src/Pure/library.ML
author haftmann
Tue Dec 20 08:38:10 2005 +0100 (2005-12-20)
changeset 18441 7488d8ea61bc
parent 18427 b7ee916ae3ec
child 18450 e57731ba01dd
permissions -rw-r--r--
removed infix prefix, introduces burrow
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(*  Title:      Pure/library.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Markus Wenzel, TU Muenchen
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Basic library: functions, options, pairs, booleans, lists, integers,
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strings, lists as sets, association lists, generic
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tables, balanced trees, orders, current directory, misc.
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*)
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infix 1 |> |-> ||> ||>> |>> |>>> #> #->;
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infix 2 ?;
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infix 3 o oo ooo oooo;
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infix 4 ~~ upto downto;
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infix orf andf \ \\ ins ins_string ins_int mem mem_int mem_string union union_int
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  union_string inter inter_int inter_string subset subset_int subset_string;
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signature BASIC_LIBRARY =
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sig
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  (*functions*)
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  val I: 'a -> 'a
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  val K: 'a -> 'b -> 'a
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  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
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  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
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  val |> : 'a * ('a -> 'b) -> 'b
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  val |-> : ('c * 'a) * ('c -> 'a -> 'b) -> 'b
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  val ||> : ('c * 'a) * ('a -> 'b) -> 'c * 'b
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  val ||>> : ('c * 'a) * ('a -> 'd * 'b) -> ('c * 'd) * 'b
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  val |>> : ('a * 'c) * ('a -> 'b) -> 'b * 'c
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  val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
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  val #> : ('a -> 'b) * ('b -> 'c) -> 'a -> 'c
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  val #-> : ('a -> 'c * 'b) * ('c -> 'b -> 'd) -> 'a -> 'd
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  val ? : ('a -> bool) * ('a -> 'a) -> 'a -> 'a
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  val ` : ('b -> 'a) -> 'b -> 'a * 'b
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  val tap: ('b -> 'a) -> 'b -> 'b
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  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
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  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
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  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
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  val funpow: int -> ('a -> 'a) -> 'a -> 'a
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  (*old options -- invalidated*)
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  datatype invalid = None of invalid
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  exception OPTION of invalid
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  (*options*)
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  val the: 'a option -> 'a
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  val these: 'a list option -> 'a list
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  val the_default: 'a -> 'a option -> 'a
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  val the_list: 'a option -> 'a list
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  val 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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  val perhaps: ('a -> 'a option) -> 'a -> 'a
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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 fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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  val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
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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 nth_list: 'a list list -> int -> 'a list
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  val split_last: 'a list -> 'a list * 'a
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  val find_index: ('a -> bool) -> 'a list -> int
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  val find_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 map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
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  val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
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  val ~~ : 'a list * 'b list -> ('a * 'b) list
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  val split_list: ('a * 'b) list -> 'a list * 'b list
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  val separate: 'a -> 'a list -> 'a list
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  val replicate: int -> 'a -> 'a list
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  val multiply: 'a list -> 'a list list -> 'a list list
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  val product: 'a list -> 'b list -> ('a * 'b) list
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  val filter: ('a -> bool) -> 'a list -> 'a list
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  val filter_out: ('a -> bool) -> 'a list -> 'a list
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  val equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
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  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val prefixes1: 'a list -> 'a list list
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  val 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_distinct: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_strings: string list -> string list
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  val sort_wrt: ('a -> string) -> 'a list -> 'a list
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  (*random numbers*)
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  exception RANDOM
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  val random: unit -> real
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  val random_range: int -> int -> int
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  val one_of: 'a list -> 'a
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  val frequency: (int * 'a) list -> 'a
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  (*current directory*)
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  val cd: string -> unit
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  val pwd: unit -> string
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  (*misc*)
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  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
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  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
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  val gensym: string -> string
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  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);
wenzelm@16705
   290
fun (x, y) ||> f = (x, f y);
wenzelm@16705
   291
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16705
   292
fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
wenzelm@16842
   293
wenzelm@16842
   294
(*reverse composition*)
haftmann@16780
   295
fun f #> g = g o f;
wenzelm@16842
   296
fun f #-> g = uncurry g o f;
wenzelm@16842
   297
haftmann@17141
   298
(*conditional application*)
wenzelm@17545
   299
fun b ? f = fn x => if b x then f x else x;
haftmann@17141
   300
wenzelm@16842
   301
(*view results*)
wenzelm@16842
   302
fun `f = fn x => (f x, x);
wenzelm@17545
   303
fun tap f = fn x => (f x; x);
wenzelm@380
   304
wenzelm@16721
   305
(*composition with multiple args*)
wenzelm@16721
   306
fun (f oo g) x y = f (g x y);
wenzelm@16721
   307
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   308
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   309
wenzelm@233
   310
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   311
fun funpow n f x =
wenzelm@233
   312
  let fun rep (0, x) = x
wenzelm@233
   313
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   314
  in rep (n, x) end;
wenzelm@160
   315
wenzelm@160
   316
wenzelm@233
   317
(** options **)
clasohm@0
   318
wenzelm@15670
   319
(*invalidate former constructors to prevent accidental use as match-all patterns!*)
wenzelm@15670
   320
datatype invalid = None of invalid;
wenzelm@15670
   321
exception OPTION of invalid;
clasohm@0
   322
wenzelm@15970
   323
val the = Option.valOf;
wenzelm@17341
   324
haftmann@17153
   325
fun these (SOME x) = x
haftmann@17313
   326
  | these _ = [];
wenzelm@17341
   327
haftmann@17313
   328
fun the_default x (SOME y) = y
haftmann@17313
   329
  | the_default x _ = x;
wenzelm@17341
   330
haftmann@17313
   331
fun the_list (SOME x) = [x]
haftmann@17313
   332
  | the_list _ = []
wenzelm@15970
   333
wenzelm@15970
   334
(*strict!*)
wenzelm@15970
   335
fun if_none NONE y = y
wenzelm@15970
   336
  | if_none (SOME x) _ = x;
wenzelm@15970
   337
wenzelm@15970
   338
fun is_some (SOME _) = true
wenzelm@15970
   339
  | is_some NONE = false;
wenzelm@15970
   340
wenzelm@15970
   341
fun is_none (SOME _) = false
wenzelm@15970
   342
  | is_none NONE = true;
wenzelm@15970
   343
wenzelm@18376
   344
fun perhaps f x = the_default x (f x);
wenzelm@18376
   345
wenzelm@6959
   346
wenzelm@17341
   347
(* exceptions *)
wenzelm@17341
   348
wenzelm@17341
   349
exception EXCEPTION of exn * string;
wenzelm@6959
   350
wenzelm@6959
   351
exception ERROR;
wenzelm@6959
   352
skalberg@15531
   353
fun try f x = SOME (f x)
skalberg@15531
   354
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => NONE;
wenzelm@6959
   355
wenzelm@6959
   356
fun can f x = is_some (try f x);
wenzelm@4139
   357
wenzelm@4139
   358
wenzelm@14868
   359
datatype 'a result =
wenzelm@14868
   360
  Result of 'a |
wenzelm@14868
   361
  Exn of exn;
wenzelm@14868
   362
wenzelm@14868
   363
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   364
wenzelm@14868
   365
fun release (Result y) = y
wenzelm@14868
   366
  | release (Exn e) = raise e;
wenzelm@14868
   367
skalberg@15531
   368
fun get_result (Result x) = SOME x
skalberg@15531
   369
  | get_result _ = NONE;
wenzelm@14868
   370
skalberg@15531
   371
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   372
  | get_exn _ = NONE;
wenzelm@14868
   373
wenzelm@14868
   374
wenzelm@4139
   375
wenzelm@233
   376
(** pairs **)
wenzelm@233
   377
wenzelm@233
   378
fun pair x y = (x, y);
wenzelm@233
   379
fun rpair x y = (y, x);
wenzelm@233
   380
wenzelm@233
   381
fun fst (x, y) = x;
wenzelm@233
   382
fun snd (x, y) = y;
wenzelm@233
   383
haftmann@17498
   384
fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2);
haftmann@17498
   385
fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
wenzelm@233
   386
wenzelm@233
   387
fun swap (x, y) = (y, x);
wenzelm@233
   388
wenzelm@4212
   389
(*apply function to components*)
wenzelm@233
   390
fun apfst f (x, y) = (f x, y);
wenzelm@233
   391
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   392
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   393
wenzelm@233
   394
wenzelm@233
   395
wenzelm@233
   396
(** booleans **)
wenzelm@233
   397
wenzelm@233
   398
(* equality *)
wenzelm@233
   399
wenzelm@233
   400
fun equal x y = x = y;
wenzelm@233
   401
fun not_equal x y = x <> y;
wenzelm@233
   402
wenzelm@233
   403
wenzelm@233
   404
(* operators for combining predicates *)
wenzelm@233
   405
wenzelm@16721
   406
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   407
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   408
wenzelm@233
   409
wenzelm@233
   410
(* predicates on lists *)
wenzelm@233
   411
wenzelm@233
   412
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   413
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   414
  let fun boolf [] = false
wenzelm@233
   415
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   416
  in boolf end;
wenzelm@233
   417
wenzelm@233
   418
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   419
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   420
  let fun boolf [] = true
wenzelm@233
   421
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   422
  in boolf end;
clasohm@0
   423
wenzelm@233
   424
wenzelm@380
   425
(* flags *)
wenzelm@380
   426
wenzelm@380
   427
fun set flag = (flag := true; true);
wenzelm@380
   428
fun reset flag = (flag := false; false);
wenzelm@380
   429
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   430
wenzelm@9118
   431
fun change r f = r := f (! r);
wenzelm@9118
   432
wenzelm@14826
   433
(*temporarily set flag, handling exceptions*)
wenzelm@2978
   434
fun setmp flag value f x =
wenzelm@2958
   435
  let
wenzelm@2958
   436
    val orig_value = ! flag;
wenzelm@2958
   437
    fun return y = (flag := orig_value; y);
wenzelm@2958
   438
  in
wenzelm@2958
   439
    flag := value;
wenzelm@2958
   440
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   441
  end;
wenzelm@2958
   442
wenzelm@380
   443
wenzelm@11853
   444
(* conditional execution *)
wenzelm@11853
   445
wenzelm@11853
   446
fun conditional b f = if b then f () else ();
wenzelm@11853
   447
wenzelm@11853
   448
wenzelm@233
   449
wenzelm@233
   450
(** lists **)
wenzelm@233
   451
skalberg@15570
   452
exception UnequalLengths;
wenzelm@233
   453
wenzelm@233
   454
fun cons x xs = x :: xs;
wenzelm@5285
   455
fun single x = [x];
wenzelm@233
   456
wenzelm@4629
   457
fun append xs ys = xs @ ys;
wenzelm@4629
   458
wenzelm@5904
   459
fun apply [] x = x
wenzelm@5904
   460
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   461
wenzelm@233
   462
wenzelm@233
   463
(* fold *)
wenzelm@233
   464
wenzelm@16654
   465
fun fold f =
wenzelm@16654
   466
  let
wenzelm@16654
   467
    fun fold_aux [] y = y
wenzelm@16654
   468
      | fold_aux (x :: xs) y = fold_aux xs (f x y);
wenzelm@16654
   469
  in fold_aux end;
wenzelm@15760
   470
wenzelm@16654
   471
fun fold_rev f =
wenzelm@16654
   472
  let
wenzelm@16654
   473
    fun fold_aux [] y = y
wenzelm@16654
   474
      | fold_aux (x :: xs) y = f x (fold_aux xs y);
wenzelm@16654
   475
  in fold_aux end;
wenzelm@16654
   476
haftmann@16869
   477
fun fold_map f =
haftmann@16691
   478
  let
haftmann@16691
   479
    fun fold_aux [] y = ([], y)
haftmann@16691
   480
      | fold_aux (x :: xs) y =
haftmann@16691
   481
          let
wenzelm@16705
   482
            val (x', y') = f x y;
wenzelm@16705
   483
            val (xs', y'') = fold_aux xs y';
haftmann@16691
   484
          in (x' :: xs', y'') end;
haftmann@16691
   485
  in fold_aux end;
haftmann@16691
   486
wenzelm@233
   487
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   488
wenzelm@233
   489
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   490
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   491
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   492
  let fun itl (e, [])  = e
wenzelm@233
   493
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   494
  in  itl end;
wenzelm@233
   495
wenzelm@233
   496
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   497
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   498
fun foldr f (l, e) =
wenzelm@233
   499
  let fun itr [] = e
wenzelm@233
   500
        | itr (a::l) = f(a, itr l)
wenzelm@233
   501
  in  itr l  end;
wenzelm@233
   502
wenzelm@233
   503
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   504
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   505
fun foldr1 f l =
wenzelm@4181
   506
  let fun itr [x] = x
wenzelm@233
   507
        | itr (x::l) = f(x, itr l)
wenzelm@233
   508
  in  itr l  end;
wenzelm@233
   509
haftmann@18050
   510
fun fold_index f =
haftmann@18050
   511
  let
haftmann@18050
   512
    fun fold_aux _  [] y = y
haftmann@18050
   513
      | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
haftmann@18050
   514
  in fold_aux 0 end;
wenzelm@14792
   515
wenzelm@16705
   516
fun foldl_map f =
wenzelm@16705
   517
  let
wenzelm@16705
   518
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   519
      | fold_aux (x, y :: ys) =
wenzelm@16705
   520
          let
wenzelm@16705
   521
            val (x', y') = f (x, y);
wenzelm@16705
   522
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   523
          in (x'', y' :: ys') end;
wenzelm@16705
   524
  in fold_aux end;
wenzelm@16705
   525
wenzelm@233
   526
wenzelm@233
   527
(* basic list functions *)
wenzelm@233
   528
wenzelm@233
   529
(*take the first n elements from a list*)
wenzelm@233
   530
fun take (n, []) = []
wenzelm@233
   531
  | take (n, x :: xs) =
wenzelm@233
   532
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   533
wenzelm@233
   534
(*drop the first n elements from a list*)
wenzelm@233
   535
fun drop (n, []) = []
wenzelm@233
   536
  | drop (n, x :: xs) =
wenzelm@233
   537
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   538
nipkow@13629
   539
fun splitAt(n,[]) = ([],[])
nipkow@13629
   540
  | splitAt(n,xs as x::ys) =
nipkow@13629
   541
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
nipkow@13629
   542
      else ([],xs)
nipkow@13629
   543
nipkow@4713
   544
fun dropwhile P [] = []
nipkow@4713
   545
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   546
wenzelm@233
   547
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   548
  raise EXCEPTION if list too short*)
haftmann@18011
   549
fun nth xs i = List.nth (xs, i);
wenzelm@233
   550
haftmann@18011
   551
(*update nth element*)
haftmann@18011
   552
fun nth_update (n, x) xs =
haftmann@18011
   553
    (case splitAt (n, xs) of
haftmann@18011
   554
      (_, []) => raise Subscript
haftmann@18011
   555
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
haftmann@18011
   556
haftmann@18011
   557
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   558
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   559
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   560
wenzelm@18286
   561
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18286
   562
skalberg@15570
   563
val last_elem = List.last;
wenzelm@233
   564
wenzelm@3762
   565
(*rear decomposition*)
skalberg@15570
   566
fun split_last [] = raise Empty
wenzelm@3762
   567
  | split_last [x] = ([], x)
wenzelm@3762
   568
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   569
wenzelm@4212
   570
(*find the position of an element in a list*)
wenzelm@4212
   571
fun find_index pred =
wenzelm@4212
   572
  let fun find _ [] = ~1
wenzelm@4212
   573
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   574
  in find 0 end;
wenzelm@3762
   575
wenzelm@4224
   576
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   577
wenzelm@4212
   578
(*find first element satisfying predicate*)
skalberg@15531
   579
fun find_first _ [] = NONE
wenzelm@4212
   580
  | find_first pred (x :: xs) =
skalberg@15531
   581
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   582
wenzelm@4916
   583
(*get first element by lookup function*)
skalberg@15531
   584
fun get_first _ [] = NONE
wenzelm@4916
   585
  | get_first f (x :: xs) =
wenzelm@4916
   586
      (case f x of
skalberg@15531
   587
        NONE => get_first f xs
wenzelm@4916
   588
      | some => some);
wenzelm@4916
   589
wenzelm@233
   590
(*flatten a list of lists to a list*)
skalberg@15531
   591
val flat = List.concat;
wenzelm@233
   592
wenzelm@12136
   593
fun unflat (xs :: xss) ys =
nipkow@13629
   594
      let val (ps,qs) = splitAt(length xs,ys)
nipkow@13629
   595
      in ps :: unflat xss qs end
wenzelm@12136
   596
  | unflat [] [] = []
skalberg@15570
   597
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   598
haftmann@18441
   599
fun burrow f xss =
haftmann@18359
   600
  unflat xss ((f o flat) xss);
haftmann@18359
   601
haftmann@18359
   602
wenzelm@233
   603
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   604
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   605
val seq = List.app;
wenzelm@233
   606
wenzelm@233
   607
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   608
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   609
  | separate _ xs = xs;
wenzelm@233
   610
wenzelm@233
   611
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   612
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   613
  let fun rep (0, xs) = xs
wenzelm@233
   614
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   615
  in
skalberg@15570
   616
    if n < 0 then raise Subscript
wenzelm@233
   617
    else rep (n, [])
wenzelm@233
   618
  end;
wenzelm@233
   619
wenzelm@14926
   620
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   621
wenzelm@4248
   622
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   623
fun multiply [] _ = []
wenzelm@18148
   624
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   625
wenzelm@14792
   626
(*direct product*)
wenzelm@14792
   627
fun product _ [] = []
wenzelm@14792
   628
  | product [] _ = []
wenzelm@14792
   629
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   630
wenzelm@233
   631
wenzelm@233
   632
(* filter *)
wenzelm@233
   633
wenzelm@233
   634
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   635
val filter = List.filter;
clasohm@0
   636
fun filter_out f = filter (not o f);
skalberg@15570
   637
val mapfilter = List.mapPartial;
wenzelm@233
   638
wenzelm@233
   639
wenzelm@233
   640
(* lists of pairs *)
wenzelm@233
   641
skalberg@15570
   642
exception UnequalLengths;
skalberg@15570
   643
haftmann@18330
   644
fun map2 _ [] [] = []
haftmann@18330
   645
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   646
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   647
haftmann@18330
   648
fun fold2 f =
haftmann@18330
   649
  let
haftmann@18330
   650
    fun fold_aux [] [] z = z
haftmann@18330
   651
      | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z)
haftmann@18330
   652
      | fold_aux _ _ _ = raise UnequalLengths;
haftmann@18330
   653
  in fold_aux end;
wenzelm@380
   654
wenzelm@4956
   655
wenzelm@233
   656
(*combine two lists forming a list of pairs:
wenzelm@233
   657
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   658
fun [] ~~ [] = []
wenzelm@233
   659
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   660
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   661
wenzelm@233
   662
(*inverse of ~~; the old 'split':
wenzelm@233
   663
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   664
val split_list = ListPair.unzip;
wenzelm@233
   665
haftmann@18330
   666
fun equal_lists eq (xs, ys) =
haftmann@18330
   667
  let
haftmann@18330
   668
    fun eq' [] [] = true
haftmann@18330
   669
      | eq' (x :: xs) (y :: ys) = eq (x, y) andalso eq' xs ys
haftmann@18330
   670
  in length xs = length ys andalso eq' xs ys end;
wenzelm@7468
   671
wenzelm@233
   672
wenzelm@233
   673
(* prefixes, suffixes *)
wenzelm@233
   674
haftmann@18441
   675
fun is_prefix _ [] _ = true
haftmann@18441
   676
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   677
  | is_prefix eq _ _ = false;
wenzelm@233
   678
wenzelm@233
   679
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   680
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   681
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   682
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   683
        | take (rxs, x :: xs) =
wenzelm@255
   684
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   685
  in  take([], xs)  end;
wenzelm@233
   686
wenzelm@233
   687
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   688
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   689
fun take_suffix _ [] = ([], [])
wenzelm@233
   690
  | take_suffix pred (x :: xs) =
wenzelm@233
   691
      (case take_suffix pred xs of
wenzelm@233
   692
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   693
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   694
wenzelm@12249
   695
fun prefixes1 [] = []
wenzelm@12249
   696
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   697
wenzelm@12249
   698
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@12249
   699
wenzelm@233
   700
wenzelm@233
   701
wenzelm@233
   702
(** integers **)
wenzelm@233
   703
wenzelm@16439
   704
fun gcd (x, y) =
paulson@15965
   705
  let fun gxd x y : IntInf.int =
nipkow@10692
   706
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   707
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   708
wenzelm@16439
   709
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   710
wenzelm@2958
   711
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   712
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   713
wenzelm@233
   714
wenzelm@233
   715
(* lists of integers *)
wenzelm@233
   716
wenzelm@233
   717
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   718
fun (from upto to) =
wenzelm@233
   719
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   720
wenzelm@233
   721
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   722
fun (from downto to) =
wenzelm@233
   723
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   724
wenzelm@233
   725
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   726
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   727
  | downto0 ([], n) = n = ~1;
wenzelm@233
   728
wenzelm@233
   729
wenzelm@233
   730
(* convert integers to strings *)
wenzelm@233
   731
wenzelm@233
   732
(*expand the number in the given base;
wenzelm@233
   733
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   734
fun radixpand (base, num) : int list =
wenzelm@233
   735
  let
wenzelm@233
   736
    fun radix (n, tail) =
wenzelm@233
   737
      if n < base then n :: tail
wenzelm@233
   738
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   739
  in radix (num, []) end;
wenzelm@233
   740
wenzelm@233
   741
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   742
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   743
fun radixstring (base, zerochar, num) =
wenzelm@233
   744
  let val offset = ord zerochar;
wenzelm@233
   745
      fun chrof n = chr (offset + n)
wenzelm@233
   746
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   747
wenzelm@233
   748
paulson@3407
   749
val string_of_int = Int.toString;
wenzelm@233
   750
paulson@3407
   751
fun string_of_indexname (a,0) = a
paulson@3407
   752
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   753
wenzelm@233
   754
wenzelm@14826
   755
(* read integers *)
wenzelm@14826
   756
wenzelm@14826
   757
fun read_radixint (radix: int, cs) : int * string list =
wenzelm@14826
   758
  let val zero = ord"0"
wenzelm@14826
   759
      val limit = zero+radix
wenzelm@14826
   760
      fun scan (num,[]) = (num,[])
wenzelm@14826
   761
        | scan (num, c::cs) =
wenzelm@14826
   762
              if  zero <= ord c  andalso  ord c < limit
wenzelm@14826
   763
              then scan(radix*num + ord c - zero, cs)
wenzelm@14826
   764
              else (num, c::cs)
wenzelm@14826
   765
  in  scan(0,cs)  end;
wenzelm@14826
   766
wenzelm@14826
   767
fun read_int cs = read_radixint (10, cs);
wenzelm@14826
   768
wenzelm@14826
   769
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
wenzelm@14826
   770
wenzelm@14826
   771
wenzelm@14826
   772
wenzelm@233
   773
(** strings **)
wenzelm@233
   774
wenzelm@16188
   775
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   776
haftmann@18011
   777
fun nth_string str i =
wenzelm@6959
   778
  (case try String.substring (str, i, 1) of
skalberg@15531
   779
    SOME s => s
skalberg@15570
   780
  | NONE => raise Subscript);
wenzelm@6312
   781
wenzelm@16188
   782
fun fold_string f str x0 =
wenzelm@6282
   783
  let
wenzelm@6282
   784
    val n = size str;
wenzelm@16188
   785
    fun iter (x, i) =
wenzelm@16188
   786
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   787
  in iter (x0, 0) end;
wenzelm@6282
   788
wenzelm@14968
   789
fun exists_string pred str =
wenzelm@14968
   790
  let
wenzelm@14968
   791
    val n = size str;
wenzelm@14968
   792
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   793
  in ex 0 end;
wenzelm@6312
   794
wenzelm@16188
   795
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   796
lcp@512
   797
(*enclose in brackets*)
lcp@512
   798
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   799
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   800
wenzelm@233
   801
(*simple quoting (does not escape special chars)*)
lcp@512
   802
val quote = enclose "\"" "\"";
wenzelm@233
   803
wenzelm@4212
   804
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   805
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   806
wenzelm@255
   807
val commas = space_implode ", ";
wenzelm@380
   808
val commas_quote = commas o map quote;
wenzelm@255
   809
wenzelm@233
   810
(*concatenate messages, one per line, into a string*)
wenzelm@255
   811
val cat_lines = space_implode "\n";
wenzelm@233
   812
wenzelm@4212
   813
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   814
fun space_explode _ "" = []
wenzelm@3832
   815
  | space_explode sep str =
wenzelm@3832
   816
      let
wenzelm@3832
   817
        fun expl chs =
wenzelm@3832
   818
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   819
            (cs, []) => [implode cs]
wenzelm@3832
   820
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   821
      in expl (explode str) end;
wenzelm@3832
   822
wenzelm@3832
   823
val split_lines = space_explode "\n";
wenzelm@3832
   824
wenzelm@14826
   825
fun prefix_lines "" txt = txt
wenzelm@14826
   826
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   827
wenzelm@7712
   828
fun untabify chs =
wenzelm@7712
   829
  let
wenzelm@7712
   830
    val tab_width = 8;
wenzelm@7712
   831
wenzelm@7712
   832
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   833
      | untab (pos, "\t") =
wenzelm@9118
   834
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   835
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   836
  in
wenzelm@7712
   837
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   838
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   839
  end;
wenzelm@7712
   840
wenzelm@16188
   841
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   842
wenzelm@16188
   843
fun unsuffix sffx s =
wenzelm@17061
   844
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   845
  else raise Fail "unsuffix";
wenzelm@5285
   846
berghofe@15060
   847
fun unprefix prfx s =
wenzelm@17061
   848
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@17061
   849
  else raise Fail "unprefix";
berghofe@15060
   850
wenzelm@10951
   851
fun replicate_string 0 _ = ""
wenzelm@10951
   852
  | replicate_string 1 a = a
wenzelm@10951
   853
  | replicate_string k a =
wenzelm@10951
   854
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   855
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   856
wenzelm@3832
   857
wenzelm@233
   858
wenzelm@16492
   859
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   860
wenzelm@233
   861
(*membership in a list*)
wenzelm@233
   862
fun x mem [] = false
wenzelm@233
   863
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   864
paulson@2175
   865
(*membership in a list, optimized version for ints*)
berghofe@1576
   866
fun (x:int) mem_int [] = false
berghofe@1576
   867
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   868
paulson@2175
   869
(*membership in a list, optimized version for strings*)
berghofe@1576
   870
fun (x:string) mem_string [] = false
berghofe@1576
   871
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   872
clasohm@0
   873
(*generalized membership test*)
wenzelm@233
   874
fun gen_mem eq (x, []) = false
wenzelm@233
   875
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   876
wenzelm@16492
   877
(*member, insert, and remove -- with canonical argument order*)
wenzelm@16492
   878
fun member eq xs x = gen_mem eq (x, xs);
wenzelm@15760
   879
fun insert eq x xs = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@15760
   880
fun remove eq x xs = if gen_mem eq (x, xs) then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   881
wenzelm@233
   882
(*insertion into list if not already there*)
paulson@2175
   883
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   884
paulson@2175
   885
(*insertion into list, optimized version for ints*)
paulson@2175
   886
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   887
paulson@2175
   888
(*insertion into list, optimized version for strings*)
paulson@2175
   889
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   890
clasohm@0
   891
(*generalized insertion*)
wenzelm@15760
   892
fun gen_ins eq (x, xs) = insert eq x xs;
wenzelm@233
   893
wenzelm@233
   894
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   895
fun xs union [] = xs
wenzelm@233
   896
  | [] union ys = ys
wenzelm@233
   897
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   898
paulson@2175
   899
(*union of sets, optimized version for ints*)
berghofe@1576
   900
fun (xs:int list) union_int [] = xs
berghofe@1576
   901
  | [] union_int ys = ys
berghofe@1576
   902
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   903
paulson@2175
   904
(*union of sets, optimized version for strings*)
berghofe@1576
   905
fun (xs:string list) union_string [] = xs
berghofe@1576
   906
  | [] union_string ys = ys
berghofe@1576
   907
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   908
clasohm@0
   909
(*generalized union*)
wenzelm@233
   910
fun gen_union eq (xs, []) = xs
wenzelm@233
   911
  | gen_union eq ([], ys) = ys
wenzelm@233
   912
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   913
wenzelm@233
   914
wenzelm@233
   915
(*intersection*)
wenzelm@233
   916
fun [] inter ys = []
wenzelm@233
   917
  | (x :: xs) inter ys =
wenzelm@233
   918
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   919
paulson@2175
   920
(*intersection, optimized version for ints*)
berghofe@1576
   921
fun ([]:int list) inter_int ys = []
berghofe@1576
   922
  | (x :: xs) inter_int ys =
berghofe@1576
   923
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   924
paulson@2175
   925
(*intersection, optimized version for strings *)
berghofe@1576
   926
fun ([]:string list) inter_string ys = []
berghofe@1576
   927
  | (x :: xs) inter_string ys =
berghofe@1576
   928
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   929
paulson@7090
   930
(*generalized intersection*)
paulson@7090
   931
fun gen_inter eq ([], ys) = []
wenzelm@12284
   932
  | gen_inter eq (x::xs, ys) =
paulson@7090
   933
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
wenzelm@12284
   934
                           else      gen_inter eq (xs, ys);
paulson@7090
   935
wenzelm@233
   936
wenzelm@233
   937
(*subset*)
wenzelm@233
   938
fun [] subset ys = true
wenzelm@233
   939
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   940
paulson@2175
   941
(*subset, optimized version for ints*)
wenzelm@16439
   942
fun ([]: int list) subset_int ys = true
berghofe@1576
   943
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   944
paulson@2175
   945
(*subset, optimized version for strings*)
wenzelm@16439
   946
fun ([]: string list) subset_string ys = true
berghofe@1576
   947
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   948
wenzelm@4363
   949
(*set equality*)
wenzelm@4363
   950
fun eq_set (xs, ys) =
wenzelm@4363
   951
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   952
paulson@2182
   953
(*set equality for strings*)
wenzelm@16439
   954
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   955
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   956
paulson@2182
   957
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   958
wenzelm@265
   959
wenzelm@233
   960
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   961
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   962
  | [] \ x = [];
wenzelm@233
   963
paulson@2243
   964
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   965
wenzelm@233
   966
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   967
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@12295
   968
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   969
wenzelm@233
   970
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   971
  first of equal elements*)
wenzelm@233
   972
fun gen_distinct eq lst =
wenzelm@233
   973
  let
wenzelm@233
   974
    val memb = gen_mem eq;
clasohm@0
   975
wenzelm@233
   976
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   977
      | dist (rev_seen, x :: xs) =
wenzelm@233
   978
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   979
          else dist (x :: rev_seen, xs);
wenzelm@233
   980
  in
wenzelm@233
   981
    dist ([], lst)
wenzelm@233
   982
  end;
wenzelm@233
   983
paulson@2243
   984
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   985
wenzelm@233
   986
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   987
fun findrep [] = []
wenzelm@233
   988
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   989
wenzelm@233
   990
wenzelm@255
   991
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   992
  order, takes first of equal elements*)
wenzelm@255
   993
fun gen_duplicates eq lst =
wenzelm@255
   994
  let
wenzelm@255
   995
    val memb = gen_mem eq;
wenzelm@255
   996
wenzelm@255
   997
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   998
      | dups (rev_dups, x :: xs) =
wenzelm@255
   999
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
  1000
            dups (rev_dups, xs)
wenzelm@255
  1001
          else dups (x :: rev_dups, xs);
wenzelm@255
  1002
  in
wenzelm@255
  1003
    dups ([], lst)
wenzelm@255
  1004
  end;
wenzelm@255
  1005
paulson@2243
  1006
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
  1007
wenzelm@16878
  1008
fun has_duplicates eq =
wenzelm@16878
  1009
  let
wenzelm@16878
  1010
    fun dups [] = false
wenzelm@16878
  1011
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
  1012
  in dups end;
wenzelm@16878
  1013
wenzelm@255
  1014
wenzelm@233
  1015
wenzelm@233
  1016
(** association lists **)
clasohm@0
  1017
wenzelm@12284
  1018
(* lists as tables *)
wenzelm@233
  1019
wenzelm@12284
  1020
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1021
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1022
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1023
wenzelm@12284
  1024
fun gen_merge_lists' _ xs [] = xs
wenzelm@12284
  1025
  | gen_merge_lists' _ [] ys = ys
wenzelm@12295
  1026
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
clasohm@0
  1027
wenzelm@12284
  1028
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
wenzelm@12284
  1029
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
haftmann@17498
  1030
fun merge_alists al = gen_merge_lists (eq_fst (op =)) al;
haftmann@17498
  1031
fun merge_alists' al = gen_merge_lists' (eq_fst (op =)) al;
wenzelm@380
  1032
clasohm@0
  1033
clasohm@0
  1034
wenzelm@233
  1035
(** balanced trees **)
wenzelm@233
  1036
wenzelm@233
  1037
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1038
wenzelm@233
  1039
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1040
fun fold_bal f [x] = x
wenzelm@233
  1041
  | fold_bal f [] = raise Balance
wenzelm@233
  1042
  | fold_bal f xs =
nipkow@13629
  1043
      let val (ps,qs) = splitAt(length xs div 2, xs)
nipkow@13629
  1044
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1045
wenzelm@233
  1046
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1047
fun access_bal (f, g, x) n i =
wenzelm@233
  1048
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1049
          if n=1 then x else
wenzelm@233
  1050
          let val n2 = n div 2
wenzelm@233
  1051
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1052
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1053
          end
wenzelm@233
  1054
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1055
wenzelm@233
  1056
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1057
fun accesses_bal (f, g, x) n =
wenzelm@233
  1058
  let fun acc n =
wenzelm@233
  1059
          if n=1 then [x] else
wenzelm@233
  1060
          let val n2 = n div 2
wenzelm@233
  1061
              val acc2 = acc n2
wenzelm@233
  1062
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1063
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1064
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1065
wenzelm@233
  1066
wenzelm@233
  1067
wenzelm@2506
  1068
(** orders **)
wenzelm@2506
  1069
wenzelm@4445
  1070
fun rev_order LESS = GREATER
wenzelm@4445
  1071
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1072
  | rev_order GREATER = LESS;
wenzelm@4445
  1073
wenzelm@4479
  1074
(*assume rel is a linear strict order*)
wenzelm@4445
  1075
fun make_ord rel (x, y) =
wenzelm@4445
  1076
  if rel (x, y) then LESS
wenzelm@4445
  1077
  else if rel (y, x) then GREATER
wenzelm@4445
  1078
  else EQUAL;
wenzelm@4445
  1079
wenzelm@15051
  1080
val int_ord = Int.compare;
wenzelm@15051
  1081
val string_ord = String.compare;
wenzelm@2506
  1082
wenzelm@16676
  1083
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1084
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1085
wenzelm@16492
  1086
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1087
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1088
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1089
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1090
wenzelm@4343
  1091
(*lexicographic product*)
wenzelm@4343
  1092
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1093
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1094
wenzelm@4343
  1095
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1096
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1097
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1098
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1099
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1100
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1101
wenzelm@4343
  1102
(*lexicographic product of lists*)
wenzelm@4343
  1103
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1104
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1105
wenzelm@2506
  1106
wenzelm@4621
  1107
(* sorting *)
wenzelm@4621
  1108
wenzelm@18427
  1109
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
  1110
fun quicksort unique ord =
wenzelm@4621
  1111
  let
wenzelm@16878
  1112
    fun qsort [] = []
wenzelm@16878
  1113
      | qsort (xs as [_]) = xs
wenzelm@18427
  1114
      | qsort (xs as [x, y]) =
wenzelm@18427
  1115
          (case ord (x, y) of
wenzelm@18427
  1116
            LESS => xs
wenzelm@18427
  1117
          | EQUAL => if unique then [x] else xs
wenzelm@18427
  1118
          | GREATER => [y, x])
wenzelm@16878
  1119
      | qsort xs =
haftmann@18011
  1120
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
  1121
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1122
    and part _ [] = ([], [], [])
wenzelm@4621
  1123
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1124
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
  1125
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
  1126
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
  1127
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1128
  in qsort end;
wenzelm@4621
  1129
wenzelm@18427
  1130
fun sort ord = quicksort false ord;
wenzelm@18427
  1131
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
  1132
wenzelm@4621
  1133
val sort_strings = sort string_ord;
wenzelm@4621
  1134
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1135
wenzelm@4621
  1136
wenzelm@2506
  1137
berghofe@14106
  1138
(** random numbers **)
berghofe@14106
  1139
berghofe@14106
  1140
exception RANDOM;
berghofe@14106
  1141
berghofe@14618
  1142
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1143
berghofe@14106
  1144
local
berghofe@14106
  1145
  val a = 16807.0;
berghofe@14106
  1146
  val m = 2147483647.0;
berghofe@14106
  1147
  val random_seed = ref 1.0;
berghofe@14106
  1148
in
berghofe@14106
  1149
berghofe@14106
  1150
fun random () =
berghofe@14106
  1151
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1152
  in (random_seed := r; r) end;
berghofe@14106
  1153
berghofe@14106
  1154
end;
berghofe@14106
  1155
berghofe@14106
  1156
fun random_range l h =
berghofe@14106
  1157
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1158
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1159
haftmann@18011
  1160
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
  1161
berghofe@14106
  1162
fun frequency xs =
berghofe@14106
  1163
  let
berghofe@14106
  1164
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
  1165
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
  1166
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1167
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1168
berghofe@14106
  1169
wenzelm@14826
  1170
(** current directory **)
wenzelm@233
  1171
paulson@2243
  1172
val cd = OS.FileSys.chDir;
wenzelm@2317
  1173
val pwd = OS.FileSys.getDir;
paulson@2243
  1174
berghofe@3606
  1175
wenzelm@4621
  1176
(** misc **)
wenzelm@233
  1177
clasohm@0
  1178
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1179
  Preserves order of elements in both lists.*)
skalberg@15570
  1180
val partition = List.partition;
clasohm@0
  1181
clasohm@0
  1182
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@16842
  1183
  let
wenzelm@16842
  1184
    fun part [] = []
wenzelm@16842
  1185
      | part (x :: ys) =
wenzelm@16842
  1186
          let val (xs, xs') = partition (fn y => eq (x, y)) ys
wenzelm@16842
  1187
          in (x::xs)::(part xs') end
wenzelm@16842
  1188
  in part end;
clasohm@0
  1189
clasohm@0
  1190
wenzelm@233
  1191
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1192
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1193
fun partition_list p i j =
wenzelm@233
  1194
  let fun part k xs =
wenzelm@233
  1195
            if k>j then
clasohm@0
  1196
              (case xs of [] => []
skalberg@15570
  1197
                         | _ => raise Fail "partition_list")
clasohm@0
  1198
            else
wenzelm@233
  1199
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1200
            in  ns :: part(k+1)rest  end
clasohm@0
  1201
  in  part i end;
clasohm@0
  1202
clasohm@0
  1203
wenzelm@233
  1204
(* generating identifiers *)
clasohm@0
  1205
paulson@4063
  1206
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1207
local
paulson@4063
  1208
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1209
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1210
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1211
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1212
             else if i=62 then "_"
wenzelm@5904
  1213
             else  (*i=63*)    "'";
paulson@4063
  1214
paulson@4063
  1215
val charVec = Vector.tabulate (64, char);
paulson@4063
  1216
wenzelm@5904
  1217
fun newid n =
wenzelm@5904
  1218
  let
wenzelm@4284
  1219
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1220
wenzelm@4284
  1221
val seedr = ref 0;
clasohm@0
  1222
paulson@4063
  1223
in
wenzelm@4284
  1224
wenzelm@12346
  1225
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1226
paulson@4063
  1227
end;
paulson@4063
  1228
paulson@4063
  1229
wenzelm@233
  1230
(* lexical scanning *)
clasohm@0
  1231
wenzelm@233
  1232
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1233
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1234
fun scanwords is_let cs =
clasohm@0
  1235
  let fun scan1 [] = []
wenzelm@233
  1236
        | scan1 cs =
wenzelm@233
  1237
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1238
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1239
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1240
wenzelm@4212
  1241
wenzelm@16439
  1242
(* stamps and serial numbers *)
wenzelm@16439
  1243
wenzelm@16439
  1244
type stamp = unit ref;
wenzelm@16439
  1245
val stamp: unit -> stamp = ref;
wenzelm@16439
  1246
wenzelm@16439
  1247
type serial = int;
wenzelm@16439
  1248
local val count = ref 0
wenzelm@16439
  1249
in fun serial () = inc count end;
wenzelm@16439
  1250
wenzelm@16535
  1251
wenzelm@16535
  1252
(* generic objects *)
wenzelm@16535
  1253
wenzelm@16535
  1254
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1255
  constructors at any time*)
wenzelm@16535
  1256
structure Object = struct type T = exn end;
wenzelm@16535
  1257
clasohm@1364
  1258
end;
clasohm@1364
  1259
wenzelm@15745
  1260
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1261
open BasicLibrary;