src/Pure/library.ML
author haftmann
Fri Oct 28 16:35:40 2005 +0200 (2005-10-28)
changeset 18011 685d95c793ff
parent 17952 00eccd84608f
child 18050 652c95961a8b
permissions -rw-r--r--
cleaned up nth, nth_update, nth_map and nth_string 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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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 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 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_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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  (*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 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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  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 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
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end;
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structure Library: LIBRARY =
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struct
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(** functions **)
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fun I x = x;
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fun K x = fn _ => x;
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fun curry f x y = f (x, y);
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fun uncurry f (x, y) = f x y;
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(*reverse application and structured results*)
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fun x |> f = f x;
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fun (x, y) |-> f = f x y;
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fun (x, y) |>> f = (f x, y);
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fun (x, y) ||> f = (x, f y);
wenzelm@16705
   290
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16705
   291
fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
wenzelm@16842
   292
wenzelm@16842
   293
(*reverse composition*)
haftmann@16780
   294
fun f #> g = g o f;
wenzelm@16842
   295
fun f #-> g = uncurry g o f;
wenzelm@16842
   296
haftmann@17141
   297
(*conditional application*)
wenzelm@17545
   298
fun b ? f = fn x => if b x then f x else x;
haftmann@17141
   299
wenzelm@16842
   300
(*view results*)
wenzelm@16842
   301
fun `f = fn x => (f x, x);
wenzelm@17545
   302
fun tap f = fn x => (f x; x);
wenzelm@380
   303
wenzelm@16721
   304
(*composition with multiple args*)
wenzelm@16721
   305
fun (f oo g) x y = f (g x y);
wenzelm@16721
   306
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   307
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   308
wenzelm@233
   309
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   310
fun funpow n f x =
wenzelm@233
   311
  let fun rep (0, x) = x
wenzelm@233
   312
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   313
  in rep (n, x) end;
wenzelm@160
   314
wenzelm@160
   315
wenzelm@233
   316
(** options **)
clasohm@0
   317
wenzelm@15670
   318
(*invalidate former constructors to prevent accidental use as match-all patterns!*)
wenzelm@15670
   319
datatype invalid = None of invalid;
wenzelm@15670
   320
exception OPTION of invalid;
clasohm@0
   321
wenzelm@15970
   322
val the = Option.valOf;
wenzelm@17341
   323
haftmann@17153
   324
fun these (SOME x) = x
haftmann@17313
   325
  | these _ = [];
wenzelm@17341
   326
haftmann@17313
   327
fun the_default x (SOME y) = y
haftmann@17313
   328
  | the_default x _ = x;
wenzelm@17341
   329
haftmann@17313
   330
fun the_list (SOME x) = [x]
haftmann@17313
   331
  | the_list _ = []
wenzelm@15970
   332
wenzelm@15970
   333
(*strict!*)
wenzelm@15970
   334
fun if_none NONE y = y
wenzelm@15970
   335
  | if_none (SOME x) _ = x;
wenzelm@15970
   336
wenzelm@15970
   337
fun is_some (SOME _) = true
wenzelm@15970
   338
  | is_some NONE = false;
wenzelm@15970
   339
wenzelm@15970
   340
fun is_none (SOME _) = false
wenzelm@15970
   341
  | is_none NONE = true;
wenzelm@15970
   342
wenzelm@6959
   343
wenzelm@17341
   344
(* exceptions *)
wenzelm@17341
   345
wenzelm@17341
   346
exception EXCEPTION of exn * string;
wenzelm@6959
   347
wenzelm@6959
   348
exception ERROR;
wenzelm@6959
   349
skalberg@15531
   350
fun try f x = SOME (f x)
skalberg@15531
   351
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => NONE;
wenzelm@6959
   352
wenzelm@6959
   353
fun can f x = is_some (try f x);
wenzelm@4139
   354
wenzelm@4139
   355
wenzelm@14868
   356
datatype 'a result =
wenzelm@14868
   357
  Result of 'a |
wenzelm@14868
   358
  Exn of exn;
wenzelm@14868
   359
wenzelm@14868
   360
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   361
wenzelm@14868
   362
fun release (Result y) = y
wenzelm@14868
   363
  | release (Exn e) = raise e;
wenzelm@14868
   364
skalberg@15531
   365
fun get_result (Result x) = SOME x
skalberg@15531
   366
  | get_result _ = NONE;
wenzelm@14868
   367
skalberg@15531
   368
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   369
  | get_exn _ = NONE;
wenzelm@14868
   370
wenzelm@14868
   371
wenzelm@4139
   372
wenzelm@233
   373
(** pairs **)
wenzelm@233
   374
wenzelm@233
   375
fun pair x y = (x, y);
wenzelm@233
   376
fun rpair x y = (y, x);
wenzelm@233
   377
wenzelm@233
   378
fun fst (x, y) = x;
wenzelm@233
   379
fun snd (x, y) = y;
wenzelm@233
   380
haftmann@17498
   381
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   382
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
wenzelm@233
   383
wenzelm@233
   384
fun swap (x, y) = (y, x);
wenzelm@233
   385
wenzelm@4212
   386
(*apply function to components*)
wenzelm@233
   387
fun apfst f (x, y) = (f x, y);
wenzelm@233
   388
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   389
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   390
wenzelm@233
   391
wenzelm@233
   392
wenzelm@233
   393
(** booleans **)
wenzelm@233
   394
wenzelm@233
   395
(* equality *)
wenzelm@233
   396
wenzelm@233
   397
fun equal x y = x = y;
wenzelm@233
   398
fun not_equal x y = x <> y;
wenzelm@233
   399
wenzelm@233
   400
wenzelm@233
   401
(* operators for combining predicates *)
wenzelm@233
   402
wenzelm@16721
   403
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   404
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   405
wenzelm@233
   406
wenzelm@233
   407
(* predicates on lists *)
wenzelm@233
   408
wenzelm@233
   409
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   410
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   411
  let fun boolf [] = false
wenzelm@233
   412
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   413
  in boolf end;
wenzelm@233
   414
wenzelm@233
   415
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   416
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   417
  let fun boolf [] = true
wenzelm@233
   418
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   419
  in boolf end;
clasohm@0
   420
wenzelm@233
   421
wenzelm@380
   422
(* flags *)
wenzelm@380
   423
wenzelm@380
   424
fun set flag = (flag := true; true);
wenzelm@380
   425
fun reset flag = (flag := false; false);
wenzelm@380
   426
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   427
wenzelm@9118
   428
fun change r f = r := f (! r);
wenzelm@9118
   429
wenzelm@14826
   430
(*temporarily set flag, handling exceptions*)
wenzelm@2978
   431
fun setmp flag value f x =
wenzelm@2958
   432
  let
wenzelm@2958
   433
    val orig_value = ! flag;
wenzelm@2958
   434
    fun return y = (flag := orig_value; y);
wenzelm@2958
   435
  in
wenzelm@2958
   436
    flag := value;
wenzelm@2958
   437
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   438
  end;
wenzelm@2958
   439
wenzelm@380
   440
wenzelm@11853
   441
(* conditional execution *)
wenzelm@11853
   442
wenzelm@11853
   443
fun conditional b f = if b then f () else ();
wenzelm@11853
   444
wenzelm@11853
   445
wenzelm@233
   446
wenzelm@233
   447
(** lists **)
wenzelm@233
   448
skalberg@15570
   449
exception UnequalLengths;
wenzelm@233
   450
wenzelm@233
   451
fun cons x xs = x :: xs;
wenzelm@5285
   452
fun single x = [x];
wenzelm@233
   453
wenzelm@4629
   454
fun append xs ys = xs @ ys;
wenzelm@4629
   455
wenzelm@5904
   456
fun apply [] x = x
wenzelm@5904
   457
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   458
wenzelm@233
   459
wenzelm@233
   460
(* fold *)
wenzelm@233
   461
wenzelm@16654
   462
fun fold f =
wenzelm@16654
   463
  let
wenzelm@16654
   464
    fun fold_aux [] y = y
wenzelm@16654
   465
      | fold_aux (x :: xs) y = fold_aux xs (f x y);
wenzelm@16654
   466
  in fold_aux end;
wenzelm@15760
   467
wenzelm@16654
   468
fun fold_rev f =
wenzelm@16654
   469
  let
wenzelm@16654
   470
    fun fold_aux [] y = y
wenzelm@16654
   471
      | fold_aux (x :: xs) y = f x (fold_aux xs y);
wenzelm@16654
   472
  in fold_aux end;
wenzelm@16654
   473
haftmann@16869
   474
fun fold_map f =
haftmann@16691
   475
  let
haftmann@16691
   476
    fun fold_aux [] y = ([], y)
haftmann@16691
   477
      | fold_aux (x :: xs) y =
haftmann@16691
   478
          let
wenzelm@16705
   479
            val (x', y') = f x y;
wenzelm@16705
   480
            val (xs', y'') = fold_aux xs y';
haftmann@16691
   481
          in (x' :: xs', y'') end;
haftmann@16691
   482
  in fold_aux end;
haftmann@16691
   483
wenzelm@233
   484
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   485
wenzelm@233
   486
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   487
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   488
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   489
  let fun itl (e, [])  = e
wenzelm@233
   490
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   491
  in  itl end;
wenzelm@233
   492
wenzelm@233
   493
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   494
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   495
fun foldr f (l, e) =
wenzelm@233
   496
  let fun itr [] = e
wenzelm@233
   497
        | itr (a::l) = f(a, itr l)
wenzelm@233
   498
  in  itr l  end;
wenzelm@233
   499
wenzelm@233
   500
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   501
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   502
fun foldr1 f l =
wenzelm@4181
   503
  let fun itr [x] = x
wenzelm@233
   504
        | itr (x::l) = f(x, itr l)
wenzelm@233
   505
  in  itr l  end;
wenzelm@233
   506
wenzelm@15760
   507
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
wenzelm@14792
   508
wenzelm@16705
   509
fun foldl_map f =
wenzelm@16705
   510
  let
wenzelm@16705
   511
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   512
      | fold_aux (x, y :: ys) =
wenzelm@16705
   513
          let
wenzelm@16705
   514
            val (x', y') = f (x, y);
wenzelm@16705
   515
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   516
          in (x'', y' :: ys') end;
wenzelm@16705
   517
  in fold_aux end;
wenzelm@16705
   518
wenzelm@233
   519
wenzelm@233
   520
(* basic list functions *)
wenzelm@233
   521
wenzelm@233
   522
(*take the first n elements from a list*)
wenzelm@233
   523
fun take (n, []) = []
wenzelm@233
   524
  | take (n, x :: xs) =
wenzelm@233
   525
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   526
wenzelm@233
   527
(*drop the first n elements from a list*)
wenzelm@233
   528
fun drop (n, []) = []
wenzelm@233
   529
  | drop (n, x :: xs) =
wenzelm@233
   530
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   531
nipkow@13629
   532
fun splitAt(n,[]) = ([],[])
nipkow@13629
   533
  | splitAt(n,xs as x::ys) =
nipkow@13629
   534
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
nipkow@13629
   535
      else ([],xs)
nipkow@13629
   536
nipkow@4713
   537
fun dropwhile P [] = []
nipkow@4713
   538
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   539
wenzelm@233
   540
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   541
  raise EXCEPTION if list too short*)
haftmann@18011
   542
fun nth xs i = List.nth (xs, i);
wenzelm@233
   543
haftmann@18011
   544
(*update nth element*)
haftmann@18011
   545
fun nth_update (n, x) xs =
haftmann@18011
   546
    (case splitAt (n, xs) of
haftmann@18011
   547
      (_, []) => raise Subscript
haftmann@18011
   548
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
haftmann@18011
   549
haftmann@18011
   550
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   551
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   552
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   553
wenzelm@233
   554
(*last element of a list*)
skalberg@15570
   555
val last_elem = List.last;
wenzelm@233
   556
wenzelm@3762
   557
(*rear decomposition*)
skalberg@15570
   558
fun split_last [] = raise Empty
wenzelm@3762
   559
  | split_last [x] = ([], x)
wenzelm@3762
   560
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   561
wenzelm@4212
   562
(*find the position of an element in a list*)
wenzelm@4212
   563
fun find_index pred =
wenzelm@4212
   564
  let fun find _ [] = ~1
wenzelm@4212
   565
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   566
  in find 0 end;
wenzelm@3762
   567
wenzelm@4224
   568
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   569
wenzelm@4212
   570
(*find first element satisfying predicate*)
skalberg@15531
   571
fun find_first _ [] = NONE
wenzelm@4212
   572
  | find_first pred (x :: xs) =
skalberg@15531
   573
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   574
wenzelm@4916
   575
(*get first element by lookup function*)
skalberg@15531
   576
fun get_first _ [] = NONE
wenzelm@4916
   577
  | get_first f (x :: xs) =
wenzelm@4916
   578
      (case f x of
skalberg@15531
   579
        NONE => get_first f xs
wenzelm@4916
   580
      | some => some);
wenzelm@4916
   581
wenzelm@233
   582
(*flatten a list of lists to a list*)
skalberg@15531
   583
val flat = List.concat;
wenzelm@233
   584
wenzelm@12136
   585
fun unflat (xs :: xss) ys =
nipkow@13629
   586
      let val (ps,qs) = splitAt(length xs,ys)
nipkow@13629
   587
      in ps :: unflat xss qs end
wenzelm@12136
   588
  | unflat [] [] = []
skalberg@15570
   589
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   590
wenzelm@233
   591
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   592
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   593
val seq = List.app;
wenzelm@233
   594
wenzelm@233
   595
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   596
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   597
  | separate _ xs = xs;
wenzelm@233
   598
wenzelm@233
   599
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   600
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   601
  let fun rep (0, xs) = xs
wenzelm@233
   602
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   603
  in
skalberg@15570
   604
    if n < 0 then raise Subscript
wenzelm@233
   605
    else rep (n, [])
wenzelm@233
   606
  end;
wenzelm@233
   607
wenzelm@14926
   608
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   609
wenzelm@4248
   610
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   611
fun multiply ([], _) = []
wenzelm@4248
   612
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   613
wenzelm@14792
   614
(*direct product*)
wenzelm@14792
   615
fun product _ [] = []
wenzelm@14792
   616
  | product [] _ = []
wenzelm@14792
   617
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   618
wenzelm@233
   619
wenzelm@233
   620
(* filter *)
wenzelm@233
   621
wenzelm@233
   622
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   623
val filter = List.filter;
clasohm@0
   624
fun filter_out f = filter (not o f);
skalberg@15570
   625
val mapfilter = List.mapPartial;
wenzelm@233
   626
wenzelm@233
   627
wenzelm@233
   628
(* lists of pairs *)
wenzelm@233
   629
skalberg@15570
   630
exception UnequalLengths;
skalberg@15570
   631
wenzelm@380
   632
fun map2 _ ([], []) = []
wenzelm@16878
   633
  | map2 f (x :: xs, y :: ys) = f (x, y) :: map2 f (xs, ys)
skalberg@15570
   634
  | map2 _ _ = raise UnequalLengths;
wenzelm@380
   635
wenzelm@380
   636
fun exists2 _ ([], []) = false
wenzelm@380
   637
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
skalberg@15570
   638
  | exists2 _ _ = raise UnequalLengths;
wenzelm@380
   639
wenzelm@380
   640
fun forall2 _ ([], []) = true
wenzelm@380
   641
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
skalberg@15570
   642
  | forall2 _ _ = raise UnequalLengths;
wenzelm@380
   643
wenzelm@4956
   644
fun seq2 _ ([], []) = ()
wenzelm@4956
   645
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
skalberg@15570
   646
  | seq2 _ _ = raise UnequalLengths;
wenzelm@4956
   647
wenzelm@233
   648
(*combine two lists forming a list of pairs:
wenzelm@233
   649
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   650
fun [] ~~ [] = []
wenzelm@233
   651
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   652
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   653
wenzelm@233
   654
(*inverse of ~~; the old 'split':
wenzelm@233
   655
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   656
val split_list = ListPair.unzip;
wenzelm@233
   657
wenzelm@7468
   658
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
wenzelm@7468
   659
wenzelm@233
   660
wenzelm@233
   661
(* prefixes, suffixes *)
wenzelm@233
   662
wenzelm@233
   663
fun [] prefix _ = true
wenzelm@233
   664
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   665
  | _ prefix _ = false;
wenzelm@233
   666
wenzelm@233
   667
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   668
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   669
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   670
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   671
        | take (rxs, x :: xs) =
wenzelm@255
   672
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   673
  in  take([], xs)  end;
wenzelm@233
   674
wenzelm@233
   675
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   676
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   677
fun take_suffix _ [] = ([], [])
wenzelm@233
   678
  | take_suffix pred (x :: xs) =
wenzelm@233
   679
      (case take_suffix pred xs of
wenzelm@233
   680
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   681
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   682
wenzelm@12249
   683
fun prefixes1 [] = []
wenzelm@12249
   684
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   685
wenzelm@12249
   686
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@12249
   687
wenzelm@233
   688
wenzelm@233
   689
wenzelm@233
   690
(** integers **)
wenzelm@233
   691
wenzelm@16439
   692
fun gcd (x, y) =
paulson@15965
   693
  let fun gxd x y : IntInf.int =
nipkow@10692
   694
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   695
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   696
wenzelm@16439
   697
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   698
wenzelm@2958
   699
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   700
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   701
wenzelm@233
   702
wenzelm@233
   703
(* lists of integers *)
wenzelm@233
   704
wenzelm@233
   705
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   706
fun (from upto to) =
wenzelm@233
   707
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   708
wenzelm@233
   709
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   710
fun (from downto to) =
wenzelm@233
   711
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   712
wenzelm@233
   713
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   714
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   715
  | downto0 ([], n) = n = ~1;
wenzelm@233
   716
wenzelm@233
   717
wenzelm@233
   718
(* convert integers to strings *)
wenzelm@233
   719
wenzelm@233
   720
(*expand the number in the given base;
wenzelm@233
   721
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   722
fun radixpand (base, num) : int list =
wenzelm@233
   723
  let
wenzelm@233
   724
    fun radix (n, tail) =
wenzelm@233
   725
      if n < base then n :: tail
wenzelm@233
   726
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   727
  in radix (num, []) end;
wenzelm@233
   728
wenzelm@233
   729
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   730
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   731
fun radixstring (base, zerochar, num) =
wenzelm@233
   732
  let val offset = ord zerochar;
wenzelm@233
   733
      fun chrof n = chr (offset + n)
wenzelm@233
   734
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   735
wenzelm@233
   736
paulson@3407
   737
val string_of_int = Int.toString;
wenzelm@233
   738
paulson@3407
   739
fun string_of_indexname (a,0) = a
paulson@3407
   740
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   741
wenzelm@233
   742
wenzelm@14826
   743
(* read integers *)
wenzelm@14826
   744
wenzelm@14826
   745
fun read_radixint (radix: int, cs) : int * string list =
wenzelm@14826
   746
  let val zero = ord"0"
wenzelm@14826
   747
      val limit = zero+radix
wenzelm@14826
   748
      fun scan (num,[]) = (num,[])
wenzelm@14826
   749
        | scan (num, c::cs) =
wenzelm@14826
   750
              if  zero <= ord c  andalso  ord c < limit
wenzelm@14826
   751
              then scan(radix*num + ord c - zero, cs)
wenzelm@14826
   752
              else (num, c::cs)
wenzelm@14826
   753
  in  scan(0,cs)  end;
wenzelm@14826
   754
wenzelm@14826
   755
fun read_int cs = read_radixint (10, cs);
wenzelm@14826
   756
wenzelm@14826
   757
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
wenzelm@14826
   758
wenzelm@14826
   759
wenzelm@14826
   760
wenzelm@233
   761
(** strings **)
wenzelm@233
   762
wenzelm@16188
   763
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   764
haftmann@18011
   765
fun nth_string str i =
wenzelm@6959
   766
  (case try String.substring (str, i, 1) of
skalberg@15531
   767
    SOME s => s
skalberg@15570
   768
  | NONE => raise Subscript);
wenzelm@6312
   769
wenzelm@16188
   770
fun fold_string f str x0 =
wenzelm@6282
   771
  let
wenzelm@6282
   772
    val n = size str;
wenzelm@16188
   773
    fun iter (x, i) =
wenzelm@16188
   774
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   775
  in iter (x0, 0) end;
wenzelm@6282
   776
wenzelm@14968
   777
fun exists_string pred str =
wenzelm@14968
   778
  let
wenzelm@14968
   779
    val n = size str;
wenzelm@14968
   780
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   781
  in ex 0 end;
wenzelm@6312
   782
wenzelm@16188
   783
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   784
lcp@512
   785
(*enclose in brackets*)
lcp@512
   786
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   787
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   788
wenzelm@233
   789
(*simple quoting (does not escape special chars)*)
lcp@512
   790
val quote = enclose "\"" "\"";
wenzelm@233
   791
wenzelm@4212
   792
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   793
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   794
wenzelm@255
   795
val commas = space_implode ", ";
wenzelm@380
   796
val commas_quote = commas o map quote;
wenzelm@255
   797
wenzelm@233
   798
(*concatenate messages, one per line, into a string*)
wenzelm@255
   799
val cat_lines = space_implode "\n";
wenzelm@233
   800
wenzelm@4212
   801
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   802
fun space_explode _ "" = []
wenzelm@3832
   803
  | space_explode sep str =
wenzelm@3832
   804
      let
wenzelm@3832
   805
        fun expl chs =
wenzelm@3832
   806
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   807
            (cs, []) => [implode cs]
wenzelm@3832
   808
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   809
      in expl (explode str) end;
wenzelm@3832
   810
wenzelm@3832
   811
val split_lines = space_explode "\n";
wenzelm@3832
   812
wenzelm@14826
   813
fun prefix_lines "" txt = txt
wenzelm@14826
   814
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   815
wenzelm@7712
   816
fun untabify chs =
wenzelm@7712
   817
  let
wenzelm@7712
   818
    val tab_width = 8;
wenzelm@7712
   819
wenzelm@7712
   820
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   821
      | untab (pos, "\t") =
wenzelm@9118
   822
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   823
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   824
  in
wenzelm@7712
   825
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   826
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   827
  end;
wenzelm@7712
   828
wenzelm@16188
   829
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   830
wenzelm@16188
   831
fun unsuffix sffx s =
wenzelm@17061
   832
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   833
  else raise Fail "unsuffix";
wenzelm@5285
   834
berghofe@15060
   835
fun unprefix prfx s =
wenzelm@17061
   836
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@17061
   837
  else raise Fail "unprefix";
berghofe@15060
   838
wenzelm@10951
   839
fun replicate_string 0 _ = ""
wenzelm@10951
   840
  | replicate_string 1 a = a
wenzelm@10951
   841
  | replicate_string k a =
wenzelm@10951
   842
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   843
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   844
wenzelm@3832
   845
wenzelm@233
   846
wenzelm@16492
   847
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   848
wenzelm@233
   849
(*membership in a list*)
wenzelm@233
   850
fun x mem [] = false
wenzelm@233
   851
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   852
paulson@2175
   853
(*membership in a list, optimized version for ints*)
berghofe@1576
   854
fun (x:int) mem_int [] = false
berghofe@1576
   855
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   856
paulson@2175
   857
(*membership in a list, optimized version for strings*)
berghofe@1576
   858
fun (x:string) mem_string [] = false
berghofe@1576
   859
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   860
clasohm@0
   861
(*generalized membership test*)
wenzelm@233
   862
fun gen_mem eq (x, []) = false
wenzelm@233
   863
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   864
wenzelm@16492
   865
(*member, insert, and remove -- with canonical argument order*)
wenzelm@16492
   866
fun member eq xs x = gen_mem eq (x, xs);
wenzelm@15760
   867
fun insert eq x xs = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@15760
   868
fun remove eq x xs = if gen_mem eq (x, xs) then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   869
wenzelm@233
   870
(*insertion into list if not already there*)
paulson@2175
   871
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   872
paulson@2175
   873
(*insertion into list, optimized version for ints*)
paulson@2175
   874
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   875
paulson@2175
   876
(*insertion into list, optimized version for strings*)
paulson@2175
   877
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   878
clasohm@0
   879
(*generalized insertion*)
wenzelm@15760
   880
fun gen_ins eq (x, xs) = insert eq x xs;
wenzelm@233
   881
wenzelm@233
   882
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   883
fun xs union [] = xs
wenzelm@233
   884
  | [] union ys = ys
wenzelm@233
   885
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   886
paulson@2175
   887
(*union of sets, optimized version for ints*)
berghofe@1576
   888
fun (xs:int list) union_int [] = xs
berghofe@1576
   889
  | [] union_int ys = ys
berghofe@1576
   890
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   891
paulson@2175
   892
(*union of sets, optimized version for strings*)
berghofe@1576
   893
fun (xs:string list) union_string [] = xs
berghofe@1576
   894
  | [] union_string ys = ys
berghofe@1576
   895
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   896
clasohm@0
   897
(*generalized union*)
wenzelm@233
   898
fun gen_union eq (xs, []) = xs
wenzelm@233
   899
  | gen_union eq ([], ys) = ys
wenzelm@233
   900
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   901
wenzelm@233
   902
wenzelm@233
   903
(*intersection*)
wenzelm@233
   904
fun [] inter ys = []
wenzelm@233
   905
  | (x :: xs) inter ys =
wenzelm@233
   906
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   907
paulson@2175
   908
(*intersection, optimized version for ints*)
berghofe@1576
   909
fun ([]:int list) inter_int ys = []
berghofe@1576
   910
  | (x :: xs) inter_int ys =
berghofe@1576
   911
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   912
paulson@2175
   913
(*intersection, optimized version for strings *)
berghofe@1576
   914
fun ([]:string list) inter_string ys = []
berghofe@1576
   915
  | (x :: xs) inter_string ys =
berghofe@1576
   916
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   917
paulson@7090
   918
(*generalized intersection*)
paulson@7090
   919
fun gen_inter eq ([], ys) = []
wenzelm@12284
   920
  | gen_inter eq (x::xs, ys) =
paulson@7090
   921
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
wenzelm@12284
   922
                           else      gen_inter eq (xs, ys);
paulson@7090
   923
wenzelm@233
   924
wenzelm@233
   925
(*subset*)
wenzelm@233
   926
fun [] subset ys = true
wenzelm@233
   927
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   928
paulson@2175
   929
(*subset, optimized version for ints*)
wenzelm@16439
   930
fun ([]: int list) subset_int ys = true
berghofe@1576
   931
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   932
paulson@2175
   933
(*subset, optimized version for strings*)
wenzelm@16439
   934
fun ([]: string list) subset_string ys = true
berghofe@1576
   935
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   936
wenzelm@4363
   937
(*set equality*)
wenzelm@4363
   938
fun eq_set (xs, ys) =
wenzelm@4363
   939
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   940
paulson@2182
   941
(*set equality for strings*)
wenzelm@16439
   942
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   943
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   944
paulson@2182
   945
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   946
wenzelm@265
   947
wenzelm@233
   948
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   949
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   950
  | [] \ x = [];
wenzelm@233
   951
paulson@2243
   952
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   953
wenzelm@233
   954
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   955
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@12295
   956
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   957
wenzelm@233
   958
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   959
  first of equal elements*)
wenzelm@233
   960
fun gen_distinct eq lst =
wenzelm@233
   961
  let
wenzelm@233
   962
    val memb = gen_mem eq;
clasohm@0
   963
wenzelm@233
   964
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   965
      | dist (rev_seen, x :: xs) =
wenzelm@233
   966
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   967
          else dist (x :: rev_seen, xs);
wenzelm@233
   968
  in
wenzelm@233
   969
    dist ([], lst)
wenzelm@233
   970
  end;
wenzelm@233
   971
paulson@2243
   972
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   973
wenzelm@233
   974
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   975
fun findrep [] = []
wenzelm@233
   976
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   977
wenzelm@233
   978
wenzelm@255
   979
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   980
  order, takes first of equal elements*)
wenzelm@255
   981
fun gen_duplicates eq lst =
wenzelm@255
   982
  let
wenzelm@255
   983
    val memb = gen_mem eq;
wenzelm@255
   984
wenzelm@255
   985
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   986
      | dups (rev_dups, x :: xs) =
wenzelm@255
   987
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   988
            dups (rev_dups, xs)
wenzelm@255
   989
          else dups (x :: rev_dups, xs);
wenzelm@255
   990
  in
wenzelm@255
   991
    dups ([], lst)
wenzelm@255
   992
  end;
wenzelm@255
   993
paulson@2243
   994
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   995
wenzelm@16878
   996
fun has_duplicates eq =
wenzelm@16878
   997
  let
wenzelm@16878
   998
    fun dups [] = false
wenzelm@16878
   999
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
  1000
  in dups end;
wenzelm@16878
  1001
wenzelm@255
  1002
wenzelm@233
  1003
wenzelm@233
  1004
(** association lists **)
clasohm@0
  1005
wenzelm@12284
  1006
(* lists as tables *)
wenzelm@233
  1007
wenzelm@12284
  1008
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1009
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1010
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1011
wenzelm@12284
  1012
fun gen_merge_lists' _ xs [] = xs
wenzelm@12284
  1013
  | gen_merge_lists' _ [] ys = ys
wenzelm@12295
  1014
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
clasohm@0
  1015
wenzelm@12284
  1016
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
wenzelm@12284
  1017
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
haftmann@17498
  1018
fun merge_alists al = gen_merge_lists (eq_fst (op =)) al;
haftmann@17498
  1019
fun merge_alists' al = gen_merge_lists' (eq_fst (op =)) al;
wenzelm@380
  1020
clasohm@0
  1021
clasohm@0
  1022
wenzelm@233
  1023
(** balanced trees **)
wenzelm@233
  1024
wenzelm@233
  1025
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1026
wenzelm@233
  1027
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1028
fun fold_bal f [x] = x
wenzelm@233
  1029
  | fold_bal f [] = raise Balance
wenzelm@233
  1030
  | fold_bal f xs =
nipkow@13629
  1031
      let val (ps,qs) = splitAt(length xs div 2, xs)
nipkow@13629
  1032
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1033
wenzelm@233
  1034
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1035
fun access_bal (f, g, x) n i =
wenzelm@233
  1036
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1037
          if n=1 then x else
wenzelm@233
  1038
          let val n2 = n div 2
wenzelm@233
  1039
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1040
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1041
          end
wenzelm@233
  1042
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1043
wenzelm@233
  1044
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1045
fun accesses_bal (f, g, x) n =
wenzelm@233
  1046
  let fun acc n =
wenzelm@233
  1047
          if n=1 then [x] else
wenzelm@233
  1048
          let val n2 = n div 2
wenzelm@233
  1049
              val acc2 = acc n2
wenzelm@233
  1050
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1051
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1052
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1053
wenzelm@233
  1054
wenzelm@233
  1055
wenzelm@2506
  1056
(** orders **)
wenzelm@2506
  1057
wenzelm@4445
  1058
fun rev_order LESS = GREATER
wenzelm@4445
  1059
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1060
  | rev_order GREATER = LESS;
wenzelm@4445
  1061
wenzelm@4479
  1062
(*assume rel is a linear strict order*)
wenzelm@4445
  1063
fun make_ord rel (x, y) =
wenzelm@4445
  1064
  if rel (x, y) then LESS
wenzelm@4445
  1065
  else if rel (y, x) then GREATER
wenzelm@4445
  1066
  else EQUAL;
wenzelm@4445
  1067
wenzelm@15051
  1068
val int_ord = Int.compare;
wenzelm@15051
  1069
val string_ord = String.compare;
wenzelm@2506
  1070
wenzelm@16676
  1071
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1072
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1073
wenzelm@16492
  1074
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1075
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1076
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1077
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1078
wenzelm@4343
  1079
(*lexicographic product*)
wenzelm@4343
  1080
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1081
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1082
wenzelm@4343
  1083
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1084
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1085
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1086
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1087
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1088
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1089
wenzelm@4343
  1090
(*lexicographic product of lists*)
wenzelm@4343
  1091
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1092
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1093
wenzelm@2506
  1094
wenzelm@4621
  1095
(* sorting *)
wenzelm@4621
  1096
wenzelm@4621
  1097
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1098
fun sort ord =
wenzelm@4621
  1099
  let
wenzelm@16878
  1100
    fun qsort [] = []
wenzelm@16878
  1101
      | qsort (xs as [_]) = xs
wenzelm@16878
  1102
      | qsort (xs as [x, y]) = if ord (x, y) = GREATER then [y, x] else xs
wenzelm@16878
  1103
      | qsort xs =
haftmann@18011
  1104
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
  1105
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1106
    and part _ [] = ([], [], [])
wenzelm@4621
  1107
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1108
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1109
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1110
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1111
  in qsort end;
wenzelm@4621
  1112
wenzelm@4621
  1113
(*sort strings*)
wenzelm@4621
  1114
val sort_strings = sort string_ord;
wenzelm@4621
  1115
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1116
berghofe@11514
  1117
fun unique_strings ([]: string list) = []
berghofe@11514
  1118
  | unique_strings [x] = [x]
berghofe@11514
  1119
  | unique_strings (x :: y :: ys) =
berghofe@11514
  1120
      if x = y then unique_strings (y :: ys)
berghofe@11514
  1121
      else x :: unique_strings (y :: ys);
wenzelm@4621
  1122
wenzelm@2506
  1123
berghofe@14106
  1124
(** random numbers **)
berghofe@14106
  1125
berghofe@14106
  1126
exception RANDOM;
berghofe@14106
  1127
berghofe@14618
  1128
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1129
berghofe@14106
  1130
local
berghofe@14106
  1131
  val a = 16807.0;
berghofe@14106
  1132
  val m = 2147483647.0;
berghofe@14106
  1133
  val random_seed = ref 1.0;
berghofe@14106
  1134
in
berghofe@14106
  1135
berghofe@14106
  1136
fun random () =
berghofe@14106
  1137
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1138
  in (random_seed := r; r) end;
berghofe@14106
  1139
berghofe@14106
  1140
end;
berghofe@14106
  1141
berghofe@14106
  1142
fun random_range l h =
berghofe@14106
  1143
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1144
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1145
haftmann@18011
  1146
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1147
berghofe@14106
  1148
fun frequency xs =
berghofe@14106
  1149
  let
berghofe@14106
  1150
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1151
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1152
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1153
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1154
berghofe@14106
  1155
wenzelm@14826
  1156
(** current directory **)
wenzelm@233
  1157
paulson@2243
  1158
val cd = OS.FileSys.chDir;
wenzelm@2317
  1159
val pwd = OS.FileSys.getDir;
paulson@2243
  1160
berghofe@3606
  1161
wenzelm@4621
  1162
(** misc **)
wenzelm@233
  1163
clasohm@0
  1164
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1165
  Preserves order of elements in both lists.*)
skalberg@15570
  1166
val partition = List.partition;
clasohm@0
  1167
clasohm@0
  1168
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@16842
  1169
  let
wenzelm@16842
  1170
    fun part [] = []
wenzelm@16842
  1171
      | part (x :: ys) =
wenzelm@16842
  1172
          let val (xs, xs') = partition (fn y => eq (x, y)) ys
wenzelm@16842
  1173
          in (x::xs)::(part xs') end
wenzelm@16842
  1174
  in part end;
clasohm@0
  1175
clasohm@0
  1176
wenzelm@233
  1177
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1178
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1179
fun partition_list p i j =
wenzelm@233
  1180
  let fun part k xs =
wenzelm@233
  1181
            if k>j then
clasohm@0
  1182
              (case xs of [] => []
skalberg@15570
  1183
                         | _ => raise Fail "partition_list")
clasohm@0
  1184
            else
wenzelm@233
  1185
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1186
            in  ns :: part(k+1)rest  end
clasohm@0
  1187
  in  part i end;
clasohm@0
  1188
clasohm@0
  1189
wenzelm@233
  1190
(* generating identifiers *)
clasohm@0
  1191
paulson@4063
  1192
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1193
local
paulson@4063
  1194
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1195
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1196
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1197
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1198
             else if i=62 then "_"
wenzelm@5904
  1199
             else  (*i=63*)    "'";
paulson@4063
  1200
paulson@4063
  1201
val charVec = Vector.tabulate (64, char);
paulson@4063
  1202
wenzelm@5904
  1203
fun newid n =
wenzelm@5904
  1204
  let
wenzelm@4284
  1205
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1206
wenzelm@4284
  1207
val seedr = ref 0;
clasohm@0
  1208
paulson@4063
  1209
in
wenzelm@4284
  1210
wenzelm@12346
  1211
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1212
paulson@4063
  1213
end;
paulson@4063
  1214
paulson@4063
  1215
wenzelm@233
  1216
(* lexical scanning *)
clasohm@0
  1217
wenzelm@233
  1218
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1219
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1220
fun scanwords is_let cs =
clasohm@0
  1221
  let fun scan1 [] = []
wenzelm@233
  1222
        | scan1 cs =
wenzelm@233
  1223
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1224
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1225
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1226
wenzelm@4212
  1227
wenzelm@16439
  1228
(* stamps and serial numbers *)
wenzelm@16439
  1229
wenzelm@16439
  1230
type stamp = unit ref;
wenzelm@16439
  1231
val stamp: unit -> stamp = ref;
wenzelm@16439
  1232
wenzelm@16439
  1233
type serial = int;
wenzelm@16439
  1234
local val count = ref 0
wenzelm@16439
  1235
in fun serial () = inc count end;
wenzelm@16439
  1236
wenzelm@16535
  1237
wenzelm@16535
  1238
(* generic objects *)
wenzelm@16535
  1239
wenzelm@16535
  1240
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1241
  constructors at any time*)
wenzelm@16535
  1242
structure Object = struct type T = exn end;
wenzelm@16535
  1243
clasohm@1364
  1244
end;
clasohm@1364
  1245
wenzelm@15745
  1246
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1247
open BasicLibrary;