
  1091
wenzelm@12284
  1092
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1093
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1094
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1095
wenzelm@12284
  1096
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
haftmann@17498
  1097
fun merge_alists al = gen_merge_lists (eq_fst (op =)) al;
clasohm@0
  1098
clasohm@0
  1099
wenzelm@233
  1100
(** balanced trees **)
wenzelm@233
  1101
wenzelm@233
  1102
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1103
wenzelm@233
  1104
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1105
fun fold_bal f [x] = x
wenzelm@233
  1106
  | fold_bal f [] = raise Balance
wenzelm@233
  1107
  | fold_bal f xs =
wenzelm@19474
  1108
      let val (ps, qs) = chop (length xs div 2) xs
nipkow@13629
  1109
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1110
wenzelm@233
  1111
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1112
fun access_bal (f, g, x) n i =
wenzelm@233
  1113
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1114
          if n=1 then x else
wenzelm@233
  1115
          let val n2 = n div 2
wenzelm@233
  1116
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1117
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1118
          end
wenzelm@233
  1119
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1120
wenzelm@233
  1121
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1122
fun accesses_bal (f, g, x) n =
wenzelm@233
  1123
  let fun acc n =
wenzelm@233
  1124
          if n=1 then [x] else
wenzelm@233
  1125
          let val n2 = n div 2
wenzelm@233
  1126
              val acc2 = acc n2
wenzelm@233
  1127
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1128
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1129
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1130
wenzelm@233
  1131
wenzelm@233
  1132
wenzelm@2506
  1133
(** orders **)
wenzelm@2506
  1134
wenzelm@18966
  1135
fun is_equal EQUAL = true
wenzelm@18966
  1136
  | is_equal _ = false;
wenzelm@18966
  1137
wenzelm@4445
  1138
fun rev_order LESS = GREATER
wenzelm@4445
  1139
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1140
  | rev_order GREATER = LESS;
wenzelm@4445
  1141
wenzelm@4479
  1142
(*assume rel is a linear strict order*)
wenzelm@4445
  1143
fun make_ord rel (x, y) =
wenzelm@4445
  1144
  if rel (x, y) then LESS
wenzelm@4445
  1145
  else if rel (y, x) then GREATER
wenzelm@4445
  1146
  else EQUAL;
wenzelm@4445
  1147
haftmann@18452
  1148
fun eq_ord ord xy =
haftmann@18452
  1149
  case ord xy
haftmann@18452
  1150
   of EQUAL => true
haftmann@18452
  1151
    | _ => false;
haftmann@18452
  1152
wenzelm@15051
  1153
val int_ord = Int.compare;
wenzelm@15051
  1154
val string_ord = String.compare;
wenzelm@2506
  1155
wenzelm@16676
  1156
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1157
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1158
wenzelm@16492
  1159
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1160
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1161
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1162
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1163
wenzelm@4343
  1164
(*lexicographic product*)
wenzelm@4343
  1165
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1166
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1167
wenzelm@4343
  1168
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1169
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1170
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1171
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1172
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1173
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1174
wenzelm@4343
  1175
(*lexicographic product of lists*)
wenzelm@4343
  1176
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1177
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1178
wenzelm@2506
  1179
wenzelm@4621
  1180
(* sorting *)
wenzelm@4621
  1181
wenzelm@18427
  1182
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
  1183
fun quicksort unique ord =
wenzelm@4621
  1184
  let
wenzelm@16878
  1185
    fun qsort [] = []
wenzelm@16878
  1186
      | qsort (xs as [_]) = xs
wenzelm@18427
  1187
      | qsort (xs as [x, y]) =
wenzelm@18427
  1188
          (case ord (x, y) of
wenzelm@18427
  1189
            LESS => xs
wenzelm@18427
  1190
          | EQUAL => if unique then [x] else xs
wenzelm@18427
  1191
          | GREATER => [y, x])
wenzelm@16878
  1192
      | qsort xs =
haftmann@18011
  1193
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
  1194
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1195
    and part _ [] = ([], [], [])
wenzelm@4621
  1196
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1197
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
  1198
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
  1199
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
  1200
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1201
  in qsort end;
wenzelm@4621
  1202
wenzelm@18427
  1203
fun sort ord = quicksort false ord;
wenzelm@18427
  1204
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
  1205
wenzelm@4621
  1206
val sort_strings = sort string_ord;
wenzelm@4621
  1207
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1208
wenzelm@4621
  1209
wenzelm@2506
  1210
berghofe@14106
  1211
(** random numbers **)
berghofe@14106
  1212
berghofe@14106
  1213
exception RANDOM;
berghofe@14106
  1214
berghofe@14618
  1215
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1216
berghofe@14106
  1217
local
berghofe@14106
  1218
  val a = 16807.0;
berghofe@14106
  1219
  val m = 2147483647.0;
berghofe@14106
  1220
  val random_seed = ref 1.0;
berghofe@14106
  1221
in
berghofe@14106
  1222
berghofe@14106
  1223
fun random () =
berghofe@14106
  1224
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1225
  in (random_seed := r; r) end;
berghofe@14106
  1226
berghofe@14106
  1227
end;
berghofe@14106
  1228
berghofe@14106
  1229
fun random_range l h =
berghofe@14106
  1230
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1231
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1232
haftmann@18011
  1233
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1234
berghofe@14106
  1235
fun frequency xs =
berghofe@14106
  1236
  let
berghofe@14106
  1237
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1238
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1239
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1240
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1241
berghofe@14106
  1242
wenzelm@14826
  1243
(** current directory **)
wenzelm@233
  1244
paulson@2243
  1245
val cd = OS.FileSys.chDir;
wenzelm@2317
  1246
val pwd = OS.FileSys.getDir;
paulson@2243
  1247
berghofe@3606
  1248
wenzelm@4621
  1249
(** misc **)
wenzelm@233
  1250
clasohm@0
  1251
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1252
  Preserves order of elements in both lists.*)
skalberg@15570
  1253
val partition = List.partition;
clasohm@0
  1254
clasohm@0
  1255
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@16842
  1256
  let
wenzelm@16842
  1257
    fun part [] = []
wenzelm@16842
  1258
      | part (x :: ys) =
wenzelm@16842
  1259
          let val (xs, xs') = partition (fn y => eq (x, y)) ys
wenzelm@16842
  1260
          in (x::xs)::(part xs') end
wenzelm@16842
  1261
  in part end;
clasohm@0
  1262
clasohm@0
  1263
wenzelm@233
  1264
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1265
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1266
fun partition_list p i j =
wenzelm@233
  1267
  let fun part k xs =
wenzelm@233
  1268
            if k>j then
clasohm@0
  1269
              (case xs of [] => []
skalberg@15570
  1270
                         | _ => raise Fail "partition_list")
clasohm@0
  1271
            else
wenzelm@233
  1272
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1273
            in  ns :: part(k+1)rest  end
clasohm@0
  1274
  in  part i end;
clasohm@0
  1275
clasohm@0
  1276
wenzelm@233
  1277
(* generating identifiers *)
clasohm@0
  1278
paulson@4063
  1279
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1280
local
paulson@4063
  1281
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1282
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1283
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1284
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1285
             else if i=62 then "_"
wenzelm@5904
  1286
             else  (*i=63*)    "'";
paulson@4063
  1287
paulson@4063
  1288
val charVec = Vector.tabulate (64, char);
paulson@4063
  1289
wenzelm@5904
  1290
fun newid n =
wenzelm@5904
  1291
  let
wenzelm@4284
  1292
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1293
wenzelm@4284
  1294
val seedr = ref 0;
clasohm@0
  1295
paulson@4063
  1296
in
wenzelm@4284
  1297
wenzelm@12346
  1298
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1299
paulson@4063
  1300
end;
paulson@4063
  1301
paulson@4063
  1302
wenzelm@233
  1303
(* lexical scanning *)
clasohm@0
  1304
wenzelm@233
  1305
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1306
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1307
fun scanwords is_let cs =
clasohm@0
  1308
  let fun scan1 [] = []
wenzelm@233
  1309
        | scan1 cs =
wenzelm@233
  1310
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1311
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1312
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1313
wenzelm@4212
  1314
wenzelm@16439
  1315
(* stamps and serial numbers *)
wenzelm@16439
  1316
wenzelm@16439
  1317
type stamp = unit ref;
wenzelm@16439
  1318
val stamp: unit -> stamp = ref;
wenzelm@16439
  1319
wenzelm@16439
  1320
type serial = int;
wenzelm@16439
  1321
local val count = ref 0
wenzelm@16439
  1322
in fun serial () = inc count end;
wenzelm@16439
  1323
wenzelm@19512
  1324
val serial_string = string_of_int o serial;
wenzelm@19512
  1325
wenzelm@16535
  1326
wenzelm@16535
  1327
(* generic objects *)
wenzelm@16535
  1328
wenzelm@16535
  1329
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1330
  constructors at any time*)
wenzelm@16535
  1331
structure Object = struct type T = exn end;
wenzelm@16535
  1332
clasohm@1364
  1333
end;
clasohm@1364
  1334
wenzelm@15745
  1335
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1336
open BasicLibrary;