src/Pure/library.ML
author wenzelm
Sat May 29 15:02:13 2004 +0200 (2004-05-29)
changeset 14826 48cfe0fe53e2
parent 14797 546365fe8349
child 14868 617e4b19a2e5
permissions -rw-r--r--
output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
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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 Munich
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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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 orf andf prefix upto downto
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  mem mem_int mem_string union union_int union_string inter inter_int
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  inter_string subset subset_int subset_string;
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infix 3 oo ooo oooo;
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signature LIBRARY =
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sig
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  (*functions*)
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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 I: 'a -> 'a
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  val K: 'a -> 'b -> 'a
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  val |> : 'a * ('a -> 'b) -> 'b
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  val |>> : ('a * 'b) * ('a -> 'c) -> 'c * 'b
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  val |>>> : ('a * 'b) * ('a -> 'c * 'd) -> 'c * ('b * 'd)
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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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  val funpow: int -> ('a -> 'a) -> 'a -> 'a
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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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  (*stamps*)
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  type stamp
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  val stamp: unit -> stamp
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  (*options*)
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  datatype 'a option = None | Some of 'a
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  exception OPTION
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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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  val apsome: ('a -> 'b) -> 'a option -> 'b option
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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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  (*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 LIST of string
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  val null: 'a list -> bool
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  val hd: 'a list -> 'a
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  val tl: 'a list -> 'a list
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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 rev_append: 'a list -> 'a list -> 'a list
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  val apply: ('a -> 'a) list -> 'a -> 'a
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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 foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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  val foldln: ('a * int -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val length: 'a list -> int
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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 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_elem: int * 'a list -> 'a
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  val map_nth_elem: int -> ('a -> 'a) -> 'a list -> 'a list
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  val last_elem: 'a list -> 'a
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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 flat: 'a list list -> 'a list
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  val unflat: 'a list list -> 'b list -> 'b list list
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  val seq: ('a -> unit) -> 'a list -> unit
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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 mapfilter: ('a -> 'b option) -> 'a list -> 'b 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: int * int -> int
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  val lcm: int * int -> 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 -> int * 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: int * int -> rat
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  val ratneg: rat -> rat
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  val rat_of_int: int -> rat
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  (*strings*)
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  val nth_elem_string: int * string -> string
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  val foldl_string: ('a * string -> 'a) -> 'a * string -> 'a
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  val exists_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 replicate_string: int -> string -> string
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  (*lists as sets*)
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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 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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  (*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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  (*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 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: ('a -> bool) -> 'a list -> 'a list * '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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end;
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structure Library: LIBRARY =
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struct
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(** functions **)
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(*handy combinators*)
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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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fun I x = x;
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fun K x y = x;
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(*reverse apply*)
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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) = let val (x', z) = f x in (x', (y, z)) end;
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(*application of (infix) operator to its left or right argument*)
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fun apl (x, f) y = f (x, y);
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fun apr (f, y) x = f (x, y);
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(*function exponentiation: f(...(f x)...) with n applications of f*)
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fun funpow n f x =
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  let fun rep (0, x) = x
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        | rep (n, x) = rep (n - 1, f x)
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  in rep (n, x) end;
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(*concatenation: 2 and 3 args*)
wenzelm@5893
   295
fun (f oo g) x y = f (g x y);
wenzelm@5893
   296
fun (f ooo g) x y z = f (g x y z);
wenzelm@6510
   297
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@6510
   298
wenzelm@160
   299
wenzelm@160
   300
wenzelm@2471
   301
(** stamps **)
wenzelm@2471
   302
wenzelm@2471
   303
type stamp = unit ref;
wenzelm@2471
   304
val stamp: unit -> stamp = ref;
wenzelm@2471
   305
wenzelm@2471
   306
wenzelm@2471
   307
wenzelm@233
   308
(** options **)
clasohm@0
   309
clasohm@0
   310
datatype 'a option = None | Some of 'a;
clasohm@0
   311
wenzelm@4139
   312
exception OPTION;
clasohm@0
   313
clasohm@0
   314
fun the (Some x) = x
wenzelm@4139
   315
  | the None = raise OPTION;
clasohm@0
   316
wenzelm@4212
   317
(*strict!*)
wenzelm@255
   318
fun if_none None y = y
wenzelm@255
   319
  | if_none (Some x) _ = x;
wenzelm@255
   320
clasohm@0
   321
fun is_some (Some _) = true
clasohm@0
   322
  | is_some None = false;
clasohm@0
   323
clasohm@0
   324
fun is_none (Some _) = false
clasohm@0
   325
  | is_none None = true;
clasohm@0
   326
wenzelm@233
   327
fun apsome f (Some x) = Some (f x)
wenzelm@233
   328
  | apsome _ None = None;
clasohm@0
   329
wenzelm@6959
   330
wenzelm@6959
   331
(* exception handling *)
wenzelm@6959
   332
wenzelm@6959
   333
exception ERROR;
wenzelm@6959
   334
wenzelm@6959
   335
fun try f x = Some (f x)
wenzelm@6959
   336
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => None;
wenzelm@6959
   337
wenzelm@6959
   338
fun can f x = is_some (try f x);
wenzelm@4139
   339
wenzelm@4139
   340
wenzelm@4139
   341
wenzelm@233
   342
(** pairs **)
wenzelm@233
   343
wenzelm@233
   344
fun pair x y = (x, y);
wenzelm@233
   345
fun rpair x y = (y, x);
wenzelm@233
   346
wenzelm@233
   347
fun fst (x, y) = x;
wenzelm@233
   348
fun snd (x, y) = y;
wenzelm@233
   349
wenzelm@233
   350
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   351
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   352
wenzelm@233
   353
fun swap (x, y) = (y, x);
wenzelm@233
   354
wenzelm@4212
   355
(*apply function to components*)
wenzelm@233
   356
fun apfst f (x, y) = (f x, y);
wenzelm@233
   357
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   358
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   359
wenzelm@233
   360
wenzelm@233
   361
wenzelm@233
   362
(** booleans **)
wenzelm@233
   363
wenzelm@233
   364
(* equality *)
wenzelm@233
   365
wenzelm@233
   366
fun equal x y = x = y;
wenzelm@233
   367
fun not_equal x y = x <> y;
wenzelm@233
   368
wenzelm@233
   369
wenzelm@233
   370
(* operators for combining predicates *)
wenzelm@233
   371
paulson@2175
   372
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   373
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   374
wenzelm@233
   375
wenzelm@233
   376
(* predicates on lists *)
wenzelm@233
   377
wenzelm@233
   378
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   379
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   380
  let fun boolf [] = false
wenzelm@233
   381
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   382
  in boolf end;
wenzelm@233
   383
wenzelm@233
   384
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   385
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   386
  let fun boolf [] = true
wenzelm@233
   387
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   388
  in boolf end;
clasohm@0
   389
wenzelm@233
   390
wenzelm@380
   391
(* flags *)
wenzelm@380
   392
wenzelm@380
   393
fun set flag = (flag := true; true);
wenzelm@380
   394
fun reset flag = (flag := false; false);
wenzelm@380
   395
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   396
wenzelm@9118
   397
fun change r f = r := f (! r);
wenzelm@9118
   398
wenzelm@14826
   399
(*temporarily set flag, handling exceptions*)
wenzelm@2978
   400
fun setmp flag value f x =
wenzelm@2958
   401
  let
wenzelm@2958
   402
    val orig_value = ! flag;
wenzelm@2958
   403
    fun return y = (flag := orig_value; y);
wenzelm@2958
   404
  in
wenzelm@2958
   405
    flag := value;
wenzelm@2958
   406
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   407
  end;
wenzelm@2958
   408
wenzelm@380
   409
wenzelm@11853
   410
(* conditional execution *)
wenzelm@11853
   411
wenzelm@11853
   412
fun conditional b f = if b then f () else ();
wenzelm@11853
   413
wenzelm@11853
   414
wenzelm@233
   415
wenzelm@233
   416
(** lists **)
wenzelm@233
   417
wenzelm@233
   418
exception LIST of string;
wenzelm@233
   419
wenzelm@233
   420
fun null [] = true
wenzelm@233
   421
  | null (_ :: _) = false;
wenzelm@233
   422
wenzelm@233
   423
fun hd [] = raise LIST "hd"
wenzelm@233
   424
  | hd (x :: _) = x;
wenzelm@233
   425
wenzelm@233
   426
fun tl [] = raise LIST "tl"
wenzelm@233
   427
  | tl (_ :: xs) = xs;
wenzelm@233
   428
wenzelm@233
   429
fun cons x xs = x :: xs;
wenzelm@5285
   430
fun single x = [x];
wenzelm@233
   431
wenzelm@4629
   432
fun append xs ys = xs @ ys;
wenzelm@4629
   433
berghofe@13794
   434
(* tail recursive version *)
berghofe@13794
   435
fun rev_append [] ys = ys
berghofe@13794
   436
  | rev_append (x :: xs) ys = rev_append xs (x :: ys);
berghofe@13794
   437
wenzelm@5904
   438
fun apply [] x = x
wenzelm@5904
   439
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   440
wenzelm@233
   441
wenzelm@233
   442
(* fold *)
wenzelm@233
   443
wenzelm@233
   444
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   445
wenzelm@233
   446
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   447
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   448
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   449
  let fun itl (e, [])  = e
wenzelm@233
   450
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   451
  in  itl end;
wenzelm@233
   452
wenzelm@233
   453
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   454
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   455
fun foldr f (l, e) =
wenzelm@233
   456
  let fun itr [] = e
wenzelm@233
   457
        | itr (a::l) = f(a, itr l)
wenzelm@233
   458
  in  itr l  end;
wenzelm@233
   459
wenzelm@233
   460
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   461
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   462
fun foldr1 f l =
wenzelm@4181
   463
  let fun itr [x] = x
wenzelm@233
   464
        | itr (x::l) = f(x, itr l)
wenzelm@233
   465
  in  itr l  end;
wenzelm@233
   466
wenzelm@14792
   467
fun fold f xs y = foldl (fn (y', x) => f x y') (y, xs);
wenzelm@14792
   468
wenzelm@4956
   469
fun foldl_map _ (x, []) = (x, [])
wenzelm@4956
   470
  | foldl_map f (x, y :: ys) =
wenzelm@4956
   471
      let
wenzelm@4956
   472
        val (x', y') = f (x, y);
wenzelm@4956
   473
        val (x'', ys') = foldl_map f (x', ys);
wenzelm@4956
   474
      in (x'', y' :: ys') end;
wenzelm@4956
   475
oheimb@11002
   476
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
wenzelm@233
   477
wenzelm@233
   478
(* basic list functions *)
wenzelm@233
   479
wenzelm@233
   480
(*length of a list, should unquestionably be a standard function*)
wenzelm@233
   481
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233
   482
        | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233
   483
in  fun length l = length1 (0, l) end;
wenzelm@233
   484
wenzelm@233
   485
(*take the first n elements from a list*)
wenzelm@233
   486
fun take (n, []) = []
wenzelm@233
   487
  | take (n, x :: xs) =
wenzelm@233
   488
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   489
wenzelm@233
   490
(*drop the first n elements from a list*)
wenzelm@233
   491
fun drop (n, []) = []
wenzelm@233
   492
  | drop (n, x :: xs) =
wenzelm@233
   493
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   494
nipkow@13629
   495
fun splitAt(n,[]) = ([],[])
nipkow@13629
   496
  | splitAt(n,xs as x::ys) =
nipkow@13629
   497
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
nipkow@13629
   498
      else ([],xs)
nipkow@13629
   499
nipkow@4713
   500
fun dropwhile P [] = []
nipkow@4713
   501
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   502
wenzelm@233
   503
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   504
  raise EXCEPTION if list too short*)
wenzelm@233
   505
fun nth_elem NL =
wenzelm@233
   506
  (case drop NL of
wenzelm@233
   507
    [] => raise LIST "nth_elem"
wenzelm@233
   508
  | x :: _ => x);
wenzelm@233
   509
wenzelm@11773
   510
fun map_nth_elem 0 f (x :: xs) = f x :: xs
wenzelm@11773
   511
  | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs
wenzelm@11773
   512
  | map_nth_elem _ _ [] = raise LIST "map_nth_elem";
wenzelm@11773
   513
wenzelm@233
   514
(*last element of a list*)
wenzelm@233
   515
fun last_elem [] = raise LIST "last_elem"
wenzelm@233
   516
  | last_elem [x] = x
wenzelm@233
   517
  | last_elem (_ :: xs) = last_elem xs;
wenzelm@233
   518
wenzelm@3762
   519
(*rear decomposition*)
wenzelm@3762
   520
fun split_last [] = raise LIST "split_last"
wenzelm@3762
   521
  | split_last [x] = ([], x)
wenzelm@3762
   522
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   523
wenzelm@4893
   524
(*update nth element*)
nipkow@13629
   525
fun nth_update x n_xs =
nipkow@13629
   526
    (case splitAt n_xs of
nipkow@13629
   527
      (_,[]) => raise LIST "nth_update"
nipkow@13629
   528
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
wenzelm@4893
   529
wenzelm@4212
   530
(*find the position of an element in a list*)
wenzelm@4212
   531
fun find_index pred =
wenzelm@4212
   532
  let fun find _ [] = ~1
wenzelm@4212
   533
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   534
  in find 0 end;
wenzelm@3762
   535
wenzelm@4224
   536
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   537
wenzelm@4212
   538
(*find first element satisfying predicate*)
wenzelm@4212
   539
fun find_first _ [] = None
wenzelm@4212
   540
  | find_first pred (x :: xs) =
wenzelm@4212
   541
      if pred x then Some x else find_first pred xs;
wenzelm@233
   542
wenzelm@4916
   543
(*get first element by lookup function*)
wenzelm@4916
   544
fun get_first _ [] = None
wenzelm@4916
   545
  | get_first f (x :: xs) =
wenzelm@4916
   546
      (case f x of
wenzelm@4916
   547
        None => get_first f xs
wenzelm@4916
   548
      | some => some);
wenzelm@4916
   549
wenzelm@233
   550
(*flatten a list of lists to a list*)
wenzelm@233
   551
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233
   552
wenzelm@12136
   553
fun unflat (xs :: xss) ys =
nipkow@13629
   554
      let val (ps,qs) = splitAt(length xs,ys)
nipkow@13629
   555
      in ps :: unflat xss qs end
wenzelm@12136
   556
  | unflat [] [] = []
wenzelm@12136
   557
  | unflat _ _ = raise LIST "unflat";
wenzelm@12136
   558
wenzelm@233
   559
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   560
  (proc x1; ...; proc xn) for side effects*)
wenzelm@233
   561
fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233
   562
  let fun seqf [] = ()
wenzelm@233
   563
        | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233
   564
  in seqf end;
wenzelm@233
   565
wenzelm@233
   566
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   567
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   568
  | separate _ xs = xs;
wenzelm@233
   569
wenzelm@233
   570
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   571
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   572
  let fun rep (0, xs) = xs
wenzelm@233
   573
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   574
  in
wenzelm@233
   575
    if n < 0 then raise LIST "replicate"
wenzelm@233
   576
    else rep (n, [])
wenzelm@233
   577
  end;
wenzelm@233
   578
wenzelm@4248
   579
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   580
fun multiply ([], _) = []
wenzelm@4248
   581
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   582
wenzelm@14792
   583
(*direct product*)
wenzelm@14792
   584
fun product _ [] = []
wenzelm@14792
   585
  | product [] _ = []
wenzelm@14792
   586
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   587
wenzelm@233
   588
wenzelm@233
   589
(* filter *)
wenzelm@233
   590
wenzelm@233
   591
(*copy the list preserving elements that satisfy the predicate*)
wenzelm@233
   592
fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0
   593
  let fun filt [] = []
wenzelm@233
   594
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233
   595
  in filt end;
clasohm@0
   596
clasohm@0
   597
fun filter_out f = filter (not o f);
clasohm@0
   598
wenzelm@233
   599
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233
   600
  | mapfilter f (x :: xs) =
wenzelm@233
   601
      (case f x of
wenzelm@233
   602
        None => mapfilter f xs
wenzelm@233
   603
      | Some y => y :: mapfilter f xs);
wenzelm@233
   604
wenzelm@233
   605
wenzelm@233
   606
(* lists of pairs *)
wenzelm@233
   607
wenzelm@380
   608
fun map2 _ ([], []) = []
wenzelm@380
   609
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380
   610
  | map2 _ _ = raise LIST "map2";
wenzelm@380
   611
wenzelm@380
   612
fun exists2 _ ([], []) = false
wenzelm@380
   613
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380
   614
  | exists2 _ _ = raise LIST "exists2";
wenzelm@380
   615
wenzelm@380
   616
fun forall2 _ ([], []) = true
wenzelm@380
   617
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380
   618
  | forall2 _ _ = raise LIST "forall2";
wenzelm@380
   619
wenzelm@4956
   620
fun seq2 _ ([], []) = ()
wenzelm@4956
   621
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
wenzelm@4956
   622
  | seq2 _ _ = raise LIST "seq2";
wenzelm@4956
   623
wenzelm@233
   624
(*combine two lists forming a list of pairs:
wenzelm@233
   625
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   626
fun [] ~~ [] = []
wenzelm@233
   627
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233
   628
  | _ ~~ _ = raise LIST "~~";
wenzelm@233
   629
wenzelm@233
   630
(*inverse of ~~; the old 'split':
wenzelm@233
   631
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233
   632
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233
   633
wenzelm@7468
   634
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
wenzelm@7468
   635
wenzelm@233
   636
wenzelm@233
   637
(* prefixes, suffixes *)
wenzelm@233
   638
wenzelm@233
   639
fun [] prefix _ = true
wenzelm@233
   640
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   641
  | _ prefix _ = false;
wenzelm@233
   642
wenzelm@233
   643
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   644
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   645
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   646
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   647
        | take (rxs, x :: xs) =
wenzelm@255
   648
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   649
  in  take([], xs)  end;
wenzelm@233
   650
wenzelm@233
   651
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   652
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   653
fun take_suffix _ [] = ([], [])
wenzelm@233
   654
  | take_suffix pred (x :: xs) =
wenzelm@233
   655
      (case take_suffix pred xs of
wenzelm@233
   656
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   657
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   658
wenzelm@12249
   659
fun prefixes1 [] = []
wenzelm@12249
   660
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   661
wenzelm@12249
   662
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@12249
   663
wenzelm@233
   664
wenzelm@233
   665
wenzelm@233
   666
(** integers **)
wenzelm@233
   667
nipkow@10692
   668
fun gcd(x,y) =
nipkow@10692
   669
  let fun gxd x y =
nipkow@10692
   670
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   671
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   672
nipkow@10692
   673
fun lcm(x,y) = (x * y) div gcd(x,y);
nipkow@10692
   674
wenzelm@2958
   675
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   676
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   677
wenzelm@233
   678
wenzelm@233
   679
(* lists of integers *)
wenzelm@233
   680
wenzelm@233
   681
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   682
fun (from upto to) =
wenzelm@233
   683
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   684
wenzelm@233
   685
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   686
fun (from downto to) =
wenzelm@233
   687
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   688
wenzelm@233
   689
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   690
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   691
  | downto0 ([], n) = n = ~1;
wenzelm@233
   692
wenzelm@233
   693
wenzelm@233
   694
(* convert integers to strings *)
wenzelm@233
   695
wenzelm@233
   696
(*expand the number in the given base;
wenzelm@233
   697
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   698
fun radixpand (base, num) : int list =
wenzelm@233
   699
  let
wenzelm@233
   700
    fun radix (n, tail) =
wenzelm@233
   701
      if n < base then n :: tail
wenzelm@233
   702
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   703
  in radix (num, []) end;
wenzelm@233
   704
wenzelm@233
   705
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   706
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   707
fun radixstring (base, zerochar, num) =
wenzelm@233
   708
  let val offset = ord zerochar;
wenzelm@233
   709
      fun chrof n = chr (offset + n)
wenzelm@233
   710
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   711
wenzelm@233
   712
paulson@3407
   713
val string_of_int = Int.toString;
wenzelm@233
   714
paulson@3407
   715
fun string_of_indexname (a,0) = a
paulson@3407
   716
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   717
wenzelm@233
   718
wenzelm@14826
   719
(* read integers *)
wenzelm@14826
   720
wenzelm@14826
   721
fun read_radixint (radix: int, cs) : int * string list =
wenzelm@14826
   722
  let val zero = ord"0"
wenzelm@14826
   723
      val limit = zero+radix
wenzelm@14826
   724
      fun scan (num,[]) = (num,[])
wenzelm@14826
   725
        | scan (num, c::cs) =
wenzelm@14826
   726
              if  zero <= ord c  andalso  ord c < limit
wenzelm@14826
   727
              then scan(radix*num + ord c - zero, cs)
wenzelm@14826
   728
              else (num, c::cs)
wenzelm@14826
   729
  in  scan(0,cs)  end;
wenzelm@14826
   730
wenzelm@14826
   731
fun read_int cs = read_radixint (10, cs);
wenzelm@14826
   732
wenzelm@14826
   733
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
wenzelm@14826
   734
wenzelm@14826
   735
wenzelm@14826
   736
wenzelm@233
   737
(** strings **)
wenzelm@233
   738
wenzelm@6312
   739
(*functions tuned for strings, avoiding explode*)
wenzelm@6312
   740
wenzelm@6312
   741
fun nth_elem_string (i, str) =
wenzelm@6959
   742
  (case try String.substring (str, i, 1) of
wenzelm@6959
   743
    Some s => s
wenzelm@6959
   744
  | None => raise LIST "nth_elem_string");
wenzelm@6312
   745
wenzelm@6282
   746
fun foldl_string f (x0, str) =
wenzelm@6282
   747
  let
wenzelm@6282
   748
    val n = size str;
wenzelm@6282
   749
    fun fold (x, i) = if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x
wenzelm@6282
   750
  in fold (x0, 0) end;
wenzelm@6282
   751
wenzelm@6312
   752
fun exists_string pred str = foldl_string (fn (b, s) => b orelse pred s) (false, str);
wenzelm@6312
   753
lcp@512
   754
(*enclose in brackets*)
lcp@512
   755
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   756
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   757
wenzelm@233
   758
(*simple quoting (does not escape special chars)*)
lcp@512
   759
val quote = enclose "\"" "\"";
wenzelm@233
   760
wenzelm@4212
   761
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   762
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   763
wenzelm@255
   764
val commas = space_implode ", ";
wenzelm@380
   765
val commas_quote = commas o map quote;
wenzelm@255
   766
wenzelm@233
   767
(*concatenate messages, one per line, into a string*)
wenzelm@255
   768
val cat_lines = space_implode "\n";
wenzelm@233
   769
wenzelm@4212
   770
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   771
fun space_explode _ "" = []
wenzelm@3832
   772
  | space_explode sep str =
wenzelm@3832
   773
      let
wenzelm@3832
   774
        fun expl chs =
wenzelm@3832
   775
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   776
            (cs, []) => [implode cs]
wenzelm@3832
   777
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   778
      in expl (explode str) end;
wenzelm@3832
   779
wenzelm@3832
   780
val split_lines = space_explode "\n";
wenzelm@3832
   781
wenzelm@14826
   782
fun prefix_lines "" txt = txt
wenzelm@14826
   783
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   784
wenzelm@7712
   785
(*untabify*)
wenzelm@7712
   786
fun untabify chs =
wenzelm@7712
   787
  let
wenzelm@7712
   788
    val tab_width = 8;
wenzelm@7712
   789
wenzelm@7712
   790
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   791
      | untab (pos, "\t") =
wenzelm@9118
   792
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   793
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   794
  in
wenzelm@7712
   795
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   796
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   797
  end;
wenzelm@7712
   798
wenzelm@5285
   799
(*append suffix*)
wenzelm@5285
   800
fun suffix sfx s = s ^ sfx;
wenzelm@5285
   801
wenzelm@5285
   802
(*remove suffix*)
wenzelm@5285
   803
fun unsuffix sfx s =
wenzelm@5285
   804
  let
wenzelm@5285
   805
    val cs = explode s;
wenzelm@5285
   806
    val prfx_len = size s - size sfx;
wenzelm@5285
   807
  in
wenzelm@5285
   808
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
wenzelm@5285
   809
      implode (take (prfx_len, cs))
wenzelm@5285
   810
    else raise LIST "unsuffix"
wenzelm@5285
   811
  end;
wenzelm@5285
   812
wenzelm@10951
   813
fun replicate_string 0 _ = ""
wenzelm@10951
   814
  | replicate_string 1 a = a
wenzelm@10951
   815
  | replicate_string k a =
wenzelm@10951
   816
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   817
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   818
wenzelm@3832
   819
wenzelm@233
   820
wenzelm@233
   821
(** lists as sets **)
wenzelm@233
   822
wenzelm@233
   823
(*membership in a list*)
wenzelm@233
   824
fun x mem [] = false
wenzelm@233
   825
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   826
paulson@2175
   827
(*membership in a list, optimized version for ints*)
berghofe@1576
   828
fun (x:int) mem_int [] = false
berghofe@1576
   829
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   830
paulson@2175
   831
(*membership in a list, optimized version for strings*)
berghofe@1576
   832
fun (x:string) mem_string [] = false
berghofe@1576
   833
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   834
clasohm@0
   835
(*generalized membership test*)
wenzelm@233
   836
fun gen_mem eq (x, []) = false
wenzelm@233
   837
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   838
wenzelm@233
   839
wenzelm@233
   840
(*insertion into list if not already there*)
paulson@2175
   841
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   842
paulson@2175
   843
(*insertion into list, optimized version for ints*)
paulson@2175
   844
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   845
paulson@2175
   846
(*insertion into list, optimized version for strings*)
paulson@2175
   847
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   848
clasohm@0
   849
(*generalized insertion*)
wenzelm@233
   850
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   851
wenzelm@233
   852
wenzelm@233
   853
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   854
fun xs union [] = xs
wenzelm@233
   855
  | [] union ys = ys
wenzelm@233
   856
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   857
paulson@2175
   858
(*union of sets, optimized version for ints*)
berghofe@1576
   859
fun (xs:int list) union_int [] = xs
berghofe@1576
   860
  | [] union_int ys = ys
berghofe@1576
   861
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   862
paulson@2175
   863
(*union of sets, optimized version for strings*)
berghofe@1576
   864
fun (xs:string list) union_string [] = xs
berghofe@1576
   865
  | [] union_string ys = ys
berghofe@1576
   866
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   867
clasohm@0
   868
(*generalized union*)
wenzelm@233
   869
fun gen_union eq (xs, []) = xs
wenzelm@233
   870
  | gen_union eq ([], ys) = ys
wenzelm@233
   871
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   872
wenzelm@233
   873
wenzelm@233
   874
(*intersection*)
wenzelm@233
   875
fun [] inter ys = []
wenzelm@233
   876
  | (x :: xs) inter ys =
wenzelm@233
   877
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   878
paulson@2175
   879
(*intersection, optimized version for ints*)
berghofe@1576
   880
fun ([]:int list) inter_int ys = []
berghofe@1576
   881
  | (x :: xs) inter_int ys =
berghofe@1576
   882
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   883
paulson@2175
   884
(*intersection, optimized version for strings *)
berghofe@1576
   885
fun ([]:string list) inter_string ys = []
berghofe@1576
   886
  | (x :: xs) inter_string ys =
berghofe@1576
   887
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   888
paulson@7090
   889
(*generalized intersection*)
paulson@7090
   890
fun gen_inter eq ([], ys) = []
wenzelm@12284
   891
  | gen_inter eq (x::xs, ys) =
paulson@7090
   892
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
wenzelm@12284
   893
                           else      gen_inter eq (xs, ys);
paulson@7090
   894
wenzelm@233
   895
wenzelm@233
   896
(*subset*)
wenzelm@233
   897
fun [] subset ys = true
wenzelm@233
   898
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   899
paulson@2175
   900
(*subset, optimized version for ints*)
berghofe@1576
   901
fun ([]:int list) subset_int ys = true
berghofe@1576
   902
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   903
paulson@2175
   904
(*subset, optimized version for strings*)
berghofe@1576
   905
fun ([]:string list) subset_string ys = true
berghofe@1576
   906
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   907
wenzelm@4363
   908
(*set equality*)
wenzelm@4363
   909
fun eq_set (xs, ys) =
wenzelm@4363
   910
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   911
paulson@2182
   912
(*set equality for strings*)
berghofe@1576
   913
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   914
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   915
paulson@2182
   916
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   917
wenzelm@265
   918
wenzelm@233
   919
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   920
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   921
  | [] \ x = [];
wenzelm@233
   922
paulson@2243
   923
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   924
wenzelm@233
   925
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   926
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@12295
   927
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   928
wenzelm@233
   929
wenzelm@233
   930
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   931
  first of equal elements*)
wenzelm@233
   932
fun gen_distinct eq lst =
wenzelm@233
   933
  let
wenzelm@233
   934
    val memb = gen_mem eq;
clasohm@0
   935
wenzelm@233
   936
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   937
      | dist (rev_seen, x :: xs) =
wenzelm@233
   938
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   939
          else dist (x :: rev_seen, xs);
wenzelm@233
   940
  in
wenzelm@233
   941
    dist ([], lst)
wenzelm@233
   942
  end;
wenzelm@233
   943
paulson@2243
   944
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   945
wenzelm@233
   946
wenzelm@233
   947
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   948
fun findrep [] = []
wenzelm@233
   949
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   950
wenzelm@233
   951
wenzelm@255
   952
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   953
  order, takes first of equal elements*)
wenzelm@255
   954
fun gen_duplicates eq lst =
wenzelm@255
   955
  let
wenzelm@255
   956
    val memb = gen_mem eq;
wenzelm@255
   957
wenzelm@255
   958
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   959
      | dups (rev_dups, x :: xs) =
wenzelm@255
   960
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   961
            dups (rev_dups, xs)
wenzelm@255
   962
          else dups (x :: rev_dups, xs);
wenzelm@255
   963
  in
wenzelm@255
   964
    dups ([], lst)
wenzelm@255
   965
  end;
wenzelm@255
   966
paulson@2243
   967
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   968
wenzelm@255
   969
wenzelm@233
   970
wenzelm@233
   971
(** association lists **)
clasohm@0
   972
wenzelm@233
   973
(*association list lookup*)
wenzelm@233
   974
fun assoc ([], key) = None
wenzelm@233
   975
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   976
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   977
paulson@2175
   978
(*association list lookup, optimized version for ints*)
berghofe@1576
   979
fun assoc_int ([], (key:int)) = None
berghofe@1576
   980
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   981
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   982
paulson@2175
   983
(*association list lookup, optimized version for strings*)
berghofe@1576
   984
fun assoc_string ([], (key:string)) = None
berghofe@1576
   985
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   986
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   987
paulson@2175
   988
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   989
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   990
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   991
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   992
wenzelm@233
   993
fun assocs ps x =
wenzelm@233
   994
  (case assoc (ps, x) of
wenzelm@233
   995
    None => []
wenzelm@233
   996
  | Some ys => ys);
wenzelm@233
   997
wenzelm@255
   998
(*two-fold association list lookup*)
wenzelm@255
   999
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
  1000
  (case assoc (aal, key1) of
wenzelm@255
  1001
    Some al => assoc (al, key2)
wenzelm@255
  1002
  | None => None);
wenzelm@255
  1003
wenzelm@233
  1004
(*generalized association list lookup*)
wenzelm@233
  1005
fun gen_assoc eq ([], key) = None
wenzelm@233
  1006
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
  1007
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
  1008
wenzelm@233
  1009
(*association list update*)
wenzelm@233
  1010
fun overwrite (al, p as (key, _)) =
wenzelm@233
  1011
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
  1012
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
  1013
        | over [] = [p]
wenzelm@233
  1014
  in over al end;
wenzelm@233
  1015
wenzelm@2522
  1016
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
  1017
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
  1018
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
  1019
        | over [] = [p]
wenzelm@2522
  1020
  in over al end;
wenzelm@2522
  1021
wenzelm@233
  1022
wenzelm@12284
  1023
(* lists as tables *)
wenzelm@233
  1024
wenzelm@12284
  1025
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1026
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1027
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1028
wenzelm@12284
  1029
fun gen_merge_lists' _ xs [] = xs
wenzelm@12284
  1030
  | gen_merge_lists' _ [] ys = ys
wenzelm@12295
  1031
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
clasohm@0
  1032
wenzelm@12284
  1033
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
wenzelm@12284
  1034
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
wenzelm@12284
  1035
fun merge_alists al = gen_merge_lists eq_fst al;
wenzelm@380
  1036
clasohm@0
  1037
clasohm@0
  1038
wenzelm@233
  1039
(** balanced trees **)
wenzelm@233
  1040
wenzelm@233
  1041
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1042
wenzelm@233
  1043
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1044
fun fold_bal f [x] = x
wenzelm@233
  1045
  | fold_bal f [] = raise Balance
wenzelm@233
  1046
  | fold_bal f xs =
nipkow@13629
  1047
      let val (ps,qs) = splitAt(length xs div 2, xs)
nipkow@13629
  1048
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1049
wenzelm@233
  1050
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1051
fun access_bal (f, g, x) n i =
wenzelm@233
  1052
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1053
          if n=1 then x else
wenzelm@233
  1054
          let val n2 = n div 2
wenzelm@233
  1055
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1056
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1057
          end
wenzelm@233
  1058
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1059
wenzelm@233
  1060
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1061
fun accesses_bal (f, g, x) n =
wenzelm@233
  1062
  let fun acc n =
wenzelm@233
  1063
          if n=1 then [x] else
wenzelm@233
  1064
          let val n2 = n div 2
wenzelm@233
  1065
              val acc2 = acc n2
wenzelm@233
  1066
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1067
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1068
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1069
wenzelm@233
  1070
wenzelm@233
  1071
wenzelm@2506
  1072
(** orders **)
wenzelm@2506
  1073
wenzelm@4445
  1074
fun rev_order LESS = GREATER
wenzelm@4445
  1075
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1076
  | rev_order GREATER = LESS;
wenzelm@4445
  1077
wenzelm@4479
  1078
(*assume rel is a linear strict order*)
wenzelm@4445
  1079
fun make_ord rel (x, y) =
wenzelm@4445
  1080
  if rel (x, y) then LESS
wenzelm@4445
  1081
  else if rel (y, x) then GREATER
wenzelm@4445
  1082
  else EQUAL;
wenzelm@4445
  1083
paulson@14472
  1084
(*Better to use Int.compare*)
wenzelm@4343
  1085
fun int_ord (i, j: int) =
wenzelm@2506
  1086
  if i < j then LESS
wenzelm@2506
  1087
  else if i = j then EQUAL
wenzelm@2506
  1088
  else GREATER;
wenzelm@2506
  1089
paulson@14472
  1090
(*Better to use String.compare*)
wenzelm@4343
  1091
fun string_ord (a, b: string) =
wenzelm@2506
  1092
  if a < b then LESS
wenzelm@2506
  1093
  else if a = b then EQUAL
wenzelm@2506
  1094
  else GREATER;
wenzelm@2506
  1095
wenzelm@4343
  1096
(*lexicographic product*)
wenzelm@4343
  1097
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1098
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1099
wenzelm@4343
  1100
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
  1101
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1102
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
  1103
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
  1104
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
  1105
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1106
wenzelm@4343
  1107
(*lexicographic product of lists*)
wenzelm@4343
  1108
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
  1109
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
  1110
wenzelm@2506
  1111
wenzelm@4621
  1112
(* sorting *)
wenzelm@4621
  1113
wenzelm@4621
  1114
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1115
fun sort ord =
wenzelm@4621
  1116
  let
wenzelm@4621
  1117
    fun qsort xs =
wenzelm@4621
  1118
      let val len = length xs in
wenzelm@4621
  1119
        if len <= 1 then xs
wenzelm@4621
  1120
        else
wenzelm@4621
  1121
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
  1122
            qsort lts @ eqs @ qsort gts
wenzelm@4621
  1123
          end
wenzelm@4621
  1124
      end
wenzelm@4621
  1125
    and part _ [] = ([], [], [])
wenzelm@4621
  1126
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1127
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1128
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1129
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1130
  in qsort end;
wenzelm@4621
  1131
wenzelm@4621
  1132
(*sort strings*)
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
berghofe@11514
  1136
fun unique_strings ([]: string list) = []
berghofe@11514
  1137
  | unique_strings [x] = [x]
berghofe@11514
  1138
  | unique_strings (x :: y :: ys) =
berghofe@11514
  1139
      if x = y then unique_strings (y :: ys)
berghofe@11514
  1140
      else x :: unique_strings (y :: ys);
wenzelm@4621
  1141
wenzelm@2506
  1142
berghofe@14106
  1143
(** random numbers **)
berghofe@14106
  1144
berghofe@14106
  1145
exception RANDOM;
berghofe@14106
  1146
berghofe@14618
  1147
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1148
berghofe@14106
  1149
local
berghofe@14106
  1150
  val a = 16807.0;
berghofe@14106
  1151
  val m = 2147483647.0;
berghofe@14106
  1152
  val random_seed = ref 1.0;
berghofe@14106
  1153
in
berghofe@14106
  1154
berghofe@14106
  1155
fun random () =
berghofe@14106
  1156
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1157
  in (random_seed := r; r) end;
berghofe@14106
  1158
berghofe@14106
  1159
end;
berghofe@14106
  1160
berghofe@14106
  1161
fun random_range l h =
berghofe@14106
  1162
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1163
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1164
berghofe@14106
  1165
fun one_of xs = nth_elem (random_range 0 (length xs - 1), xs);
berghofe@14106
  1166
berghofe@14106
  1167
fun frequency xs =
berghofe@14106
  1168
  let
berghofe@14106
  1169
    val sum = foldl op + (0, map fst xs);
berghofe@14106
  1170
    fun pick n ((k, x) :: xs) =
berghofe@14106
  1171
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1172
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1173
berghofe@14106
  1174
wenzelm@14826
  1175
(** current directory **)
wenzelm@233
  1176
paulson@2243
  1177
val cd = OS.FileSys.chDir;
wenzelm@2317
  1178
val pwd = OS.FileSys.getDir;
paulson@2243
  1179
berghofe@3606
  1180
wenzelm@233
  1181
nipkow@10692
  1182
(** rational numbers **)
nipkow@10692
  1183
nipkow@10692
  1184
datatype rat = Rat of bool * int * int
nipkow@10692
  1185
wenzelm@14826
  1186
exception RAT of string;
wenzelm@14826
  1187
nipkow@10692
  1188
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
nipkow@10692
  1189
nipkow@10692
  1190
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
nipkow@10692
  1191
  let val absp = abs p
nipkow@10692
  1192
      val m = gcd(absp,q)
nipkow@10692
  1193
  in Rat(a = (0 <= p), absp div m, q div m) end;
nipkow@10692
  1194
nipkow@10692
  1195
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
nipkow@10692
  1196
  let val den = lcm(q,s)
nipkow@10692
  1197
      val p = p*(den div q) and r = r*(den div s)
nipkow@10692
  1198
      val num = (if a then p else ~p) + (if b then r else ~r)
nipkow@10692
  1199
  in ratnorm(true,num,den) end;
nipkow@10692
  1200
nipkow@10692
  1201
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
nipkow@10692
  1202
wenzelm@14826
  1203
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p)
nipkow@10692
  1204
nipkow@10692
  1205
fun int_ratdiv(p,q) =
wenzelm@14826
  1206
  if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q)
nipkow@10692
  1207
nipkow@10692
  1208
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
nipkow@10692
  1209
nipkow@10692
  1210
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
nipkow@10692
  1211
nipkow@10692
  1212
wenzelm@4621
  1213
(** misc **)
wenzelm@233
  1214
wenzelm@233
  1215
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1216
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1217
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1218
  in map keypair end;
clasohm@0
  1219
wenzelm@233
  1220
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1221
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1222
fun keyfilter [] searchkey = []
wenzelm@233
  1223
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1224
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1225
      else keyfilter pairs searchkey;
clasohm@0
  1226
clasohm@0
  1227
clasohm@0
  1228
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1229
  Preserves order of elements in both lists.*)
clasohm@0
  1230
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
  1231
    let fun part ([], answer) = answer
wenzelm@233
  1232
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
  1233
            then  part (xs, (x::ys, ns))
wenzelm@233
  1234
            else  part (xs, (ys, x::ns))
wenzelm@233
  1235
    in  part (rev ys, ([], []))  end;
clasohm@0
  1236
clasohm@0
  1237
clasohm@0
  1238
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1239
    let fun part [] = []
wenzelm@233
  1240
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1241
                           in (x::xs)::(part xs') end
clasohm@0
  1242
    in part end;
clasohm@0
  1243
clasohm@0
  1244
wenzelm@233
  1245
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1246
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1247
fun partition_list p i j =
wenzelm@233
  1248
  let fun part k xs =
wenzelm@233
  1249
            if k>j then
clasohm@0
  1250
              (case xs of [] => []
clasohm@0
  1251
                         | _ => raise LIST "partition_list")
clasohm@0
  1252
            else
wenzelm@233
  1253
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1254
            in  ns :: part(k+1)rest  end
clasohm@0
  1255
  in  part i end;
clasohm@0
  1256
clasohm@0
  1257
wenzelm@233
  1258
(* generating identifiers *)
clasohm@0
  1259
paulson@4063
  1260
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1261
local
paulson@4063
  1262
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1263
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1264
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1265
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1266
             else if i=62 then "_"
wenzelm@5904
  1267
             else  (*i=63*)    "'";
paulson@4063
  1268
paulson@4063
  1269
val charVec = Vector.tabulate (64, char);
paulson@4063
  1270
wenzelm@5904
  1271
fun newid n =
wenzelm@5904
  1272
  let
wenzelm@4284
  1273
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1274
wenzelm@4284
  1275
val seedr = ref 0;
clasohm@0
  1276
paulson@4063
  1277
in
wenzelm@4284
  1278
wenzelm@12346
  1279
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1280
paulson@4063
  1281
end;
paulson@4063
  1282
paulson@4063
  1283
wenzelm@233
  1284
(* lexical scanning *)
clasohm@0
  1285
wenzelm@233
  1286
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1287
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1288
fun scanwords is_let cs =
clasohm@0
  1289
  let fun scan1 [] = []
wenzelm@233
  1290
        | scan1 cs =
wenzelm@233
  1291
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1292
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1293
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1294
wenzelm@4212
  1295
clasohm@1364
  1296
end;
clasohm@1364
  1297
clasohm@1364
  1298
open Library;