src/Pure/library.ML
author ballarin
Mon, 11 Apr 2005 12:34:34 +0200
changeset 15696 1da4ce092c0b
parent 15670 963cd3f7976c
child 15745 33bb955b2e73
permissions -rw-r--r--
First release of interpretation commands.
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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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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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  val is_none: 'a option -> bool
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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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  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 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 fold_rev: ('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 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_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: 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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    (* CB: note alternative Syntax.string_of_vname has nicer syntax *)
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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 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*)
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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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  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_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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signature LIBRARY_CLOSED =
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sig
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  include LIBRARY
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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 apsome: ('a -> 'b) -> 'a option -> 'b option
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  val rev_append: 'a list -> 'a list -> 'a list
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  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
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  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
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  val take: int * 'a list -> 'a list
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  val drop: int * 'a list -> 'a list
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  val nth_elem: int * 'a list -> 'a
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  val last_elem: 'a list -> 'a
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  val flat: 'a list list -> 'a list
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  val seq: ('a -> unit) -> 'a list -> unit
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  val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val filter: ('a -> bool) -> 'a list -> 'a list
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  val mapfilter: ('a -> 'b option) -> 'a list -> 'b list
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end;
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structure Library: LIBRARY_CLOSED =
1364
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struct
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233
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(** functions **)
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233
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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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380
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(*reverse apply*)
410
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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;
380
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233
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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*)
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fun (f oo g) x y = f (g x y);
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fun (f ooo g) x y z = f (g x y z);
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fun (f oooo g) x y z w = f (g x y z w);
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(** stamps **)
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type stamp = unit ref;
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val stamp: unit -> stamp = ref;
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(** options **)
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val the = valOf;
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fun if_none opt a = getOpt (opt, a);
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val is_some = isSome;
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fun is_none opt = not (isSome opt);
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val apsome = Option.map;
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(*invalidate former constructors to prevent accidental use as match-all patterns!*)
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datatype invalid = None of invalid;
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exception OPTION of invalid;
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(* exception handling *)
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exception ERROR;
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fun try f x = SOME (f x)
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  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => NONE;
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fun can f x = is_some (try f x);
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datatype 'a result =
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  Result of 'a |
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  Exn of exn;
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fun capture f x = Result (f x) handle e => Exn e;
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fun release (Result y) = y
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  | release (Exn e) = raise e;
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fun get_result (Result x) = SOME x
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  | get_result _ = NONE;
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fun get_exn (Exn exn) = SOME exn
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  | get_exn _ = NONE;
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(** pairs **)
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fun pair x y = (x, y);
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fun rpair x y = (y, x);
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fun fst (x, y) = x;
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fun snd (x, y) = y;
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fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
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fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
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fun swap (x, y) = (y, x);
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(*apply function to components*)
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fun apfst f (x, y) = (f x, y);
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fun apsnd f (x, y) = (x, f y);
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fun pairself f (x, y) = (f x, f y);
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(** booleans **)
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(* equality *)
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fun equal x y = x = y;
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fun not_equal x y = x <> y;
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(* operators for combining predicates *)
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fun (p orf q) = fn x => p x orelse q x;
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fun (p andf q) = fn x => p x andalso q x;
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(* predicates on lists *)
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(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
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fun exists (pred: 'a -> bool) : 'a list -> bool =
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  let fun boolf [] = false
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        | boolf (x :: xs) = pred x orelse boolf xs
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  in boolf end;
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(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
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fun forall (pred: 'a -> bool) : 'a list -> bool =
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  let fun boolf [] = true
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        | boolf (x :: xs) = pred x andalso boolf xs
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  in boolf end;
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(* flags *)
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fun set flag = (flag := true; true);
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fun reset flag = (flag := false; false);
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fun toggle flag = (flag := not (! flag); ! flag);
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fun change r f = r := f (! r);
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(*temporarily set flag, handling exceptions*)
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fun setmp flag value f x =
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  let
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    val orig_value = ! flag;
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    fun return y = (flag := orig_value; y);
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  in
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    flag := value;
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    return (f x handle exn => (return (); raise exn))
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  end;
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(* conditional execution *)
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fun conditional b f = if b then f () else ();
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(** lists **)
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exception UnequalLengths;
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fun cons x xs = x :: xs;
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fun single x = [x];
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fun append xs ys = xs @ ys;
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   446
(* tail recursive version *)
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fun rev_append xs ys = List.revAppend(xs,ys);
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e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
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fun apply [] x = x
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  | apply (f :: fs) x = apply fs (f x);
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(* fold *)
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(*the following versions of fold are designed to fit nicely with infixes*)
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(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
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    for operators that associate to the left (TAIL RECURSIVE)*)
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fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
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  let fun itl (e, [])  = e
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        | itl (e, a::l) = itl (f(e, a), l)
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  in  itl end;
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(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
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    for operators that associate to the right (not tail recursive)*)
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fun foldr f (l, e) =
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  let fun itr [] = e
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        | itr (a::l) = f(a, itr l)
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  in  itr l  end;
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(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
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   472
    for n > 0, operators that associate to the right (not tail recursive)*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   473
fun foldr1 f l =
4181
wenzelm
parents: 4139
diff changeset
   474
  let fun itr [x] = x
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   475
        | itr (x::l) = f(x, itr l)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   476
  in  itr l  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   477
14792
b7dac2fae5bb added fold, product; removed transitive_closure;
wenzelm
parents: 14618
diff changeset
   478
fun fold f xs y = foldl (fn (y', x) => f x y') (y, xs);
15035
8c57751cd43f added fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b;
wenzelm
parents: 14981
diff changeset
   479
fun fold_rev f xs y = foldr (fn (x, y') => f x y') (xs, y);
14792
b7dac2fae5bb added fold, product; removed transitive_closure;
wenzelm
parents: 14618
diff changeset
   480
4956
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   481
fun foldl_map _ (x, []) = (x, [])
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   482
  | foldl_map f (x, y :: ys) =
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   483
      let
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   484
        val (x', y') = f (x, y);
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   485
        val (x'', ys') = foldl_map f (x', ys);
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   486
      in (x'', y' :: ys') end;
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   487
11002
e33dfe9bde39 added foldln
oheimb
parents: 10951
diff changeset
   488
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   489
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   490
(* basic list functions *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   491
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   492
(*take the first n elements from a list*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   493
fun take (n, []) = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   494
  | take (n, x :: xs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   495
      if n > 0 then x :: take (n - 1, xs) else [];
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   496
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   497
(*drop the first n elements from a list*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   498
fun drop (n, []) = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   499
  | drop (n, x :: xs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   500
      if n > 0 then drop (n - 1, xs) else x :: xs;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   501
13629
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   502
fun splitAt(n,[]) = ([],[])
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   503
  | splitAt(n,xs as x::ys) =
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   504
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   505
      else ([],xs)
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   506
4713
bea2ab2e360b New simplifier flag for mutual simplification.
nipkow
parents: 4692
diff changeset
   507
fun dropwhile P [] = []
bea2ab2e360b New simplifier flag for mutual simplification.
nipkow
parents: 4692
diff changeset
   508
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
bea2ab2e360b New simplifier flag for mutual simplification.
nipkow
parents: 4692
diff changeset
   509
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   510
(*return nth element of a list, where 0 designates the first element;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   511
  raise EXCEPTION if list too short*)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   512
fun nth_elem (i,xs) = List.nth(xs,i);
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   513
11773
983d2db52062 map_nth_elem;
wenzelm
parents: 11514
diff changeset
   514
fun map_nth_elem 0 f (x :: xs) = f x :: xs
983d2db52062 map_nth_elem;
wenzelm
parents: 11514
diff changeset
   515
  | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   516
  | map_nth_elem _ _ [] = raise Subscript;
11773
983d2db52062 map_nth_elem;
wenzelm
parents: 11514
diff changeset
   517
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   518
(*last element of a list*)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   519
val last_elem = List.last;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   520
3762
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   521
(*rear decomposition*)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   522
fun split_last [] = raise Empty
3762
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   523
  | split_last [x] = ([], x)
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   524
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   525
4893
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   526
(*update nth element*)
13629
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   527
fun nth_update x n_xs =
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   528
    (case splitAt n_xs of
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   529
      (_,[]) => raise Subscript
13629
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   530
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
4893
df9d6eef16d5 added nth_update: 'a -> int * 'a list -> 'a list;
wenzelm
parents: 4849
diff changeset
   531
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   532
(*find the position of an element in a list*)
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   533
fun find_index pred =
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   534
  let fun find _ [] = ~1
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   535
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   536
  in find 0 end;
3762
f20b071a429a added split_last;
wenzelm
parents: 3699
diff changeset
   537
4224
79e205c3a82c made SML/NJ happy;
wenzelm
parents: 4212
diff changeset
   538
fun find_index_eq x = find_index (equal x);
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   539
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   540
(*find first element satisfying predicate*)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   541
fun find_first _ [] = NONE
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   542
  | find_first pred (x :: xs) =
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   543
      if pred x then SOME x else find_first pred xs;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   544
4916
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   545
(*get first element by lookup function*)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   546
fun get_first _ [] = NONE
4916
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   547
  | get_first f (x :: xs) =
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   548
      (case f x of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   549
        NONE => get_first f xs
4916
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   550
      | some => some);
fe8b0c82691b get_first: ('a -> 'b option) -> 'a list -> 'b option;
wenzelm
parents: 4893
diff changeset
   551
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   552
(*flatten a list of lists to a list*)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   553
val flat = List.concat;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   554
12136
74156e7bb22e added unflat;
wenzelm
parents: 11853
diff changeset
   555
fun unflat (xs :: xss) ys =
13629
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   556
      let val (ps,qs) = splitAt(length xs,ys)
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
   557
      in ps :: unflat xss qs end
12136
74156e7bb22e added unflat;
wenzelm
parents: 11853
diff changeset
   558
  | unflat [] [] = []
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   559
  | unflat _ _ = raise UnequalLengths;
12136
74156e7bb22e added unflat;
wenzelm
parents: 11853
diff changeset
   560
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   561
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   562
  (proc x1; ...; proc xn) for side effects*)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   563
val seq = List.app;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   564
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   565
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   566
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   567
  | separate _ xs = xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   568
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   569
(*make the list [x, x, ..., x] of length n*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   570
fun replicate n (x: 'a) : 'a list =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   571
  let fun rep (0, xs) = xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   572
        | rep (n, xs) = rep (n - 1, x :: xs)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   573
  in
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   574
    if n < 0 then raise Subscript
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   575
    else rep (n, [])
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   576
  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   577
14926
d2baf4b79424 added translate_string;
wenzelm
parents: 14868
diff changeset
   578
fun translate_string f = String.translate (f o String.str);
d2baf4b79424 added translate_string;
wenzelm
parents: 14868
diff changeset
   579
4248
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
   580
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
   581
fun multiply ([], _) = []
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
   582
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
5e8a31c41d44 added get_error: 'a error -> string option, get_ok: 'a error -> 'a option;
wenzelm
parents: 4224
diff changeset
   583
14792
b7dac2fae5bb added fold, product; removed transitive_closure;
wenzelm
parents: 14618
diff changeset
   584
(*direct product*)
b7dac2fae5bb added fold, product; removed transitive_closure;
wenzelm
parents: 14618
diff changeset
   585
fun product _ [] = []
b7dac2fae5bb added fold, product; removed transitive_closure;
wenzelm
parents: 14618
diff changeset
   586
  | product [] _ = []
b7dac2fae5bb added fold, product; removed transitive_closure;
wenzelm
parents: 14618
diff changeset
   587
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
b7dac2fae5bb added fold, product; removed transitive_closure;
wenzelm
parents: 14618
diff changeset
   588
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   589
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   590
(* filter *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   591
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   592
(*copy the list preserving elements that satisfy the predicate*)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   593
val filter = List.filter;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   594
fun filter_out f = filter (not o f);
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   595
val mapfilter = List.mapPartial;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   596
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   597
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   598
(* lists of pairs *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   599
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   600
exception UnequalLengths;
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   601
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   602
fun map2 _ ([], []) = []
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   603
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   604
  | map2 _ _ = raise UnequalLengths;
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   605
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   606
fun exists2 _ ([], []) = false
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   607
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   608
  | exists2 _ _ = raise UnequalLengths;
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   609
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   610
fun forall2 _ ([], []) = true
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   611
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   612
  | forall2 _ _ = raise UnequalLengths;
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   613
4956
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   614
fun seq2 _ ([], []) = ()
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   615
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   616
  | seq2 _ _ = raise UnequalLengths;
4956
a7538e43896e added foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list;
wenzelm
parents: 4945
diff changeset
   617
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   618
(*combine two lists forming a list of pairs:
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   619
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   620
fun [] ~~ [] = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   621
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   622
  | _ ~~ _ = raise UnequalLengths;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   623
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   624
(*inverse of ~~; the old 'split':
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   625
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   626
val split_list = ListPair.unzip;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   627
7468
6ce03d2f7d91 equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool;
wenzelm
parents: 7090
diff changeset
   628
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
6ce03d2f7d91 equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool;
wenzelm
parents: 7090
diff changeset
   629
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   630
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   631
(* prefixes, suffixes *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   632
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   633
fun [] prefix _ = true
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   634
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   635
  | _ prefix _ = false;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   636
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   637
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   638
   where xi is the first element that does not satisfy the predicate*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   639
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   640
  let fun take (rxs, []) = (rev rxs, [])
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   641
        | take (rxs, x :: xs) =
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   642
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   643
  in  take([], xs)  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   644
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   645
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   646
   where xi is the last element that does not satisfy the predicate*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   647
fun take_suffix _ [] = ([], [])
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   648
  | take_suffix pred (x :: xs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   649
      (case take_suffix pred xs of
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   650
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   651
      | (prfx, sffx) => (x :: prfx, sffx));
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   652
12249
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   653
fun prefixes1 [] = []
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   654
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   655
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   656
fun suffixes1 xs = map rev (prefixes1 (rev xs));
dd9a51255855 added prefixes1, suffixes1;
wenzelm
parents: 12136
diff changeset
   657
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   658
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   659
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   660
(** integers **)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   661
10692
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   662
fun gcd(x,y) =
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   663
  let fun gxd x y =
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   664
    if y = 0 then x else gxd y (x mod y)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   665
  in if x < y then gxd y x else gxd x y end;
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   666
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   667
fun lcm(x,y) = (x * y) div gcd(x,y);
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
   668
2958
7837471d2f27 improved inc, dec;
wenzelm
parents: 2806
diff changeset
   669
fun inc i = (i := ! i + 1; ! i);
7837471d2f27 improved inc, dec;
wenzelm
parents: 2806
diff changeset
   670
fun dec i = (i := ! i - 1; ! i);
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   671
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   672
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   673
(* lists of integers *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   674
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   675
(*make the list [from, from + 1, ..., to]*)
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   676
fun (from upto to) =
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   677
  if from > to then [] else from :: ((from + 1) upto to);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   678
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   679
(*make the list [from, from - 1, ..., to]*)
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   680
fun (from downto to) =
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   681
  if from < to then [] else from :: ((from - 1) downto to);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   682
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   683
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   684
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   685
  | downto0 ([], n) = n = ~1;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   686
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   687
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   688
(* convert integers to strings *)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   689
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   690
(*expand the number in the given base;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   691
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   692
fun radixpand (base, num) : int list =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   693
  let
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   694
    fun radix (n, tail) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   695
      if n < base then n :: tail
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   696
      else radix (n div base, (n mod base) :: tail)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   697
  in radix (num, []) end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   698
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   699
(*expands a number into a string of characters starting from "zerochar";
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   700
  example: radixstring (2, "0", 8) gives "1000"*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   701
fun radixstring (base, zerochar, num) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   702
  let val offset = ord zerochar;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   703
      fun chrof n = chr (offset + n)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   704
  in implode (map chrof (radixpand (base, num))) end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   705
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   706
3407
afd288caf573 Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents: 3393
diff changeset
   707
val string_of_int = Int.toString;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   708
3407
afd288caf573 Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents: 3393
diff changeset
   709
fun string_of_indexname (a,0) = a
afd288caf573 Removal of radixstring from string_of_int; addition of string_of_indexname
paulson
parents: 3393
diff changeset
   710
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   711
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   712
14826
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   713
(* read integers *)
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   714
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   715
fun read_radixint (radix: int, cs) : int * string list =
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   716
  let val zero = ord"0"
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   717
      val limit = zero+radix
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   718
      fun scan (num,[]) = (num,[])
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   719
        | scan (num, c::cs) =
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   720
              if  zero <= ord c  andalso  ord c < limit
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   721
              then scan(radix*num + ord c - zero, cs)
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   722
              else (num, c::cs)
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   723
  in  scan(0,cs)  end;
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   724
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   725
fun read_int cs = read_radixint (10, cs);
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   726
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   727
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   728
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   729
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   730
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   731
(** strings **)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   732
6312
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   733
(*functions tuned for strings, avoiding explode*)
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   734
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   735
fun nth_elem_string (i, str) =
6959
d33b1629eaf9 try/can: pass Interrupt and ERROR;
wenzelm
parents: 6642
diff changeset
   736
  (case try String.substring (str, i, 1) of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   737
    SOME s => s
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   738
  | NONE => raise Subscript);
6312
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   739
6282
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   740
fun foldl_string f (x0, str) =
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   741
  let
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   742
    val n = size str;
14968
9db3d2be8cdf tuned exists_string;
wenzelm
parents: 14926
diff changeset
   743
    fun fold (x, i) =
9db3d2be8cdf tuned exists_string;
wenzelm
parents: 14926
diff changeset
   744
      if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x;
6282
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   745
  in fold (x0, 0) end;
589671bebbb3 foldl_string;
wenzelm
parents: 5966
diff changeset
   746
14968
9db3d2be8cdf tuned exists_string;
wenzelm
parents: 14926
diff changeset
   747
fun exists_string pred str =
9db3d2be8cdf tuned exists_string;
wenzelm
parents: 14926
diff changeset
   748
  let
9db3d2be8cdf tuned exists_string;
wenzelm
parents: 14926
diff changeset
   749
    val n = size str;
9db3d2be8cdf tuned exists_string;
wenzelm
parents: 14926
diff changeset
   750
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
9db3d2be8cdf tuned exists_string;
wenzelm
parents: 14926
diff changeset
   751
  in ex 0 end;
6312
d361b0a99e31 added nth_elem_string, exists_string;
wenzelm
parents: 6282
diff changeset
   752
512
55755ed9fab9 Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents: 410
diff changeset
   753
(*enclose in brackets*)
55755ed9fab9 Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents: 410
diff changeset
   754
fun enclose lpar rpar str = lpar ^ str ^ rpar;
6642
732af87c0650 strip_quotes replaced by unenclose;
wenzelm
parents: 6510
diff changeset
   755
fun unenclose str = String.substring (str, 1, size str - 2);
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   756
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   757
(*simple quoting (does not escape special chars)*)
512
55755ed9fab9 Pure/library/enclose, Pure/Syntax/pretty/enclose: renamed from parents
lcp
parents: 410
diff changeset
   758
val quote = enclose "\"" "\"";
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   759
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   760
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   761
fun space_implode a bs = implode (separate a bs);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   762
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   763
val commas = space_implode ", ";
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
   764
val commas_quote = commas o map quote;
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   765
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   766
(*concatenate messages, one per line, into a string*)
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   767
val cat_lines = space_implode "\n";
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   768
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
   769
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
3832
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   770
fun space_explode _ "" = []
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   771
  | space_explode sep str =
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   772
      let
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   773
        fun expl chs =
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   774
          (case take_prefix (not_equal sep) chs of
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   775
            (cs, []) => [implode cs]
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   776
          | (cs, _ :: cs') => implode cs :: expl cs');
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   777
      in expl (explode str) end;
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   778
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   779
val split_lines = space_explode "\n";
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   780
14826
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   781
fun prefix_lines "" txt = txt
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   782
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
   783
7712
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   784
(*untabify*)
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   785
fun untabify chs =
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   786
  let
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   787
    val tab_width = 8;
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   788
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   789
    fun untab (_, "\n") = (0, ["\n"])
9118
62367f8fef02 added change: 'a ref -> ('a -> 'a) -> unit;
wenzelm
parents: 8999
diff changeset
   790
      | untab (pos, "\t") =
62367f8fef02 added change: 'a ref -> ('a -> 'a) -> unit;
wenzelm
parents: 8999
diff changeset
   791
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
7712
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   792
      | untab (pos, c) = (pos + 1, [c]);
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   793
  in
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   794
    if not (exists (equal "\t") chs) then chs
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   795
    else flat (#2 (foldl_map untab (0, chs)))
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   796
  end;
c522ec2adc37 added untabify;
wenzelm
parents: 7468
diff changeset
   797
5285
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   798
(*append suffix*)
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   799
fun suffix sfx s = s ^ sfx;
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   800
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   801
(*remove suffix*)
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   802
fun unsuffix sfx s =
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   803
  let
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   804
    val cs = explode s;
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   805
    val prfx_len = size s - size sfx;
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   806
  in
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   807
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   808
      implode (take (prfx_len, cs))
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   809
    else raise Fail "unsuffix"
5285
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   810
  end;
2d1425492fb3 val single: 'a -> 'a list;
wenzelm
parents: 5112
diff changeset
   811
15060
7b4abcfae4e1 Added function unprefix.
berghofe
parents: 15051
diff changeset
   812
(*remove prefix*)
7b4abcfae4e1 Added function unprefix.
berghofe
parents: 15051
diff changeset
   813
fun unprefix prfx s =
7b4abcfae4e1 Added function unprefix.
berghofe
parents: 15051
diff changeset
   814
  let val (prfx', sfx) = splitAt (size prfx, explode s)
7b4abcfae4e1 Added function unprefix.
berghofe
parents: 15051
diff changeset
   815
  in
7b4abcfae4e1 Added function unprefix.
berghofe
parents: 15051
diff changeset
   816
    if implode prfx' = prfx then implode sfx
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   817
    else raise Fail "unprefix"
15060
7b4abcfae4e1 Added function unprefix.
berghofe
parents: 15051
diff changeset
   818
  end;
7b4abcfae4e1 Added function unprefix.
berghofe
parents: 15051
diff changeset
   819
10951
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   820
fun replicate_string 0 _ = ""
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   821
  | replicate_string 1 a = a
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   822
  | replicate_string k a =
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   823
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   824
      else replicate_string (k div 2) (a ^ a) ^ a;
ddb9b820d8a5 added replicate_string;
wenzelm
parents: 10692
diff changeset
   825
3832
17a20a2af8f5 fixed space_explode, old one retained as BAD_space_explode;
wenzelm
parents: 3762
diff changeset
   826
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   827
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   828
(** lists as sets **)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   829
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   830
(*membership in a list*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   831
fun x mem [] = false
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   832
  | x mem (y :: ys) = x = y orelse x mem ys;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   833
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   834
(*membership in a list, optimized version for ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   835
fun (x:int) mem_int [] = false
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   836
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   837
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   838
(*membership in a list, optimized version for strings*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   839
fun (x:string) mem_string [] = false
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   840
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   841
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   842
(*generalized membership test*)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   843
fun gen_mem eq (x, []) = false
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   844
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   845
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   846
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   847
(*insertion into list if not already there*)
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   848
fun (x ins xs) = if x mem xs then xs else x :: xs;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   849
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   850
(*insertion into list, optimized version for ints*)
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   851
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   852
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   853
(*insertion into list, optimized version for strings*)
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   854
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   855
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   856
(*generalized insertion*)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   857
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   858
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   859
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   860
(*union of sets represented as lists: no repetitions*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   861
fun xs union [] = xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   862
  | [] union ys = ys
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   863
  | (x :: xs) union ys = xs union (x ins ys);
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   864
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   865
(*union of sets, optimized version for ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   866
fun (xs:int list) union_int [] = xs
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   867
  | [] union_int ys = ys
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   868
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   869
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   870
(*union of sets, optimized version for strings*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   871
fun (xs:string list) union_string [] = xs
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   872
  | [] union_string ys = ys
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   873
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   874
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   875
(*generalized union*)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   876
fun gen_union eq (xs, []) = xs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   877
  | gen_union eq ([], ys) = ys
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   878
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   879
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   880
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   881
(*intersection*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   882
fun [] inter ys = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   883
  | (x :: xs) inter ys =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   884
      if x mem ys then x :: (xs inter ys) else xs inter ys;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   885
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   886
(*intersection, optimized version for ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   887
fun ([]:int list) inter_int ys = []
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   888
  | (x :: xs) inter_int ys =
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   889
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   890
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   891
(*intersection, optimized version for strings *)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   892
fun ([]:string list) inter_string ys = []
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   893
  | (x :: xs) inter_string ys =
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   894
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   895
7090
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   896
(*generalized intersection*)
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   897
fun gen_inter eq ([], ys) = []
12284
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
   898
  | gen_inter eq (x::xs, ys) =
7090
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   899
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
12284
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
   900
                           else      gen_inter eq (xs, ys);
7090
dd30a72880c7 added gen_inter
paulson
parents: 6959
diff changeset
   901
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   902
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   903
(*subset*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   904
fun [] subset ys = true
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   905
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   906
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   907
(*subset, optimized version for ints*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   908
fun ([]:int list) subset_int ys = true
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   909
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   910
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   911
(*subset, optimized version for strings*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   912
fun ([]:string list) subset_string ys = true
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   913
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   914
4363
b449831f03f4 added eq_set;
wenzelm
parents: 4343
diff changeset
   915
(*set equality*)
b449831f03f4 added eq_set;
wenzelm
parents: 4343
diff changeset
   916
fun eq_set (xs, ys) =
b449831f03f4 added eq_set;
wenzelm
parents: 4343
diff changeset
   917
  xs = ys orelse (xs subset ys andalso ys subset xs);
b449831f03f4 added eq_set;
wenzelm
parents: 4343
diff changeset
   918
2182
29e56f003599 Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents: 2175
diff changeset
   919
(*set equality for strings*)
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   920
fun eq_set_string ((xs:string list), ys) =
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   921
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   922
2182
29e56f003599 Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents: 2175
diff changeset
   923
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
29e56f003599 Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents: 2175
diff changeset
   924
265
443dc2c37583 added eq_set;
wenzelm
parents: 255
diff changeset
   925
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   926
(*removing an element from a list WITHOUT duplicates*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   927
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   928
  | [] \ x = [];
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   929
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
   930
fun ys \\ xs = foldl (op \) (ys,xs);
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   931
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   932
(*removing an element from a list -- possibly WITH duplicates*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   933
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
12295
83f747db967c clarified order in gen_merge_lists';
wenzelm
parents: 12284
diff changeset
   934
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   935
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   936
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   937
(*makes a list of the distinct members of the input; preserves order, takes
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   938
  first of equal elements*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   939
fun gen_distinct eq lst =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   940
  let
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   941
    val memb = gen_mem eq;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   942
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   943
    fun dist (rev_seen, []) = rev rev_seen
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   944
      | dist (rev_seen, x :: xs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   945
          if memb (x, rev_seen) then dist (rev_seen, xs)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   946
          else dist (x :: rev_seen, xs);
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   947
  in
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   948
    dist ([], lst)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   949
  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   950
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
   951
fun distinct l = gen_distinct (op =) l;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   952
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   953
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   954
(*returns the tail beginning with the first repeated element, or []*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   955
fun findrep [] = []
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   956
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   957
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   958
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   959
(*returns a list containing all repeated elements exactly once; preserves
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   960
  order, takes first of equal elements*)
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   961
fun gen_duplicates eq lst =
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   962
  let
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   963
    val memb = gen_mem eq;
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   964
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   965
    fun dups (rev_dups, []) = rev rev_dups
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   966
      | dups (rev_dups, x :: xs) =
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   967
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   968
            dups (rev_dups, xs)
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   969
          else dups (x :: rev_dups, xs);
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   970
  in
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   971
    dups ([], lst)
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   972
  end;
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   973
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
   974
fun duplicates l = gen_duplicates (op =) l;
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   975
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
   976
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   977
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   978
(** association lists **)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   979
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   980
(*association list lookup*)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   981
fun assoc ([], key) = NONE
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   982
  | assoc ((keyi, xi) :: pairs, key) =
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   983
      if key = keyi then SOME xi else assoc (pairs, key);
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
   984
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   985
(*association list lookup, optimized version for ints*)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   986
fun assoc_int ([], (key:int)) = NONE
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   987
  | assoc_int ((keyi, xi) :: pairs, key) =
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   988
      if key = keyi then SOME xi else assoc_int (pairs, key);
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   989
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   990
(*association list lookup, optimized version for strings*)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   991
fun assoc_string ([], (key:string)) = NONE
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   992
  | assoc_string ((keyi, xi) :: pairs, key) =
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   993
      if key = keyi then SOME xi else assoc_string (pairs, key);
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   994
2175
21fde76bc742 Updated syntax; shortened comments; put in monomorphic versions of ins
paulson
parents: 2157
diff changeset
   995
(*association list lookup, optimized version for string*ints*)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   996
fun assoc_string_int ([], (key:string*int)) = NONE
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   997
  | assoc_string_int ((keyi, xi) :: pairs, key) =
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
   998
      if key = keyi then SOME xi else assoc_string_int (pairs, key);
1576
af8f43f742a0 Added some optimized versions of functions dealing with sets
berghofe
parents: 1460
diff changeset
   999
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1000
fun assocs ps x =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1001
  (case assoc (ps, x) of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
  1002
    NONE => []
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
  1003
  | SOME ys => ys);
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1004
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
  1005
(*two-fold association list lookup*)
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
  1006
fun assoc2 (aal, (key1, key2)) =
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
  1007
  (case assoc (aal, key1) of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
  1008
    SOME al => assoc (al, key2)
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
  1009
  | NONE => NONE);
255
ee132db91681 added if_none, parents, commas, gen_duplicates, duplicates, assoc2;
wenzelm
parents: 245
diff changeset
  1010
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1011
(*generalized association list lookup*)
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
  1012
fun gen_assoc eq ([], key) = NONE
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1013
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15263
diff changeset
  1014
      if eq (key, keyi) then SOME xi else gen_assoc eq (pairs, key);
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1015
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1016
(*association list update*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1017
fun overwrite (al, p as (key, _)) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1018
  let fun over ((q as (keyi, _)) :: pairs) =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1019
            if keyi = key then p :: pairs else q :: (over pairs)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1020
        | over [] = [p]
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1021
  in over al end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1022
2522
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1023
fun gen_overwrite eq (al, p as (key, _)) =
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1024
  let fun over ((q as (keyi, _)) :: pairs) =
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1025
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1026
        | over [] = [p]
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1027
  in over al end;
a1a18530c4ac added gen_overwrite;
wenzelm
parents: 2506
diff changeset
  1028
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1029
12284
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
  1030
(* lists as tables *)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1031
12284
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
  1032
fun gen_merge_lists _ xs [] = xs
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
  1033
  | gen_merge_lists _ [] ys = ys
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
  1034
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1035
12284
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
  1036
fun gen_merge_lists' _ xs [] = xs
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
  1037
  | gen_merge_lists' _ [] ys = ys
12295
83f747db967c clarified order in gen_merge_lists';
wenzelm
parents: 12284
diff changeset
  1038
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1039
12284
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
  1040
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
  1041
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
131e743d168a added gen_merge_lists(') and merge_lists(');
wenzelm
parents: 12260
diff changeset
  1042
fun merge_alists al = gen_merge_lists eq_fst al;
15263
b40e91201039 Added function merge_alists'.
berghofe
parents: 15060
diff changeset
  1043
fun merge_alists' al = gen_merge_lists' eq_fst al;
380
daca5b594fb3 added infix op also: 'a * ('a -> 'b) -> 'b;
wenzelm
parents: 265
diff changeset
  1044
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1045
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1046
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1047
(** balanced trees **)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1048
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1049
exception Balance;      (*indicates non-positive argument to balancing fun*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1050
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1051
(*balanced folding; avoids deep nesting*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1052
fun fold_bal f [x] = x
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1053
  | fold_bal f [] = raise Balance
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1054
  | fold_bal f xs =
13629
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
  1055
      let val (ps,qs) = splitAt(length xs div 2, xs)
a46362d2b19b take/drop -> splitAt
nipkow
parents: 13488
diff changeset
  1056
      in  f (fold_bal f ps, fold_bal f qs)  end;
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1057
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1058
(*construct something of the form f(...g(...(x)...)) for balanced access*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1059
fun access_bal (f, g, x) n i =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1060
  let fun acc n i =     (*1<=i<=n*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1061
          if n=1 then x else
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1062
          let val n2 = n div 2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1063
          in  if i<=n2 then f (acc n2 i)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1064
                       else g (acc (n-n2) (i-n2))
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1065
          end
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1066
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1067
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1068
(*construct ALL such accesses; could try harder to share recursive calls!*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1069
fun accesses_bal (f, g, x) n =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1070
  let fun acc n =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1071
          if n=1 then [x] else
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1072
          let val n2 = n div 2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1073
              val acc2 = acc n2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1074
          in  if n-n2=n2 then map f acc2 @ map g acc2
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1075
                         else map f acc2 @ map g (acc (n-n2)) end
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1076
  in  if 1<=n then acc n else raise Balance  end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1077
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1078
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1079
2506
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1080
(** orders **)
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1081
4445
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1082
fun rev_order LESS = GREATER
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1083
  | rev_order EQUAL = EQUAL
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1084
  | rev_order GREATER = LESS;
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1085
4479
708d7c26db5b improved comment;
wenzelm
parents: 4445
diff changeset
  1086
(*assume rel is a linear strict order*)
4445
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1087
fun make_ord rel (x, y) =
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1088
  if rel (x, y) then LESS
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1089
  else if rel (y, x) then GREATER
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1090
  else EQUAL;
de74b549f976 added rev_order, make_ord;
wenzelm
parents: 4363
diff changeset
  1091
15051
0dbbab9f77fe int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents: 15035
diff changeset
  1092
val int_ord = Int.compare;
0dbbab9f77fe int_ord = Int.compare, string_ord = String.compare;
wenzelm
parents: 15035
diff changeset
  1093
val string_ord = String.compare;
2506
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1094
4343
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1095
(*lexicographic product*)
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1096
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1097
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1098
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1099
(*dictionary order -- in general NOT well-founded!*)
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1100
fun dict_ord _ ([], []) = EQUAL
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1101
  | dict_ord _ ([], _ :: _) = LESS
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1102
  | dict_ord _ (_ :: _, []) = GREATER
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1103
  | dict_ord elem_ord (x :: xs, y :: ys) =
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1104
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1105
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1106
(*lexicographic product of lists*)
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1107
fun list_ord elem_ord (xs, ys) =
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1108
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
9849fb57c395 added prod_ord, dict_ord, list_ord;
wenzelm
parents: 4326
diff changeset
  1109
2506
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1110
4621
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1111
(* sorting *)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1112
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1113
(*quicksort (stable, i.e. does not reorder equal elements)*)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1114
fun sort ord =
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1115
  let
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1116
    fun qsort xs =
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1117
      let val len = length xs in
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1118
        if len <= 1 then xs
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1119
        else
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1120
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1121
            qsort lts @ eqs @ qsort gts
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1122
          end
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1123
      end
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1124
    and part _ [] = ([], [], [])
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1125
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1126
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1127
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1128
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1129
  in qsort end;
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1130
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1131
(*sort strings*)
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1132
val sort_strings = sort string_ord;
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1133
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1134
11514
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1135
fun unique_strings ([]: string list) = []
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1136
  | unique_strings [x] = [x]
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1137
  | unique_strings (x :: y :: ys) =
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1138
      if x = y then unique_strings (y :: ys)
a12def3d1847 Added function unique_strings.
berghofe
parents: 11021
diff changeset
  1139
      else x :: unique_strings (y :: ys);
4621
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1140
2506
965127966331 added datatype order;
wenzelm
parents: 2471
diff changeset
  1141
14106
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1142
(** random numbers **)
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1143
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1144
exception RANDOM;
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1145
14618
068bb99f3ebd Fixed bug in rmod that caused an overflow exception in SML/NJ.
berghofe
parents: 14472
diff changeset
  1146
fun rmod x y = x - y * Real.realFloor (x / y);
14106
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1147
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1148
local
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1149
  val a = 16807.0;
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1150
  val m = 2147483647.0;
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1151
  val random_seed = ref 1.0;
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1152
in
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1153
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1154
fun random () =
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1155
  let val r = rmod (a * !random_seed) m
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1156
  in (random_seed := r; r) end;
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1157
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1158
end;
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1159
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1160
fun random_range l h =
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1161
  if h < l orelse l < 0 then raise RANDOM
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1162
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1163
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1164
fun one_of xs = nth_elem (random_range 0 (length xs - 1), xs);
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1165
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1166
fun frequency xs =
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1167
  let
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1168
    val sum = foldl op + (0, map fst xs);
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1169
    fun pick n ((k, x) :: xs) =
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1170
      if n <= k then x else pick (n - k) xs
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1171
  in pick (random_range 1 sum) xs end;
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1172
bbf708a7e27f Added several functions for producing random numbers.
berghofe
parents: 13794
diff changeset
  1173
14826
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
  1174
(** current directory **)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1175
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
  1176
val cd = OS.FileSys.chDir;
2317
672015b535d7 added pwd;
wenzelm
parents: 2303
diff changeset
  1177
val pwd = OS.FileSys.getDir;
2243
3ebeaaacfbd1 Eta-expanded some declarations that are illegal under value polymorphism
paulson
parents: 2196
diff changeset
  1178
3606
5d7073700fbc Added function "file_exists".
berghofe
parents: 3553
diff changeset
  1179
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1180
10692
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1181
(** rational numbers **)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1182
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1183
datatype rat = Rat of bool * int * int
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1184
14826
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
  1185
exception RAT of string;
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
  1186
10692
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1187
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1188
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1189
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1190
  let val absp = abs p
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1191
      val m = gcd(absp,q)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1192
  in Rat(a = (0 <= p), absp div m, q div m) end;
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1193
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1194
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1195
  let val den = lcm(q,s)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1196
      val p = p*(den div q) and r = r*(den div s)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1197
      val num = (if a then p else ~p) + (if b then r else ~r)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1198
  in ratnorm(true,num,den) end;
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1199
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1200
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1201
14826
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
  1202
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p)
10692
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1203
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1204
fun int_ratdiv(p,q) =
14826
48cfe0fe53e2 output channels and diagnostics moved to General/output.ML; added read_int etc. from term.ML; removed obsolete mtree; type rat uses exception RAT;
wenzelm
parents: 14797
diff changeset
  1205
  if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q)
10692
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1206
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1207
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1208
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1209
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1210
6077fd933575 added rational arithmetic
nipkow
parents: 9830
diff changeset
  1211
4621
79e6a11ba8a9 added explicit signature;
wenzelm
parents: 4616
diff changeset
  1212
(** misc **)
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1213
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1214
(*use the keyfun to make a list of (x, key) pairs*)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1215
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1216
  let fun keypair x = (x, keyfun x)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1217
  in map keypair end;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1218
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1219
(*given a list of (x, key) pairs and a searchkey
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1220
  return the list of xs from each pair whose key equals searchkey*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1221
fun keyfilter [] searchkey = []
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1222
  | keyfilter ((x, key) :: pairs) searchkey =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1223
      if key = searchkey then x :: keyfilter pairs searchkey
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1224
      else keyfilter pairs searchkey;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1225
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1226
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1227
(*Partition list into elements that satisfy predicate and those that don't.
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1228
  Preserves order of elements in both lists.*)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1229
val partition = List.partition;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1230
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1231
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1232
fun partition_eq (eq:'a * 'a -> bool) =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1233
    let fun part [] = []
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1234
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1235
                           in (x::xs)::(part xs') end
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1236
    in part end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1237
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1238
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1239
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1240
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1241
fun partition_list p i j =
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1242
  let fun part k xs =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1243
            if k>j then
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1244
              (case xs of [] => []
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1245
                         | _ => raise Fail "partition_list")
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1246
            else
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1247
            let val (ns, rest) = partition (p k) xs;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1248
            in  ns :: part(k+1)rest  end
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1249
  in  part i end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1250
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1251
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1252
(* generating identifiers *)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1253
4063
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1254
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1255
local
4063
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1256
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1257
fun char i =      if i<26 then chr (ord "A" + i)
5904
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1258
             else if i<52 then chr (ord "a" + i - 26)
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1259
             else if i<62 then chr (ord"0" + i - 52)
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1260
             else if i=62 then "_"
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1261
             else  (*i=63*)    "'";
4063
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1262
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1263
val charVec = Vector.tabulate (64, char);
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1264
5904
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1265
fun newid n =
e077a0e66563 val apply: ('a -> 'a) list -> 'a -> 'a;
wenzelm
parents: 5893
diff changeset
  1266
  let
4284
eb65491ae776 removed merge_opts;
wenzelm
parents: 4255
diff changeset
  1267
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
2003
b48f066d52dc Addition of gensym
paulson
parents: 1628
diff changeset
  1268
4284
eb65491ae776 removed merge_opts;
wenzelm
parents: 4255
diff changeset
  1269
val seedr = ref 0;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1270
4063
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1271
in
4284
eb65491ae776 removed merge_opts;
wenzelm
parents: 4255
diff changeset
  1272
12346
e7b1956f4eae removed questionable init_gensym;
wenzelm
parents: 12295
diff changeset
  1273
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
2003
b48f066d52dc Addition of gensym
paulson
parents: 1628
diff changeset
  1274
4063
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1275
end;
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1276
0b19014b9155 Faster lexing
paulson
parents: 4046
diff changeset
  1277
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1278
(* lexical scanning *)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1279
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1280
(*scan a list of characters into "words" composed of "letters" (recognized by
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1281
  is_let) and separated by any number of non-"letters"*)
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1282
fun scanwords is_let cs =
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
  1283
  let fun scan1 [] = []
233
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1284
        | scan1 cs =
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1285
            let val (lets, rest) = take_prefix is_let cs
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1286
            in implode lets :: scanwords is_let rest end;
efd6b4bb14dd major cleanup and reorganisation;
wenzelm
parents: 205
diff changeset
  1287
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
24
f3d4ff75d9f2 added functions that operate on filenames: split_filename (originally located
clasohm
parents: 0
diff changeset
  1288
4212
68c7b37f8721 major cleanup;
wenzelm
parents: 4194
diff changeset
  1289
1364
8ea1a962ad72 files now define a structure to allow SML/NJ to optimize the code
clasohm
parents: 1290
diff changeset
  1290
end;
8ea1a962ad72 files now define a structure to allow SML/NJ to optimize the code
clasohm
parents: 1290
diff changeset
  1291
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1292
structure OpenLibrary: LIBRARY = Library;
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
  1293
open OpenLibrary;