src/Pure/library.ML
author wenzelm
Thu Apr 07 09:27:33 2005 +0200 (2005-04-07)
changeset 15670 963cd3f7976c
parent 15570 8d8c70b41bab
child 15696 1da4ce092c0b
permissions -rw-r--r--
invalidated former constructors None/OPTION to prevent accidental use as match-all patterns!
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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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  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 =
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struct
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(** functions **)
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(*handy combinators*)
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fun curry f x y = f (x, y);
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fun uncurry f (x, y) = f x y;
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fun I x = x;
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fun K x y = x;
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(*reverse apply*)
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fun (x |> f) = f x;
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fun ((x, y) |>> f) = (f x, y);
wenzelm@8418
   296
fun ((x, y) |>>> f) = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@380
   297
wenzelm@233
   298
(*application of (infix) operator to its left or right argument*)
wenzelm@233
   299
fun apl (x, f) y = f (x, y);
wenzelm@233
   300
fun apr (f, y) x = f (x, y);
clasohm@0
   301
wenzelm@233
   302
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   303
fun funpow n f x =
wenzelm@233
   304
  let fun rep (0, x) = x
wenzelm@233
   305
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   306
  in rep (n, x) end;
wenzelm@160
   307
wenzelm@5893
   308
(*concatenation: 2 and 3 args*)
wenzelm@5893
   309
fun (f oo g) x y = f (g x y);
wenzelm@5893
   310
fun (f ooo g) x y z = f (g x y z);
wenzelm@6510
   311
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@6510
   312
wenzelm@160
   313
wenzelm@160
   314
wenzelm@2471
   315
(** stamps **)
wenzelm@2471
   316
wenzelm@2471
   317
type stamp = unit ref;
wenzelm@2471
   318
val stamp: unit -> stamp = ref;
wenzelm@2471
   319
wenzelm@2471
   320
wenzelm@2471
   321
wenzelm@233
   322
(** options **)
clasohm@0
   323
skalberg@15570
   324
val the = valOf;
wenzelm@15670
   325
fun if_none opt a = getOpt (opt, a);
skalberg@15570
   326
val is_some = isSome;
wenzelm@15670
   327
fun is_none opt = not (isSome opt);
wenzelm@15670
   328
val apsome = Option.map;
clasohm@0
   329
wenzelm@15670
   330
(*invalidate former constructors to prevent accidental use as match-all patterns!*)
wenzelm@15670
   331
datatype invalid = None of invalid;
wenzelm@15670
   332
exception OPTION of invalid;
clasohm@0
   333
wenzelm@6959
   334
wenzelm@6959
   335
(* exception handling *)
wenzelm@6959
   336
wenzelm@6959
   337
exception ERROR;
wenzelm@6959
   338
skalberg@15531
   339
fun try f x = SOME (f x)
skalberg@15531
   340
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => NONE;
wenzelm@6959
   341
wenzelm@6959
   342
fun can f x = is_some (try f x);
wenzelm@4139
   343
wenzelm@4139
   344
wenzelm@14868
   345
datatype 'a result =
wenzelm@14868
   346
  Result of 'a |
wenzelm@14868
   347
  Exn of exn;
wenzelm@14868
   348
wenzelm@14868
   349
fun capture f x = Result (f x) handle e => Exn e;
wenzelm@14868
   350
wenzelm@14868
   351
fun release (Result y) = y
wenzelm@14868
   352
  | release (Exn e) = raise e;
wenzelm@14868
   353
skalberg@15531
   354
fun get_result (Result x) = SOME x
skalberg@15531
   355
  | get_result _ = NONE;
wenzelm@14868
   356
skalberg@15531
   357
fun get_exn (Exn exn) = SOME exn
skalberg@15531
   358
  | get_exn _ = NONE;
wenzelm@14868
   359
wenzelm@14868
   360
wenzelm@4139
   361
wenzelm@233
   362
(** pairs **)
wenzelm@233
   363
wenzelm@233
   364
fun pair x y = (x, y);
wenzelm@233
   365
fun rpair x y = (y, x);
wenzelm@233
   366
wenzelm@233
   367
fun fst (x, y) = x;
wenzelm@233
   368
fun snd (x, y) = y;
wenzelm@233
   369
wenzelm@233
   370
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   371
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   372
wenzelm@233
   373
fun swap (x, y) = (y, x);
wenzelm@233
   374
wenzelm@4212
   375
(*apply function to components*)
wenzelm@233
   376
fun apfst f (x, y) = (f x, y);
wenzelm@233
   377
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   378
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   379
wenzelm@233
   380
wenzelm@233
   381
wenzelm@233
   382
(** booleans **)
wenzelm@233
   383
wenzelm@233
   384
(* equality *)
wenzelm@233
   385
wenzelm@233
   386
fun equal x y = x = y;
wenzelm@233
   387
fun not_equal x y = x <> y;
wenzelm@233
   388
wenzelm@233
   389
wenzelm@233
   390
(* operators for combining predicates *)
wenzelm@233
   391
paulson@2175
   392
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   393
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   394
wenzelm@233
   395
wenzelm@233
   396
(* predicates on lists *)
wenzelm@233
   397
wenzelm@233
   398
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   399
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   400
  let fun boolf [] = false
wenzelm@233
   401
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   402
  in boolf end;
wenzelm@233
   403
wenzelm@233
   404
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   405
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   406
  let fun boolf [] = true
wenzelm@233
   407
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   408
  in boolf end;
clasohm@0
   409
wenzelm@233
   410
wenzelm@380
   411
(* flags *)
wenzelm@380
   412
wenzelm@380
   413
fun set flag = (flag := true; true);
wenzelm@380
   414
fun reset flag = (flag := false; false);
wenzelm@380
   415
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   416
wenzelm@9118
   417
fun change r f = r := f (! r);
wenzelm@9118
   418
wenzelm@14826
   419
(*temporarily set flag, handling exceptions*)
wenzelm@2978
   420
fun setmp flag value f x =
wenzelm@2958
   421
  let
wenzelm@2958
   422
    val orig_value = ! flag;
wenzelm@2958
   423
    fun return y = (flag := orig_value; y);
wenzelm@2958
   424
  in
wenzelm@2958
   425
    flag := value;
wenzelm@2958
   426
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   427
  end;
wenzelm@2958
   428
wenzelm@380
   429
wenzelm@11853
   430
(* conditional execution *)
wenzelm@11853
   431
wenzelm@11853
   432
fun conditional b f = if b then f () else ();
wenzelm@11853
   433
wenzelm@11853
   434
wenzelm@233
   435
wenzelm@233
   436
(** lists **)
wenzelm@233
   437
skalberg@15570
   438
exception UnequalLengths;
wenzelm@233
   439
wenzelm@233
   440
fun cons x xs = x :: xs;
wenzelm@5285
   441
fun single x = [x];
wenzelm@233
   442
wenzelm@4629
   443
fun append xs ys = xs @ ys;
wenzelm@4629
   444
berghofe@13794
   445
(* tail recursive version *)
skalberg@15531
   446
fun rev_append xs ys = List.revAppend(xs,ys);
berghofe@13794
   447
wenzelm@5904
   448
fun apply [] x = x
wenzelm@5904
   449
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   450
wenzelm@233
   451
wenzelm@233
   452
(* fold *)
wenzelm@233
   453
wenzelm@233
   454
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   455
wenzelm@233
   456
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   457
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   458
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   459
  let fun itl (e, [])  = e
wenzelm@233
   460
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   461
  in  itl end;
wenzelm@233
   462
wenzelm@233
   463
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   464
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   465
fun foldr f (l, e) =
wenzelm@233
   466
  let fun itr [] = e
wenzelm@233
   467
        | itr (a::l) = f(a, itr l)
wenzelm@233
   468
  in  itr l  end;
wenzelm@233
   469
wenzelm@233
   470
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   471
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   472
fun foldr1 f l =
wenzelm@4181
   473
  let fun itr [x] = x
wenzelm@233
   474
        | itr (x::l) = f(x, itr l)
wenzelm@233
   475
  in  itr l  end;
wenzelm@233
   476
wenzelm@14792
   477
fun fold f xs y = foldl (fn (y', x) => f x y') (y, xs);
wenzelm@15035
   478
fun fold_rev f xs y = foldr (fn (x, y') => f x y') (xs, y);
wenzelm@14792
   479
wenzelm@4956
   480
fun foldl_map _ (x, []) = (x, [])
wenzelm@4956
   481
  | foldl_map f (x, y :: ys) =
wenzelm@4956
   482
      let
wenzelm@4956
   483
        val (x', y') = f (x, y);
wenzelm@4956
   484
        val (x'', ys') = foldl_map f (x', ys);
wenzelm@4956
   485
      in (x'', y' :: ys') end;
wenzelm@4956
   486
oheimb@11002
   487
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
wenzelm@233
   488
wenzelm@233
   489
(* basic list functions *)
wenzelm@233
   490
wenzelm@233
   491
(*take the first n elements from a list*)
wenzelm@233
   492
fun take (n, []) = []
wenzelm@233
   493
  | take (n, x :: xs) =
wenzelm@233
   494
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   495
wenzelm@233
   496
(*drop the first n elements from a list*)
wenzelm@233
   497
fun drop (n, []) = []
wenzelm@233
   498
  | drop (n, x :: xs) =
wenzelm@233
   499
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   500
nipkow@13629
   501
fun splitAt(n,[]) = ([],[])
nipkow@13629
   502
  | splitAt(n,xs as x::ys) =
nipkow@13629
   503
      if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end
nipkow@13629
   504
      else ([],xs)
nipkow@13629
   505
nipkow@4713
   506
fun dropwhile P [] = []
nipkow@4713
   507
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   508
wenzelm@233
   509
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   510
  raise EXCEPTION if list too short*)
skalberg@15570
   511
fun nth_elem (i,xs) = List.nth(xs,i);
wenzelm@233
   512
wenzelm@11773
   513
fun map_nth_elem 0 f (x :: xs) = f x :: xs
wenzelm@11773
   514
  | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs
skalberg@15570
   515
  | map_nth_elem _ _ [] = raise Subscript;
wenzelm@11773
   516
wenzelm@233
   517
(*last element of a list*)
skalberg@15570
   518
val last_elem = List.last;
wenzelm@233
   519
wenzelm@3762
   520
(*rear decomposition*)
skalberg@15570
   521
fun split_last [] = raise Empty
wenzelm@3762
   522
  | split_last [x] = ([], x)
wenzelm@3762
   523
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   524
wenzelm@4893
   525
(*update nth element*)
nipkow@13629
   526
fun nth_update x n_xs =
nipkow@13629
   527
    (case splitAt n_xs of
skalberg@15570
   528
      (_,[]) => raise Subscript
nipkow@13629
   529
    | (prfx, _ :: sffx') => prfx @ (x :: sffx'))
wenzelm@4893
   530
wenzelm@4212
   531
(*find the position of an element in a list*)
wenzelm@4212
   532
fun find_index pred =
wenzelm@4212
   533
  let fun find _ [] = ~1
wenzelm@4212
   534
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   535
  in find 0 end;
wenzelm@3762
   536
wenzelm@4224
   537
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   538
wenzelm@4212
   539
(*find first element satisfying predicate*)
skalberg@15531
   540
fun find_first _ [] = NONE
wenzelm@4212
   541
  | find_first pred (x :: xs) =
skalberg@15531
   542
      if pred x then SOME x else find_first pred xs;
wenzelm@233
   543
wenzelm@4916
   544
(*get first element by lookup function*)
skalberg@15531
   545
fun get_first _ [] = NONE
wenzelm@4916
   546
  | get_first f (x :: xs) =
wenzelm@4916
   547
      (case f x of
skalberg@15531
   548
        NONE => get_first f xs
wenzelm@4916
   549
      | some => some);
wenzelm@4916
   550
wenzelm@233
   551
(*flatten a list of lists to a list*)
skalberg@15531
   552
val flat = List.concat;
wenzelm@233
   553
wenzelm@12136
   554
fun unflat (xs :: xss) ys =
nipkow@13629
   555
      let val (ps,qs) = splitAt(length xs,ys)
nipkow@13629
   556
      in ps :: unflat xss qs end
wenzelm@12136
   557
  | unflat [] [] = []
skalberg@15570
   558
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   559
wenzelm@233
   560
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   561
  (proc x1; ...; proc xn) for side effects*)
skalberg@15570
   562
val seq = List.app;
wenzelm@233
   563
wenzelm@233
   564
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   565
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   566
  | separate _ xs = xs;
wenzelm@233
   567
wenzelm@233
   568
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   569
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   570
  let fun rep (0, xs) = xs
wenzelm@233
   571
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   572
  in
skalberg@15570
   573
    if n < 0 then raise Subscript
wenzelm@233
   574
    else rep (n, [])
wenzelm@233
   575
  end;
wenzelm@233
   576
wenzelm@14926
   577
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   578
wenzelm@4248
   579
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   580
fun multiply ([], _) = []
wenzelm@4248
   581
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   582
wenzelm@14792
   583
(*direct product*)
wenzelm@14792
   584
fun product _ [] = []
wenzelm@14792
   585
  | product [] _ = []
wenzelm@14792
   586
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   587
wenzelm@233
   588
wenzelm@233
   589
(* filter *)
wenzelm@233
   590
wenzelm@233
   591
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   592
val filter = List.filter;
clasohm@0
   593
fun filter_out f = filter (not o f);
skalberg@15570
   594
val mapfilter = List.mapPartial;
wenzelm@233
   595
wenzelm@233
   596
wenzelm@233
   597
(* lists of pairs *)
wenzelm@233
   598
skalberg@15570
   599
exception UnequalLengths;
skalberg@15570
   600
wenzelm@380
   601
fun map2 _ ([], []) = []
wenzelm@380
   602
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
skalberg@15570
   603
  | map2 _ _ = raise UnequalLengths;
wenzelm@380
   604
wenzelm@380
   605
fun exists2 _ ([], []) = false
wenzelm@380
   606
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
skalberg@15570
   607
  | exists2 _ _ = raise UnequalLengths;
wenzelm@380
   608
wenzelm@380
   609
fun forall2 _ ([], []) = true
wenzelm@380
   610
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
skalberg@15570
   611
  | forall2 _ _ = raise UnequalLengths;
wenzelm@380
   612
wenzelm@4956
   613
fun seq2 _ ([], []) = ()
wenzelm@4956
   614
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
skalberg@15570
   615
  | seq2 _ _ = raise UnequalLengths;
wenzelm@4956
   616
wenzelm@233
   617
(*combine two lists forming a list of pairs:
wenzelm@233
   618
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   619
fun [] ~~ [] = []
wenzelm@233
   620
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   621
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   622
wenzelm@233
   623
(*inverse of ~~; the old 'split':
wenzelm@233
   624
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   625
val split_list = ListPair.unzip;
wenzelm@233
   626
wenzelm@7468
   627
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
wenzelm@7468
   628
wenzelm@233
   629
wenzelm@233
   630
(* prefixes, suffixes *)
wenzelm@233
   631
wenzelm@233
   632
fun [] prefix _ = true
wenzelm@233
   633
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   634
  | _ prefix _ = false;
wenzelm@233
   635
wenzelm@233
   636
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   637
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   638
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   639
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   640
        | take (rxs, x :: xs) =
wenzelm@255
   641
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   642
  in  take([], xs)  end;
wenzelm@233
   643
wenzelm@233
   644
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   645
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   646
fun take_suffix _ [] = ([], [])
wenzelm@233
   647
  | take_suffix pred (x :: xs) =
wenzelm@233
   648
      (case take_suffix pred xs of
wenzelm@233
   649
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   650
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   651
wenzelm@12249
   652
fun prefixes1 [] = []
wenzelm@12249
   653
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   654
wenzelm@12249
   655
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@12249
   656
wenzelm@233
   657
wenzelm@233
   658
wenzelm@233
   659
(** integers **)
wenzelm@233
   660
nipkow@10692
   661
fun gcd(x,y) =
nipkow@10692
   662
  let fun gxd x y =
nipkow@10692
   663
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   664
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   665
nipkow@10692
   666
fun lcm(x,y) = (x * y) div gcd(x,y);
nipkow@10692
   667
wenzelm@2958
   668
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   669
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   670
wenzelm@233
   671
wenzelm@233
   672
(* lists of integers *)
wenzelm@233
   673
wenzelm@233
   674
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   675
fun (from upto to) =
wenzelm@233
   676
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   677
wenzelm@233
   678
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   679
fun (from downto to) =
wenzelm@233
   680
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   681
wenzelm@233
   682
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   683
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   684
  | downto0 ([], n) = n = ~1;
wenzelm@233
   685
wenzelm@233
   686
wenzelm@233
   687
(* convert integers to strings *)
wenzelm@233
   688
wenzelm@233
   689
(*expand the number in the given base;
wenzelm@233
   690
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   691
fun radixpand (base, num) : int list =
wenzelm@233
   692
  let
wenzelm@233
   693
    fun radix (n, tail) =
wenzelm@233
   694
      if n < base then n :: tail
wenzelm@233
   695
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   696
  in radix (num, []) end;
wenzelm@233
   697
wenzelm@233
   698
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   699
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   700
fun radixstring (base, zerochar, num) =
wenzelm@233
   701
  let val offset = ord zerochar;
wenzelm@233
   702
      fun chrof n = chr (offset + n)
wenzelm@233
   703
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   704
wenzelm@233
   705
paulson@3407
   706
val string_of_int = Int.toString;
wenzelm@233
   707
paulson@3407
   708
fun string_of_indexname (a,0) = a
paulson@3407
   709
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   710
wenzelm@233
   711
wenzelm@14826
   712
(* read integers *)
wenzelm@14826
   713
wenzelm@14826
   714
fun read_radixint (radix: int, cs) : int * string list =
wenzelm@14826
   715
  let val zero = ord"0"
wenzelm@14826
   716
      val limit = zero+radix
wenzelm@14826
   717
      fun scan (num,[]) = (num,[])
wenzelm@14826
   718
        | scan (num, c::cs) =
wenzelm@14826
   719
              if  zero <= ord c  andalso  ord c < limit
wenzelm@14826
   720
              then scan(radix*num + ord c - zero, cs)
wenzelm@14826
   721
              else (num, c::cs)
wenzelm@14826
   722
  in  scan(0,cs)  end;
wenzelm@14826
   723
wenzelm@14826
   724
fun read_int cs = read_radixint (10, cs);
wenzelm@14826
   725
wenzelm@14826
   726
fun oct_char s = chr (#1 (read_radixint (8, explode s)));
wenzelm@14826
   727
wenzelm@14826
   728
wenzelm@14826
   729
wenzelm@233
   730
(** strings **)
wenzelm@233
   731
wenzelm@6312
   732
(*functions tuned for strings, avoiding explode*)
wenzelm@6312
   733
wenzelm@6312
   734
fun nth_elem_string (i, str) =
wenzelm@6959
   735
  (case try String.substring (str, i, 1) of
skalberg@15531
   736
    SOME s => s
skalberg@15570
   737
  | NONE => raise Subscript);
wenzelm@6312
   738
wenzelm@6282
   739
fun foldl_string f (x0, str) =
wenzelm@6282
   740
  let
wenzelm@6282
   741
    val n = size str;
wenzelm@14968
   742
    fun fold (x, i) =
wenzelm@14968
   743
      if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x;
wenzelm@6282
   744
  in fold (x0, 0) end;
wenzelm@6282
   745
wenzelm@14968
   746
fun exists_string pred str =
wenzelm@14968
   747
  let
wenzelm@14968
   748
    val n = size str;
wenzelm@14968
   749
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   750
  in ex 0 end;
wenzelm@6312
   751
lcp@512
   752
(*enclose in brackets*)
lcp@512
   753
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   754
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   755
wenzelm@233
   756
(*simple quoting (does not escape special chars)*)
lcp@512
   757
val quote = enclose "\"" "\"";
wenzelm@233
   758
wenzelm@4212
   759
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   760
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   761
wenzelm@255
   762
val commas = space_implode ", ";
wenzelm@380
   763
val commas_quote = commas o map quote;
wenzelm@255
   764
wenzelm@233
   765
(*concatenate messages, one per line, into a string*)
wenzelm@255
   766
val cat_lines = space_implode "\n";
wenzelm@233
   767
wenzelm@4212
   768
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   769
fun space_explode _ "" = []
wenzelm@3832
   770
  | space_explode sep str =
wenzelm@3832
   771
      let
wenzelm@3832
   772
        fun expl chs =
wenzelm@3832
   773
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   774
            (cs, []) => [implode cs]
wenzelm@3832
   775
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   776
      in expl (explode str) end;
wenzelm@3832
   777
wenzelm@3832
   778
val split_lines = space_explode "\n";
wenzelm@3832
   779
wenzelm@14826
   780
fun prefix_lines "" txt = txt
wenzelm@14826
   781
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   782
wenzelm@7712
   783
(*untabify*)
wenzelm@7712
   784
fun untabify chs =
wenzelm@7712
   785
  let
wenzelm@7712
   786
    val tab_width = 8;
wenzelm@7712
   787
wenzelm@7712
   788
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   789
      | untab (pos, "\t") =
wenzelm@9118
   790
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   791
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   792
  in
wenzelm@7712
   793
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   794
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   795
  end;
wenzelm@7712
   796
wenzelm@5285
   797
(*append suffix*)
wenzelm@5285
   798
fun suffix sfx s = s ^ sfx;
wenzelm@5285
   799
wenzelm@5285
   800
(*remove suffix*)
wenzelm@5285
   801
fun unsuffix sfx s =
wenzelm@5285
   802
  let
wenzelm@5285
   803
    val cs = explode s;
wenzelm@5285
   804
    val prfx_len = size s - size sfx;
wenzelm@5285
   805
  in
wenzelm@5285
   806
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
wenzelm@5285
   807
      implode (take (prfx_len, cs))
skalberg@15570
   808
    else raise Fail "unsuffix"
wenzelm@5285
   809
  end;
wenzelm@5285
   810
berghofe@15060
   811
(*remove prefix*)
berghofe@15060
   812
fun unprefix prfx s =
berghofe@15060
   813
  let val (prfx', sfx) = splitAt (size prfx, explode s)
berghofe@15060
   814
  in
berghofe@15060
   815
    if implode prfx' = prfx then implode sfx
skalberg@15570
   816
    else raise Fail "unprefix"
berghofe@15060
   817
  end;
berghofe@15060
   818
wenzelm@10951
   819
fun replicate_string 0 _ = ""
wenzelm@10951
   820
  | replicate_string 1 a = a
wenzelm@10951
   821
  | replicate_string k a =
wenzelm@10951
   822
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   823
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   824
wenzelm@3832
   825
wenzelm@233
   826
wenzelm@233
   827
(** lists as sets **)
wenzelm@233
   828
wenzelm@233
   829
(*membership in a list*)
wenzelm@233
   830
fun x mem [] = false
wenzelm@233
   831
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   832
paulson@2175
   833
(*membership in a list, optimized version for ints*)
berghofe@1576
   834
fun (x:int) mem_int [] = false
berghofe@1576
   835
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   836
paulson@2175
   837
(*membership in a list, optimized version for strings*)
berghofe@1576
   838
fun (x:string) mem_string [] = false
berghofe@1576
   839
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   840
clasohm@0
   841
(*generalized membership test*)
wenzelm@233
   842
fun gen_mem eq (x, []) = false
wenzelm@233
   843
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   844
wenzelm@233
   845
wenzelm@233
   846
(*insertion into list if not already there*)
paulson@2175
   847
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   848
paulson@2175
   849
(*insertion into list, optimized version for ints*)
paulson@2175
   850
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   851
paulson@2175
   852
(*insertion into list, optimized version for strings*)
paulson@2175
   853
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   854
clasohm@0
   855
(*generalized insertion*)
wenzelm@233
   856
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   857
wenzelm@233
   858
wenzelm@233
   859
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   860
fun xs union [] = xs
wenzelm@233
   861
  | [] union ys = ys
wenzelm@233
   862
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   863
paulson@2175
   864
(*union of sets, optimized version for ints*)
berghofe@1576
   865
fun (xs:int list) union_int [] = xs
berghofe@1576
   866
  | [] union_int ys = ys
berghofe@1576
   867
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   868
paulson@2175
   869
(*union of sets, optimized version for strings*)
berghofe@1576
   870
fun (xs:string list) union_string [] = xs
berghofe@1576
   871
  | [] union_string ys = ys
berghofe@1576
   872
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   873
clasohm@0
   874
(*generalized union*)
wenzelm@233
   875
fun gen_union eq (xs, []) = xs
wenzelm@233
   876
  | gen_union eq ([], ys) = ys
wenzelm@233
   877
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   878
wenzelm@233
   879
wenzelm@233
   880
(*intersection*)
wenzelm@233
   881
fun [] inter ys = []
wenzelm@233
   882
  | (x :: xs) inter ys =
wenzelm@233
   883
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   884
paulson@2175
   885
(*intersection, optimized version for ints*)
berghofe@1576
   886
fun ([]:int list) inter_int ys = []
berghofe@1576
   887
  | (x :: xs) inter_int ys =
berghofe@1576
   888
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   889
paulson@2175
   890
(*intersection, optimized version for strings *)
berghofe@1576
   891
fun ([]:string list) inter_string ys = []
berghofe@1576
   892
  | (x :: xs) inter_string ys =
berghofe@1576
   893
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   894
paulson@7090
   895
(*generalized intersection*)
paulson@7090
   896
fun gen_inter eq ([], ys) = []
wenzelm@12284
   897
  | gen_inter eq (x::xs, ys) =
paulson@7090
   898
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
wenzelm@12284
   899
                           else      gen_inter eq (xs, ys);
paulson@7090
   900
wenzelm@233
   901
wenzelm@233
   902
(*subset*)
wenzelm@233
   903
fun [] subset ys = true
wenzelm@233
   904
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   905
paulson@2175
   906
(*subset, optimized version for ints*)
berghofe@1576
   907
fun ([]:int list) subset_int ys = true
berghofe@1576
   908
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   909
paulson@2175
   910
(*subset, optimized version for strings*)
berghofe@1576
   911
fun ([]:string list) subset_string ys = true
berghofe@1576
   912
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   913
wenzelm@4363
   914
(*set equality*)
wenzelm@4363
   915
fun eq_set (xs, ys) =
wenzelm@4363
   916
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   917
paulson@2182
   918
(*set equality for strings*)
berghofe@1576
   919
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   920
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   921
paulson@2182
   922
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   923
wenzelm@265
   924
wenzelm@233
   925
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   926
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   927
  | [] \ x = [];
wenzelm@233
   928
paulson@2243
   929
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   930
wenzelm@233
   931
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   932
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@12295
   933
fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   934
wenzelm@233
   935
wenzelm@233
   936
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   937
  first of equal elements*)
wenzelm@233
   938
fun gen_distinct eq lst =
wenzelm@233
   939
  let
wenzelm@233
   940
    val memb = gen_mem eq;
clasohm@0
   941
wenzelm@233
   942
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   943
      | dist (rev_seen, x :: xs) =
wenzelm@233
   944
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   945
          else dist (x :: rev_seen, xs);
wenzelm@233
   946
  in
wenzelm@233
   947
    dist ([], lst)
wenzelm@233
   948
  end;
wenzelm@233
   949
paulson@2243
   950
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   951
wenzelm@233
   952
wenzelm@233
   953
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   954
fun findrep [] = []
wenzelm@233
   955
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   956
wenzelm@233
   957
wenzelm@255
   958
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   959
  order, takes first of equal elements*)
wenzelm@255
   960
fun gen_duplicates eq lst =
wenzelm@255
   961
  let
wenzelm@255
   962
    val memb = gen_mem eq;
wenzelm@255
   963
wenzelm@255
   964
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   965
      | dups (rev_dups, x :: xs) =
wenzelm@255
   966
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   967
            dups (rev_dups, xs)
wenzelm@255
   968
          else dups (x :: rev_dups, xs);
wenzelm@255
   969
  in
wenzelm@255
   970
    dups ([], lst)
wenzelm@255
   971
  end;
wenzelm@255
   972
paulson@2243
   973
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   974
wenzelm@255
   975
wenzelm@233
   976
wenzelm@233
   977
(** association lists **)
clasohm@0
   978
wenzelm@233
   979
(*association list lookup*)
skalberg@15531
   980
fun assoc ([], key) = NONE
wenzelm@233
   981
  | assoc ((keyi, xi) :: pairs, key) =
skalberg@15531
   982
      if key = keyi then SOME xi else assoc (pairs, key);
wenzelm@233
   983
paulson@2175
   984
(*association list lookup, optimized version for ints*)
skalberg@15531
   985
fun assoc_int ([], (key:int)) = NONE
berghofe@1576
   986
  | assoc_int ((keyi, xi) :: pairs, key) =
skalberg@15531
   987
      if key = keyi then SOME xi else assoc_int (pairs, key);
berghofe@1576
   988
paulson@2175
   989
(*association list lookup, optimized version for strings*)
skalberg@15531
   990
fun assoc_string ([], (key:string)) = NONE
berghofe@1576
   991
  | assoc_string ((keyi, xi) :: pairs, key) =
skalberg@15531
   992
      if key = keyi then SOME xi else assoc_string (pairs, key);
berghofe@1576
   993
paulson@2175
   994
(*association list lookup, optimized version for string*ints*)
skalberg@15531
   995
fun assoc_string_int ([], (key:string*int)) = NONE
berghofe@1576
   996
  | assoc_string_int ((keyi, xi) :: pairs, key) =
skalberg@15531
   997
      if key = keyi then SOME xi else assoc_string_int (pairs, key);
berghofe@1576
   998
wenzelm@233
   999
fun assocs ps x =
wenzelm@233
  1000
  (case assoc (ps, x) of
skalberg@15531
  1001
    NONE => []
skalberg@15531
  1002
  | SOME ys => ys);
wenzelm@233
  1003
wenzelm@255
  1004
(*two-fold association list lookup*)
wenzelm@255
  1005
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
  1006
  (case assoc (aal, key1) of
skalberg@15531
  1007
    SOME al => assoc (al, key2)
skalberg@15531
  1008
  | NONE => NONE);
wenzelm@255
  1009
wenzelm@233
  1010
(*generalized association list lookup*)
skalberg@15531
  1011
fun gen_assoc eq ([], key) = NONE
wenzelm@233
  1012
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
skalberg@15531
  1013
      if eq (key, keyi) then SOME xi else gen_assoc eq (pairs, key);
wenzelm@233
  1014
wenzelm@233
  1015
(*association list update*)
wenzelm@233
  1016
fun overwrite (al, p as (key, _)) =
wenzelm@233
  1017
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
  1018
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
  1019
        | over [] = [p]
wenzelm@233
  1020
  in over al end;
wenzelm@233
  1021
wenzelm@2522
  1022
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
  1023
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
  1024
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
  1025
        | over [] = [p]
wenzelm@2522
  1026
  in over al end;
wenzelm@2522
  1027
wenzelm@233
  1028
wenzelm@12284
  1029
(* lists as tables *)
wenzelm@233
  1030
wenzelm@12284
  1031
fun gen_merge_lists _ xs [] = xs
wenzelm@12284
  1032
  | gen_merge_lists _ [] ys = ys
wenzelm@12284
  1033
  | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs);
clasohm@0
  1034
wenzelm@12284
  1035
fun gen_merge_lists' _ xs [] = xs
wenzelm@12284
  1036
  | gen_merge_lists' _ [] ys = ys
wenzelm@12295
  1037
  | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs;
clasohm@0
  1038
wenzelm@12284
  1039
fun merge_lists xs ys = gen_merge_lists (op =) xs ys;
wenzelm@12284
  1040
fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys;
wenzelm@12284
  1041
fun merge_alists al = gen_merge_lists eq_fst al;
berghofe@15263
  1042
fun merge_alists' al = gen_merge_lists' eq_fst al;
wenzelm@380
  1043
clasohm@0
  1044
clasohm@0
  1045
wenzelm@233
  1046
(** balanced trees **)
wenzelm@233
  1047
wenzelm@233
  1048
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1049
wenzelm@233
  1050
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1051
fun fold_bal f [x] = x
wenzelm@233
  1052
  | fold_bal f [] = raise Balance
wenzelm@233
  1053
  | fold_bal f xs =
nipkow@13629
  1054
      let val (ps,qs) = splitAt(length xs div 2, xs)
nipkow@13629
  1055
      in  f (fold_bal f ps, fold_bal f qs)  end;
wenzelm@233
  1056
wenzelm@233
  1057
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1058
fun access_bal (f, g, x) n i =
wenzelm@233
  1059
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1060
          if n=1 then x else
wenzelm@233
  1061
          let val n2 = n div 2
wenzelm@233
  1062
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1063
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1064
          end
wenzelm@233
  1065
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1066
wenzelm@233
  1067
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1068
fun accesses_bal (f, g, x) n =
wenzelm@233
  1069
  let fun acc n =
wenzelm@233
  1070
          if n=1 then [x] else
wenzelm@233
  1071
          let val n2 = n div 2
wenzelm@233
  1072
              val acc2 = acc n2
wenzelm@233
  1073
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1074
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1075
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1076
wenzelm@233
  1077
wenzelm@233
  1078
wenzelm@2506
  1079
(** orders **)
wenzelm@2506
  1080
wenzelm@4445
  1081
fun rev_order LESS = GREATER
wenzelm@4445
  1082
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1083
  | rev_order GREATER = LESS;
wenzelm@4445
  1084
wenzelm@4479
  1085
(*assume rel is a linear strict order*)
wenzelm@4445
  1086
fun make_ord rel (x, y) =
wenzelm@4445
  1087
  if rel (x, y) then LESS
wenzelm@4445
  1088
  else if rel (y, x) then GREATER
wenzelm@4445
  1089
  else EQUAL;
wenzelm@4445
  1090
wenzelm@15051
  1091
val int_ord = Int.compare;
wenzelm@15051
  1092
val string_ord = String.compare;
wenzelm@2506
  1093
wenzelm@4343
  1094
(*lexicographic product*)
wenzelm@4343
  1095
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1096
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1097
wenzelm@4343
  1098
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
  1099
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1100
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
  1101
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
  1102
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
  1103
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1104
wenzelm@4343
  1105
(*lexicographic product of lists*)
wenzelm@4343
  1106
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
  1107
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
  1108
wenzelm@2506
  1109
wenzelm@4621
  1110
(* sorting *)
wenzelm@4621
  1111
wenzelm@4621
  1112
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1113
fun sort ord =
wenzelm@4621
  1114
  let
wenzelm@4621
  1115
    fun qsort xs =
wenzelm@4621
  1116
      let val len = length xs in
wenzelm@4621
  1117
        if len <= 1 then xs
wenzelm@4621
  1118
        else
wenzelm@4621
  1119
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
  1120
            qsort lts @ eqs @ qsort gts
wenzelm@4621
  1121
          end
wenzelm@4621
  1122
      end
wenzelm@4621
  1123
    and part _ [] = ([], [], [])
wenzelm@4621
  1124
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1125
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1126
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1127
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1128
  in qsort end;
wenzelm@4621
  1129
wenzelm@4621
  1130
(*sort strings*)
wenzelm@4621
  1131
val sort_strings = sort string_ord;
wenzelm@4621
  1132
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1133
berghofe@11514
  1134
fun unique_strings ([]: string list) = []
berghofe@11514
  1135
  | unique_strings [x] = [x]
berghofe@11514
  1136
  | unique_strings (x :: y :: ys) =
berghofe@11514
  1137
      if x = y then unique_strings (y :: ys)
berghofe@11514
  1138
      else x :: unique_strings (y :: ys);
wenzelm@4621
  1139
wenzelm@2506
  1140
berghofe@14106
  1141
(** random numbers **)
berghofe@14106
  1142
berghofe@14106
  1143
exception RANDOM;
berghofe@14106
  1144
berghofe@14618
  1145
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
  1146
berghofe@14106
  1147
local
berghofe@14106
  1148
  val a = 16807.0;
berghofe@14106
  1149
  val m = 2147483647.0;
berghofe@14106
  1150
  val random_seed = ref 1.0;
berghofe@14106
  1151
in
berghofe@14106
  1152
berghofe@14106
  1153
fun random () =
berghofe@14106
  1154
  let val r = rmod (a * !random_seed) m
berghofe@14106
  1155
  in (random_seed := r; r) end;
berghofe@14106
  1156
berghofe@14106
  1157
end;
berghofe@14106
  1158
berghofe@14106
  1159
fun random_range l h =
berghofe@14106
  1160
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
  1161
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
  1162
berghofe@14106
  1163
fun one_of xs = nth_elem (random_range 0 (length xs - 1), xs);
berghofe@14106
  1164
berghofe@14106
  1165
fun frequency xs =
berghofe@14106
  1166
  let
berghofe@14106
  1167
    val sum = foldl op + (0, map fst xs);
berghofe@14106
  1168
    fun pick n ((k, x) :: xs) =
berghofe@14106
  1169
      if n <= k then x else pick (n - k) xs
berghofe@14106
  1170
  in pick (random_range 1 sum) xs end;
berghofe@14106
  1171
berghofe@14106
  1172
wenzelm@14826
  1173
(** current directory **)
wenzelm@233
  1174
paulson@2243
  1175
val cd = OS.FileSys.chDir;
wenzelm@2317
  1176
val pwd = OS.FileSys.getDir;
paulson@2243
  1177
berghofe@3606
  1178
wenzelm@233
  1179
nipkow@10692
  1180
(** rational numbers **)
nipkow@10692
  1181
nipkow@10692
  1182
datatype rat = Rat of bool * int * int
nipkow@10692
  1183
wenzelm@14826
  1184
exception RAT of string;
wenzelm@14826
  1185
nipkow@10692
  1186
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
nipkow@10692
  1187
nipkow@10692
  1188
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
nipkow@10692
  1189
  let val absp = abs p
nipkow@10692
  1190
      val m = gcd(absp,q)
nipkow@10692
  1191
  in Rat(a = (0 <= p), absp div m, q div m) end;
nipkow@10692
  1192
nipkow@10692
  1193
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
nipkow@10692
  1194
  let val den = lcm(q,s)
nipkow@10692
  1195
      val p = p*(den div q) and r = r*(den div s)
nipkow@10692
  1196
      val num = (if a then p else ~p) + (if b then r else ~r)
nipkow@10692
  1197
  in ratnorm(true,num,den) end;
nipkow@10692
  1198
nipkow@10692
  1199
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
nipkow@10692
  1200
wenzelm@14826
  1201
fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p)
nipkow@10692
  1202
nipkow@10692
  1203
fun int_ratdiv(p,q) =
wenzelm@14826
  1204
  if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q)
nipkow@10692
  1205
nipkow@10692
  1206
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
nipkow@10692
  1207
nipkow@10692
  1208
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
nipkow@10692
  1209
nipkow@10692
  1210
wenzelm@4621
  1211
(** misc **)
wenzelm@233
  1212
wenzelm@233
  1213
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1214
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1215
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1216
  in map keypair end;
clasohm@0
  1217
wenzelm@233
  1218
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1219
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1220
fun keyfilter [] searchkey = []
wenzelm@233
  1221
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1222
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1223
      else keyfilter pairs searchkey;
clasohm@0
  1224
clasohm@0
  1225
clasohm@0
  1226
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1227
  Preserves order of elements in both lists.*)
skalberg@15570
  1228
val partition = List.partition;
clasohm@0
  1229
clasohm@0
  1230
clasohm@0
  1231
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1232
    let fun part [] = []
wenzelm@233
  1233
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1234
                           in (x::xs)::(part xs') end
clasohm@0
  1235
    in part end;
clasohm@0
  1236
clasohm@0
  1237
wenzelm@233
  1238
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1239
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1240
fun partition_list p i j =
wenzelm@233
  1241
  let fun part k xs =
wenzelm@233
  1242
            if k>j then
clasohm@0
  1243
              (case xs of [] => []
skalberg@15570
  1244
                         | _ => raise Fail "partition_list")
clasohm@0
  1245
            else
wenzelm@233
  1246
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1247
            in  ns :: part(k+1)rest  end
clasohm@0
  1248
  in  part i end;
clasohm@0
  1249
clasohm@0
  1250
wenzelm@233
  1251
(* generating identifiers *)
clasohm@0
  1252
paulson@4063
  1253
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1254
local
paulson@4063
  1255
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1256
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1257
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1258
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1259
             else if i=62 then "_"
wenzelm@5904
  1260
             else  (*i=63*)    "'";
paulson@4063
  1261
paulson@4063
  1262
val charVec = Vector.tabulate (64, char);
paulson@4063
  1263
wenzelm@5904
  1264
fun newid n =
wenzelm@5904
  1265
  let
wenzelm@4284
  1266
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1267
wenzelm@4284
  1268
val seedr = ref 0;
clasohm@0
  1269
paulson@4063
  1270
in
wenzelm@4284
  1271
wenzelm@12346
  1272
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@2003
  1273
paulson@4063
  1274
end;
paulson@4063
  1275
paulson@4063
  1276
wenzelm@233
  1277
(* lexical scanning *)
clasohm@0
  1278
wenzelm@233
  1279
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1280
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1281
fun scanwords is_let cs =
clasohm@0
  1282
  let fun scan1 [] = []
wenzelm@233
  1283
        | scan1 cs =
wenzelm@233
  1284
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1285
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1286
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1287
wenzelm@4212
  1288
clasohm@1364
  1289
end;
clasohm@1364
  1290
skalberg@15570
  1291
structure OpenLibrary: LIBRARY = Library;
skalberg@15570
  1292
open OpenLibrary;