src/Pure/library.ML
author wenzelm
Sat Jul 28 20:40:29 2007 +0200 (2007-07-28)
changeset 24023 6fd65e2e0dba
parent 23963 c2ee97a963db
child 24049 e4adf8175149
permissions -rw-r--r--
setmp: NAMED_CRITICAL;
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(*  Title:      Pure/library.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Markus Wenzel, TU Muenchen
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Basic library: functions, options, pairs, booleans, lists, integers,
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strings, lists as sets, orders, current directory, misc.
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See also General/basics.ML for the most fundamental concepts.
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*)
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infix 1 |>>>
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infix 2 ?
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infix 3 o oo ooo oooo
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infix 4 ~~ upto downto
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infix orf andf \ \\ mem mem_int mem_string union union_int
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  union_string inter inter_int inter_string subset subset_int subset_string
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signature BASIC_LIBRARY =
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sig
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  (*functions*)
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  val undefined: 'a -> 'b
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  val I: 'a -> 'a
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  val K: 'a -> 'b -> 'a
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  val flip: ('a -> 'b -> 'c) -> 'b -> 'a -> 'c
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  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
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  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
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  val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd)
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  val ? : bool * ('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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  val funpow: int -> ('a -> 'a) -> 'a -> 'a
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  (*errors*)
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  exception SYS_ERROR of string
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  val sys_error: string -> 'a
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  exception ERROR of string
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  val error: string -> 'a
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  val cat_error: string -> string -> 'a
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  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
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  (*pairs*)
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  val pair: 'a -> 'b -> 'a * 'b
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  val rpair: 'a -> 'b -> 'b * 'a
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  val fst: 'a * 'b -> 'a
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  val snd: 'a * 'b -> 'b
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  val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool
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  val swap: 'a * 'b -> 'b * 'a
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  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
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  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
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  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
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  (*booleans*)
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  val equal: ''a -> ''a -> bool
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  val not_equal: ''a -> ''a -> bool
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  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val exists: ('a -> bool) -> 'a list -> bool
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  val forall: ('a -> bool) -> 'a list -> bool
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  val set: bool ref -> bool
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  val reset: bool ref -> bool
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  val toggle: bool ref -> bool
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  val change: 'a ref -> ('a -> 'a) -> unit
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  val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  (*lists*)
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  exception UnequalLengths
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  val single: 'a -> 'a list
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  val the_single: 'a list -> 'a
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  val singleton: ('a list -> 'b list) -> 'a -> 'b
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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 foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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  val flat: 'a list list -> 'a list
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  val unflat: 'a list list -> 'b list -> 'b list list
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  val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list
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  val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd
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  val maps: ('a -> 'b list) -> 'a list -> 'b list
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  val chop: int -> 'a list -> 'a list * 'a list
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  val dropwhile: ('a -> bool) -> 'a list -> 'a list
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  val nth: 'a list -> int -> 'a
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  val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list
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  val nth_list: 'a list list -> int -> 'a list
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  val map_index: (int * 'a -> 'b) -> 'a list -> 'b list
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  val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b
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  val split_last: 'a list -> 'a list * 'a
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  val find_index: ('a -> bool) -> 'a list -> int
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  val find_index_eq: ''a -> ''a list -> int
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  val find_first: ('a -> bool) -> 'a list -> 'a option
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  val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option
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  val get_first: ('a -> 'b option) -> 'a list -> 'b option
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  val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
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  val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c
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  val zip_options: 'a list -> 'b option list -> ('a * 'b) list
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  val ~~ : 'a list * 'b list -> ('a * 'b) list
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  val split_list: ('a * 'b) list -> 'a list * 'b list
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  val separate: 'a -> 'a list -> 'a list
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  val replicate: int -> 'a -> 'a list
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  val multiply: 'a list -> 'a list list -> 'a list list
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  val product: 'a list -> 'b list -> ('a * 'b) list
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  val filter: ('a -> bool) -> 'a list -> 'a list
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  val filter_out: ('a -> bool) -> 'a list -> 'a list
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  val map_filter: ('a -> 'b option) -> 'a list -> 'b list
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  val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool
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  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b 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 prefixes: 'a list -> 'a list list
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  val suffixes1: 'a list -> 'a list list
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  val suffixes: 'a list -> 'a list list
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  (*integers*)
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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 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 signed_string_of_int: int -> string
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  val string_of_indexname: string * int -> string
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  val read_intinf: int -> string list -> IntInf.int * string list
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  val read_int: string list -> int * string list
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  val oct_char: string -> string
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  (*strings*)
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  val nth_string: string -> int -> string
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  val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a
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  val exists_string: (string -> bool) -> string -> bool
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  val forall_string: (string -> bool) -> string -> bool
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  val enclose: string -> string -> string -> string
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  val unenclose: string -> string
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  val quote: string -> string
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  val space_implode: string -> string list -> string
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  val commas: string list -> string
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  val commas_quote: string list -> string
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  val cat_lines: string list -> string
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  val space_explode: string -> string -> string list
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  val split_lines: string -> string list
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  val prefix_lines: string -> string -> string
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  val untabify: string list -> string list
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  val prefix: string -> string -> string
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  val suffix: string -> string -> string
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  val unprefix: string -> string -> string
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  val unsuffix: string -> string -> string
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  val replicate_string: int -> string -> string
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  val translate_string: (string -> string) -> string -> string
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  (*lists as sets -- see also Pure/General/ord_list.ML*)
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  val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool
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  val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list
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  val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list
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  val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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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 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 gen_eq_set: ('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 distinct: ('a * 'a -> bool) -> 'a list -> 'a list
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  val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
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  val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool
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  (*lists as multisets*)
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  val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list
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  val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  (*orders*)
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  val is_equal: order -> bool
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  val rev_order: order -> order
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  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
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  val int_ord: int * int -> order
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  val string_ord: string * string -> order
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  val fast_string_ord: string * string -> order
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  val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order
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  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
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  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val sort: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_strings: string list -> string list
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  val sort_wrt: ('a -> string) -> 'a list -> 'a list
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  (*random numbers*)
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  exception RANDOM
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  val random: unit -> real
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  val random_range: int -> int -> int
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  val one_of: 'a list -> 'a
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  val frequency: (int * 'a) list -> 'a
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  (*misc*)
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  val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b
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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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  type stamp
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  val stamp: unit -> stamp
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  type serial
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  val serial: unit -> serial
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  val serial_string: unit -> string
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  structure Object: sig type T end
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end;
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signature LIBRARY =
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sig
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  include BASIC_LIBRARY
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  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
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  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
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  val take: int * 'a list -> 'a list
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  val drop: int * 'a list -> 'a list
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  val last_elem: 'a list -> 'a
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end;
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structure Library: LIBRARY =
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struct
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(* functions *)
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fun undefined _ = raise Match;
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fun I x = x;
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fun K x = fn _ => x;
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fun flip f x y = f y x;
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fun curry f x y = f (x, y);
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fun uncurry f (x, y) = f x y;
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(*application and structured results -- old version*)
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fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end;
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(*conditional application*)
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fun b ? f = fn x => if b then f x else x;
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(*composition with multiple 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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(*function exponentiation: f(...(f x)...) with n applications of f*)
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fun funpow 0 _ x = x
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  | funpow n f x = funpow (n - 1) f (f x);
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(* errors *)
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exception SYS_ERROR of string;
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fun sys_error msg = raise SYS_ERROR msg;
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exception ERROR of string;
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fun error msg = raise ERROR msg;
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fun cat_error "" msg = error msg
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  | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2);
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fun assert_all pred list msg =
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  let
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    fun ass [] = ()
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      | ass (x :: xs) = if pred x then ass xs else error (msg x);
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  in ass list end;
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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 eq ((x1, _), (x2, _)) = eq (x1, x2);
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fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2);
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fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2);
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fun swap (x, y) = (y, x);
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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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(*polymorphic equality*)
wenzelm@233
   304
fun equal x y = x = y;
wenzelm@233
   305
fun not_equal x y = x <> y;
wenzelm@233
   306
wenzelm@21395
   307
(*combining predicates*)
wenzelm@16721
   308
fun p orf q = fn x => p x orelse q x;
wenzelm@16721
   309
fun p andf q = fn x => p x andalso q x;
wenzelm@233
   310
wenzelm@233
   311
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   312
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   313
  let fun boolf [] = false
wenzelm@233
   314
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   315
  in boolf end;
wenzelm@233
   316
wenzelm@233
   317
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   318
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   319
  let fun boolf [] = true
wenzelm@233
   320
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   321
  in boolf end;
clasohm@0
   322
wenzelm@19644
   323
wenzelm@380
   324
(* flags *)
wenzelm@380
   325
wenzelm@380
   326
fun set flag = (flag := true; true);
wenzelm@380
   327
fun reset flag = (flag := false; false);
wenzelm@380
   328
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   329
wenzelm@9118
   330
fun change r f = r := f (! r);
wenzelm@9118
   331
wenzelm@18712
   332
(*temporarily set flag during execution*)
wenzelm@23932
   333
fun setmp_noncritical flag value f x =
wenzelm@2958
   334
  let
wenzelm@2958
   335
    val orig_value = ! flag;
wenzelm@18712
   336
    val _ = flag := value;
wenzelm@23963
   337
    val result = Exn.capture f x;
wenzelm@18712
   338
    val _ = flag := orig_value;
wenzelm@23963
   339
  in Exn.release result end;
wenzelm@2958
   340
wenzelm@24023
   341
fun setmp flag value f x = NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x);
wenzelm@23932
   342
wenzelm@19644
   343
wenzelm@21395
   344
wenzelm@233
   345
(** lists **)
wenzelm@233
   346
skalberg@15570
   347
exception UnequalLengths;
wenzelm@233
   348
wenzelm@5285
   349
fun single x = [x];
wenzelm@233
   350
wenzelm@20882
   351
fun the_single [x] = x
wenzelm@20882
   352
  | the_single _ = raise Empty;
wenzelm@20882
   353
wenzelm@20882
   354
fun singleton f x = the_single (f [x]);
wenzelm@19273
   355
wenzelm@5904
   356
fun apply [] x = x
wenzelm@5904
   357
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   358
wenzelm@233
   359
wenzelm@21395
   360
(* fold -- old versions *)
haftmann@16691
   361
wenzelm@233
   362
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   363
wenzelm@233
   364
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   365
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   366
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   367
  let fun itl (e, [])  = e
wenzelm@233
   368
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   369
  in  itl end;
wenzelm@233
   370
wenzelm@233
   371
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   372
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   373
fun foldr f (l, e) =
wenzelm@233
   374
  let fun itr [] = e
wenzelm@233
   375
        | itr (a::l) = f(a, itr l)
wenzelm@233
   376
  in  itr l  end;
wenzelm@233
   377
wenzelm@233
   378
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   379
    for n > 0, operators that associate to the right (not tail recursive)*)
paulson@20443
   380
fun foldr1 f [] = raise Empty
wenzelm@20510
   381
  | foldr1 f l =
paulson@20443
   382
      let fun itr [x] = x
wenzelm@20510
   383
            | itr (x::l) = f(x, itr l)
paulson@20443
   384
      in  itr l  end;
wenzelm@233
   385
wenzelm@16705
   386
fun foldl_map f =
wenzelm@16705
   387
  let
wenzelm@16705
   388
    fun fold_aux (x, []) = (x, [])
wenzelm@16705
   389
      | fold_aux (x, y :: ys) =
wenzelm@16705
   390
          let
wenzelm@16705
   391
            val (x', y') = f (x, y);
wenzelm@16705
   392
            val (x'', ys') = fold_aux (x', ys);
wenzelm@16705
   393
          in (x'', y' :: ys') end;
wenzelm@16705
   394
  in fold_aux end;
wenzelm@16705
   395
wenzelm@233
   396
wenzelm@233
   397
(* basic list functions *)
wenzelm@233
   398
wenzelm@20510
   399
fun eq_list eq (list1, list2) =
haftmann@20348
   400
  let
wenzelm@20510
   401
    fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys)
wenzelm@20510
   402
      | eq_lst _ = true;
wenzelm@20510
   403
  in length list1 = length list2 andalso eq_lst (list1, list2) end;
haftmann@20348
   404
wenzelm@19483
   405
fun maps f [] = []
wenzelm@19483
   406
  | maps f (x :: xs) = f x @ maps f xs;
wenzelm@19483
   407
wenzelm@23220
   408
fun chop 0 xs = ([], xs)
wenzelm@23220
   409
  | chop _ [] = ([], [])
wenzelm@23220
   410
  | chop n (x :: xs) = chop (n - 1) xs |>> cons x;
wenzelm@19011
   411
wenzelm@233
   412
(*take the first n elements from a list*)
wenzelm@233
   413
fun take (n, []) = []
wenzelm@233
   414
  | take (n, x :: xs) =
wenzelm@233
   415
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   416
wenzelm@233
   417
(*drop the first n elements from a list*)
wenzelm@233
   418
fun drop (n, []) = []
wenzelm@233
   419
  | drop (n, x :: xs) =
wenzelm@233
   420
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   421
nipkow@4713
   422
fun dropwhile P [] = []
nipkow@4713
   423
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   424
wenzelm@233
   425
(*return nth element of a list, where 0 designates the first element;
wenzelm@18461
   426
  raise Subscript if list too short*)
haftmann@18011
   427
fun nth xs i = List.nth (xs, i);
wenzelm@233
   428
wenzelm@18461
   429
fun nth_list xss i = nth xss i handle Subscript => [];
wenzelm@18461
   430
haftmann@18011
   431
fun nth_map 0 f (x :: xs) = f x :: xs
haftmann@18011
   432
  | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs
haftmann@18011
   433
  | nth_map _ _ [] = raise Subscript;
wenzelm@11773
   434
haftmann@18514
   435
fun map_index f =
haftmann@18514
   436
  let
haftmann@18514
   437
    fun mapp _ [] = []
haftmann@18514
   438
      | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs
haftmann@18514
   439
  in mapp 0 end;
haftmann@18514
   440
haftmann@21118
   441
fun fold_index f =
haftmann@21118
   442
  let
haftmann@21118
   443
    fun fold_aux _ [] y = y
haftmann@21118
   444
      | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y);
haftmann@21118
   445
  in fold_aux 0 end;
haftmann@21118
   446
skalberg@15570
   447
val last_elem = List.last;
wenzelm@233
   448
wenzelm@3762
   449
(*rear decomposition*)
skalberg@15570
   450
fun split_last [] = raise Empty
wenzelm@3762
   451
  | split_last [x] = ([], x)
wenzelm@3762
   452
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   453
wenzelm@4212
   454
(*find the position of an element in a list*)
wenzelm@4212
   455
fun find_index pred =
wenzelm@4212
   456
  let fun find _ [] = ~1
wenzelm@4212
   457
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   458
  in find 0 end;
wenzelm@3762
   459
wenzelm@4224
   460
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   461
wenzelm@4212
   462
(*find first element satisfying predicate*)
paulson@22593
   463
val find_first = List.find;
wenzelm@233
   464
wenzelm@4916
   465
(*get first element by lookup function*)
skalberg@15531
   466
fun get_first _ [] = NONE
wenzelm@4916
   467
  | get_first f (x :: xs) =
wenzelm@4916
   468
      (case f x of
skalberg@15531
   469
        NONE => get_first f xs
wenzelm@4916
   470
      | some => some);
wenzelm@4916
   471
haftmann@19233
   472
fun get_index f =
haftmann@19233
   473
  let
haftmann@19233
   474
    fun get _ [] = NONE
wenzelm@19461
   475
      | get i (x :: xs) =
haftmann@19233
   476
          case f x
wenzelm@19461
   477
           of NONE => get (i + 1) xs
haftmann@19233
   478
            | SOME y => SOME (i, y)
haftmann@19233
   479
  in get 0 end;
haftmann@19233
   480
skalberg@15531
   481
val flat = List.concat;
wenzelm@233
   482
wenzelm@12136
   483
fun unflat (xs :: xss) ys =
wenzelm@19424
   484
      let val (ps, qs) = chop (length xs) ys
nipkow@13629
   485
      in ps :: unflat xss qs end
wenzelm@12136
   486
  | unflat [] [] = []
skalberg@15570
   487
  | unflat _ _ = raise UnequalLengths;
wenzelm@12136
   488
wenzelm@21479
   489
fun burrow f xss = unflat xss (f (flat xss));
haftmann@18359
   490
haftmann@18549
   491
fun fold_burrow f xss s =
haftmann@18549
   492
  apfst (unflat xss) (f (flat xss) s);
haftmann@18359
   493
wenzelm@233
   494
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   495
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   496
  | separate _ xs = xs;
wenzelm@233
   497
wenzelm@233
   498
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   499
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   500
  let fun rep (0, xs) = xs
wenzelm@233
   501
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   502
  in
skalberg@15570
   503
    if n < 0 then raise Subscript
wenzelm@233
   504
    else rep (n, [])
wenzelm@233
   505
  end;
wenzelm@233
   506
wenzelm@14926
   507
fun translate_string f = String.translate (f o String.str);
wenzelm@14926
   508
wenzelm@4248
   509
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@18148
   510
fun multiply [] _ = []
wenzelm@18148
   511
  | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss;
wenzelm@4248
   512
wenzelm@14792
   513
(*direct product*)
wenzelm@14792
   514
fun product _ [] = []
wenzelm@14792
   515
  | product [] _ = []
wenzelm@14792
   516
  | product (x :: xs) ys = map (pair x) ys @ product xs ys;
wenzelm@14792
   517
wenzelm@233
   518
wenzelm@233
   519
(* filter *)
wenzelm@233
   520
wenzelm@233
   521
(*copy the list preserving elements that satisfy the predicate*)
skalberg@15531
   522
val filter = List.filter;
clasohm@0
   523
fun filter_out f = filter (not o f);
wenzelm@19483
   524
val map_filter = List.mapPartial;
wenzelm@233
   525
wenzelm@233
   526
wenzelm@233
   527
(* lists of pairs *)
wenzelm@233
   528
skalberg@15570
   529
exception UnequalLengths;
skalberg@15570
   530
haftmann@18330
   531
fun map2 _ [] [] = []
haftmann@18330
   532
  | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys
haftmann@18330
   533
  | map2 _ _ _ = raise UnequalLengths;
wenzelm@380
   534
wenzelm@23220
   535
fun fold2 f [] [] z = z
wenzelm@23220
   536
  | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z)
wenzelm@23220
   537
  | fold2 f _ _ _ = raise UnequalLengths;
wenzelm@380
   538
wenzelm@19799
   539
fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys
wenzelm@19799
   540
  | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys
wenzelm@19799
   541
  | zip_options _ [] = []
wenzelm@19799
   542
  | zip_options [] _ = raise UnequalLengths;
wenzelm@4956
   543
wenzelm@233
   544
(*combine two lists forming a list of pairs:
wenzelm@233
   545
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   546
fun [] ~~ [] = []
wenzelm@233
   547
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
skalberg@15570
   548
  | _ ~~ _ = raise UnequalLengths;
wenzelm@233
   549
wenzelm@233
   550
(*inverse of ~~; the old 'split':
wenzelm@233
   551
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
skalberg@15570
   552
val split_list = ListPair.unzip;
wenzelm@233
   553
wenzelm@233
   554
wenzelm@233
   555
(* prefixes, suffixes *)
wenzelm@233
   556
haftmann@18441
   557
fun is_prefix _ [] _ = true
haftmann@18441
   558
  | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys
haftmann@18441
   559
  | is_prefix eq _ _ = false;
wenzelm@233
   560
wenzelm@233
   561
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   562
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   563
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   564
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   565
        | take (rxs, x :: xs) =
wenzelm@255
   566
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   567
  in  take([], xs)  end;
wenzelm@233
   568
haftmann@20108
   569
fun chop_prefix eq ([], ys) = ([], ([], ys))
haftmann@20108
   570
  | chop_prefix eq (xs, []) = ([], (xs, []))
wenzelm@23220
   571
  | chop_prefix eq (xs as x :: xs', ys as y :: ys') =
haftmann@20108
   572
      if eq (x, y) then
haftmann@20108
   573
        let val (ps', xys'') = chop_prefix eq (xs', ys')
wenzelm@23220
   574
        in (x :: ps', xys'') end
haftmann@20108
   575
      else ([], (xs, ys));
haftmann@20108
   576
wenzelm@233
   577
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   578
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   579
fun take_suffix _ [] = ([], [])
wenzelm@233
   580
  | take_suffix pred (x :: xs) =
wenzelm@233
   581
      (case take_suffix pred xs of
wenzelm@233
   582
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   583
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   584
wenzelm@12249
   585
fun prefixes1 [] = []
wenzelm@12249
   586
  | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs);
wenzelm@12249
   587
wenzelm@19011
   588
fun prefixes xs = [] :: prefixes1 xs;
wenzelm@19011
   589
wenzelm@12249
   590
fun suffixes1 xs = map rev (prefixes1 (rev xs));
wenzelm@19011
   591
fun suffixes xs = [] :: suffixes1 xs;
wenzelm@233
   592
wenzelm@23220
   593
wenzelm@23220
   594
wenzelm@233
   595
(** integers **)
wenzelm@233
   596
wenzelm@2958
   597
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   598
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   599
wenzelm@233
   600
wenzelm@233
   601
(* lists of integers *)
wenzelm@233
   602
wenzelm@233
   603
(*make the list [from, from + 1, ..., to]*)
wenzelm@21859
   604
fun (i upto j) =
wenzelm@21859
   605
  if i > j then [] else i :: (i + 1 upto j);
wenzelm@233
   606
wenzelm@233
   607
(*make the list [from, from - 1, ..., to]*)
wenzelm@21859
   608
fun (i downto j) =
wenzelm@21859
   609
  if i < j then [] else i :: (i - 1 downto j);
wenzelm@233
   610
wenzelm@233
   611
wenzelm@233
   612
(* convert integers to strings *)
wenzelm@233
   613
wenzelm@233
   614
(*expand the number in the given base;
wenzelm@233
   615
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   616
fun radixpand (base, num) : int list =
wenzelm@233
   617
  let
wenzelm@233
   618
    fun radix (n, tail) =
wenzelm@233
   619
      if n < base then n :: tail
wenzelm@233
   620
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   621
  in radix (num, []) end;
wenzelm@233
   622
wenzelm@233
   623
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   624
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   625
fun radixstring (base, zerochar, num) =
wenzelm@233
   626
  let val offset = ord zerochar;
wenzelm@233
   627
      fun chrof n = chr (offset + n)
wenzelm@233
   628
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   629
wenzelm@233
   630
paulson@3407
   631
val string_of_int = Int.toString;
wenzelm@233
   632
wenzelm@21942
   633
fun signed_string_of_int i =
wenzelm@21942
   634
  if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i;
wenzelm@21942
   635
wenzelm@23220
   636
fun string_of_indexname (a, 0) = a
wenzelm@23220
   637
  | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i;
wenzelm@233
   638
wenzelm@233
   639
wenzelm@14826
   640
(* read integers *)
wenzelm@14826
   641
wenzelm@20095
   642
fun read_intinf radix cs =
wenzelm@20095
   643
  let
wenzelm@20095
   644
    val zero = ord "0";
wenzelm@20095
   645
    val limit = zero + radix;
wenzelm@20095
   646
    fun scan (num, []) = (num, [])
wenzelm@20095
   647
      | scan (num, c :: cs) =
wenzelm@20095
   648
        if zero <= ord c andalso ord c < limit then
wenzelm@20095
   649
          scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs)
wenzelm@20095
   650
        else (num, c :: cs);
wenzelm@21859
   651
  in scan (IntInf.fromInt 0, cs) end;
wenzelm@14826
   652
wenzelm@20095
   653
fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs);
wenzelm@14826
   654
wenzelm@20095
   655
fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s))));
wenzelm@14826
   656
wenzelm@14826
   657
wenzelm@14826
   658
wenzelm@233
   659
(** strings **)
wenzelm@233
   660
wenzelm@16188
   661
(* functions tuned for strings, avoiding explode *)
wenzelm@6312
   662
haftmann@18011
   663
fun nth_string str i =
wenzelm@6959
   664
  (case try String.substring (str, i, 1) of
skalberg@15531
   665
    SOME s => s
skalberg@15570
   666
  | NONE => raise Subscript);
wenzelm@6312
   667
wenzelm@16188
   668
fun fold_string f str x0 =
wenzelm@6282
   669
  let
wenzelm@6282
   670
    val n = size str;
wenzelm@16188
   671
    fun iter (x, i) =
wenzelm@16188
   672
      if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x;
wenzelm@16188
   673
  in iter (x0, 0) end;
wenzelm@6282
   674
wenzelm@14968
   675
fun exists_string pred str =
wenzelm@14968
   676
  let
wenzelm@14968
   677
    val n = size str;
wenzelm@14968
   678
    fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1));
wenzelm@14968
   679
  in ex 0 end;
wenzelm@6312
   680
wenzelm@16188
   681
fun forall_string pred = not o exists_string (not o pred);
wenzelm@16188
   682
lcp@512
   683
(*enclose in brackets*)
lcp@512
   684
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   685
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   686
wenzelm@233
   687
(*simple quoting (does not escape special chars)*)
lcp@512
   688
val quote = enclose "\"" "\"";
wenzelm@233
   689
wenzelm@4212
   690
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   691
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   692
wenzelm@255
   693
val commas = space_implode ", ";
wenzelm@380
   694
val commas_quote = commas o map quote;
wenzelm@255
   695
wenzelm@233
   696
(*concatenate messages, one per line, into a string*)
wenzelm@255
   697
val cat_lines = space_implode "\n";
wenzelm@233
   698
wenzelm@4212
   699
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   700
fun space_explode _ "" = []
paulson@21899
   701
  | space_explode sep s = String.fields (fn c => str c = sep) s;
wenzelm@3832
   702
wenzelm@3832
   703
val split_lines = space_explode "\n";
wenzelm@3832
   704
wenzelm@14826
   705
fun prefix_lines "" txt = txt
wenzelm@14826
   706
  | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@14826
   707
wenzelm@7712
   708
fun untabify chs =
wenzelm@7712
   709
  let
wenzelm@7712
   710
    val tab_width = 8;
wenzelm@7712
   711
wenzelm@22582
   712
    fun untab pos [] ys = rev ys
berghofe@22256
   713
      | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys)
berghofe@22256
   714
      | untab pos ("\t" :: xs) ys =
wenzelm@22582
   715
          let val d = tab_width - (pos mod tab_width)
wenzelm@23718
   716
          in untab (pos + d) xs (funpow d (cons " ") ys) end
berghofe@22256
   717
      | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys);
wenzelm@7712
   718
  in
wenzelm@19301
   719
    if not (exists (fn c => c = "\t") chs) then chs
berghofe@22256
   720
    else untab 0 chs []
wenzelm@7712
   721
  end;
wenzelm@7712
   722
wenzelm@18681
   723
fun prefix prfx s = prfx ^ s;
wenzelm@16188
   724
fun suffix sffx s = s ^ sffx;
wenzelm@5285
   725
wenzelm@18681
   726
fun unprefix prfx s =
wenzelm@18681
   727
  if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx)
wenzelm@18681
   728
  else raise Fail "unprefix";
wenzelm@18681
   729
wenzelm@16188
   730
fun unsuffix sffx s =
wenzelm@17061
   731
  if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx)
wenzelm@17061
   732
  else raise Fail "unsuffix";
wenzelm@5285
   733
wenzelm@10951
   734
fun replicate_string 0 _ = ""
wenzelm@10951
   735
  | replicate_string 1 a = a
wenzelm@10951
   736
  | replicate_string k a =
wenzelm@10951
   737
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   738
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   739
wenzelm@233
   740
wenzelm@23220
   741
wenzelm@16492
   742
(** lists as sets -- see also Pure/General/ord_list.ML **)
wenzelm@233
   743
wenzelm@18923
   744
(*canonical member, insert, remove*)
wenzelm@18923
   745
fun member eq list x =
wenzelm@18923
   746
  let
wenzelm@18923
   747
    fun memb [] = false
wenzelm@18923
   748
      | memb (y :: ys) = eq (x, y) orelse memb ys;
wenzelm@18923
   749
  in memb list end;
berghofe@1576
   750
wenzelm@18923
   751
fun insert eq x xs = if member eq xs x then xs else x :: xs;
wenzelm@18923
   752
fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs;
wenzelm@233
   753
wenzelm@19301
   754
fun subtract eq = fold (remove eq);
wenzelm@19301
   755
wenzelm@18923
   756
fun merge _ ([], ys) = ys
wenzelm@18923
   757
  | merge eq (xs, ys) = fold_rev (insert eq) ys xs;
clasohm@0
   758
wenzelm@18923
   759
(*old-style infixes*)
wenzelm@18923
   760
fun x mem xs = member (op =) xs x;
wenzelm@18923
   761
fun (x: int) mem_int xs = member (op =) xs x;
wenzelm@18923
   762
fun (x: string) mem_string xs = member (op =) xs x;
berghofe@1576
   763
wenzelm@233
   764
wenzelm@233
   765
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   766
fun xs union [] = xs
wenzelm@233
   767
  | [] union ys = ys
haftmann@20854
   768
  | (x :: xs) union ys = xs union (insert (op =) x ys);
clasohm@0
   769
paulson@2175
   770
(*union of sets, optimized version for ints*)
berghofe@1576
   771
fun (xs:int list) union_int [] = xs
berghofe@1576
   772
  | [] union_int ys = ys
haftmann@20854
   773
  | (x :: xs) union_int ys = xs union_int (insert (op =) x ys);
berghofe@1576
   774
paulson@2175
   775
(*union of sets, optimized version for strings*)
berghofe@1576
   776
fun (xs:string list) union_string [] = xs
berghofe@1576
   777
  | [] union_string ys = ys
haftmann@20854
   778
  | (x :: xs) union_string ys = xs union_string (insert (op =) x ys);
berghofe@1576
   779
clasohm@0
   780
(*generalized union*)
wenzelm@233
   781
fun gen_union eq (xs, []) = xs
wenzelm@233
   782
  | gen_union eq ([], ys) = ys
wenzelm@18923
   783
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys);
wenzelm@233
   784
wenzelm@233
   785
wenzelm@233
   786
(*intersection*)
wenzelm@233
   787
fun [] inter ys = []
wenzelm@233
   788
  | (x :: xs) inter ys =
wenzelm@233
   789
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   790
paulson@2175
   791
(*intersection, optimized version for ints*)
berghofe@1576
   792
fun ([]:int list) inter_int ys = []
berghofe@1576
   793
  | (x :: xs) inter_int ys =
berghofe@1576
   794
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   795
paulson@2175
   796
(*intersection, optimized version for strings *)
berghofe@1576
   797
fun ([]:string list) inter_string ys = []
berghofe@1576
   798
  | (x :: xs) inter_string ys =
berghofe@1576
   799
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   800
paulson@7090
   801
(*generalized intersection*)
paulson@7090
   802
fun gen_inter eq ([], ys) = []
wenzelm@12284
   803
  | gen_inter eq (x::xs, ys) =
wenzelm@18923
   804
      if member eq ys x then x :: gen_inter eq (xs, ys)
wenzelm@18923
   805
      else gen_inter eq (xs, ys);
paulson@7090
   806
wenzelm@233
   807
wenzelm@233
   808
(*subset*)
wenzelm@233
   809
fun [] subset ys = true
wenzelm@233
   810
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   811
paulson@2175
   812
(*subset, optimized version for ints*)
wenzelm@16439
   813
fun ([]: int list) subset_int ys = true
berghofe@1576
   814
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   815
paulson@2175
   816
(*subset, optimized version for strings*)
wenzelm@16439
   817
fun ([]: string list) subset_string ys = true
berghofe@1576
   818
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   819
wenzelm@4363
   820
(*set equality*)
wenzelm@4363
   821
fun eq_set (xs, ys) =
wenzelm@4363
   822
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   823
paulson@2182
   824
(*set equality for strings*)
wenzelm@16439
   825
fun eq_set_string ((xs: string list), ys) =
berghofe@1576
   826
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   827
wenzelm@18923
   828
fun gen_subset eq (xs, ys) = forall (member eq ys) xs;
paulson@2182
   829
wenzelm@19301
   830
fun gen_eq_set eq (xs, ys) =
haftmann@20348
   831
  eq_list eq (xs, ys) orelse
wenzelm@19301
   832
    (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs));
wenzelm@19301
   833
wenzelm@265
   834
wenzelm@233
   835
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   836
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   837
  | [] \ x = [];
paulson@2243
   838
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   839
wenzelm@233
   840
wenzelm@233
   841
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   842
  first of equal elements*)
wenzelm@19046
   843
fun distinct eq lst =
wenzelm@233
   844
  let
wenzelm@233
   845
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   846
      | dist (rev_seen, x :: xs) =
wenzelm@18923
   847
          if member eq rev_seen x then dist (rev_seen, xs)
wenzelm@233
   848
          else dist (x :: rev_seen, xs);
wenzelm@19046
   849
  in dist ([], lst) end;
wenzelm@233
   850
wenzelm@255
   851
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   852
  order, takes first of equal elements*)
wenzelm@18966
   853
fun duplicates eq lst =
wenzelm@255
   854
  let
wenzelm@255
   855
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   856
      | dups (rev_dups, x :: xs) =
wenzelm@18923
   857
          if member eq rev_dups x orelse not (member eq xs x) then
wenzelm@255
   858
            dups (rev_dups, xs)
wenzelm@255
   859
          else dups (x :: rev_dups, xs);
wenzelm@18966
   860
  in dups ([], lst) end;
wenzelm@255
   861
wenzelm@16878
   862
fun has_duplicates eq =
wenzelm@16878
   863
  let
wenzelm@16878
   864
    fun dups [] = false
wenzelm@16878
   865
      | dups (x :: xs) = member eq xs x orelse dups xs;
wenzelm@16878
   866
  in dups end;
wenzelm@16878
   867
wenzelm@255
   868
wenzelm@23220
   869
nipkow@22142
   870
(** lists as multisets **)
nipkow@22142
   871
nipkow@22142
   872
fun remove1 _ _ [] = raise Empty
wenzelm@23220
   873
  | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs;
nipkow@22142
   874
wenzelm@23220
   875
fun submultiset _ ([], _)  = true
wenzelm@23220
   876
  | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys);
wenzelm@233
   877
clasohm@0
   878
clasohm@0
   879
wenzelm@2506
   880
(** orders **)
wenzelm@2506
   881
wenzelm@18966
   882
fun is_equal EQUAL = true
wenzelm@18966
   883
  | is_equal _ = false;
wenzelm@18966
   884
wenzelm@4445
   885
fun rev_order LESS = GREATER
wenzelm@4445
   886
  | rev_order EQUAL = EQUAL
wenzelm@4445
   887
  | rev_order GREATER = LESS;
wenzelm@4445
   888
wenzelm@4479
   889
(*assume rel is a linear strict order*)
wenzelm@4445
   890
fun make_ord rel (x, y) =
wenzelm@4445
   891
  if rel (x, y) then LESS
wenzelm@4445
   892
  else if rel (y, x) then GREATER
wenzelm@4445
   893
  else EQUAL;
wenzelm@4445
   894
wenzelm@15051
   895
val int_ord = Int.compare;
wenzelm@15051
   896
val string_ord = String.compare;
wenzelm@2506
   897
wenzelm@16676
   898
fun fast_string_ord (s1, s2) =
wenzelm@16676
   899
  (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord);
wenzelm@16676
   900
wenzelm@16492
   901
fun option_ord ord (SOME x, SOME y) = ord (x, y)
wenzelm@16492
   902
  | option_ord _ (NONE, NONE) = EQUAL
wenzelm@16492
   903
  | option_ord _ (NONE, SOME _) = LESS
wenzelm@16492
   904
  | option_ord _ (SOME _, NONE) = GREATER;
wenzelm@16492
   905
wenzelm@4343
   906
(*lexicographic product*)
wenzelm@4343
   907
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   908
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   909
wenzelm@4343
   910
(*dictionary order -- in general NOT well-founded!*)
wenzelm@16984
   911
fun dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@16984
   912
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord)
wenzelm@16984
   913
  | dict_ord _ ([], []) = EQUAL
wenzelm@4343
   914
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@16984
   915
  | dict_ord _ (_ :: _, []) = GREATER;
wenzelm@4343
   916
wenzelm@4343
   917
(*lexicographic product of lists*)
wenzelm@4343
   918
fun list_ord elem_ord (xs, ys) =
wenzelm@16676
   919
  (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   920
wenzelm@2506
   921
wenzelm@4621
   922
(* sorting *)
wenzelm@4621
   923
wenzelm@18427
   924
(*quicksort -- stable, i.e. does not reorder equal elements*)
wenzelm@18427
   925
fun quicksort unique ord =
wenzelm@4621
   926
  let
wenzelm@16878
   927
    fun qsort [] = []
wenzelm@16878
   928
      | qsort (xs as [_]) = xs
wenzelm@18427
   929
      | qsort (xs as [x, y]) =
wenzelm@18427
   930
          (case ord (x, y) of
wenzelm@18427
   931
            LESS => xs
wenzelm@18427
   932
          | EQUAL => if unique then [x] else xs
wenzelm@18427
   933
          | GREATER => [y, x])
wenzelm@16878
   934
      | qsort xs =
haftmann@18011
   935
          let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs
wenzelm@16878
   936
          in qsort lts @ eqs @ qsort gts end
wenzelm@4621
   937
    and part _ [] = ([], [], [])
wenzelm@4621
   938
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
   939
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@18427
   940
      | add EQUAL x (lts, [], gts) = (lts, [x], gts)
wenzelm@18427
   941
      | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts)
wenzelm@4621
   942
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
   943
  in qsort end;
wenzelm@4621
   944
wenzelm@18427
   945
fun sort ord = quicksort false ord;
wenzelm@18427
   946
fun sort_distinct ord = quicksort true ord;
wenzelm@18427
   947
wenzelm@4621
   948
val sort_strings = sort string_ord;
wenzelm@4621
   949
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
   950
wenzelm@4621
   951
wenzelm@2506
   952
berghofe@14106
   953
(** random numbers **)
berghofe@14106
   954
berghofe@14106
   955
exception RANDOM;
berghofe@14106
   956
berghofe@14618
   957
fun rmod x y = x - y * Real.realFloor (x / y);
berghofe@14106
   958
berghofe@14106
   959
local
berghofe@14106
   960
  val a = 16807.0;
berghofe@14106
   961
  val m = 2147483647.0;
berghofe@14106
   962
  val random_seed = ref 1.0;
berghofe@14106
   963
in
berghofe@14106
   964
wenzelm@23922
   965
fun random () = CRITICAL (fn () =>
wenzelm@23922
   966
  let val r = rmod (a * ! random_seed) m
wenzelm@23922
   967
  in (random_seed := r; r) end);
berghofe@14106
   968
berghofe@14106
   969
end;
berghofe@14106
   970
berghofe@14106
   971
fun random_range l h =
berghofe@14106
   972
  if h < l orelse l < 0 then raise RANDOM
berghofe@14106
   973
  else l + Real.floor (rmod (random ()) (real (h - l + 1)));
berghofe@14106
   974
haftmann@18011
   975
fun one_of xs = nth xs (random_range 0 (length xs - 1));
berghofe@14106
   976
berghofe@14106
   977
fun frequency xs =
berghofe@14106
   978
  let
berghofe@14106
   979
    val sum = foldl op + (0, map fst xs);
wenzelm@17756
   980
    fun pick n ((k: int, x) :: xs) =
berghofe@14106
   981
      if n <= k then x else pick (n - k) xs
berghofe@14106
   982
  in pick (random_range 1 sum) xs end;
berghofe@14106
   983
berghofe@14106
   984
wenzelm@23220
   985
wenzelm@4621
   986
(** misc **)
wenzelm@233
   987
wenzelm@19644
   988
fun divide_and_conquer decomp x =
wenzelm@19644
   989
  let val (ys, recomb) = decomp x
wenzelm@19644
   990
  in recomb (map (divide_and_conquer decomp) ys) end;
wenzelm@19644
   991
clasohm@0
   992
wenzelm@233
   993
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
   994
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
   995
fun partition_list p i j =
wenzelm@233
   996
  let fun part k xs =
wenzelm@233
   997
            if k>j then
clasohm@0
   998
              (case xs of [] => []
skalberg@15570
   999
                         | _ => raise Fail "partition_list")
clasohm@0
  1000
            else
wenzelm@19691
  1001
            let val (ns, rest) = List.partition (p k) xs;
wenzelm@233
  1002
            in  ns :: part(k+1)rest  end
clasohm@0
  1003
  in  part i end;
clasohm@0
  1004
wenzelm@19691
  1005
fun partition_eq (eq:'a * 'a -> bool) =
wenzelm@19691
  1006
  let
wenzelm@19691
  1007
    fun part [] = []
wenzelm@19691
  1008
      | part (x :: ys) =
wenzelm@19691
  1009
          let val (xs, xs') = List.partition (fn y => eq (x, y)) ys
wenzelm@19691
  1010
          in (x::xs)::(part xs') end
wenzelm@19691
  1011
  in part end;
wenzelm@19691
  1012
wenzelm@19691
  1013
clasohm@0
  1014
wenzelm@233
  1015
(* generating identifiers *)
clasohm@0
  1016
paulson@4063
  1017
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
wenzelm@22369
  1018
local
wenzelm@22369
  1019
(*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*)
wenzelm@22582
  1020
fun gensym_char i =
paulson@22368
  1021
  if i<26 then chr (ord "A" + i)
paulson@22368
  1022
  else if i<52 then chr (ord "a" + i - 26)
wenzelm@22369
  1023
  else chr (ord "0" + i - 52);
paulson@4063
  1024
wenzelm@22369
  1025
val char_vec = Vector.tabulate (62, gensym_char);
wenzelm@22369
  1026
fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n)));
wenzelm@4284
  1027
paulson@22368
  1028
val gensym_seed = ref 0;
paulson@2003
  1029
wenzelm@22369
  1030
in
wenzelm@23922
  1031
  fun gensym pre = pre ^ newid (CRITICAL (fn () => inc gensym_seed));
wenzelm@22369
  1032
end;
paulson@4063
  1033
paulson@4063
  1034
wenzelm@16439
  1035
(* stamps and serial numbers *)
wenzelm@16439
  1036
wenzelm@16439
  1037
type stamp = unit ref;
wenzelm@16439
  1038
val stamp: unit -> stamp = ref;
wenzelm@16439
  1039
wenzelm@16439
  1040
type serial = int;
wenzelm@16439
  1041
local val count = ref 0
wenzelm@23922
  1042
in fun serial () = CRITICAL (fn () => inc count) end;
wenzelm@16439
  1043
wenzelm@19512
  1044
val serial_string = string_of_int o serial;
wenzelm@19512
  1045
wenzelm@16535
  1046
wenzelm@16535
  1047
(* generic objects *)
wenzelm@16535
  1048
wenzelm@16535
  1049
(*note that the builtin exception datatype may be extended by new
wenzelm@16535
  1050
  constructors at any time*)
wenzelm@16535
  1051
structure Object = struct type T = exn end;
wenzelm@16535
  1052
clasohm@1364
  1053
end;
clasohm@1364
  1054
wenzelm@15745
  1055
structure BasicLibrary: BASIC_LIBRARY = Library;
wenzelm@15745
  1056
open BasicLibrary;