src/Pure/library.ML
author wenzelm
Mon Aug 01 19:20:38 2005 +0200 (2005-08-01)
changeset 16984 abc48b981e60
parent 16878 07213f0e291f
child 17028 a497f621bfd4
permissions -rw-r--r--
tuned dict_ord;
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(*  Title:      Pure/library.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Markus Wenzel, TU Muenchen
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Basic library: functions, options, pairs, booleans, lists, integers,
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rational numbers, strings, lists as sets, association lists, generic
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tables, balanced trees, orders, current directory, misc.
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*)
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infix |> |-> ||> ||>> |>> |>>> #> #-> ~~ \ \\ ins ins_string ins_int
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  orf andf prefix upto downto mem mem_int mem_string union union_int
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  union_string inter inter_int inter_string subset subset_int
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  subset_string;
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infix 3 oo ooo oooo;
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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 ` : ('b -> 'a) -> 'b -> 'a * '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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  val apl: 'a * ('a * 'b -> 'c) -> 'b -> 'c
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  val apr: ('a * 'b -> 'c) * 'b -> 'a -> 'c
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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 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 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 * 'b) * (''a * 'c) -> bool
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  val eq_snd: ('a * ''b) * ('c * ''b) -> bool
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  val swap: 'a * 'b -> 'b * 'a
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  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
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  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
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  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
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  (*booleans*)
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  val equal: ''a -> ''a -> bool
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  val not_equal: ''a -> ''a -> bool
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  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val exists: ('a -> bool) -> 'a list -> bool
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  val forall: ('a -> bool) -> 'a list -> bool
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  val set: bool ref -> bool
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  val reset: bool ref -> bool
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  val toggle: bool ref -> bool
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  val change: 'a ref -> ('a -> 'a) -> unit
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  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val conditional: bool -> (unit -> unit) -> unit
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  (*lists*)
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  exception UnequalLengths
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  val cons: 'a -> 'a list -> 'a list
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  val single: 'a -> 'a list
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  val append: 'a list -> 'a list -> 'a list
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  val apply: ('a -> 'a) list -> 'a -> 'a
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  val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val fold_map: ('a -> 'b -> 'c * 'b) -> 'a list -> 'b -> 'c list * 'b
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  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val foldln: ('a * int -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val unflat: 'a list list -> 'b list -> 'b list list
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  val splitAt: int * 'a list -> 'a list * 'a list
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  val dropwhile: ('a -> bool) -> 'a list -> 'a list
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  val map_nth_elem: int -> ('a -> 'a) -> 'a list -> 'a list
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  val split_last: 'a list -> 'a list * 'a
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  val nth_update: 'a -> int * 'a list -> 'a list
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  val find_index: ('a -> bool) -> 'a list -> int
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  val find_index_eq: ''a -> ''a list -> int
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  val find_first: ('a -> bool) -> 'a list -> 'a option
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  val get_first: ('a -> 'b option) -> 'a list -> 'b option
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  val separate: 'a -> 'a list -> 'a list
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  val replicate: int -> 'a -> 'a list
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  val multiply: 'a list * 'a list list -> 'a list list
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  val product: 'a list -> 'b list -> ('a * 'b) list
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  val filter: ('a -> bool) -> 'a list -> 'a list
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  val filter_out: ('a -> bool) -> 'a list -> 'a list
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  val map2: ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list
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  val exists2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val forall2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val seq2: ('a * 'b -> unit) -> 'a list * 'b list -> unit
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  val ~~ : 'a list * 'b list -> ('a * 'b) list
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  val split_list: ('a * 'b) list -> 'a list * 'b list
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  val equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val prefix: ''a list * ''a list -> bool
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  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val prefixes1: 'a list -> 'a list list
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  val suffixes1: 'a list -> 'a list list
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  (*integers*)
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  val gcd: IntInf.int * IntInf.int -> IntInf.int
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  val lcm: IntInf.int * IntInf.int -> IntInf.int
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  val inc: int ref -> int
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  val dec: int ref -> int
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  val upto: int * int -> int list
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  val downto: int * int -> int list
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  val downto0: int list * int -> bool
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  val radixpand: int * int -> int list
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  val radixstring: int * string * int -> string
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  val string_of_int: int -> string
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  val string_of_indexname: string * int -> string
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  val read_radixint: int * string list -> int * string list
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  val read_int: string list -> int * string list
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  val oct_char: string -> string
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  (*rational numbers*)
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  type rat
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  exception RAT of string
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  val rep_rat: rat -> IntInf.int * IntInf.int
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  val ratadd: rat * rat -> rat
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  val ratmul: rat * rat -> rat
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  val ratinv: rat -> rat
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  val int_ratdiv: IntInf.int * IntInf.int -> rat
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  val ratneg: rat -> rat
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  val rat_of_int: int -> rat
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  val rat_of_intinf: IntInf.int -> rat
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  (*strings*)
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  val nth_elem_string: int * string -> string
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  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
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  val exists_string: (string -> bool) -> string -> bool
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  val forall_string: (string -> bool) -> string -> bool
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  val enclose: string -> string -> string -> string
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  val unenclose: string -> string
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  val quote: string -> string
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  val space_implode: string -> string list -> string
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  val commas: string list -> string
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  val commas_quote: string list -> string
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  val cat_lines: string list -> string
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  val space_explode: string -> string -> string list
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  val split_lines: string -> string list
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  val prefix_lines: string -> string -> string
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  val untabify: string list -> string list
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  val suffix: string -> string -> string
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  val unsuffix: string -> string -> string
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  val unprefix: string -> string -> string
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  val replicate_string: int -> string -> string
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  val translate_string: (string -> string) -> string -> string
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  (*lists as sets -- see also Pure/General/ord_list.ML*)
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  val mem: ''a * ''a list -> bool
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  val mem_int: int * int list -> bool
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  val mem_string: string * string list -> bool
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  val gen_mem: ('a * 'b -> bool) -> 'a * 'b list -> bool
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  val ins: ''a * ''a list -> ''a list
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  val ins_int: int * int list -> int list
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  val ins_string: string * string list -> string list
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  val gen_ins: ('a * 'a -> bool) -> 'a * 'a list -> 'a list
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  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
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  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
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  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val union: ''a list * ''a list -> ''a list
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  val union_int: int list * int list -> int list
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  val union_string: string list * string list -> string list
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  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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  val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
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  val inter: ''a list * ''a list -> ''a list
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  val inter_int: int list * int list -> int list
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  val inter_string: string list * string list -> string list
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  val subset: ''a list * ''a list -> bool
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  val subset_int: int list * int list -> bool
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  val subset_string: string list * string list -> bool
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  val eq_set: ''a list * ''a list -> bool
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  val eq_set_string: string list * string list -> bool
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  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val \ : ''a list * ''a -> ''a list
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  val \\ : ''a list * ''a list -> ''a list
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  val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list
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  val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
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  val gen_distinct: ('a * 'a -> bool) -> 'a list -> 'a list
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  val distinct: ''a list -> ''a list
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  val findrep: ''a list -> ''a list
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  val gen_duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
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  val duplicates: ''a list -> ''a list
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  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
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  (*association lists*)
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  val assoc: (''a * 'b) list * ''a -> 'b option
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  val assoc_int: (int * 'a) list * int -> 'a option
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  val assoc_string: (string * 'a) list * string -> 'a option
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  val assoc_string_int: ((string * int) * 'a) list * (string * int) -> 'a option
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  val assocs: (''a * 'b list) list -> ''a -> 'b list
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  val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) -> 'c option
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  val gen_assoc: ('a * 'b -> bool) -> ('b * 'c) list * 'a -> 'c option
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  val overwrite: (''a * 'b) list * (''a * 'b) -> (''a * 'b) list
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  val gen_overwrite: ('a * 'a -> bool) -> ('a * 'b) list * ('a * 'b) -> ('a * 'b) list
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  (*lists as tables*)
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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 make_keylist: ('a -> 'b) -> 'a list -> ('a * 'b) list
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  val keyfilter: ('a * ''b) list -> ''b -> 'a list
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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
skalberg@15570
   286
  val nth_elem: int * 'a list -> 'a
skalberg@15570
   287
  val last_elem: 'a list -> 'a
skalberg@15570
   288
  val flat: 'a list list -> 'a list
skalberg@15570
   289
  val seq: ('a -> unit) -> 'a list -> unit
skalberg@15570
   290
  val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
skalberg@15570
   291
  val mapfilter: ('a -> 'b option) -> 'a list -> 'b list
skalberg@15570
   292
end;
skalberg@15570
   293
wenzelm@15745
   294
structure Library: LIBRARY =
clasohm@1364
   295
struct
clasohm@0
   296
wenzelm@4995
   297
wenzelm@233
   298
(** functions **)
clasohm@0
   299
wenzelm@16842
   300
fun I x = x;
wenzelm@16842
   301
fun K x = fn _ => x;
wenzelm@233
   302
fun curry f x y = f (x, y);
wenzelm@233
   303
fun uncurry f (x, y) = f x y;
clasohm@0
   304
wenzelm@16705
   305
(*reverse application and structured results*)
wenzelm@16705
   306
fun x |> f = f x;
wenzelm@16705
   307
fun (x, y) |-> f = f x y;
wenzelm@16705
   308
fun (x, y) |>> f = (f x, y);
wenzelm@16705
   309
fun (x, y) ||> f = (x, f y);
wenzelm@16705
   310
fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@16705
   311
fun (x, y) ||>> f = let val (z, y') = f y in ((x, z), y') end;
wenzelm@16842
   312
wenzelm@16842
   313
(*reverse composition*)
haftmann@16780
   314
fun f #> g = g o f;
wenzelm@16842
   315
fun f #-> g = uncurry g o f;
wenzelm@16842
   316
wenzelm@16842
   317
(*view results*)
wenzelm@16842
   318
fun `f = fn x => (f x, x);
wenzelm@380
   319
wenzelm@16721
   320
(*composition with multiple args*)
wenzelm@16721
   321
fun (f oo g) x y = f (g x y);
wenzelm@16721
   322
fun (f ooo g) x y z = f (g x y z);
wenzelm@16721
   323
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@16721
   324
wenzelm@233
   325
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   326
fun funpow n f x =
wenzelm@233
   327
  let fun rep (0, x) = x
wenzelm@233
   328
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   329
  in rep (n, x) end;
wenzelm@160
   330
wenzelm@16842
   331
(*application of (infix) operator to its left or right argument*)
wenzelm@16842
   332
fun apl (x, f) y = f (x, y);
wenzelm@16842
   333
fun apr (f, y) x = f (x, y);
wenzelm@160
   334
wenzelm@160
   335
wenzelm@233
   336
(** options **)
clasohm@0
   337
wenzelm@15670
   338
(*invalidate former constructors to prevent accidental use as match-all patterns!*)
wenzelm@15670
   339
datatype invalid = None of invalid;
wenzelm@15670
   340
exception OPTION of invalid;
clasohm@0
   341
wenzelm@15970
   342
val the = Option.valOf;
wenzelm@15970
   343
wenzelm@15970
   344
(*strict!*)
wenzelm@15970
   345
fun if_none NONE y = y
wenzelm@15970
   346
  | if_none (SOME x) _ = x;
wenzelm@15970
   347
wenzelm@15970
   348
fun is_some (SOME _) = true
wenzelm@15970
   349
  | is_some NONE = false;
wenzelm@15970
   350
wenzelm@15970
   351
fun is_none (SOME _) = false
wenzelm@15970
   352
  | is_none NONE = true;
wenzelm@15970
   353
wenzelm@6959
   354
wenzelm@6959
   355
(* exception handling *)
wenzelm@6959
   356
wenzelm@6959
   357
exception ERROR;
wenzelm@6959
   358
skalberg@15531
   359
fun try f x = SOME (f x)
skalberg@15531
   360
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => NONE;
wenzelm@6959
   361
wenzelm@6959
   362
fun can f x = is_some (try f x);
wenzelm@4139
   363
wenzelm@4139
   364
wenzelm@14868
   365
datatype 'a result =
wenzelm@14868
   366
  Result of 'a |
wenzelm@14868
   367
  Exn of exn;
wenzelm@14868
   368
wenzelm@14868
   369
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   370
wenzelm@14868
   371
fun release (Result y) = y
wenzelm@14868
   372
  | release (Exn e) = raise e;
wenzelm@14868
   373
skalberg@15531
   374
fun get_result (Result x) = SOME x
skalberg@15531
   375
  | get_result _ = NONE;
wenzelm@14868
   376
skalberg@15531
   377
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   378
  | get_exn _ = NONE;
wenzelm@14868
   379
wenzelm@14868
   380
wenzelm@4139
   381
wenzelm@233
   382
(** pairs **)
wenzelm@233
   383
wenzelm@233
   384
fun pair x y = (x, y);
wenzelm@233
   385
fun rpair x y = (y, x);
wenzelm@233
   386
wenzelm@233
   387
fun fst (x, y) = x;
wenzelm@233
   388
fun snd (x, y) = y;
wenzelm@233
   389
wenzelm@233
   390
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   391
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   392
wenzelm@233
   393
fun swap (x, y) = (y, x);
wenzelm@233
   394
wenzelm@4212
   395
(*apply function to components*)
wenzelm@233
   396
fun apfst f (x, y) = (f x, y);
wenzelm@233
   397
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   398
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   399
wenzelm@233
   400
wenzelm@233
   401
wenzelm@233
   402
(** booleans **)
wenzelm@233
   403
wenzelm@233
   404
(* equality *)
wenzelm@233
   405
wenzelm@233
   406
fun equal x y = x = y;
wenzelm@233
   407
fun not_equal x y = x <> y;
wenzelm@233
   408
wenzelm@233
   409
wenzelm@233
   410
(* operators for combining predicates *)
wenzelm@233
   411
wenzelm@16721
   412
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   413
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   414
wenzelm@233
   415
wenzelm@233
   416
(* predicates on lists *)
wenzelm@233
   417
wenzelm@233
   418
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   419
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   420
  let fun boolf [] = false
wenzelm@233
   421
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   422
  in boolf end;
wenzelm@233
   423
wenzelm@233
   424
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   425
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   426
  let fun boolf [] = true
wenzelm@233
   427
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   428
  in boolf end;
clasohm@0
   429
wenzelm@233
   430
wenzelm@380
   431
(* flags *)
wenzelm@380
   432
wenzelm@380
   433
fun set flag = (flag := true; true);
wenzelm@380
   434
fun reset flag = (flag := false; false);
wenzelm@380
   435
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   436
wenzelm@9118
   437
fun change r f = r := f (! r);
wenzelm@9118
   438
wenzelm@14826
   439
(*temporarily set flag, handling exceptions*)
wenzelm@2978
   440
fun setmp flag value f x =
wenzelm@2958
   441
  let
wenzelm@2958
   442
    val orig_value = ! flag;
wenzelm@2958
   443
    fun return y = (flag := orig_value; y);
wenzelm@2958
   444
  in
wenzelm@2958
   445
    flag := value;
wenzelm@2958
   446
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   447
  end;
wenzelm@2958
   448
wenzelm@380
   449
wenzelm@11853
   450
(* conditional execution *)
wenzelm@11853
   451
wenzelm@11853
   452
fun conditional b f = if b then f () else ();
wenzelm@11853
   453
wenzelm@11853
   454
wenzelm@233
   455
wenzelm@233
   456
(** lists **)
wenzelm@233
   457
skalberg@15570
   458
exception UnequalLengths;
wenzelm@233
   459
wenzelm@233
   460
fun cons x xs = x :: xs;
wenzelm@5285
   461
fun single x = [x];
wenzelm@233
   462
wenzelm@4629
   463
fun append xs ys = xs @ ys;
wenzelm@4629
   464
wenzelm@5904
   465
fun apply [] x = x
wenzelm@5904
   466
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   467
wenzelm@233
   468
wenzelm@233
   469
(* fold *)
wenzelm@233
   470
wenzelm@16654
   471
fun fold f =
wenzelm@16654
   472
  let
wenzelm@16654
   473
    fun fold_aux [] y = y
wenzelm@16654
   474
      | fold_aux (x :: xs) y = fold_aux xs (f x y);
wenzelm@16654
   475
  in fold_aux end;
wenzelm@15760
   476
wenzelm@16654
   477
fun fold_rev f =
wenzelm@16654
   478
  let
wenzelm@16654
   479
    fun fold_aux [] y = y
wenzelm@16654
   480
      | fold_aux (x :: xs) y = f x (fold_aux xs y);
wenzelm@16654
   481
  in fold_aux end;
wenzelm@16654
   482
haftmann@16869
   483
fun fold_map f =
haftmann@16691
   484
  let
haftmann@16691
   485
    fun fold_aux [] y = ([], y)
haftmann@16691
   486
      | fold_aux (x :: xs) y =
haftmann@16691
   487
          let
wenzelm@16705
   488
            val (x', y') = f x y;
wenzelm@16705
   489
            val (xs', y'') = fold_aux xs y';
haftmann@16691
   490
          in (x' :: xs', y'') end;
haftmann@16691
   491
  in fold_aux end;
haftmann@16691
   492
wenzelm@233
   493
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   494
wenzelm@233
   495
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   496
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   497
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   498
  let fun itl (e, [])  = e
wenzelm@233
   499
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   500
  in  itl end;
wenzelm@233
   501
wenzelm@233
   502
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   503
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   504
fun foldr f (l, e) =
wenzelm@233
   505
  let fun itr [] = e
wenzelm@233
   506
        | itr (a::l) = f(a, itr l)
wenzelm@233
   507
  in  itr l  end;
wenzelm@233
   508
wenzelm@233
   509
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   510
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   511
fun foldr1 f l =
wenzelm@4181
   512
  let fun itr [x] = x
wenzelm@233
   513
        | itr (x::l) = f(x, itr l)
wenzelm@233
   514
  in  itr l  end;
wenzelm@233
   515
wenzelm@15760
   516
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
wenzelm@14792
   517
wenzelm@16705
   518
fun foldl_map f =
wenzelm@16705
   519
  let
wenzelm@16705
   520
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   521
      | fold_aux (x, y :: ys) =
wenzelm@16705
   522
          let
wenzelm@16705
   523
            val (x', y') = f (x, y);
wenzelm@16705
   524
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   525
          in (x'', y' :: ys') end;
wenzelm@16705
   526
  in fold_aux end;
wenzelm@16705
   527
wenzelm@233
   528
wenzelm@233
   529
(* basic list functions *)
wenzelm@233
   530
wenzelm@233
   531
(*take the first n elements from a list*)
wenzelm@233
   532
fun take (n, []) = []
wenzelm@233
   533
  | take (n, x :: xs) =
wenzelm@233
   534
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   535
wenzelm@233
   536
(*drop the first n elements from a list*)
wenzelm@233
   537
fun drop (n, []) = []
wenzelm@233
   538
  | drop (n, x :: xs) =
wenzelm@233
   539
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   540
nipkow@13629
   541
fun splitAt(n,[]) = ([],[])
nipkow@13629
   542
  | splitAt(n,xs as x::ys) =
nipkow@13629
   543
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
nipkow@13629
   544
      else ([],xs)
nipkow@13629
   545
nipkow@4713
   546
fun dropwhile P [] = []
nipkow@4713
   547
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   548
wenzelm@233
   549
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   550
  raise EXCEPTION if list too short*)
skalberg@15570
   551
fun nth_elem (i,xs) = List.nth(xs,i);
wenzelm@233
   552
wenzelm@11773
   553
fun map_nth_elem 0 f (x :: xs) = f x :: xs
wenzelm@11773
   554
  | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs
skalberg@15570
   555
  | map_nth_elem _ _ [] = raise Subscript;
wenzelm@11773
   556
wenzelm@233
   557
(*last element of a list*)
skalberg@15570
   558
val last_elem = List.last;
wenzelm@233
   559
wenzelm@3762
   560
(*rear decomposition*)
skalberg@15570
   561
fun split_last [] = raise Empty
wenzelm@3762
   562
  | split_last [x] = ([], x)
wenzelm@3762
   563
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   564
wenzelm@4893
   565
(*update nth element*)
nipkow@13629
   566
fun nth_update x n_xs =
nipkow@13629
   567
    (case splitAt n_xs of
skalberg@15570
   568
      (_,[]) => raise Subscript
nipkow@13629
   569
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
wenzelm@4893
   570
wenzelm@4212
   571
(*find the position of an element in a list*)
wenzelm@4212
   572
fun find_index pred =
wenzelm@4212
   573
  let fun find _ [] = ~1
wenzelm@4212
   574
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   575
  in find 0 end;
wenzelm@3762
   576
wenzelm@4224
   577
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   578
wenzelm@4212
   579
(*find first element satisfying predicate*)
skalberg@15531
   580
fun find_first _ [] = NONE
wenzelm@4212
   581
  | find_first pred (x :: xs) =
skalberg@15531
   582
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   583
wenzelm@4916
   584
(*get first element by lookup function*)
skalberg@15531
   585
fun get_first _ [] = NONE
wenzelm@4916
   586
  | get_first f (x :: xs) =
wenzelm@4916
   587
      (case f x of
skalberg@15531
   588
        NONE => get_first f xs
wenzelm@4916
   589
      | some => some);
wenzelm@4916
   590
wenzelm@233
   591
(*flatten a list of lists to a list*)
skalberg@15531
   592
val flat = List.concat;
wenzelm@233
   593
wenzelm@12136
   594
fun unflat (xs :: xss) ys =
nipkow@13629
   595
      let val (ps,qs) = splitAt(length xs,ys)
nipkow@13629
   596
      in ps :: unflat xss qs end
wenzelm@12136
   597
  | unflat [] [] = []
skalberg@15570
   598
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   599
wenzelm@233
   600
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   601
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   602
val seq = List.app;
wenzelm@233
   603
wenzelm@233
   604
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   605
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   606
  | separate _ xs = xs;
wenzelm@233
   607
wenzelm@233
   608
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   609
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   610
  let fun rep (0, xs) = xs
wenzelm@233
   611
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   612
  in
skalberg@15570
   613
    if n < 0 then raise Subscript
wenzelm@233
   614
    else rep (n, [])
wenzelm@233
   615
  end;
wenzelm@233
   616
wenzelm@14926
   617
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   618
wenzelm@4248
   619
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   620
fun multiply ([], _) = []
wenzelm@4248
   621
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   622
wenzelm@14792
   623
(*direct product*)
wenzelm@14792
   624
fun product _ [] = []
wenzelm@14792
   625
  | product [] _ = []
wenzelm@14792
   626
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   627
wenzelm@233
   628
wenzelm@233
   629
(* filter *)
wenzelm@233
   630
wenzelm@233
   631
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   632
val filter = List.filter;
clasohm@0
   633
fun filter_out f = filter (not o f);
skalberg@15570
   634
val mapfilter = List.mapPartial;
wenzelm@233
   635
wenzelm@233
   636
wenzelm@233
   637
(* lists of pairs *)
wenzelm@233
   638
skalberg@15570
   639
exception UnequalLengths;
skalberg@15570
   640
wenzelm@380
   641
fun map2 _ ([], []) = []
wenzelm@16878
   642
  | map2 f (x :: xs, y :: ys) = f (x, y) :: map2 f (xs, ys)
skalberg@15570
   643
  | map2 _ _ = raise UnequalLengths;
wenzelm@380
   644
wenzelm@380
   645
fun exists2 _ ([], []) = false
wenzelm@380
   646
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
skalberg@15570
   647
  | exists2 _ _ = raise UnequalLengths;
wenzelm@380
   648
wenzelm@380
   649
fun forall2 _ ([], []) = true
wenzelm@380
   650
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
skalberg@15570
   651
  | forall2 _ _ = raise UnequalLengths;
wenzelm@380
   652
wenzelm@4956
   653
fun seq2 _ ([], []) = ()
wenzelm@4956
   654
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
skalberg@15570
   655
  | seq2 _ _ = raise UnequalLengths;
wenzelm@4956
   656
wenzelm@233
   657
(*combine two lists forming a list of pairs:
wenzelm@233
   658
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   659
fun [] ~~ [] = []
wenzelm@233
   660
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   661
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   662
wenzelm@233
   663
(*inverse of ~~; the old 'split':
wenzelm@233
   664
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   665
val split_list = ListPair.unzip;
wenzelm@233
   666
wenzelm@7468
   667
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
wenzelm@7468
   668
wenzelm@233
   669
wenzelm@233
   670
(* prefixes, suffixes *)
wenzelm@233
   671
wenzelm@233
   672
fun [] prefix _ = true
wenzelm@233
   673
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   674
  | _ prefix _ = false;
wenzelm@233
   675
wenzelm@233
   676
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   677
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   678
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   679
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   680
        | take (rxs, x :: xs) =
wenzelm@255
   681
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   682
  in  take([], xs)  end;
wenzelm@233
   683
wenzelm@233
   684
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   685
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   686
fun take_suffix _ [] = ([], [])
wenzelm@233
   687
  | take_suffix pred (x :: xs) =
wenzelm@233
   688
      (case take_suffix pred xs of
wenzelm@233
   689
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   690
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   691
wenzelm@12249
   692
fun prefixes1 [] = []
wenzelm@12249
   693
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   694
wenzelm@12249
   695
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@12249
   696
wenzelm@233
   697
wenzelm@233
   698
wenzelm@233
   699
(** integers **)
wenzelm@233
   700
wenzelm@16439
   701
fun gcd (x, y) =
paulson@15965
   702
  let fun gxd x y : IntInf.int =
nipkow@10692
   703
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   704
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   705
wenzelm@16439
   706
fun lcm (x, y) = (x * y) div gcd (x, y);
nipkow@10692
   707
wenzelm@2958
   708
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   709
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   710
wenzelm@233
   711
wenzelm@233
   712
(* lists of integers *)
wenzelm@233
   713
wenzelm@233
   714
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   715
fun (from upto to) =
wenzelm@233
   716
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   717
wenzelm@233
   718
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   719
fun (from downto to) =
wenzelm@233
   720
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   721
wenzelm@233
   722
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   723
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   724
  | downto0 ([], n) = n = ~1;
wenzelm@233
   725
wenzelm@233
   726
wenzelm@233
   727
(* convert integers to strings *)
wenzelm@233
   728
wenzelm@233
   729
(*expand the number in the given base;
wenzelm@233
   730
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   731
fun radixpand (base, num) : int list =
wenzelm@233
   732
  let
wenzelm@233
   733
    fun radix (n, tail) =
wenzelm@233
   734
      if n < base then n :: tail
wenzelm@233
   735
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   736
  in radix (num, []) end;
wenzelm@233
   737
wenzelm@233
   738
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   739
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   740
fun radixstring (base, zerochar, num) =
wenzelm@233
   741
  let val offset = ord zerochar;
wenzelm@233
   742
      fun chrof n = chr (offset + n)
wenzelm@233
   743
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   744
wenzelm@233
   745
paulson@3407
   746
val string_of_int = Int.toString;
wenzelm@233
   747
paulson@3407
   748
fun string_of_indexname (a,0) = a
paulson@3407
   749
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   750
wenzelm@233
   751
wenzelm@14826
   752
(* read integers *)
wenzelm@14826
   753
wenzelm@14826
   754
fun read_radixint (radix: int, cs) : int * string list =
wenzelm@14826
   755
  let val zero = ord"0"
wenzelm@14826
   756
      val limit = zero+radix
wenzelm@14826
   757
      fun scan (num,[]) = (num,[])
wenzelm@14826
   758
        | scan (num, c::cs) =
wenzelm@14826
   759
              if  zero <= ord c  andalso  ord c < limit
wenzelm@14826
   760
              then scan(radix*num + ord c - zero, cs)
wenzelm@14826
   761
              else (num, c::cs)
wenzelm@14826
   762
  in  scan(0,cs)  end;
wenzelm@14826
   763
wenzelm@14826
   764
fun read_int cs = read_radixint (10, cs);
wenzelm@14826
   765
wenzelm@14826
   766
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
wenzelm@14826
   767
wenzelm@14826
   768
wenzelm@14826
   769
wenzelm@233
   770
(** strings **)
wenzelm@233
   771
wenzelm@16188
   772
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   773
wenzelm@6312
   774
fun nth_elem_string (i, str) =
wenzelm@6959
   775
  (case try String.substring (str, i, 1) of
skalberg@15531
   776
    SOME s => s
skalberg@15570
   777
  | NONE => raise Subscript);
wenzelm@6312
   778
wenzelm@16188
   779
fun fold_string f str x0 =
wenzelm@6282
   780
  let
wenzelm@6282
   781
    val n = size str;
wenzelm@16188
   782
    fun iter (x, i) =
wenzelm@16188
   783
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   784
  in iter (x0, 0) end;
wenzelm@6282
   785
wenzelm@14968
   786
fun exists_string pred str =
wenzelm@14968
   787
  let
wenzelm@14968
   788
    val n = size str;
wenzelm@14968
   789
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   790
  in ex 0 end;
wenzelm@6312
   791
wenzelm@16188
   792
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   793
lcp@512
   794
(*enclose in brackets*)
lcp@512
   795
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   796
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   797
wenzelm@233
   798
(*simple quoting (does not escape special chars)*)
lcp@512
   799
val quote = enclose "\"" "\"";
wenzelm@233
   800
wenzelm@4212
   801
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   802
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   803
wenzelm@255
   804
val commas = space_implode ", ";
wenzelm@380
   805
val commas_quote = commas o map quote;
wenzelm@255
   806
wenzelm@233
   807
(*concatenate messages, one per line, into a string*)
wenzelm@255
   808
val cat_lines = space_implode "\n";
wenzelm@233
   809
wenzelm@4212
   810
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   811
fun space_explode _ "" = []
wenzelm@3832
   812
  | space_explode sep str =
wenzelm@3832
   813
      let
wenzelm@3832
   814
        fun expl chs =
wenzelm@3832
   815
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   816
            (cs, []) => [implode cs]
wenzelm@3832
   817
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   818
      in expl (explode str) end;
wenzelm@3832
   819
wenzelm@3832
   820
val split_lines = space_explode "\n";
wenzelm@3832
   821
wenzelm@14826
   822
fun prefix_lines "" txt = txt
wenzelm@14826
   823
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   824
wenzelm@7712
   825
fun untabify chs =
wenzelm@7712
   826
  let
wenzelm@7712
   827
    val tab_width = 8;
wenzelm@7712
   828
wenzelm@7712
   829
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   830
      | untab (pos, "\t") =
wenzelm@9118
   831
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   832
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   833
  in
wenzelm@7712
   834
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   835
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   836
  end;
wenzelm@7712
   837
wenzelm@16188
   838
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   839
wenzelm@16188
   840
fun unsuffix sffx s =
wenzelm@16188
   841
  let val m = size sffx; val n = size s - m in
wenzelm@16188
   842
    if n >= 0 andalso String.substring (s, n, m) = sffx then String.substring (s, 0, n)
skalberg@15570
   843
    else raise Fail "unsuffix"
wenzelm@5285
   844
  end;
wenzelm@5285
   845
berghofe@15060
   846
fun unprefix prfx s =
wenzelm@16188
   847
  let val m = size prfx; val n = size s - m in
wenzelm@16188
   848
    if String.isPrefix prfx s then String.substring (s, m, n)
skalberg@15570
   849
    else raise Fail "unprefix"
berghofe@15060
   850
  end;
berghofe@15060
   851
wenzelm@10951
   852
fun replicate_string 0 _ = ""
wenzelm@10951
   853
  | replicate_string 1 a = a
wenzelm@10951
   854
  | replicate_string k a =
wenzelm@10951
   855
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   856
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   857
wenzelm@3832
   858
wenzelm@233
   859
wenzelm@16492
   860
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   861
wenzelm@233
   862
(*membership in a list*)
wenzelm@233
   863
fun x mem [] = false
wenzelm@233
   864
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   865
paulson@2175
   866
(*membership in a list, optimized version for ints*)
berghofe@1576
   867
fun (x:int) mem_int [] = false
berghofe@1576
   868
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   869
paulson@2175
   870
(*membership in a list, optimized version for strings*)
berghofe@1576
   871
fun (x:string) mem_string [] = false
berghofe@1576
   872
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   873
clasohm@0
   874
(*generalized membership test*)
wenzelm@233
   875
fun gen_mem eq (x, []) = false
wenzelm@233
   876
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   877
wenzelm@16492
   878
(*member, insert, and remove -- with canonical argument order*)
wenzelm@16492
   879
fun member eq xs x = gen_mem eq (x, xs);
wenzelm@15760
   880
fun insert eq x xs = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@15760
   881
fun remove eq x xs = if gen_mem eq (x, xs) then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   882
wenzelm@233
   883
(*insertion into list if not already there*)
paulson@2175
   884
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   885
paulson@2175
   886
(*insertion into list, optimized version for ints*)
paulson@2175
   887
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   888
paulson@2175
   889
(*insertion into list, optimized version for strings*)
paulson@2175
   890
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   891
clasohm@0
   892
(*generalized insertion*)
wenzelm@15760
   893
fun gen_ins eq (x, xs) = insert eq x xs;
wenzelm@233
   894
wenzelm@233
   895
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   896
fun xs union [] = xs
wenzelm@233
   897
  | [] union ys = ys
wenzelm@233
   898
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   899
paulson@2175
   900
(*union of sets, optimized version for ints*)
berghofe@1576
   901
fun (xs:int list) union_int [] = xs
berghofe@1576
   902
  | [] union_int ys = ys
berghofe@1576
   903
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   904
paulson@2175
   905
(*union of sets, optimized version for strings*)
berghofe@1576
   906
fun (xs:string list) union_string [] = xs
berghofe@1576
   907
  | [] union_string ys = ys
berghofe@1576
   908
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   909
clasohm@0
   910
(*generalized union*)
wenzelm@233
   911
fun gen_union eq (xs, []) = xs
wenzelm@233
   912
  | gen_union eq ([], ys) = ys
wenzelm@233
   913
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   914
wenzelm@233
   915
wenzelm@233
   916
(*intersection*)
wenzelm@233
   917
fun [] inter ys = []
wenzelm@233
   918
  | (x :: xs) inter ys =
wenzelm@233
   919
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   920
paulson@2175
   921
(*intersection, optimized version for ints*)
berghofe@1576
   922
fun ([]:int list) inter_int ys = []
berghofe@1576
   923
  | (x :: xs) inter_int ys =
berghofe@1576
   924
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   925
paulson@2175
   926
(*intersection, optimized version for strings *)
berghofe@1576
   927
fun ([]:string list) inter_string ys = []
berghofe@1576
   928
  | (x :: xs) inter_string ys =
berghofe@1576
   929
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   930
paulson@7090
   931
(*generalized intersection*)
paulson@7090
   932
fun gen_inter eq ([], ys) = []
wenzelm@12284
   933
  | gen_inter eq (x::xs, ys) =
paulson@7090
   934
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
wenzelm@12284
   935
                           else      gen_inter eq (xs, ys);
paulson@7090
   936
wenzelm@233
   937
wenzelm@233
   938
(*subset*)
wenzelm@233
   939
fun [] subset ys = true
wenzelm@233
   940
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   941
paulson@2175
   942
(*subset, optimized version for ints*)
wenzelm@16439
   943
fun ([]: int list) subset_int ys = true
berghofe@1576
   944
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   945
paulson@2175
   946
(*subset, optimized version for strings*)
wenzelm@16439
   947
fun ([]: string list) subset_string ys = true
berghofe@1576
   948
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   949
wenzelm@4363
   950
(*set equality*)
wenzelm@4363
   951
fun eq_set (xs, ys) =
wenzelm@4363
   952
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   953
paulson@2182
   954
(*set equality for strings*)
wenzelm@16439
   955
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   956
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   957
paulson@2182
   958
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   959
wenzelm@265
   960
wenzelm@233
   961
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   962
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   963
  | [] \ x = [];
wenzelm@233
   964
paulson@2243
   965
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   966
wenzelm@233
   967
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   968
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@12295
   969
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   970
wenzelm@233
   971
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   972
  first of equal elements*)
wenzelm@233
   973
fun gen_distinct eq lst =
wenzelm@233
   974
  let
wenzelm@233
   975
    val memb = gen_mem eq;
clasohm@0
   976
wenzelm@233
   977
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   978
      | dist (rev_seen, x :: xs) =
wenzelm@233
   979
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   980
          else dist (x :: rev_seen, xs);
wenzelm@233
   981
  in
wenzelm@233
   982
    dist ([], lst)
wenzelm@233
   983
  end;
wenzelm@233
   984
paulson@2243
   985
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   986
wenzelm@233
   987
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   988
fun findrep [] = []
wenzelm@233
   989
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   990
wenzelm@233
   991
wenzelm@255
   992
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   993
  order, takes first of equal elements*)
wenzelm@255
   994
fun gen_duplicates eq lst =
wenzelm@255
   995
  let
wenzelm@255
   996
    val memb = gen_mem eq;
wenzelm@255
   997
wenzelm@255
   998
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   999
      | dups (rev_dups, x :: xs) =
wenzelm@255
  1000
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
  1001
            dups (rev_dups, xs)
wenzelm@255
  1002
          else dups (x :: rev_dups, xs);
wenzelm@255
  1003
  in
wenzelm@255
  1004
    dups ([], lst)
wenzelm@255
  1005
  end;
wenzelm@255
  1006
paulson@2243
  1007
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
  1008
wenzelm@16878
  1009
fun has_duplicates eq =
wenzelm@16878
  1010
  let
wenzelm@16878
  1011
    fun dups [] = false
wenzelm@16878
  1012
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
  1013
  in dups end;
wenzelm@16878
  1014
wenzelm@255
  1015
wenzelm@233
  1016
wenzelm@233
  1017
(** association lists **)
clasohm@0
  1018
wenzelm@233
  1019
(*association list lookup*)
skalberg@15531
  1020
fun assoc ([], key) = NONE
wenzelm@233
  1021
  | assoc ((keyi, xi) :: pairs, key) =
skalberg@15531
  1022
      if key = keyi then SOME xi else assoc (pairs, key);
wenzelm@233
  1023
paulson@2175
  1024
(*association list lookup, optimized version for ints*)
skalberg@15531
  1025
fun assoc_int ([], (key:int)) = NONE
berghofe@1576
  1026
  | assoc_int ((keyi, xi) :: pairs, key) =
skalberg@15531
  1027
      if key = keyi then SOME xi else assoc_int (pairs, key);
berghofe@1576
  1028
paulson@2175
  1029
(*association list lookup, optimized version for strings*)
skalberg@15531
  1030
fun assoc_string ([], (key:string)) = NONE
berghofe@1576
  1031
  | assoc_string ((keyi, xi) :: pairs, key) =
skalberg@15531
  1032
      if key = keyi then SOME xi else assoc_string (pairs, key);
berghofe@1576
  1033
paulson@2175
  1034
(*association list lookup, optimized version for string*ints*)
skalberg@15531
  1035
fun assoc_string_int ([], (key:string*int)) = NONE
berghofe@1576
  1036
  | assoc_string_int ((keyi, xi) :: pairs, key) =
skalberg@15531
  1037
      if key = keyi then SOME xi else assoc_string_int (pairs, key);
berghofe@1576
  1038
wenzelm@233
  1039
fun assocs ps x =
wenzelm@233
  1040
  (case assoc (ps, x) of
skalberg@15531
  1041
    NONE => []
skalberg@15531
  1042
  | SOME ys => ys);
wenzelm@233
  1043
wenzelm@255
  1044
(*two-fold association list lookup*)
wenzelm@255
  1045
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
  1046
  (case assoc (aal, key1) of
skalberg@15531
  1047
    SOME al => assoc (al, key2)
skalberg@15531
  1048
  | NONE => NONE);
wenzelm@255
  1049
wenzelm@233
  1050
(*generalized association list lookup*)
skalberg@15531
  1051
fun gen_assoc eq ([], key) = NONE
wenzelm@233
  1052
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
skalberg@15531
  1053
      if eq (key, keyi) then SOME xi else gen_assoc eq (pairs, key);
wenzelm@233
  1054
wenzelm@233
  1055
(*association list update*)
wenzelm@233
  1056
fun overwrite (al, p as (key, _)) =
wenzelm@233
  1057
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
  1058
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
  1059
        | over [] = [p]
wenzelm@233
  1060
  in over al end;
wenzelm@233
  1061
wenzelm@2522
  1062
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
  1063
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
  1064
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
  1065
        | over [] = [p]
wenzelm@2522
  1066
  in over al end;
wenzelm@2522
  1067
wenzelm@233
  1068
wenzelm@12284
  1069
(* lists as tables *)
wenzelm@233
  1070
wenzelm@12284
  1071
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1072
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1073
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1074
wenzelm@12284
  1075
fun gen_merge_lists' _ xs [] = xs
wenzelm@12284
  1076
  | gen_merge_lists' _ [] ys = ys
wenzelm@12295
  1077
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
clasohm@0
  1078
wenzelm@12284
  1079
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
wenzelm@12284
  1080
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
wenzelm@12284
  1081
fun merge_alists al = gen_merge_lists eq_fst al;
berghofe@15263
  1082
fun merge_alists' al = gen_merge_lists' eq_fst al;
wenzelm@380
  1083
clasohm@0
  1084
clasohm@0
  1085
wenzelm@233
  1086
(** balanced trees **)
wenzelm@233
  1087
wenzelm@233
  1088
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1089
wenzelm@233
  1090
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1091
fun fold_bal f [x] = x
wenzelm@233
  1092
  | fold_bal f [] = raise Balance
wenzelm@233
  1093
  | fold_bal f xs =
nipkow@13629
  1094
      let val (ps,qs) = splitAt(length xs div 2, xs)
nipkow@13629
  1095
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1096
wenzelm@233
  1097
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1098
fun access_bal (f, g, x) n i =
wenzelm@233
  1099
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1100
          if n=1 then x else
wenzelm@233
  1101
          let val n2 = n div 2
wenzelm@233
  1102
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1103
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1104
          end
wenzelm@233
  1105
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1106
wenzelm@233
  1107
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1108
fun accesses_bal (f, g, x) n =
wenzelm@233
  1109
  let fun acc n =
wenzelm@233
  1110
          if n=1 then [x] else
wenzelm@233
  1111
          let val n2 = n div 2
wenzelm@233
  1112
              val acc2 = acc n2
wenzelm@233
  1113
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1114
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1115
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1116
wenzelm@233
  1117
wenzelm@233
  1118
wenzelm@2506
  1119
(** orders **)
wenzelm@2506
  1120
wenzelm@4445
  1121
fun rev_order LESS = GREATER
wenzelm@4445
  1122
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1123
  | rev_order GREATER = LESS;
wenzelm@4445
  1124
wenzelm@4479
  1125
(*assume rel is a linear strict order*)
wenzelm@4445
  1126
fun make_ord rel (x, y) =
wenzelm@4445
  1127
  if rel (x, y) then LESS
wenzelm@4445
  1128
  else if rel (y, x) then GREATER
wenzelm@4445
  1129
  else EQUAL;
wenzelm@4445
  1130
wenzelm@15051
  1131
val int_ord = Int.compare;
wenzelm@15051
  1132
val string_ord = String.compare;
wenzelm@2506
  1133
wenzelm@16676
  1134
fun fast_string_ord (s1, s2) =
wenzelm@16676
  1135
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
  1136
wenzelm@16492
  1137
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
  1138
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
  1139
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
  1140
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
  1141
wenzelm@4343
  1142
(*lexicographic product*)
wenzelm@4343
  1143
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1144
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1145
wenzelm@4343
  1146
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
  1147
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
  1148
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
  1149
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1150
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
  1151
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
  1152
wenzelm@4343
  1153
(*lexicographic product of lists*)
wenzelm@4343
  1154
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
  1155
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1156
wenzelm@2506
  1157
wenzelm@4621
  1158
(* sorting *)
wenzelm@4621
  1159
wenzelm@4621
  1160
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1161
fun sort ord =
wenzelm@4621
  1162
  let
wenzelm@16878
  1163
    fun qsort [] = []
wenzelm@16878
  1164
      | qsort (xs as [_]) = xs
wenzelm@16878
  1165
      | qsort (xs as [x, y]) = if ord (x, y) = GREATER then [y, x] else xs
wenzelm@16878
  1166
      | qsort xs =
wenzelm@16878
  1167
          let val (lts, eqs, gts) = part (nth_elem (length xs div 2, xs)) xs
wenzelm@16878
  1168
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
  1169
    and part _ [] = ([], [], [])
wenzelm@4621
  1170
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1171
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1172
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1173
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1174
  in qsort end;
wenzelm@4621
  1175
wenzelm@4621
  1176
(*sort strings*)
wenzelm@4621
  1177
val sort_strings = sort string_ord;
wenzelm@4621
  1178
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1179
berghofe@11514
  1180
fun unique_strings ([]: string list) = []
berghofe@11514
  1181
  | unique_strings [x] = [x]
berghofe@11514
  1182
  | unique_strings (x :: y :: ys) =
berghofe@11514
  1183
      if x = y then unique_strings (y :: ys)
berghofe@11514
  1184
      else x :: unique_strings (y :: ys);
wenzelm@4621
  1185
wenzelm@2506
  1186
berghofe@14106
  1187
(** random numbers **)
berghofe@14106
  1188
berghofe@14106
  1189
exception RANDOM;
berghofe@14106
  1190
berghofe@14618
  1191
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1192
berghofe@14106
  1193
local
berghofe@14106
  1194
  val a = 16807.0;
berghofe@14106
  1195
  val m = 2147483647.0;
berghofe@14106
  1196
  val random_seed = ref 1.0;
berghofe@14106
  1197
in
berghofe@14106
  1198
berghofe@14106
  1199
fun random () =
berghofe@14106
  1200
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1201
  in (random_seed := r; r) end;
berghofe@14106
  1202
berghofe@14106
  1203
end;
berghofe@14106
  1204
berghofe@14106
  1205
fun random_range l h =
berghofe@14106
  1206
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1207
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1208
berghofe@14106
  1209
fun one_of xs = nth_elem (random_range 0 (length xs - 1), xs);
berghofe@14106
  1210
berghofe@14106
  1211
fun frequency xs =
berghofe@14106
  1212
  let
berghofe@14106
  1213
    val sum = foldl op + (0, map fst xs);
berghofe@14106
  1214
    fun pick n ((k, x) :: xs) =
berghofe@14106
  1215
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1216
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1217
berghofe@14106
  1218
wenzelm@14826
  1219
(** current directory **)
wenzelm@233
  1220
paulson@2243
  1221
val cd = OS.FileSys.chDir;
wenzelm@2317
  1222
val pwd = OS.FileSys.getDir;
paulson@2243
  1223
berghofe@3606
  1224
wenzelm@233
  1225
nipkow@10692
  1226
(** rational numbers **)
nipkow@10692
  1227
paulson@15965
  1228
datatype rat = Rat of bool * IntInf.int * IntInf.int
nipkow@10692
  1229
wenzelm@14826
  1230
exception RAT of string;
wenzelm@14826
  1231
nipkow@10692
  1232
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
nipkow@10692
  1233
nipkow@10692
  1234
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
nipkow@10692
  1235
  let val absp = abs p
nipkow@10692
  1236
      val m = gcd(absp,q)
nipkow@10692
  1237
  in Rat(a = (0 <= p), absp div m, q div m) end;
nipkow@10692
  1238
nipkow@10692
  1239
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
nipkow@10692
  1240
  let val den = lcm(q,s)
nipkow@10692
  1241
      val p = p*(den div q) and r = r*(den div s)
nipkow@10692
  1242
      val num = (if a then p else ~p) + (if b then r else ~r)
nipkow@10692
  1243
  in ratnorm(true,num,den) end;
nipkow@10692
  1244
nipkow@10692
  1245
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
nipkow@10692
  1246
wenzelm@14826
  1247
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p)
nipkow@10692
  1248
nipkow@10692
  1249
fun int_ratdiv(p,q) =
wenzelm@14826
  1250
  if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q)
nipkow@10692
  1251
nipkow@10692
  1252
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
nipkow@10692
  1253
paulson@15965
  1254
fun rat_of_intinf i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
paulson@15965
  1255
paulson@15965
  1256
fun rat_of_int i = rat_of_intinf (IntInf.fromInt i);
nipkow@10692
  1257
nipkow@10692
  1258
wenzelm@4621
  1259
(** misc **)
wenzelm@233
  1260
wenzelm@233
  1261
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1262
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1263
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1264
  in map keypair end;
clasohm@0
  1265
wenzelm@233
  1266
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1267
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1268
fun keyfilter [] searchkey = []
wenzelm@233
  1269
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1270
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1271
      else keyfilter pairs searchkey;
clasohm@0
  1272
clasohm@0
  1273
clasohm@0
  1274
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1275
  Preserves order of elements in both lists.*)
skalberg@15570
  1276
val partition = List.partition;
clasohm@0
  1277
clasohm@0
  1278
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@16842
  1279
  let
wenzelm@16842
  1280
    fun part [] = []
wenzelm@16842
  1281
      | part (x :: ys) =
wenzelm@16842
  1282
          let val (xs, xs') = partition (fn y => eq (x, y)) ys
wenzelm@16842
  1283
          in (x::xs)::(part xs') end
wenzelm@16842
  1284
  in part end;
clasohm@0
  1285
clasohm@0
  1286
wenzelm@233
  1287
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1288
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1289
fun partition_list p i j =
wenzelm@233
  1290
  let fun part k xs =
wenzelm@233
  1291
            if k>j then
clasohm@0
  1292
              (case xs of [] => []
skalberg@15570
  1293
                         | _ => raise Fail "partition_list")
clasohm@0
  1294
            else
wenzelm@233
  1295
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1296
            in  ns :: part(k+1)rest  end
clasohm@0
  1297
  in  part i end;
clasohm@0
  1298
clasohm@0
  1299
wenzelm@233
  1300
(* generating identifiers *)
clasohm@0
  1301
paulson@4063
  1302
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1303
local
paulson@4063
  1304
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1305
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1306
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1307
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1308
             else if i=62 then "_"
wenzelm@5904
  1309
             else  (*i=63*)    "'";
paulson@4063
  1310
paulson@4063
  1311
val charVec = Vector.tabulate (64, char);
paulson@4063
  1312
wenzelm@5904
  1313
fun newid n =
wenzelm@5904
  1314
  let
wenzelm@4284
  1315
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1316
wenzelm@4284
  1317
val seedr = ref 0;
clasohm@0
  1318
paulson@4063
  1319
in
wenzelm@4284
  1320
wenzelm@12346
  1321
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1322
paulson@4063
  1323
end;
paulson@4063
  1324
paulson@4063
  1325
wenzelm@233
  1326
(* lexical scanning *)
clasohm@0
  1327
wenzelm@233
  1328
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1329
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1330
fun scanwords is_let cs =
clasohm@0
  1331
  let fun scan1 [] = []
wenzelm@233
  1332
        | scan1 cs =
wenzelm@233
  1333
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1334
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1335
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1336
wenzelm@4212
  1337
wenzelm@16439
  1338
(* stamps and serial numbers *)
wenzelm@16439
  1339
wenzelm@16439
  1340
type stamp = unit ref;
wenzelm@16439
  1341
val stamp: unit -> stamp = ref;
wenzelm@16439
  1342
wenzelm@16439
  1343
type serial = int;
wenzelm@16439
  1344
local val count = ref 0
wenzelm@16439
  1345
in fun serial () = inc count end;
wenzelm@16439
  1346
wenzelm@16535
  1347
wenzelm@16535
  1348
(* generic objects *)
wenzelm@16535
  1349
wenzelm@16535
  1350
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1351
  constructors at any time*)
wenzelm@16535
  1352
structure Object = struct type T = exn end;
wenzelm@16535
  1353
clasohm@1364
  1354
end;
clasohm@1364
  1355
wenzelm@15745
  1356
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1357
open BasicLibrary;