src/Pure/library.ML
author paulson
Mon Oct 10 15:35:29 2005 +0200 (2005-10-10)
changeset 17819 1241e5d31d5b
parent 17756 d4a35f82fbb4
child 17822 3830b0a41d51
permissions -rw-r--r--
small tidy-up of utility functions
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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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rational numbers, 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 prefix \ \\ 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 if_none: 'a option -> 'a -> 'a
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  val is_some: 'a option -> bool
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  val is_none: 'a option -> bool
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  exception EXCEPTION of exn * string
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  exception ERROR
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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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  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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  (*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 swap: 'a * 'b -> 'b * 'a
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  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
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  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
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  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
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  (*booleans*)
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  val equal: ''a -> ''a -> bool
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  val not_equal: ''a -> ''a -> bool
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  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val exists: ('a -> bool) -> 'a list -> bool
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  val forall: ('a -> bool) -> 'a list -> bool
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  val set: bool ref -> bool
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  val reset: bool ref -> bool
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  val toggle: bool ref -> bool
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  val change: 'a ref -> ('a -> 'a) -> unit
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  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val conditional: bool -> (unit -> unit) -> unit
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  (*lists*)
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  exception UnequalLengths
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  val cons: 'a -> 'a list -> 'a list
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  val single: 'a -> '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 foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val foldln: ('a * int -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val unflat: 'a list list -> 'b list -> 'b list list
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  val splitAt: int * 'a list -> 'a list * 'a list
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  val dropwhile: ('a -> bool) -> 'a list -> 'a list
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  val map_nth_elem: int -> ('a -> 'a) -> 'a list -> 'a list
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  val split_last: 'a list -> 'a list * 'a
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  val nth_update: 'a -> int * 'a list -> 'a list
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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_first: ('a -> 'b option) -> 'a list -> 'b option
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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 map2: ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list
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  val exists2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val forall2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val seq2: ('a * 'b -> unit) -> 'a list * 'b list -> unit
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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 equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val prefix: ''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 suffixes1: '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_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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  (*rational numbers*)
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  type rat
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  exception RAT of string
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  val rep_rat: rat -> IntInf.int * IntInf.int
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  val ratge0: rat -> bool
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  val ratgt0: rat -> bool
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  val ratle: rat * rat -> bool
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  val ratlt: rat * rat -> bool
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  val ratadd: rat * rat -> rat
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  val ratmul: rat * rat -> rat
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  val ratinv: rat -> rat
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  val int_ratdiv: IntInf.int * IntInf.int -> rat
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  val ratneg: rat -> rat
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  val rat_of_int: int -> rat
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  val rat_of_intinf: IntInf.int -> rat
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  val rat0: rat
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  (*strings*)
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  val nth_elem_string: int * string -> 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 suffix: string -> string -> string
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  val unsuffix: string -> string -> string
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  val unprefix: 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 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 gen_mem: ('a * 'b -> bool) -> 'a * 'b 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 gen_ins: ('a * 'a -> bool) -> 'a * 'a list -> 'a list
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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 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 \ : ''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 gen_distinct: ('a * 'a -> bool) -> 'a list -> 'a list
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  val distinct: ''a list -> ''a list
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  val findrep: ''a list -> ''a list
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  val gen_duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
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  val duplicates: ''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 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_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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  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 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_strings: string list -> string list
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  val sort_wrt: ('a -> string) -> 'a list -> 'a list
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  val unique_strings: string list -> string 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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  val scanwords: (string -> bool) -> string list -> string list
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  val string_of_pid: Posix.Process.pid -> string
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  type stamp
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  val stamp: unit -> stamp
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  type serial
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  val serial: unit -> serial
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  structure Object: sig type T end
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end;
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signature LIBRARY =
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sig
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  include BASIC_LIBRARY
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  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
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  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
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  val take: int * 'a list -> 'a list
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  val drop: int * 'a list -> 'a list
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  val nth_elem: int * 'a list -> 'a
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  val last_elem: 'a list -> 'a
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  val flat: 'a list list -> 'a list
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  val seq: ('a -> unit) -> 'a list -> unit
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  val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val mapfilter: ('a -> 'b option) -> 'a list -> 'b list
skalberg@15570
   290
end;
skalberg@15570
   291
wenzelm@15745
   292
structure Library: LIBRARY =
clasohm@1364
   293
struct
clasohm@0
   294
wenzelm@4995
   295
wenzelm@233
   296
(** functions **)
clasohm@0
   297
wenzelm@16842
   298
fun I x = x;
wenzelm@16842
   299
fun K x = fn _ => x;
wenzelm@233
   300
fun curry f x y = f (x, y);
wenzelm@233
   301
fun uncurry f (x, y) = f x y;
clasohm@0
   302
wenzelm@16705
   303
(*reverse application and structured results*)
wenzelm@16705
   304
fun x |> f = f x;
wenzelm@16705
   305
fun (x, y) |-> f = f x y;
wenzelm@16705
   306
fun (x, y) |>> f = (f x, y);
wenzelm@16705
   307
fun (x, y) ||> f = (x, f y);
wenzelm@16705
   308
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16705
   309
fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
wenzelm@16842
   310
wenzelm@16842
   311
(*reverse composition*)
haftmann@16780
   312
fun f #> g = g o f;
wenzelm@16842
   313
fun f #-> g = uncurry g o f;
wenzelm@16842
   314
haftmann@17141
   315
(*conditional application*)
wenzelm@17545
   316
fun b ? f = fn x => if b x then f x else x;
haftmann@17141
   317
wenzelm@16842
   318
(*view results*)
wenzelm@16842
   319
fun `f = fn x => (f x, x);
wenzelm@17545
   320
fun tap f = fn x => (f x; x);
wenzelm@380
   321
wenzelm@16721
   322
(*composition with multiple args*)
wenzelm@16721
   323
fun (f oo g) x y = f (g x y);
wenzelm@16721
   324
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   325
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   326
wenzelm@233
   327
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   328
fun funpow n f x =
wenzelm@233
   329
  let fun rep (0, x) = x
wenzelm@233
   330
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   331
  in rep (n, x) end;
wenzelm@160
   332
wenzelm@160
   333
wenzelm@233
   334
(** options **)
clasohm@0
   335
wenzelm@15670
   336
(*invalidate former constructors to prevent accidental use as match-all patterns!*)
wenzelm@15670
   337
datatype invalid = None of invalid;
wenzelm@15670
   338
exception OPTION of invalid;
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
(*strict!*)
wenzelm@15970
   352
fun if_none NONE y = y
wenzelm@15970
   353
  | if_none (SOME x) _ = x;
wenzelm@15970
   354
wenzelm@15970
   355
fun is_some (SOME _) = true
wenzelm@15970
   356
  | is_some NONE = false;
wenzelm@15970
   357
wenzelm@15970
   358
fun is_none (SOME _) = false
wenzelm@15970
   359
  | is_none NONE = true;
wenzelm@15970
   360
wenzelm@6959
   361
wenzelm@17341
   362
(* exceptions *)
wenzelm@17341
   363
wenzelm@17341
   364
exception EXCEPTION of exn * string;
wenzelm@6959
   365
wenzelm@6959
   366
exception ERROR;
wenzelm@6959
   367
skalberg@15531
   368
fun try f x = SOME (f x)
skalberg@15531
   369
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => NONE;
wenzelm@6959
   370
wenzelm@6959
   371
fun can f x = is_some (try f x);
wenzelm@4139
   372
wenzelm@4139
   373
wenzelm@14868
   374
datatype 'a result =
wenzelm@14868
   375
  Result of 'a |
wenzelm@14868
   376
  Exn of exn;
wenzelm@14868
   377
wenzelm@14868
   378
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   379
wenzelm@14868
   380
fun release (Result y) = y
wenzelm@14868
   381
  | release (Exn e) = raise e;
wenzelm@14868
   382
skalberg@15531
   383
fun get_result (Result x) = SOME x
skalberg@15531
   384
  | get_result _ = NONE;
wenzelm@14868
   385
skalberg@15531
   386
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   387
  | get_exn _ = NONE;
wenzelm@14868
   388
wenzelm@14868
   389
wenzelm@4139
   390
wenzelm@233
   391
(** pairs **)
wenzelm@233
   392
wenzelm@233
   393
fun pair x y = (x, y);
wenzelm@233
   394
fun rpair x y = (y, x);
wenzelm@233
   395
wenzelm@233
   396
fun fst (x, y) = x;
wenzelm@233
   397
fun snd (x, y) = y;
wenzelm@233
   398
haftmann@17498
   399
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   400
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
wenzelm@233
   401
wenzelm@233
   402
fun swap (x, y) = (y, x);
wenzelm@233
   403
wenzelm@4212
   404
(*apply function to components*)
wenzelm@233
   405
fun apfst f (x, y) = (f x, y);
wenzelm@233
   406
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   407
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   408
wenzelm@233
   409
wenzelm@233
   410
wenzelm@233
   411
(** booleans **)
wenzelm@233
   412
wenzelm@233
   413
(* equality *)
wenzelm@233
   414
wenzelm@233
   415
fun equal x y = x = y;
wenzelm@233
   416
fun not_equal x y = x <> y;
wenzelm@233
   417
wenzelm@233
   418
wenzelm@233
   419
(* operators for combining predicates *)
wenzelm@233
   420
wenzelm@16721
   421
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   422
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   423
wenzelm@233
   424
wenzelm@233
   425
(* predicates on lists *)
wenzelm@233
   426
wenzelm@233
   427
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   428
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   429
  let fun boolf [] = false
wenzelm@233
   430
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   431
  in boolf end;
wenzelm@233
   432
wenzelm@233
   433
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   434
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   435
  let fun boolf [] = true
wenzelm@233
   436
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   437
  in boolf end;
clasohm@0
   438
wenzelm@233
   439
wenzelm@380
   440
(* flags *)
wenzelm@380
   441
wenzelm@380
   442
fun set flag = (flag := true; true);
wenzelm@380
   443
fun reset flag = (flag := false; false);
wenzelm@380
   444
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   445
wenzelm@9118
   446
fun change r f = r := f (! r);
wenzelm@9118
   447
wenzelm@14826
   448
(*temporarily set flag, handling exceptions*)
wenzelm@2978
   449
fun setmp flag value f x =
wenzelm@2958
   450
  let
wenzelm@2958
   451
    val orig_value = ! flag;
wenzelm@2958
   452
    fun return y = (flag := orig_value; y);
wenzelm@2958
   453
  in
wenzelm@2958
   454
    flag := value;
wenzelm@2958
   455
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   456
  end;
wenzelm@2958
   457
wenzelm@380
   458
wenzelm@11853
   459
(* conditional execution *)
wenzelm@11853
   460
wenzelm@11853
   461
fun conditional b f = if b then f () else ();
wenzelm@11853
   462
wenzelm@11853
   463
wenzelm@233
   464
wenzelm@233
   465
(** lists **)
wenzelm@233
   466
skalberg@15570
   467
exception UnequalLengths;
wenzelm@233
   468
wenzelm@233
   469
fun cons x xs = x :: xs;
wenzelm@5285
   470
fun single x = [x];
wenzelm@233
   471
wenzelm@4629
   472
fun append xs ys = xs @ ys;
wenzelm@4629
   473
wenzelm@5904
   474
fun apply [] x = x
wenzelm@5904
   475
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   476
wenzelm@233
   477
wenzelm@233
   478
(* fold *)
wenzelm@233
   479
wenzelm@16654
   480
fun fold f =
wenzelm@16654
   481
  let
wenzelm@16654
   482
    fun fold_aux [] y = y
wenzelm@16654
   483
      | fold_aux (x :: xs) y = fold_aux xs (f x y);
wenzelm@16654
   484
  in fold_aux end;
wenzelm@15760
   485
wenzelm@16654
   486
fun fold_rev f =
wenzelm@16654
   487
  let
wenzelm@16654
   488
    fun fold_aux [] y = y
wenzelm@16654
   489
      | fold_aux (x :: xs) y = f x (fold_aux xs y);
wenzelm@16654
   490
  in fold_aux end;
wenzelm@16654
   491
haftmann@16869
   492
fun fold_map f =
haftmann@16691
   493
  let
haftmann@16691
   494
    fun fold_aux [] y = ([], y)
haftmann@16691
   495
      | fold_aux (x :: xs) y =
haftmann@16691
   496
          let
wenzelm@16705
   497
            val (x', y') = f x y;
wenzelm@16705
   498
            val (xs', y'') = fold_aux xs y';
haftmann@16691
   499
          in (x' :: xs', y'') end;
haftmann@16691
   500
  in fold_aux end;
haftmann@16691
   501
wenzelm@233
   502
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   503
wenzelm@233
   504
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   505
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   506
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   507
  let fun itl (e, [])  = e
wenzelm@233
   508
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   509
  in  itl end;
wenzelm@233
   510
wenzelm@233
   511
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   512
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   513
fun foldr f (l, e) =
wenzelm@233
   514
  let fun itr [] = e
wenzelm@233
   515
        | itr (a::l) = f(a, itr l)
wenzelm@233
   516
  in  itr l  end;
wenzelm@233
   517
wenzelm@233
   518
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   519
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   520
fun foldr1 f l =
wenzelm@4181
   521
  let fun itr [x] = x
wenzelm@233
   522
        | itr (x::l) = f(x, itr l)
wenzelm@233
   523
  in  itr l  end;
wenzelm@233
   524
wenzelm@15760
   525
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
wenzelm@14792
   526
wenzelm@16705
   527
fun foldl_map f =
wenzelm@16705
   528
  let
wenzelm@16705
   529
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   530
      | fold_aux (x, y :: ys) =
wenzelm@16705
   531
          let
wenzelm@16705
   532
            val (x', y') = f (x, y);
wenzelm@16705
   533
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   534
          in (x'', y' :: ys') end;
wenzelm@16705
   535
  in fold_aux end;
wenzelm@16705
   536
wenzelm@233
   537
wenzelm@233
   538
(* basic list functions *)
wenzelm@233
   539
wenzelm@233
   540
(*take the first n elements from a list*)
wenzelm@233
   541
fun take (n, []) = []
wenzelm@233
   542
  | take (n, x :: xs) =
wenzelm@233
   543
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   544
wenzelm@233
   545
(*drop the first n elements from a list*)
wenzelm@233
   546
fun drop (n, []) = []
wenzelm@233
   547
  | drop (n, x :: xs) =
wenzelm@233
   548
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   549
nipkow@13629
   550
fun splitAt(n,[]) = ([],[])
nipkow@13629
   551
  | splitAt(n,xs as x::ys) =
nipkow@13629
   552
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
nipkow@13629
   553
      else ([],xs)
nipkow@13629
   554
nipkow@4713
   555
fun dropwhile P [] = []
nipkow@4713
   556
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   557
wenzelm@233
   558
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   559
  raise EXCEPTION if list too short*)
skalberg@15570
   560
fun nth_elem (i,xs) = List.nth(xs,i);
wenzelm@233
   561
wenzelm@11773
   562
fun map_nth_elem 0 f (x :: xs) = f x :: xs
wenzelm@11773
   563
  | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs
skalberg@15570
   564
  | map_nth_elem _ _ [] = raise Subscript;
wenzelm@11773
   565
wenzelm@233
   566
(*last element of a list*)
skalberg@15570
   567
val last_elem = List.last;
wenzelm@233
   568
wenzelm@3762
   569
(*rear decomposition*)
skalberg@15570
   570
fun split_last [] = raise Empty
wenzelm@3762
   571
  | split_last [x] = ([], x)
wenzelm@3762
   572
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   573
wenzelm@4893
   574
(*update nth element*)
nipkow@13629
   575
fun nth_update x n_xs =
nipkow@13629
   576
    (case splitAt n_xs of
skalberg@15570
   577
      (_,[]) => raise Subscript
nipkow@13629
   578
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
wenzelm@4893
   579
wenzelm@4212
   580
(*find the position of an element in a list*)
wenzelm@4212
   581
fun find_index pred =
wenzelm@4212
   582
  let fun find _ [] = ~1
wenzelm@4212
   583
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   584
  in find 0 end;
wenzelm@3762
   585
wenzelm@4224
   586
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   587
wenzelm@4212
   588
(*find first element satisfying predicate*)
skalberg@15531
   589
fun find_first _ [] = NONE
wenzelm@4212
   590
  | find_first pred (x :: xs) =
skalberg@15531
   591
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   592
wenzelm@4916
   593
(*get first element by lookup function*)
skalberg@15531
   594
fun get_first _ [] = NONE
wenzelm@4916
   595
  | get_first f (x :: xs) =
wenzelm@4916
   596
      (case f x of
skalberg@15531
   597
        NONE => get_first f xs
wenzelm@4916
   598
      | some => some);
wenzelm@4916
   599
wenzelm@233
   600
(*flatten a list of lists to a list*)
skalberg@15531
   601
val flat = List.concat;
wenzelm@233
   602
wenzelm@12136
   603
fun unflat (xs :: xss) ys =
nipkow@13629
   604
      let val (ps,qs) = splitAt(length xs,ys)
nipkow@13629
   605
      in ps :: unflat xss qs end
wenzelm@12136
   606
  | unflat [] [] = []
skalberg@15570
   607
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   608
wenzelm@233
   609
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   610
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   611
val seq = List.app;
wenzelm@233
   612
wenzelm@233
   613
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   614
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   615
  | separate _ xs = xs;
wenzelm@233
   616
wenzelm@233
   617
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   618
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   619
  let fun rep (0, xs) = xs
wenzelm@233
   620
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   621
  in
skalberg@15570
   622
    if n < 0 then raise Subscript
wenzelm@233
   623
    else rep (n, [])
wenzelm@233
   624
  end;
wenzelm@233
   625
wenzelm@14926
   626
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   627
wenzelm@4248
   628
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   629
fun multiply ([], _) = []
wenzelm@4248
   630
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   631
wenzelm@14792
   632
(*direct product*)
wenzelm@14792
   633
fun product _ [] = []
wenzelm@14792
   634
  | product [] _ = []
wenzelm@14792
   635
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   636
wenzelm@233
   637
wenzelm@233
   638
(* filter *)
wenzelm@233
   639
wenzelm@233
   640
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   641
val filter = List.filter;
clasohm@0
   642
fun filter_out f = filter (not o f);
skalberg@15570
   643
val mapfilter = List.mapPartial;
wenzelm@233
   644
wenzelm@233
   645
wenzelm@233
   646
(* lists of pairs *)
wenzelm@233
   647
skalberg@15570
   648
exception UnequalLengths;
skalberg@15570
   649
wenzelm@380
   650
fun map2 _ ([], []) = []
wenzelm@16878
   651
  | map2 f (x :: xs, y :: ys) = f (x, y) :: map2 f (xs, ys)
skalberg@15570
   652
  | map2 _ _ = raise UnequalLengths;
wenzelm@380
   653
wenzelm@380
   654
fun exists2 _ ([], []) = false
wenzelm@380
   655
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
skalberg@15570
   656
  | exists2 _ _ = raise UnequalLengths;
wenzelm@380
   657
wenzelm@380
   658
fun forall2 _ ([], []) = true
wenzelm@380
   659
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
skalberg@15570
   660
  | forall2 _ _ = raise UnequalLengths;
wenzelm@380
   661
wenzelm@4956
   662
fun seq2 _ ([], []) = ()
wenzelm@4956
   663
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
skalberg@15570
   664
  | seq2 _ _ = raise UnequalLengths;
wenzelm@4956
   665
wenzelm@233
   666
(*combine two lists forming a list of pairs:
wenzelm@233
   667
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   668
fun [] ~~ [] = []
wenzelm@233
   669
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   670
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   671
wenzelm@233
   672
(*inverse of ~~; the old 'split':
wenzelm@233
   673
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   674
val split_list = ListPair.unzip;
wenzelm@233
   675
wenzelm@7468
   676
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
wenzelm@7468
   677
wenzelm@233
   678
wenzelm@233
   679
(* prefixes, suffixes *)
wenzelm@233
   680
wenzelm@233
   681
fun [] prefix _ = true
wenzelm@233
   682
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   683
  | _ prefix _ = false;
wenzelm@233
   684
wenzelm@233
   685
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   686
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   687
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   688
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   689
        | take (rxs, x :: xs) =
wenzelm@255
   690
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   691
  in  take([], xs)  end;
wenzelm@233
   692
wenzelm@233
   693
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   694
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   695
fun take_suffix _ [] = ([], [])
wenzelm@233
   696
  | take_suffix pred (x :: xs) =
wenzelm@233
   697
      (case take_suffix pred xs of
wenzelm@233
   698
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   699
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   700
wenzelm@12249
   701
fun prefixes1 [] = []
wenzelm@12249
   702
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   703
wenzelm@12249
   704
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@12249
   705
wenzelm@233
   706
wenzelm@233
   707
wenzelm@233
   708
(** integers **)
wenzelm@233
   709
wenzelm@16439
   710
fun gcd (x, y) =
paulson@15965
   711
  let fun gxd x y : IntInf.int =
nipkow@10692
   712
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   713
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   714
wenzelm@16439
   715
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   716
wenzelm@2958
   717
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   718
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   719
wenzelm@233
   720
wenzelm@233
   721
(* lists of integers *)
wenzelm@233
   722
wenzelm@233
   723
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   724
fun (from upto to) =
wenzelm@233
   725
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   726
wenzelm@233
   727
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   728
fun (from downto to) =
wenzelm@233
   729
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   730
wenzelm@233
   731
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   732
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   733
  | downto0 ([], n) = n = ~1;
wenzelm@233
   734
wenzelm@233
   735
wenzelm@233
   736
(* convert integers to strings *)
wenzelm@233
   737
wenzelm@233
   738
(*expand the number in the given base;
wenzelm@233
   739
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   740
fun radixpand (base, num) : int list =
wenzelm@233
   741
  let
wenzelm@233
   742
    fun radix (n, tail) =
wenzelm@233
   743
      if n < base then n :: tail
wenzelm@233
   744
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   745
  in radix (num, []) end;
wenzelm@233
   746
wenzelm@233
   747
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   748
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   749
fun radixstring (base, zerochar, num) =
wenzelm@233
   750
  let val offset = ord zerochar;
wenzelm@233
   751
      fun chrof n = chr (offset + n)
wenzelm@233
   752
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   753
wenzelm@233
   754
paulson@3407
   755
val string_of_int = Int.toString;
wenzelm@233
   756
paulson@3407
   757
fun string_of_indexname (a,0) = a
paulson@3407
   758
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   759
wenzelm@233
   760
wenzelm@14826
   761
(* read integers *)
wenzelm@14826
   762
wenzelm@14826
   763
fun read_radixint (radix: int, cs) : int * string list =
wenzelm@14826
   764
  let val zero = ord"0"
wenzelm@14826
   765
      val limit = zero+radix
wenzelm@14826
   766
      fun scan (num,[]) = (num,[])
wenzelm@14826
   767
        | scan (num, c::cs) =
wenzelm@14826
   768
              if  zero <= ord c  andalso  ord c < limit
wenzelm@14826
   769
              then scan(radix*num + ord c - zero, cs)
wenzelm@14826
   770
              else (num, c::cs)
wenzelm@14826
   771
  in  scan(0,cs)  end;
wenzelm@14826
   772
wenzelm@14826
   773
fun read_int cs = read_radixint (10, cs);
wenzelm@14826
   774
wenzelm@14826
   775
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
wenzelm@14826
   776
wenzelm@14826
   777
wenzelm@14826
   778
wenzelm@233
   779
(** strings **)
wenzelm@233
   780
wenzelm@16188
   781
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   782
wenzelm@6312
   783
fun nth_elem_string (i, str) =
wenzelm@6959
   784
  (case try String.substring (str, i, 1) of
skalberg@15531
   785
    SOME s => s
skalberg@15570
   786
  | NONE => raise Subscript);
wenzelm@6312
   787
wenzelm@16188
   788
fun fold_string f str x0 =
wenzelm@6282
   789
  let
wenzelm@6282
   790
    val n = size str;
wenzelm@16188
   791
    fun iter (x, i) =
wenzelm@16188
   792
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   793
  in iter (x0, 0) end;
wenzelm@6282
   794
wenzelm@14968
   795
fun exists_string pred str =
wenzelm@14968
   796
  let
wenzelm@14968
   797
    val n = size str;
wenzelm@14968
   798
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   799
  in ex 0 end;
wenzelm@6312
   800
wenzelm@16188
   801
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   802
lcp@512
   803
(*enclose in brackets*)
lcp@512
   804
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   805
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   806
wenzelm@233
   807
(*simple quoting (does not escape special chars)*)
lcp@512
   808
val quote = enclose "\"" "\"";
wenzelm@233
   809
wenzelm@4212
   810
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   811
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   812
wenzelm@255
   813
val commas = space_implode ", ";
wenzelm@380
   814
val commas_quote = commas o map quote;
wenzelm@255
   815
wenzelm@233
   816
(*concatenate messages, one per line, into a string*)
wenzelm@255
   817
val cat_lines = space_implode "\n";
wenzelm@233
   818
wenzelm@4212
   819
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   820
fun space_explode _ "" = []
wenzelm@3832
   821
  | space_explode sep str =
wenzelm@3832
   822
      let
wenzelm@3832
   823
        fun expl chs =
wenzelm@3832
   824
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   825
            (cs, []) => [implode cs]
wenzelm@3832
   826
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   827
      in expl (explode str) end;
wenzelm@3832
   828
wenzelm@3832
   829
val split_lines = space_explode "\n";
wenzelm@3832
   830
wenzelm@14826
   831
fun prefix_lines "" txt = txt
wenzelm@14826
   832
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   833
wenzelm@7712
   834
fun untabify chs =
wenzelm@7712
   835
  let
wenzelm@7712
   836
    val tab_width = 8;
wenzelm@7712
   837
wenzelm@7712
   838
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   839
      | untab (pos, "\t") =
wenzelm@9118
   840
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   841
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   842
  in
wenzelm@7712
   843
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   844
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   845
  end;
wenzelm@7712
   846
wenzelm@16188
   847
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   848
wenzelm@16188
   849
fun unsuffix sffx s =
wenzelm@17061
   850
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   851
  else raise Fail "unsuffix";
wenzelm@5285
   852
berghofe@15060
   853
fun unprefix prfx s =
wenzelm@17061
   854
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@17061
   855
  else raise Fail "unprefix";
berghofe@15060
   856
wenzelm@10951
   857
fun replicate_string 0 _ = ""
wenzelm@10951
   858
  | replicate_string 1 a = a
wenzelm@10951
   859
  | replicate_string k a =
wenzelm@10951
   860
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   861
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   862
wenzelm@3832
   863
wenzelm@233
   864
wenzelm@16492
   865
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   866
wenzelm@233
   867
(*membership in a list*)
wenzelm@233
   868
fun x mem [] = false
wenzelm@233
   869
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   870
paulson@2175
   871
(*membership in a list, optimized version for ints*)
berghofe@1576
   872
fun (x:int) mem_int [] = false
berghofe@1576
   873
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   874
paulson@2175
   875
(*membership in a list, optimized version for strings*)
berghofe@1576
   876
fun (x:string) mem_string [] = false
berghofe@1576
   877
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   878
clasohm@0
   879
(*generalized membership test*)
wenzelm@233
   880
fun gen_mem eq (x, []) = false
wenzelm@233
   881
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   882
wenzelm@16492
   883
(*member, insert, and remove -- with canonical argument order*)
wenzelm@16492
   884
fun member eq xs x = gen_mem eq (x, xs);
wenzelm@15760
   885
fun insert eq x xs = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@15760
   886
fun remove eq x xs = if gen_mem eq (x, xs) then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   887
wenzelm@233
   888
(*insertion into list if not already there*)
paulson@2175
   889
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   890
paulson@2175
   891
(*insertion into list, optimized version for ints*)
paulson@2175
   892
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   893
paulson@2175
   894
(*insertion into list, optimized version for strings*)
paulson@2175
   895
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   896
clasohm@0
   897
(*generalized insertion*)
wenzelm@15760
   898
fun gen_ins eq (x, xs) = insert eq x xs;
wenzelm@233
   899
wenzelm@233
   900
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   901
fun xs union [] = xs
wenzelm@233
   902
  | [] union ys = ys
wenzelm@233
   903
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   904
paulson@2175
   905
(*union of sets, optimized version for ints*)
berghofe@1576
   906
fun (xs:int list) union_int [] = xs
berghofe@1576
   907
  | [] union_int ys = ys
berghofe@1576
   908
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   909
paulson@2175
   910
(*union of sets, optimized version for strings*)
berghofe@1576
   911
fun (xs:string list) union_string [] = xs
berghofe@1576
   912
  | [] union_string ys = ys
berghofe@1576
   913
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   914
clasohm@0
   915
(*generalized union*)
wenzelm@233
   916
fun gen_union eq (xs, []) = xs
wenzelm@233
   917
  | gen_union eq ([], ys) = ys
wenzelm@233
   918
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   919
wenzelm@233
   920
wenzelm@233
   921
(*intersection*)
wenzelm@233
   922
fun [] inter ys = []
wenzelm@233
   923
  | (x :: xs) inter ys =
wenzelm@233
   924
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   925
paulson@2175
   926
(*intersection, optimized version for ints*)
berghofe@1576
   927
fun ([]:int list) inter_int ys = []
berghofe@1576
   928
  | (x :: xs) inter_int ys =
berghofe@1576
   929
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   930
paulson@2175
   931
(*intersection, optimized version for strings *)
berghofe@1576
   932
fun ([]:string list) inter_string ys = []
berghofe@1576
   933
  | (x :: xs) inter_string ys =
berghofe@1576
   934
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   935
paulson@7090
   936
(*generalized intersection*)
paulson@7090
   937
fun gen_inter eq ([], ys) = []
wenzelm@12284
   938
  | gen_inter eq (x::xs, ys) =
paulson@7090
   939
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
wenzelm@12284
   940
                           else      gen_inter eq (xs, ys);
paulson@7090
   941
wenzelm@233
   942
wenzelm@233
   943
(*subset*)
wenzelm@233
   944
fun [] subset ys = true
wenzelm@233
   945
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   946
paulson@2175
   947
(*subset, optimized version for ints*)
wenzelm@16439
   948
fun ([]: int list) subset_int ys = true
berghofe@1576
   949
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   950
paulson@2175
   951
(*subset, optimized version for strings*)
wenzelm@16439
   952
fun ([]: string list) subset_string ys = true
berghofe@1576
   953
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   954
wenzelm@4363
   955
(*set equality*)
wenzelm@4363
   956
fun eq_set (xs, ys) =
wenzelm@4363
   957
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   958
paulson@2182
   959
(*set equality for strings*)
wenzelm@16439
   960
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   961
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   962
paulson@2182
   963
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   964
wenzelm@265
   965
wenzelm@233
   966
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   967
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   968
  | [] \ x = [];
wenzelm@233
   969
paulson@2243
   970
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   971
wenzelm@233
   972
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   973
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@12295
   974
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   975
wenzelm@233
   976
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   977
  first of equal elements*)
wenzelm@233
   978
fun gen_distinct eq lst =
wenzelm@233
   979
  let
wenzelm@233
   980
    val memb = gen_mem eq;
clasohm@0
   981
wenzelm@233
   982
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   983
      | dist (rev_seen, x :: xs) =
wenzelm@233
   984
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   985
          else dist (x :: rev_seen, xs);
wenzelm@233
   986
  in
wenzelm@233
   987
    dist ([], lst)
wenzelm@233
   988
  end;
wenzelm@233
   989
paulson@2243
   990
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   991
wenzelm@233
   992
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   993
fun findrep [] = []
wenzelm@233
   994
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   995
wenzelm@233
   996
wenzelm@255
   997
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   998
  order, takes first of equal elements*)
wenzelm@255
   999
fun gen_duplicates eq lst =
wenzelm@255
  1000
  let
wenzelm@255
  1001
    val memb = gen_mem eq;
wenzelm@255
  1002
wenzelm@255
  1003
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
  1004
      | dups (rev_dups, x :: xs) =
wenzelm@255
  1005
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
  1006
            dups (rev_dups, xs)
wenzelm@255
  1007
          else dups (x :: rev_dups, xs);
wenzelm@255
  1008
  in
wenzelm@255
  1009
    dups ([], lst)
wenzelm@255
  1010
  end;
wenzelm@255
  1011
paulson@2243
  1012
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
  1013
wenzelm@16878
  1014
fun has_duplicates eq =
wenzelm@16878
  1015
  let
wenzelm@16878
  1016
    fun dups [] = false
wenzelm@16878
  1017
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
  1018
  in dups end;
wenzelm@16878
  1019
wenzelm@255
  1020
wenzelm@233
  1021
wenzelm@233
  1022
(** association lists **)
clasohm@0
  1023
wenzelm@12284
  1024
(* lists as tables *)
wenzelm@233
  1025
wenzelm@12284
  1026
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1027
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1028
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1029
wenzelm@12284
  1030
fun gen_merge_lists' _ xs [] = xs
wenzelm@12284
  1031
  | gen_merge_lists' _ [] ys = ys
wenzelm@12295
  1032
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
clasohm@0
  1033
wenzelm@12284
  1034
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
wenzelm@12284
  1035
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
haftmann@17498
  1036
fun merge_alists al = gen_merge_lists (eq_fst (op =)) al;
haftmann@17498
  1037
fun merge_alists' al = gen_merge_lists' (eq_fst (op =)) al;
wenzelm@380
  1038
clasohm@0
  1039
clasohm@0
  1040
wenzelm@233
  1041
(** balanced trees **)
wenzelm@233
  1042
wenzelm@233
  1043
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1044
wenzelm@233
  1045
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1046
fun fold_bal f [x] = x
wenzelm@233
  1047
  | fold_bal f [] = raise Balance
wenzelm@233
  1048
  | fold_bal f xs =
nipkow@13629
  1049
      let val (ps,qs) = splitAt(length xs div 2, xs)
nipkow@13629
  1050
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1051
wenzelm@233
  1052
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1053
fun access_bal (f, g, x) n i =
wenzelm@233
  1054
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1055
          if n=1 then x else
wenzelm@233
  1056
          let val n2 = n div 2
wenzelm@233
  1057
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1058
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1059
          end
wenzelm@233
  1060
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1061
wenzelm@233
  1062
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1063
fun accesses_bal (f, g, x) n =
wenzelm@233
  1064
  let fun acc n =
wenzelm@233
  1065
          if n=1 then [x] else
wenzelm@233
  1066
          let val n2 = n div 2
wenzelm@233
  1067
              val acc2 = acc n2
wenzelm@233
  1068
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1069
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1070
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1071
wenzelm@233
  1072
wenzelm@233
  1073
wenzelm@2506
  1074
(** orders **)
wenzelm@2506
  1075
wenzelm@4445
  1076
fun rev_order LESS = GREATER
wenzelm@4445
  1077
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1078
  | rev_order GREATER = LESS;
wenzelm@4445
  1079
wenzelm@4479
  1080
(*assume rel is a linear strict order*)
wenzelm@4445
  1081
fun make_ord rel (x, y) =
wenzelm@4445
  1082
  if rel (x, y) then LESS
wenzelm@4445
  1083
  else if rel (y, x) then GREATER
wenzelm@4445
  1084
  else EQUAL;
wenzelm@4445
  1085
wenzelm@15051
  1086
val int_ord = Int.compare;
wenzelm@15051
  1087
val string_ord = String.compare;
wenzelm@2506
  1088
wenzelm@16676
  1089
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1090
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1091
wenzelm@16492
  1092
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1093
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1094
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1095
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1096
wenzelm@4343
  1097
(*lexicographic product*)
wenzelm@4343
  1098
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1099
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1100
wenzelm@4343
  1101
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1102
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1103
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1104
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1105
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1106
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1107
wenzelm@4343
  1108
(*lexicographic product of lists*)
wenzelm@4343
  1109
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1110
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1111
wenzelm@2506
  1112
wenzelm@4621
  1113
(* sorting *)
wenzelm@4621
  1114
wenzelm@4621
  1115
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1116
fun sort ord =
wenzelm@4621
  1117
  let
wenzelm@16878
  1118
    fun qsort [] = []
wenzelm@16878
  1119
      | qsort (xs as [_]) = xs
wenzelm@16878
  1120
      | qsort (xs as [x, y]) = if ord (x, y) = GREATER then [y, x] else xs
wenzelm@16878
  1121
      | qsort xs =
wenzelm@16878
  1122
          let val (lts, eqs, gts) = part (nth_elem (length xs div 2, xs)) xs
wenzelm@16878
  1123
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1124
    and part _ [] = ([], [], [])
wenzelm@4621
  1125
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1126
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1127
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1128
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1129
  in qsort end;
wenzelm@4621
  1130
wenzelm@4621
  1131
(*sort strings*)
wenzelm@4621
  1132
val sort_strings = sort string_ord;
wenzelm@4621
  1133
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1134
berghofe@11514
  1135
fun unique_strings ([]: string list) = []
berghofe@11514
  1136
  | unique_strings [x] = [x]
berghofe@11514
  1137
  | unique_strings (x :: y :: ys) =
berghofe@11514
  1138
      if x = y then unique_strings (y :: ys)
berghofe@11514
  1139
      else x :: unique_strings (y :: ys);
wenzelm@4621
  1140
wenzelm@2506
  1141
berghofe@14106
  1142
(** random numbers **)
berghofe@14106
  1143
berghofe@14106
  1144
exception RANDOM;
berghofe@14106
  1145
berghofe@14618
  1146
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1147
berghofe@14106
  1148
local
berghofe@14106
  1149
  val a = 16807.0;
berghofe@14106
  1150
  val m = 2147483647.0;
berghofe@14106
  1151
  val random_seed = ref 1.0;
berghofe@14106
  1152
in
berghofe@14106
  1153
berghofe@14106
  1154
fun random () =
berghofe@14106
  1155
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1156
  in (random_seed := r; r) end;
berghofe@14106
  1157
berghofe@14106
  1158
end;
berghofe@14106
  1159
berghofe@14106
  1160
fun random_range l h =
berghofe@14106
  1161
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1162
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1163
berghofe@14106
  1164
fun one_of xs = nth_elem (random_range 0 (length xs - 1), xs);
berghofe@14106
  1165
berghofe@14106
  1166
fun frequency xs =
berghofe@14106
  1167
  let
berghofe@14106
  1168
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1169
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1170
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1171
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1172
berghofe@14106
  1173
wenzelm@14826
  1174
(** current directory **)
wenzelm@233
  1175
paulson@2243
  1176
val cd = OS.FileSys.chDir;
wenzelm@2317
  1177
val pwd = OS.FileSys.getDir;
paulson@2243
  1178
berghofe@3606
  1179
wenzelm@233
  1180
nipkow@10692
  1181
(** rational numbers **)
nipkow@17028
  1182
(* Keep them normalized! *)
nipkow@10692
  1183
paulson@15965
  1184
datatype rat = Rat of bool * IntInf.int * IntInf.int
nipkow@10692
  1185
wenzelm@14826
  1186
exception RAT of string;
wenzelm@14826
  1187
nipkow@10692
  1188
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
nipkow@10692
  1189
nipkow@10692
  1190
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
nipkow@10692
  1191
  let val absp = abs p
nipkow@10692
  1192
      val m = gcd(absp,q)
nipkow@10692
  1193
  in Rat(a = (0 <= p), absp div m, q div m) end;
nipkow@10692
  1194
nipkow@17028
  1195
fun ratcommon(p,q,r,s) =
nipkow@10692
  1196
  let val den = lcm(q,s)
nipkow@17028
  1197
  in (p*(den div q), r*(den div s), den) end
nipkow@17028
  1198
nipkow@17028
  1199
fun ratge0(Rat(a,p,q)) = a;
nipkow@17028
  1200
fun ratgt0(Rat(a,p,q)) = a andalso p > 0;
nipkow@17028
  1201
nipkow@17028
  1202
fun ratle(Rat(a,p,q),Rat(b,r,s)) =
nipkow@17028
  1203
  not a andalso b orelse
nipkow@17028
  1204
  a = b andalso
nipkow@17028
  1205
    let val (p,r,_) = ratcommon(p,q,r,s)
nipkow@17028
  1206
    in if a then p <= r else r <= p end
nipkow@17028
  1207
nipkow@17028
  1208
fun ratlt(Rat(a,p,q),Rat(b,r,s)) =
nipkow@17028
  1209
  not a andalso b orelse
nipkow@17028
  1210
  a = b andalso
nipkow@17028
  1211
    let val (p,r,_) = ratcommon(p,q,r,s)
nipkow@17028
  1212
    in if a then p < r else r < p end
nipkow@17028
  1213
nipkow@17028
  1214
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
nipkow@17032
  1215
  let val (p,r,den) = ratcommon(p,q,r,s)
nipkow@10692
  1216
      val num = (if a then p else ~p) + (if b then r else ~r)
nipkow@10692
  1217
  in ratnorm(true,num,den) end;
nipkow@10692
  1218
nipkow@10692
  1219
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
nipkow@10692
  1220
wenzelm@14826
  1221
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p)
nipkow@10692
  1222
nipkow@10692
  1223
fun int_ratdiv(p,q) =
wenzelm@14826
  1224
  if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q)
nipkow@10692
  1225
nipkow@10692
  1226
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
nipkow@10692
  1227
paulson@15965
  1228
fun rat_of_intinf i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
paulson@15965
  1229
paulson@15965
  1230
fun rat_of_int i = rat_of_intinf (IntInf.fromInt i);
nipkow@10692
  1231
wenzelm@17341
  1232
val rat0 = rat_of_int 0;
wenzelm@17341
  1233
nipkow@10692
  1234
wenzelm@4621
  1235
(** misc **)
wenzelm@233
  1236
clasohm@0
  1237
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1238
  Preserves order of elements in both lists.*)
skalberg@15570
  1239
val partition = List.partition;
clasohm@0
  1240
clasohm@0
  1241
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@16842
  1242
  let
wenzelm@16842
  1243
    fun part [] = []
wenzelm@16842
  1244
      | part (x :: ys) =
wenzelm@16842
  1245
          let val (xs, xs') = partition (fn y => eq (x, y)) ys
wenzelm@16842
  1246
          in (x::xs)::(part xs') end
wenzelm@16842
  1247
  in part end;
clasohm@0
  1248
clasohm@0
  1249
wenzelm@233
  1250
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1251
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1252
fun partition_list p i j =
wenzelm@233
  1253
  let fun part k xs =
wenzelm@233
  1254
            if k>j then
clasohm@0
  1255
              (case xs of [] => []
skalberg@15570
  1256
                         | _ => raise Fail "partition_list")
clasohm@0
  1257
            else
wenzelm@233
  1258
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1259
            in  ns :: part(k+1)rest  end
clasohm@0
  1260
  in  part i end;
clasohm@0
  1261
clasohm@0
  1262
wenzelm@233
  1263
(* generating identifiers *)
clasohm@0
  1264
paulson@4063
  1265
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1266
local
paulson@4063
  1267
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1268
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1269
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1270
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1271
             else if i=62 then "_"
wenzelm@5904
  1272
             else  (*i=63*)    "'";
paulson@4063
  1273
paulson@4063
  1274
val charVec = Vector.tabulate (64, char);
paulson@4063
  1275
wenzelm@5904
  1276
fun newid n =
wenzelm@5904
  1277
  let
wenzelm@4284
  1278
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1279
wenzelm@4284
  1280
val seedr = ref 0;
clasohm@0
  1281
paulson@4063
  1282
in
wenzelm@4284
  1283
wenzelm@12346
  1284
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1285
paulson@4063
  1286
end;
paulson@4063
  1287
paulson@17819
  1288
(*Convert a process ID to a decimal string (chiefly for tracing)*)
paulson@17819
  1289
fun string_of_pid pid = 
paulson@17819
  1290
    Word.fmt StringCvt.DEC (Word.fromLargeWord (Posix.Process.pidToWord pid));
paulson@17819
  1291
paulson@4063
  1292
wenzelm@233
  1293
(* lexical scanning *)
clasohm@0
  1294
wenzelm@233
  1295
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1296
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1297
fun scanwords is_let cs =
clasohm@0
  1298
  let fun scan1 [] = []
wenzelm@233
  1299
        | scan1 cs =
wenzelm@233
  1300
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1301
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1302
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1303
wenzelm@4212
  1304
wenzelm@16439
  1305
(* stamps and serial numbers *)
wenzelm@16439
  1306
wenzelm@16439
  1307
type stamp = unit ref;
wenzelm@16439
  1308
val stamp: unit -> stamp = ref;
wenzelm@16439
  1309
wenzelm@16439
  1310
type serial = int;
wenzelm@16439
  1311
local val count = ref 0
wenzelm@16439
  1312
in fun serial () = inc count end;
wenzelm@16439
  1313
wenzelm@16535
  1314
wenzelm@16535
  1315
(* generic objects *)
wenzelm@16535
  1316
wenzelm@16535
  1317
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1318
  constructors at any time*)
wenzelm@16535
  1319
structure Object = struct type T = exn end;
wenzelm@16535
  1320
clasohm@1364
  1321
end;
clasohm@1364
  1322
wenzelm@15745
  1323
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1324
open BasicLibrary;