wenzelm@41: (* Title: Pure/library.ML wenzelm@233: Author: Lawrence C Paulson, Cambridge University Computer Laboratory wenzelm@16188: Author: Markus Wenzel, TU Muenchen clasohm@0: haftmann@28732: Basic library: functions, pairs, booleans, lists, integers, wenzelm@23424: strings, lists as sets, orders, current directory, misc. wenzelm@21395: wenzelm@21395: See also General/basics.ML for the most fundamental concepts. clasohm@0: *) clasohm@0: wenzelm@21395: infix 2 ? wenzelm@21395: infix 3 o oo ooo oooo wenzelm@21395: infix 4 ~~ upto downto haftmann@36692: infix orf andf wenzelm@5893: wenzelm@15745: signature BASIC_LIBRARY = wenzelm@4621: sig wenzelm@4621: (*functions*) wenzelm@23860: val undefined: 'a -> 'b wenzelm@16842: val I: 'a -> 'a wenzelm@16842: val K: 'a -> 'b -> 'a wenzelm@4621: val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c wenzelm@4621: val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c wenzelm@21565: val ? : bool * ('a -> 'a) -> 'a -> 'a wenzelm@16721: val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b wenzelm@16721: val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b wenzelm@16721: val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b wenzelm@16842: val funpow: int -> ('a -> 'a) -> 'a -> 'a haftmann@31250: val funpow_yield: int -> ('a -> 'b * 'a) -> 'a -> 'b list * 'a clasohm@1364: wenzelm@4621: (*pairs*) wenzelm@4621: val pair: 'a -> 'b -> 'a * 'b wenzelm@4621: val rpair: 'a -> 'b -> 'b * 'a wenzelm@4621: val fst: 'a * 'b -> 'a wenzelm@4621: val snd: 'a * 'b -> 'b haftmann@17498: val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool haftmann@17498: val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool haftmann@19454: val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool wenzelm@4621: val swap: 'a * 'b -> 'b * 'a wenzelm@4621: val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c wenzelm@4621: val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b wenzelm@59058: val apply2: ('a -> 'b) -> 'a * 'a -> 'b * 'b wenzelm@4621: wenzelm@4621: (*booleans*) wenzelm@4621: val equal: ''a -> ''a -> bool wenzelm@4621: val not_equal: ''a -> ''a -> bool wenzelm@4621: val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool wenzelm@4621: val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool wenzelm@4621: val exists: ('a -> bool) -> 'a list -> bool wenzelm@4621: val forall: ('a -> bool) -> 'a list -> bool wenzelm@4621: wenzelm@4621: (*lists*) wenzelm@5285: val single: 'a -> 'a list wenzelm@20882: val the_single: 'a list -> 'a wenzelm@19273: val singleton: ('a list -> 'b list) -> 'a -> 'b haftmann@25061: val yield_singleton: ('a list -> 'c -> 'b list * 'c) -> 'a -> 'c -> 'b * 'c wenzelm@25058: val perhaps_apply: ('a -> 'a option) list -> 'a -> 'a option wenzelm@25058: val perhaps_loop: ('a -> 'a option) -> 'a -> 'a option berghofe@25681: val foldl1: ('a * 'a -> 'a) -> 'a list -> 'a wenzelm@15760: val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a wenzelm@46891: val eq_list: ('a * 'a -> bool) -> 'a list * 'a list -> bool wenzelm@21395: val maps: ('a -> 'b list) -> 'a list -> 'b list wenzelm@25549: val filter: ('a -> bool) -> 'a list -> 'a list wenzelm@25549: val filter_out: ('a -> bool) -> 'a list -> 'a list wenzelm@25549: val map_filter: ('a -> 'b option) -> 'a list -> 'b list haftmann@33955: val take: int -> 'a list -> 'a list haftmann@33955: val drop: int -> 'a list -> 'a list wenzelm@19011: val chop: int -> 'a list -> 'a list * 'a list wenzelm@46891: val chop_groups: int -> 'a list -> 'a list list haftmann@18278: val nth: 'a list -> int -> 'a wenzelm@46891: val nth_list: 'a list list -> int -> 'a list haftmann@18011: val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list haftmann@24846: val nth_drop: int -> 'a list -> 'a list haftmann@18514: val map_index: (int * 'a -> 'b) -> 'a list -> 'b list haftmann@18514: val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b haftmann@33063: val map_range: (int -> 'a) -> int -> 'a list haftmann@52271: val fold_range: (int -> 'a -> 'a) -> int -> 'a -> 'a wenzelm@4621: val split_last: 'a list -> 'a list * 'a wenzelm@46891: val find_first: ('a -> bool) -> 'a list -> 'a option wenzelm@4621: val find_index: ('a -> bool) -> 'a list -> int wenzelm@46891: val get_first: ('a -> 'b option) -> 'a list -> 'b option haftmann@19233: val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option wenzelm@46891: val flat: 'a list list -> 'a list wenzelm@46891: val unflat: 'a list list -> 'b list -> 'b list list wenzelm@46891: val grouped: int -> (('a list -> 'b list) -> 'c list list -> 'd list list) -> wenzelm@46891: ('a -> 'b) -> 'c list -> 'd list wenzelm@46891: val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list wenzelm@46891: val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list wenzelm@46891: val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd wenzelm@46891: val separate: 'a -> 'a list -> 'a list wenzelm@46891: val surround: 'a -> 'a list -> 'a list wenzelm@46891: val replicate: int -> 'a -> 'a list wenzelm@46891: val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list wenzelm@46891: val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c haftmann@18330: val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list haftmann@18330: val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c wenzelm@46891: val map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list wenzelm@19799: val zip_options: 'a list -> 'b option list -> ('a * 'b) list haftmann@18330: val ~~ : 'a list * 'b list -> ('a * 'b) list haftmann@18330: val split_list: ('a * 'b) list -> 'a list * 'b list wenzelm@46891: val burrow_fst: ('a list -> 'b list) -> ('a * 'c) list -> ('b * 'c) list wenzelm@67522: val take_prefix: ('a -> bool) -> 'a list -> 'a list wenzelm@67522: val drop_prefix: ('a -> bool) -> 'a list -> 'a list wenzelm@67522: val chop_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list wenzelm@67522: val take_suffix: ('a -> bool) -> 'a list -> 'a list wenzelm@67522: val drop_suffix: ('a -> bool) -> 'a list -> 'a list wenzelm@67522: val chop_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list haftmann@18441: val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool wenzelm@67521: val chop_common_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list) wenzelm@12249: val prefixes1: 'a list -> 'a list list wenzelm@19011: val prefixes: 'a list -> 'a list list wenzelm@12249: val suffixes1: 'a list -> 'a list list wenzelm@19011: val suffixes: 'a list -> 'a list list wenzelm@61707: val trim: ('a -> bool) -> 'a list -> 'a list wenzelm@4621: wenzelm@4621: (*integers*) wenzelm@4621: val upto: int * int -> int list wenzelm@4621: val downto: int * int -> int list wenzelm@68087: val hex_digit: int -> string wenzelm@4621: val radixpand: int * int -> int list wenzelm@4621: val radixstring: int * string * int -> string wenzelm@4621: val string_of_int: int -> string wenzelm@21942: val signed_string_of_int: int -> string wenzelm@4621: val string_of_indexname: string * int -> string wenzelm@24630: val read_radix_int: int -> string list -> int * string list wenzelm@14826: val read_int: string list -> int * string list wenzelm@14826: val oct_char: string -> string wenzelm@4621: wenzelm@4621: (*strings*) haftmann@18011: val nth_string: string -> int -> string wenzelm@16188: val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a wenzelm@6312: val exists_string: (string -> bool) -> string -> bool wenzelm@16188: val forall_string: (string -> bool) -> string -> bool wenzelm@28025: val first_field: string -> string -> (string * string) option wenzelm@4621: val enclose: string -> string -> string -> string wenzelm@6642: val unenclose: string -> string wenzelm@4621: val quote: string -> string wenzelm@55033: val cartouche: string -> string wenzelm@4621: val space_implode: string -> string list -> string wenzelm@4621: val commas: string list -> string wenzelm@4621: val commas_quote: string list -> string wenzelm@4621: val cat_lines: string list -> string wenzelm@4621: val space_explode: string -> string -> string list wenzelm@14826: val split_lines: string -> string list wenzelm@56038: val plain_words: string -> string wenzelm@5942: val prefix_lines: string -> string -> string wenzelm@18681: val prefix: string -> string -> string wenzelm@5285: val suffix: string -> string -> string wenzelm@18681: val unprefix: string -> string -> string wenzelm@5285: val unsuffix: string -> string -> string wenzelm@47499: val trim_line: string -> string wenzelm@65904: val trim_split_lines: string -> string list wenzelm@67179: val normalize_lines: string -> string wenzelm@10951: val replicate_string: int -> string -> string wenzelm@14926: val translate_string: (string -> string) -> string -> string wenzelm@65934: val encode_lines: string -> string wenzelm@65934: val decode_lines: string -> string haftmann@63304: val align_right: string -> int -> string -> string kleing@29882: val match_string: string -> string -> bool wenzelm@4621: wenzelm@41516: (*reals*) wenzelm@41516: val string_of_real: real -> string wenzelm@41516: val signed_string_of_real: real -> string wenzelm@41516: wenzelm@16492: (*lists as sets -- see also Pure/General/ord_list.ML*) wenzelm@18923: val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool wenzelm@18923: val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list wenzelm@18923: val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list wenzelm@24049: val update: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list haftmann@33042: val union: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list wenzelm@19301: val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list haftmann@33049: val inter: ('a * 'b -> bool) -> 'b list -> 'a list -> 'a list wenzelm@18923: val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list haftmann@33038: val subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool wenzelm@42403: val eq_set: ('a * 'a -> bool) -> 'a list * 'a list -> bool wenzelm@19046: val distinct: ('a * 'a -> bool) -> 'a list -> 'a list wenzelm@18966: val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list wenzelm@16878: val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool wenzelm@46891: val map_transpose: ('a list -> 'b) -> 'a list list -> 'b list wenzelm@4621: wenzelm@23220: (*lists as multisets*) nipkow@22142: val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list haftmann@33078: val combine: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list haftmann@33079: val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool wenzelm@4621: wenzelm@4621: (*orders*) wenzelm@18966: val is_equal: order -> bool wenzelm@67560: val is_less: order -> bool wenzelm@67560: val is_less_equal: order -> bool wenzelm@67560: val is_greater: order -> bool wenzelm@67560: val is_greater_equal: order -> bool wenzelm@4621: val rev_order: order -> order wenzelm@4621: val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order wenzelm@25224: val bool_ord: bool * bool -> order wenzelm@4621: val int_ord: int * int -> order wenzelm@4621: val string_ord: string * string -> order wenzelm@16676: val fast_string_ord: string * string -> order wenzelm@16492: val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order wenzelm@4621: val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order wenzelm@4621: val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order wenzelm@4621: val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order wenzelm@4621: val sort: ('a * 'a -> order) -> 'a list -> 'a list wenzelm@18427: val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list wenzelm@4621: val sort_strings: string list -> string list wenzelm@60924: val sort_by: ('a -> string) -> 'a list -> 'a list wenzelm@30558: val tag_list: int -> 'a list -> (int * 'a) list wenzelm@30558: val untag_list: (int * 'a) list -> 'a list wenzelm@30558: val order_list: (int * 'a) list -> 'a list wenzelm@4621: wenzelm@4621: (*misc*) wenzelm@19644: val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b wenzelm@32978: val divide_and_conquer': ('a -> 'b -> ('a list * ('c list * 'b -> 'c * 'b)) * 'b) -> wenzelm@32978: 'a -> 'b -> 'c * 'b wenzelm@4621: val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list wenzelm@4621: val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list wenzelm@40509: type serial = int wenzelm@16439: val serial: unit -> serial wenzelm@19512: val serial_string: unit -> string wenzelm@45626: eqtype stamp wenzelm@45626: val stamp: unit -> stamp wenzelm@51368: structure Any: sig type T = exn end wenzelm@43603: val getenv: string -> string wenzelm@43603: val getenv_strict: string -> string wenzelm@4621: end; wenzelm@4621: wenzelm@15745: signature LIBRARY = skalberg@15570: sig wenzelm@15745: include BASIC_LIBRARY skalberg@15570: val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a skalberg@15570: val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b skalberg@15570: end; skalberg@15570: wenzelm@15745: structure Library: LIBRARY = clasohm@1364: struct clasohm@0: wenzelm@21395: (* functions *) clasohm@0: wenzelm@23860: fun undefined _ = raise Match; wenzelm@23860: wenzelm@16842: fun I x = x; wenzelm@16842: fun K x = fn _ => x; wenzelm@233: fun curry f x y = f (x, y); wenzelm@233: fun uncurry f (x, y) = f x y; clasohm@0: haftmann@17141: (*conditional application*) wenzelm@21565: fun b ? f = fn x => if b then f x else x; haftmann@17141: wenzelm@16721: (*composition with multiple args*) wenzelm@16721: fun (f oo g) x y = f (g x y); wenzelm@16721: fun (f ooo g) x y z = f (g x y z); wenzelm@16721: fun (f oooo g) x y z w = f (g x y z w); wenzelm@16721: haftmann@31250: (*function exponentiation: f (... (f x) ...) with n applications of f*) haftmann@31250: fun funpow (0 : int) _ = I haftmann@31250: | funpow n f = f #> funpow (n - 1) f; wenzelm@160: haftmann@31250: fun funpow_yield (0 : int) _ x = ([], x) haftmann@31250: | funpow_yield n f x = x |> f ||>> funpow_yield (n - 1) f |>> op ::; wenzelm@160: wenzelm@40318: wenzelm@21395: (* pairs *) wenzelm@233: wenzelm@233: fun pair x y = (x, y); wenzelm@233: fun rpair x y = (y, x); wenzelm@233: wenzelm@233: fun fst (x, y) = x; wenzelm@233: fun snd (x, y) = y; wenzelm@233: haftmann@17498: fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2); haftmann@17498: fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2); haftmann@19454: fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2); wenzelm@233: wenzelm@233: fun swap (x, y) = (y, x); wenzelm@233: wenzelm@233: fun apfst f (x, y) = (f x, y); wenzelm@233: fun apsnd f (x, y) = (x, f y); wenzelm@59058: fun apply2 f (x, y) = (f x, f y); wenzelm@233: wenzelm@233: wenzelm@21395: (* booleans *) wenzelm@233: wenzelm@21395: (*polymorphic equality*) wenzelm@233: fun equal x y = x = y; wenzelm@233: fun not_equal x y = x <> y; wenzelm@233: wenzelm@21395: (*combining predicates*) wenzelm@16721: fun p orf q = fn x => p x orelse q x; wenzelm@16721: fun p andf q = fn x => p x andalso q x; wenzelm@233: wenzelm@25752: val exists = List.exists; wenzelm@25752: val forall = List.all; clasohm@0: wenzelm@19644: wenzelm@21395: wenzelm@233: (** lists **) wenzelm@233: wenzelm@5285: fun single x = [x]; wenzelm@233: wenzelm@20882: fun the_single [x] = x wenzelm@47060: | the_single _ = raise List.Empty; wenzelm@20882: wenzelm@20882: fun singleton f x = the_single (f [x]); wenzelm@19273: haftmann@25061: fun yield_singleton f x = f [x] #>> the_single; haftmann@25061: wenzelm@25058: fun perhaps_apply funs arg = wenzelm@25058: let wenzelm@25058: fun app [] res = res wenzelm@25058: | app (f :: fs) (changed, x) = wenzelm@25058: (case f x of wenzelm@25058: NONE => app fs (changed, x) wenzelm@25058: | SOME x' => app fs (true, x')); wenzelm@25058: in (case app funs (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end; wenzelm@25058: wenzelm@25058: fun perhaps_loop f arg = wenzelm@25058: let wenzelm@25058: fun loop (changed, x) = wenzelm@25058: (case f x of wenzelm@25058: NONE => (changed, x) wenzelm@25058: | SOME x' => loop (true, x')); wenzelm@25058: in (case loop (false, arg) of (false, _) => NONE | (true, arg') => SOME arg') end; wenzelm@25058: wenzelm@233: wenzelm@21395: (* fold -- old versions *) haftmann@16691: wenzelm@233: (*the following versions of fold are designed to fit nicely with infixes*) clasohm@0: wenzelm@233: (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn wenzelm@233: for operators that associate to the left (TAIL RECURSIVE)*) wenzelm@233: fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a = wenzelm@233: let fun itl (e, []) = e wenzelm@233: | itl (e, a::l) = itl (f(e, a), l) wenzelm@233: in itl end; wenzelm@233: wenzelm@233: (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) wenzelm@233: for operators that associate to the right (not tail recursive)*) wenzelm@233: fun foldr f (l, e) = wenzelm@233: let fun itr [] = e wenzelm@233: | itr (a::l) = f(a, itr l) wenzelm@233: in itr l end; wenzelm@233: berghofe@25681: (* (op @) [x1, ..., xn] ===> ((x1 @ x2) @ x3) ... @ xn berghofe@25681: for operators that associate to the left (TAIL RECURSIVE)*) wenzelm@47060: fun foldl1 f [] = raise List.Empty berghofe@25681: | foldl1 f (x :: xs) = foldl f (x, xs); berghofe@25681: wenzelm@233: (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn)) wenzelm@233: for n > 0, operators that associate to the right (not tail recursive)*) wenzelm@47060: fun foldr1 f [] = raise List.Empty wenzelm@20510: | foldr1 f l = paulson@20443: let fun itr [x] = x wenzelm@20510: | itr (x::l) = f(x, itr l) paulson@20443: in itr l end; wenzelm@233: wenzelm@233: wenzelm@233: (* basic list functions *) wenzelm@233: wenzelm@20510: fun eq_list eq (list1, list2) = wenzelm@42403: pointer_eq (list1, list2) orelse wenzelm@42403: let wenzelm@42403: fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys) wenzelm@42403: | eq_lst _ = true; wenzelm@42403: in length list1 = length list2 andalso eq_lst (list1, list2) end; haftmann@20348: wenzelm@19483: fun maps f [] = [] wenzelm@19483: | maps f (x :: xs) = f x @ maps f xs; wenzelm@19483: haftmann@25538: val filter = List.filter; haftmann@25538: fun filter_out f = filter (not o f); haftmann@25538: val map_filter = List.mapPartial; haftmann@25538: haftmann@33955: fun take (0: int) xs = [] haftmann@33955: | take _ [] = [] haftmann@34059: | take n (x :: xs) = x :: take (n - 1) xs; haftmann@33955: haftmann@33955: fun drop (0: int) xs = xs haftmann@33955: | drop _ [] = [] haftmann@34059: | drop n (x :: xs) = drop (n - 1) xs; haftmann@33955: wenzelm@24593: fun chop (0: int) xs = ([], xs) wenzelm@23220: | chop _ [] = ([], []) wenzelm@23220: | chop n (x :: xs) = chop (n - 1) xs |>> cons x; wenzelm@19011: wenzelm@46891: fun chop_groups n list = wenzelm@46891: (case chop (Int.max (n, 1)) list of wenzelm@46891: ([], _) => [] wenzelm@46891: | (g, rest) => g :: chop_groups n rest); wenzelm@46891: wenzelm@46891: wenzelm@233: (*return nth element of a list, where 0 designates the first element; wenzelm@18461: raise Subscript if list too short*) haftmann@18011: fun nth xs i = List.nth (xs, i); wenzelm@233: wenzelm@43278: fun nth_list xss i = nth xss i handle General.Subscript => []; wenzelm@18461: haftmann@18011: fun nth_map 0 f (x :: xs) = f x :: xs haftmann@18011: | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs wenzelm@24593: | nth_map (_: int) _ [] = raise Subscript; wenzelm@11773: haftmann@24846: fun nth_drop n xs = haftmann@24846: List.take (xs, n) @ List.drop (xs, n + 1); haftmann@24846: haftmann@18514: fun map_index f = haftmann@18514: let haftmann@52271: fun map_aux (_: int) [] = [] haftmann@52271: | map_aux i (x :: xs) = f (i, x) :: map_aux (i + 1) xs haftmann@52271: in map_aux 0 end; haftmann@18514: haftmann@21118: fun fold_index f = haftmann@21118: let wenzelm@24593: fun fold_aux (_: int) [] y = y haftmann@52271: | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y) haftmann@21118: in fold_aux 0 end; haftmann@21118: haftmann@33063: fun map_range f i = haftmann@33063: let haftmann@52271: fun map_aux (k: int) = haftmann@52271: if k < i then f k :: map_aux (k + 1) else [] haftmann@52271: in map_aux 0 end; haftmann@52271: haftmann@52271: fun fold_range f i = haftmann@52271: let haftmann@52271: fun fold_aux (k: int) y = haftmann@52271: if k < i then fold_aux (k + 1) (f k y) else y haftmann@52271: in fold_aux 0 end; haftmann@52271: haftmann@33063: wenzelm@3762: (*rear decomposition*) wenzelm@47060: fun split_last [] = raise List.Empty wenzelm@3762: | split_last [x] = ([], x) wenzelm@3762: | split_last (x :: xs) = apfst (cons x) (split_last xs); wenzelm@3762: wenzelm@46891: (*find first element satisfying predicate*) wenzelm@46891: val find_first = List.find; wenzelm@46891: ballarin@29209: (*find position of first element satisfying a predicate*) wenzelm@4212: fun find_index pred = wenzelm@24593: let fun find (_: int) [] = ~1 wenzelm@4212: | find n (x :: xs) = if pred x then n else find (n + 1) xs; wenzelm@4212: in find 0 end; wenzelm@3762: wenzelm@4916: (*get first element by lookup function*) skalberg@15531: fun get_first _ [] = NONE wenzelm@4916: | get_first f (x :: xs) = wenzelm@4916: (case f x of skalberg@15531: NONE => get_first f xs wenzelm@4916: | some => some); wenzelm@4916: haftmann@19233: fun get_index f = haftmann@19233: let wenzelm@69237: fun get_aux (_: int) [] = NONE wenzelm@69237: | get_aux i (x :: xs) = wenzelm@46838: (case f x of wenzelm@69237: NONE => get_aux (i + 1) xs wenzelm@46838: | SOME y => SOME (i, y)) wenzelm@69237: in get_aux 0 end; haftmann@19233: skalberg@15531: val flat = List.concat; wenzelm@233: wenzelm@12136: fun unflat (xs :: xss) ys = wenzelm@19424: let val (ps, qs) = chop (length xs) ys nipkow@13629: in ps :: unflat xss qs end wenzelm@12136: | unflat [] [] = [] wenzelm@40722: | unflat _ _ = raise ListPair.UnequalLengths; wenzelm@12136: wenzelm@46891: fun grouped n comb f = chop_groups n #> comb (map f) #> flat; wenzelm@46891: wenzelm@21479: fun burrow f xss = unflat xss (f (flat xss)); haftmann@18359: wenzelm@24864: fun burrow_options f os = map (try hd) (burrow f (map the_list os)); wenzelm@24864: haftmann@18549: fun fold_burrow f xss s = haftmann@18549: apfst (unflat xss) (f (flat xss) s); haftmann@18359: wenzelm@233: (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) wenzelm@233: fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs wenzelm@233: | separate _ xs = xs; wenzelm@233: wenzelm@25980: fun surround s (x :: xs) = s :: x :: surround s xs wenzelm@25980: | surround s [] = [s]; wenzelm@25980: wenzelm@233: (*make the list [x, x, ..., x] of length n*) wenzelm@24593: fun replicate (n: int) x = wenzelm@233: let fun rep (0, xs) = xs wenzelm@233: | rep (n, xs) = rep (n - 1, x :: xs) wenzelm@233: in skalberg@15570: if n < 0 then raise Subscript wenzelm@233: else rep (n, []) wenzelm@233: end; wenzelm@233: wenzelm@4248: wenzelm@25549: (* direct product *) wenzelm@25549: haftmann@25538: fun map_product f _ [] = [] haftmann@25538: | map_product f [] _ = [] haftmann@25538: | map_product f (x :: xs) ys = map (f x) ys @ map_product f xs ys; wenzelm@233: haftmann@25538: fun fold_product f _ [] z = z haftmann@25538: | fold_product f [] _ z = z haftmann@25538: | fold_product f (x :: xs) ys z = z |> fold (f x) ys |> fold_product f xs ys; wenzelm@233: wenzelm@25549: wenzelm@25549: (* lists of pairs *) wenzelm@233: haftmann@18330: fun map2 _ [] [] = [] haftmann@18330: | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys wenzelm@40722: | map2 _ _ _ = raise ListPair.UnequalLengths; wenzelm@380: wenzelm@58633: fun fold2 _ [] [] z = z wenzelm@23220: | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z) wenzelm@58633: | fold2 _ _ _ _ = raise ListPair.UnequalLengths; wenzelm@380: wenzelm@58633: fun map_split _ [] = ([], []) haftmann@25943: | map_split f (x :: xs) = haftmann@25943: let haftmann@25943: val (y, w) = f x; haftmann@25943: val (ys, ws) = map_split f xs; haftmann@25943: in (y :: ys, w :: ws) end; haftmann@25943: wenzelm@19799: fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys wenzelm@19799: | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys wenzelm@19799: | zip_options _ [] = [] wenzelm@40722: | zip_options [] _ = raise ListPair.UnequalLengths; wenzelm@4956: wenzelm@233: (*combine two lists forming a list of pairs: wenzelm@233: [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) wenzelm@233: fun [] ~~ [] = [] wenzelm@233: | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) wenzelm@40722: | _ ~~ _ = raise ListPair.UnequalLengths; wenzelm@233: wenzelm@233: (*inverse of ~~; the old 'split': wenzelm@233: [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) skalberg@15570: val split_list = ListPair.unzip; wenzelm@233: haftmann@28347: fun burrow_fst f xs = split_list xs |>> f |> op ~~; haftmann@28347: wenzelm@233: wenzelm@67522: (* take, drop, chop, trim according to predicate *) wenzelm@67522: wenzelm@67522: fun take_prefix pred list = wenzelm@67522: let wenzelm@67522: fun take res (x :: xs) = if pred x then take (x :: res) xs else rev res wenzelm@67522: | take res [] = rev res; wenzelm@67522: in take [] list end; wenzelm@67522: wenzelm@67522: fun drop_prefix pred list = wenzelm@67522: let wenzelm@67522: fun drop (x :: xs) = if pred x then drop xs else x :: xs wenzelm@67522: | drop [] = []; wenzelm@67522: in drop list end; wenzelm@67522: wenzelm@67522: fun chop_prefix pred list = wenzelm@67522: let wenzelm@67522: val prfx = take_prefix pred list; wenzelm@67522: val sffx = drop (length prfx) list; wenzelm@67522: in (prfx, sffx) end; wenzelm@67522: wenzelm@67522: fun take_suffix pred list = wenzelm@67522: let wenzelm@67522: fun take res (x :: xs) = if pred x then take (x :: res) xs else res wenzelm@67522: | take res [] = res; wenzelm@67522: in take [] (rev list) end; wenzelm@67522: wenzelm@67522: fun drop_suffix pred list = wenzelm@67522: let wenzelm@67522: fun drop (x :: xs) = if pred x then drop xs else rev (x :: xs) wenzelm@67522: | drop [] = []; wenzelm@67522: in drop (rev list) end; wenzelm@67522: wenzelm@67522: fun chop_suffix pred list = wenzelm@67522: let wenzelm@67522: val prfx = drop_suffix pred list; wenzelm@67522: val sffx = drop (length prfx) list; wenzelm@67522: in (prfx, sffx) end; wenzelm@67522: wenzelm@67522: fun trim pred = drop_prefix pred #> drop_suffix pred; wenzelm@67522: wenzelm@67522: wenzelm@233: (* prefixes, suffixes *) wenzelm@233: haftmann@18441: fun is_prefix _ [] _ = true haftmann@18441: | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys haftmann@18441: | is_prefix eq _ _ = false; wenzelm@233: wenzelm@67521: fun chop_common_prefix eq ([], ys) = ([], ([], ys)) wenzelm@67521: | chop_common_prefix eq (xs, []) = ([], (xs, [])) wenzelm@67521: | chop_common_prefix eq (xs as x :: xs', ys as y :: ys') = wenzelm@67521: if eq (x, y) then wenzelm@67521: let val (ps', xys'') = chop_common_prefix eq (xs', ys') wenzelm@67521: in (x :: ps', xys'') end wenzelm@67521: else ([], (xs, ys)); wenzelm@67521: wenzelm@12249: fun prefixes1 [] = [] wenzelm@12249: | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); wenzelm@12249: wenzelm@19011: fun prefixes xs = [] :: prefixes1 xs; wenzelm@19011: wenzelm@12249: fun suffixes1 xs = map rev (prefixes1 (rev xs)); wenzelm@19011: fun suffixes xs = [] :: suffixes1 xs; wenzelm@233: wenzelm@23220: wenzelm@233: (** integers **) wenzelm@233: wenzelm@233: (* lists of integers *) wenzelm@233: wenzelm@233: (*make the list [from, from + 1, ..., to]*) wenzelm@24593: fun ((i: int) upto j) = wenzelm@21859: if i > j then [] else i :: (i + 1 upto j); wenzelm@233: wenzelm@233: (*make the list [from, from - 1, ..., to]*) wenzelm@24593: fun ((i: int) downto j) = wenzelm@21859: if i < j then [] else i :: (i - 1 downto j); wenzelm@233: wenzelm@233: wenzelm@233: (* convert integers to strings *) wenzelm@233: wenzelm@68087: (*hexadecimal*) wenzelm@68087: fun hex_digit i = wenzelm@68087: if i < 10 then chr (Char.ord #"0" + i) else chr (Char.ord #"a" + i - 10); wenzelm@68087: wenzelm@233: (*expand the number in the given base; wenzelm@233: example: radixpand (2, 8) gives [1, 0, 0, 0]*) wenzelm@233: fun radixpand (base, num) : int list = wenzelm@233: let wenzelm@233: fun radix (n, tail) = wenzelm@233: if n < base then n :: tail wenzelm@233: else radix (n div base, (n mod base) :: tail) wenzelm@233: in radix (num, []) end; wenzelm@233: wenzelm@233: (*expands a number into a string of characters starting from "zerochar"; wenzelm@233: example: radixstring (2, "0", 8) gives "1000"*) wenzelm@233: fun radixstring (base, zerochar, num) = wenzelm@233: let val offset = ord zerochar; wenzelm@233: fun chrof n = chr (offset + n) wenzelm@233: in implode (map chrof (radixpand (base, num))) end; wenzelm@233: wenzelm@233: wenzelm@41492: local wenzelm@64275: val zero = Char.ord #"0"; wenzelm@57909: val small_int = 10000: int; wenzelm@57909: val small_int_table = Vector.tabulate (small_int, Int.toString); wenzelm@41492: in wenzelm@41492: wenzelm@41492: fun string_of_int i = wenzelm@41492: if i < 0 then Int.toString i wenzelm@41492: else if i < 10 then chr (zero + i) wenzelm@57909: else if i < small_int then Vector.sub (small_int_table, i) wenzelm@41492: else Int.toString i; wenzelm@41492: wenzelm@41492: end; wenzelm@233: wenzelm@21942: fun signed_string_of_int i = wenzelm@21942: if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i; wenzelm@21942: wenzelm@23220: fun string_of_indexname (a, 0) = a wenzelm@23220: | string_of_indexname (a, i) = a ^ "_" ^ string_of_int i; wenzelm@233: wenzelm@233: wenzelm@14826: (* read integers *) wenzelm@14826: wenzelm@24630: fun read_radix_int radix cs = wenzelm@20095: let wenzelm@64275: val zero = Char.ord #"0"; wenzelm@20095: val limit = zero + radix; wenzelm@20095: fun scan (num, []) = (num, []) wenzelm@20095: | scan (num, c :: cs) = wenzelm@50637: if zero <= ord c andalso ord c < limit then wenzelm@50637: scan (radix * num + (ord c - zero), cs) wenzelm@50637: else (num, c :: cs); wenzelm@24630: in scan (0, cs) end; wenzelm@14826: wenzelm@24630: val read_int = read_radix_int 10; wenzelm@14826: wenzelm@40627: fun oct_char s = chr (#1 (read_radix_int 8 (raw_explode s))); wenzelm@14826: wenzelm@14826: wenzelm@14826: wenzelm@233: (** strings **) wenzelm@233: wenzelm@16188: (* functions tuned for strings, avoiding explode *) wenzelm@6312: haftmann@18011: fun nth_string str i = wenzelm@6959: (case try String.substring (str, i, 1) of skalberg@15531: SOME s => s skalberg@15570: | NONE => raise Subscript); wenzelm@6312: wenzelm@16188: fun fold_string f str x0 = wenzelm@6282: let wenzelm@6282: val n = size str; wenzelm@16188: fun iter (x, i) = wenzelm@16188: if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x; wenzelm@16188: in iter (x0, 0) end; wenzelm@6282: wenzelm@14968: fun exists_string pred str = wenzelm@14968: let wenzelm@14968: val n = size str; wenzelm@14968: fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1)); wenzelm@14968: in ex 0 end; wenzelm@6312: wenzelm@16188: fun forall_string pred = not o exists_string (not o pred); wenzelm@16188: wenzelm@28025: fun first_field sep str = wenzelm@28022: let wenzelm@28025: val n = size sep; wenzelm@28022: val len = size str; wenzelm@28022: fun find i = wenzelm@28022: if i + n > len then NONE wenzelm@28025: else if String.substring (str, i, n) = sep then SOME i wenzelm@28022: else find (i + 1); wenzelm@28025: in wenzelm@28025: (case find 0 of wenzelm@28025: NONE => NONE wenzelm@28025: | SOME i => SOME (String.substring (str, 0, i), String.extract (str, i + n, NONE))) wenzelm@28025: end; wenzelm@28022: lcp@512: (*enclose in brackets*) lcp@512: fun enclose lpar rpar str = lpar ^ str ^ rpar; wenzelm@6642: fun unenclose str = String.substring (str, 1, size str - 2); wenzelm@255: wenzelm@233: (*simple quoting (does not escape special chars)*) lcp@512: val quote = enclose "\"" "\""; wenzelm@233: wenzelm@62529: val cartouche = enclose "\" "\"; wenzelm@55033: wenzelm@59469: val space_implode = String.concatWith; wenzelm@233: wenzelm@255: val commas = space_implode ", "; wenzelm@380: val commas_quote = commas o map quote; wenzelm@255: wenzelm@255: val cat_lines = space_implode "\n"; wenzelm@233: wenzelm@4212: (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*) wenzelm@3832: fun space_explode _ "" = [] paulson@21899: | space_explode sep s = String.fields (fn c => str c = sep) s; wenzelm@3832: wenzelm@3832: val split_lines = space_explode "\n"; wenzelm@3832: wenzelm@56038: fun plain_words s = space_explode "_" s |> space_implode " "; wenzelm@56038: wenzelm@14826: fun prefix_lines "" txt = txt wenzelm@14826: | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines; wenzelm@14826: wenzelm@18681: fun prefix prfx s = prfx ^ s; wenzelm@16188: fun suffix sffx s = s ^ sffx; wenzelm@5285: wenzelm@18681: fun unprefix prfx s = wenzelm@18681: if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx) wenzelm@18681: else raise Fail "unprefix"; wenzelm@18681: wenzelm@16188: fun unsuffix sffx s = wenzelm@17061: if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx) wenzelm@17061: else raise Fail "unsuffix"; wenzelm@5285: wenzelm@65904: fun trim_line s = wenzelm@65904: if String.isSuffix "\r\n" s wenzelm@65904: then String.substring (s, 0, size s - 2) wenzelm@65904: else if String.isSuffix "\r" s orelse String.isSuffix "\n" s wenzelm@65904: then String.substring (s, 0, size s - 1) wenzelm@65904: else s; wenzelm@65904: wenzelm@65904: val trim_split_lines = trim_line #> split_lines #> map trim_line; wenzelm@47499: wenzelm@67179: fun normalize_lines str = wenzelm@67179: if exists_string (fn s => s = "\r") str then wenzelm@67179: split_lines str |> map trim_line |> cat_lines wenzelm@67179: else str; wenzelm@67179: wenzelm@24593: fun replicate_string (0: int) _ = "" wenzelm@10951: | replicate_string 1 a = a wenzelm@10951: | replicate_string k a = wenzelm@10951: if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) wenzelm@10951: else replicate_string (k div 2) (a ^ a) ^ a; wenzelm@10951: haftmann@31250: fun translate_string f = String.translate (f o String.str); haftmann@31250: wenzelm@65934: val encode_lines = translate_string (fn "\n" => "\v" | c => c); wenzelm@65934: val decode_lines = translate_string (fn "\v" => "\n" | c => c); wenzelm@65934: haftmann@63304: fun align_right c k s = haftmann@63304: let haftmann@63304: val _ = if size c <> 1 orelse size s > k haftmann@63304: then raise Fail "align_right" else () haftmann@63304: in replicate_string (k - size s) c ^ s end; haftmann@63304: kleing@29882: (*crude matching of str against simple glob pat*) kleing@29882: fun match_string pat str = kleing@29882: let kleing@29882: fun match [] _ = true kleing@29882: | match (p :: ps) s = kleing@29882: size p <= size s andalso kleing@29882: (case try (unprefix p) s of kleing@29882: SOME s' => match ps s' kleing@29882: | NONE => match (p :: ps) (String.substring (s, 1, size s - 1))); kleing@29882: in match (space_explode "*" pat) str end; wenzelm@23220: wenzelm@35976: wenzelm@41516: (** reals **) wenzelm@41516: wenzelm@41516: val string_of_real = Real.fmt (StringCvt.GEN NONE); wenzelm@41516: wenzelm@41516: fun signed_string_of_real x = wenzelm@41516: if x < 0.0 then "-" ^ string_of_real (~ x) else string_of_real x; wenzelm@41516: wenzelm@41516: wenzelm@35976: wenzelm@16492: (** lists as sets -- see also Pure/General/ord_list.ML **) wenzelm@233: wenzelm@26439: (* canonical operations *) wenzelm@26439: wenzelm@18923: fun member eq list x = wenzelm@18923: let wenzelm@18923: fun memb [] = false wenzelm@18923: | memb (y :: ys) = eq (x, y) orelse memb ys; wenzelm@18923: in memb list end; berghofe@1576: wenzelm@18923: fun insert eq x xs = if member eq xs x then xs else x :: xs; wenzelm@18923: fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs; wenzelm@24049: fun update eq x xs = cons x (remove eq x xs); wenzelm@233: haftmann@33049: fun inter eq xs = filter (member eq xs); haftmann@33049: haftmann@33042: fun union eq = fold (insert eq); wenzelm@19301: fun subtract eq = fold (remove eq); wenzelm@19301: wenzelm@30572: fun merge eq (xs, ys) = wenzelm@30572: if pointer_eq (xs, ys) then xs wenzelm@30572: else if null xs then ys wenzelm@30572: else fold_rev (insert eq) ys xs; clasohm@0: wenzelm@26439: haftmann@33050: (* subset and set equality *) haftmann@33050: haftmann@33038: fun subset eq (xs, ys) = forall (member eq ys) xs; berghofe@1576: haftmann@33038: fun eq_set eq (xs, ys) = haftmann@20348: eq_list eq (xs, ys) orelse haftmann@33038: (subset eq (xs, ys) andalso subset (eq o swap) (ys, xs)); wenzelm@19301: wenzelm@265: wenzelm@233: (*makes a list of the distinct members of the input; preserves order, takes wenzelm@233: first of equal elements*) wenzelm@19046: fun distinct eq lst = wenzelm@233: let wenzelm@233: fun dist (rev_seen, []) = rev rev_seen wenzelm@233: | dist (rev_seen, x :: xs) = wenzelm@18923: if member eq rev_seen x then dist (rev_seen, xs) wenzelm@233: else dist (x :: rev_seen, xs); wenzelm@19046: in dist ([], lst) end; wenzelm@233: wenzelm@255: (*returns a list containing all repeated elements exactly once; preserves wenzelm@255: order, takes first of equal elements*) wenzelm@18966: fun duplicates eq lst = wenzelm@255: let wenzelm@255: fun dups (rev_dups, []) = rev rev_dups wenzelm@255: | dups (rev_dups, x :: xs) = wenzelm@18923: if member eq rev_dups x orelse not (member eq xs x) then wenzelm@255: dups (rev_dups, xs) wenzelm@255: else dups (x :: rev_dups, xs); wenzelm@18966: in dups ([], lst) end; wenzelm@255: wenzelm@16878: fun has_duplicates eq = wenzelm@16878: let wenzelm@16878: fun dups [] = false wenzelm@16878: | dups (x :: xs) = member eq xs x orelse dups xs; wenzelm@16878: in dups end; wenzelm@16878: wenzelm@255: haftmann@32352: (* matrices *) haftmann@32352: haftmann@32352: fun map_transpose f xss = haftmann@32352: let wenzelm@40722: val n = wenzelm@40722: (case distinct (op =) (map length xss) of wenzelm@40722: [] => 0 haftmann@32352: | [n] => n wenzelm@40722: | _ => raise ListPair.UnequalLengths); haftmann@33206: in map_range (fn m => f (map (fn xs => nth xs m) xss)) n end; haftmann@32352: haftmann@32352: wenzelm@23220: nipkow@22142: (** lists as multisets **) nipkow@22142: haftmann@33078: fun remove1 eq x [] = [] haftmann@33078: | remove1 eq x (y :: ys) = if eq (x, y) then ys else y :: remove1 eq x ys; nipkow@22142: haftmann@33078: fun combine eq xs ys = fold (remove1 eq) ys xs @ ys; wenzelm@233: haftmann@33079: fun submultiset _ ([], _) = true haftmann@33079: | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys); haftmann@33079: clasohm@0: clasohm@0: wenzelm@2506: (** orders **) wenzelm@2506: wenzelm@67560: fun is_equal ord = ord = EQUAL; wenzelm@67560: fun is_less ord = ord = LESS; wenzelm@67560: fun is_less_equal ord = ord = LESS orelse ord = EQUAL; wenzelm@67560: fun is_greater ord = ord = GREATER; wenzelm@67560: fun is_greater_equal ord = ord = GREATER orelse ord = EQUAL; wenzelm@18966: wenzelm@4445: fun rev_order LESS = GREATER wenzelm@4445: | rev_order EQUAL = EQUAL wenzelm@4445: | rev_order GREATER = LESS; wenzelm@4445: wenzelm@4479: (*assume rel is a linear strict order*) wenzelm@4445: fun make_ord rel (x, y) = wenzelm@4445: if rel (x, y) then LESS wenzelm@4445: else if rel (y, x) then GREATER wenzelm@4445: else EQUAL; wenzelm@4445: wenzelm@25224: fun bool_ord (false, true) = LESS wenzelm@25224: | bool_ord (true, false) = GREATER wenzelm@25224: | bool_ord _ = EQUAL; wenzelm@25224: wenzelm@15051: val int_ord = Int.compare; wenzelm@15051: val string_ord = String.compare; wenzelm@2506: wenzelm@16676: fun fast_string_ord (s1, s2) = wenzelm@43793: if pointer_eq (s1, s2) then EQUAL wenzelm@43793: else (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord); wenzelm@16676: wenzelm@16492: fun option_ord ord (SOME x, SOME y) = ord (x, y) wenzelm@16492: | option_ord _ (NONE, NONE) = EQUAL wenzelm@16492: | option_ord _ (NONE, SOME _) = LESS wenzelm@16492: | option_ord _ (SOME _, NONE) = GREATER; wenzelm@16492: wenzelm@4343: (*lexicographic product*) wenzelm@4343: fun prod_ord a_ord b_ord ((x, y), (x', y')) = wenzelm@4343: (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord); wenzelm@4343: wenzelm@4343: (*dictionary order -- in general NOT well-founded!*) wenzelm@16984: fun dict_ord elem_ord (x :: xs, y :: ys) = wenzelm@16984: (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord) wenzelm@16984: | dict_ord _ ([], []) = EQUAL wenzelm@4343: | dict_ord _ ([], _ :: _) = LESS wenzelm@16984: | dict_ord _ (_ :: _, []) = GREATER; wenzelm@4343: wenzelm@4343: (*lexicographic product of lists*) wenzelm@4343: fun list_ord elem_ord (xs, ys) = wenzelm@16676: (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord); wenzelm@4343: wenzelm@2506: wenzelm@4621: (* sorting *) wenzelm@4621: wenzelm@48271: (*stable mergesort -- preserves order of equal elements*) wenzelm@48271: fun mergesort unique ord = wenzelm@4621: let wenzelm@48271: fun merge (xs as x :: xs') (ys as y :: ys') = wenzelm@48271: (case ord (x, y) of wenzelm@48271: LESS => x :: merge xs' ys wenzelm@48271: | EQUAL => wenzelm@48271: if unique then merge xs ys' wenzelm@48271: else x :: merge xs' ys wenzelm@48271: | GREATER => y :: merge xs ys') wenzelm@48271: | merge [] ys = ys wenzelm@48271: | merge xs [] = xs; wenzelm@48271: wenzelm@48271: fun merge_all [xs] = xs wenzelm@48271: | merge_all xss = merge_all (merge_pairs xss) wenzelm@48271: and merge_pairs (xs :: ys :: xss) = merge xs ys :: merge_pairs xss wenzelm@48271: | merge_pairs xss = xss; wenzelm@48271: wenzelm@48271: fun runs (x :: y :: xs) = wenzelm@18427: (case ord (x, y) of wenzelm@48271: LESS => ascending y [x] xs wenzelm@48271: | EQUAL => wenzelm@48271: if unique then runs (x :: xs) wenzelm@48271: else ascending y [x] xs wenzelm@48271: | GREATER => descending y [x] xs) wenzelm@48271: | runs xs = [xs] wenzelm@4621: wenzelm@48271: and ascending x xs (zs as y :: ys) = wenzelm@48271: (case ord (x, y) of wenzelm@48271: LESS => ascending y (x :: xs) ys wenzelm@48271: | EQUAL => wenzelm@48271: if unique then ascending x xs ys wenzelm@48271: else ascending y (x :: xs) ys wenzelm@48271: | GREATER => rev (x :: xs) :: runs zs) wenzelm@48271: | ascending x xs [] = [rev (x :: xs)] wenzelm@48271: wenzelm@48271: and descending x xs (zs as y :: ys) = wenzelm@48271: (case ord (x, y) of wenzelm@48271: GREATER => descending y (x :: xs) ys wenzelm@48271: | EQUAL => wenzelm@48271: if unique then descending x xs ys wenzelm@48271: else (x :: xs) :: runs zs wenzelm@48271: | LESS => (x :: xs) :: runs zs) wenzelm@48271: | descending x xs [] = [x :: xs]; wenzelm@48271: wenzelm@48271: in merge_all o runs end; wenzelm@48271: wenzelm@48271: fun sort ord = mergesort false ord; wenzelm@48271: fun sort_distinct ord = mergesort true ord; wenzelm@18427: wenzelm@4621: val sort_strings = sort string_ord; wenzelm@60924: fun sort_by key xs = sort (string_ord o apply2 key) xs; wenzelm@4621: wenzelm@4621: wenzelm@30558: (* items tagged by integer index *) wenzelm@30558: wenzelm@30558: (*insert tags*) wenzelm@30558: fun tag_list k [] = [] haftmann@30570: | tag_list k (x :: xs) = (k:int, x) :: tag_list (k + 1) xs; wenzelm@30558: wenzelm@30558: (*remove tags and suppress duplicates -- list is assumed sorted!*) wenzelm@30558: fun untag_list [] = [] wenzelm@30558: | untag_list [(k: int, x)] = [x] wenzelm@30558: | untag_list ((k, x) :: (rest as (k', x') :: _)) = wenzelm@30558: if k = k' then untag_list rest wenzelm@30558: else x :: untag_list rest; wenzelm@30558: wenzelm@30558: (*return list elements in original order*) wenzelm@59058: fun order_list list = untag_list (sort (int_ord o apply2 fst) list); wenzelm@30558: wenzelm@30558: wenzelm@2506: wenzelm@4621: (** misc **) wenzelm@233: wenzelm@19644: fun divide_and_conquer decomp x = wenzelm@19644: let val (ys, recomb) = decomp x wenzelm@19644: in recomb (map (divide_and_conquer decomp) ys) end; wenzelm@19644: wenzelm@32978: fun divide_and_conquer' decomp x s = wenzelm@32978: let val ((ys, recomb), s') = decomp x s wenzelm@32978: in recomb (fold_map (divide_and_conquer' decomp) ys s') end; wenzelm@32978: clasohm@0: wenzelm@233: (*Partition a list into buckets [ bi, b(i+1), ..., bj ] clasohm@0: putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) clasohm@0: fun partition_list p i j = wenzelm@37851: let wenzelm@37851: fun part (k: int) xs = wenzelm@37851: if k > j then wenzelm@37851: (case xs of wenzelm@37851: [] => [] wenzelm@37851: | _ => raise Fail "partition_list") wenzelm@37851: else wenzelm@37851: let val (ns, rest) = List.partition (p k) xs wenzelm@37851: in ns :: part (k + 1) rest end; wenzelm@37851: in part (i: int) end; clasohm@0: wenzelm@37851: fun partition_eq (eq: 'a * 'a -> bool) = wenzelm@19691: let wenzelm@19691: fun part [] = [] wenzelm@19691: | part (x :: ys) = wenzelm@19691: let val (xs, xs') = List.partition (fn y => eq (x, y)) ys wenzelm@37851: in (x :: xs) :: part xs' end; wenzelm@19691: in part end; wenzelm@19691: wenzelm@19691: wenzelm@45626: (* serial numbers and abstract stamps *) wenzelm@16439: wenzelm@16439: type serial = int; wenzelm@62918: val serial = Counter.make (); wenzelm@19512: val serial_string = string_of_int o serial; wenzelm@19512: wenzelm@45626: datatype stamp = Stamp of serial; wenzelm@45626: fun stamp () = Stamp (serial ()); wenzelm@45626: wenzelm@16535: wenzelm@51368: (* values of any type *) wenzelm@16535: wenzelm@16535: (*note that the builtin exception datatype may be extended by new wenzelm@16535: constructors at any time*) wenzelm@51368: structure Any = struct type T = exn end; wenzelm@16535: wenzelm@43603: wenzelm@43603: (* getenv *) wenzelm@43603: wenzelm@43603: fun getenv x = wenzelm@43603: (case OS.Process.getEnv x of wenzelm@43603: NONE => "" wenzelm@43603: | SOME y => y); wenzelm@43603: wenzelm@43603: fun getenv_strict x = wenzelm@43603: (case getenv x of wenzelm@43603: "" => error ("Undefined Isabelle environment variable: " ^ quote x) wenzelm@43603: | y => y); wenzelm@43603: clasohm@1364: end; clasohm@1364: wenzelm@32188: structure Basic_Library: BASIC_LIBRARY = Library; wenzelm@32188: open Basic_Library;