wenzelm@41: (* Title: Pure/library.ML clasohm@0: ID: $Id$ wenzelm@233: Author: Lawrence C Paulson, Cambridge University Computer Laboratory wenzelm@16188: Author: Markus Wenzel, TU Muenchen clasohm@0: wenzelm@233: Basic library: functions, options, 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 1 |>>> wenzelm@21395: infix 2 ? wenzelm@21395: infix 3 o oo ooo oooo wenzelm@21395: infix 4 ~~ upto downto haftmann@20854: infix orf andf \ \\ mem mem_int mem_string union union_int wenzelm@21395: union_string inter inter_int inter_string subset subset_int subset_string 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 haftmann@21335: val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd) 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 clasohm@1364: wenzelm@18681: (*errors*) wenzelm@19542: exception SYS_ERROR of string wenzelm@19542: val sys_error: string -> 'a wenzelm@18681: exception ERROR of string wenzelm@18681: val error: string -> 'a wenzelm@18681: val cat_error: string -> string -> 'a wenzelm@18681: val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit wenzelm@18681: 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@4621: val pairself: ('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: val set: bool ref -> bool wenzelm@4621: val reset: bool ref -> bool wenzelm@4621: val toggle: bool ref -> bool wenzelm@9118: val change: 'a ref -> ('a -> 'a) -> unit wenzelm@28157: val change_result: 'a ref -> ('a -> 'b * 'a) -> 'b wenzelm@23932: val setmp_noncritical: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c wenzelm@4621: val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c wenzelm@25797: val setmp_thread_data: 'a Universal.tag -> 'a -> 'a -> ('b -> 'c) -> 'b -> 'c wenzelm@4621: wenzelm@4621: (*lists*) skalberg@15570: exception UnequalLengths 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@5904: val apply: ('a -> 'a) list -> 'a -> 'a 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 haftmann@18278: val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list wenzelm@19461: val flat: 'a list list -> 'a list wenzelm@19424: val unflat: 'a list list -> 'b list -> 'b list list haftmann@18441: val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list wenzelm@24864: val burrow_options: ('a list -> 'b list) -> 'a option list -> 'b option list haftmann@18549: val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd 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 wenzelm@19011: val chop: int -> 'a list -> 'a list * 'a list nipkow@4713: val dropwhile: ('a -> bool) -> 'a list -> 'a list haftmann@18278: val nth: 'a list -> int -> 'a haftmann@18011: val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list haftmann@24846: val nth_drop: int -> 'a list -> 'a list wenzelm@18286: val nth_list: 'a list list -> int -> '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 wenzelm@4621: val split_last: 'a list -> 'a list * 'a wenzelm@4621: val find_index: ('a -> bool) -> 'a list -> int wenzelm@4621: val find_index_eq: ''a -> ''a list -> int wenzelm@4621: val find_first: ('a -> bool) -> 'a list -> 'a option haftmann@19233: val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option wenzelm@4916: val get_first: ('a -> 'b option) -> 'a list -> 'b option haftmann@19454: val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool 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@19799: val zip_options: 'a list -> 'b option list -> ('a * 'b) list haftmann@18330: val ~~ : 'a list * 'b list -> ('a * 'b) list haftmann@25943: val map_split: ('a -> 'b * 'c) -> 'a list -> 'b list * 'c list haftmann@18330: val split_list: ('a * 'b) list -> 'a list * 'b list haftmann@26449: val map_product: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list haftmann@26449: val fold_product: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c wenzelm@4621: val separate: 'a -> 'a list -> 'a list wenzelm@25980: val surround: 'a -> 'a list -> 'a list wenzelm@4621: val replicate: int -> 'a -> 'a list haftmann@18441: val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool wenzelm@4621: val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list haftmann@20108: val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list) wenzelm@4621: val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a 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@4621: wenzelm@4621: (*integers*) wenzelm@4621: val inc: int ref -> int wenzelm@4621: val dec: int ref -> int wenzelm@4621: val upto: int * int -> int list wenzelm@4621: val downto: int * int -> int list 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@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@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@10951: val replicate_string: int -> string -> string wenzelm@14926: val translate_string: (string -> string) -> string -> string wenzelm@25549: val multiply: 'a list -> 'a list list -> 'a list list wenzelm@4621: 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 wenzelm@19301: val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list wenzelm@18923: val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list wenzelm@4621: val mem: ''a * ''a list -> bool wenzelm@4621: val mem_int: int * int list -> bool wenzelm@4621: val mem_string: string * string list -> bool wenzelm@4621: val union: ''a list * ''a list -> ''a list wenzelm@4621: val union_int: int list * int list -> int list wenzelm@4621: val union_string: string list * string list -> string list wenzelm@4621: val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list paulson@7090: val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list wenzelm@4621: val inter: ''a list * ''a list -> ''a list wenzelm@4621: val inter_int: int list * int list -> int list wenzelm@4621: val inter_string: string list * string list -> string list wenzelm@4621: val subset: ''a list * ''a list -> bool wenzelm@4621: val subset_int: int list * int list -> bool wenzelm@4621: val subset_string: string list * string list -> bool wenzelm@4621: val eq_set: ''a list * ''a list -> bool wenzelm@4621: val eq_set_string: string list * string list -> bool wenzelm@4621: val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool wenzelm@19301: val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool wenzelm@4621: val \ : ''a list * ''a -> ''a list wenzelm@4621: val \\ : ''a list * ''a list -> ''a list 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@4621: wenzelm@23220: (*lists as multisets*) nipkow@22142: val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list wenzelm@23220: val submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool wenzelm@4621: wenzelm@4621: (*orders*) wenzelm@18966: val is_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@4621: val sort_wrt: ('a -> string) -> 'a list -> 'a list wenzelm@4621: berghofe@14106: (*random numbers*) berghofe@14106: exception RANDOM berghofe@14106: val random: unit -> real berghofe@14106: val random_range: int -> int -> int berghofe@14106: val one_of: 'a list -> 'a berghofe@14106: val frequency: (int * 'a) list -> 'a berghofe@14106: wenzelm@4621: (*misc*) wenzelm@19644: val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> '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@4621: val gensym: string -> string wenzelm@16439: type stamp wenzelm@16439: val stamp: unit -> stamp wenzelm@16439: type serial wenzelm@16439: val serial: unit -> serial wenzelm@19512: val serial_string: unit -> string wenzelm@16535: structure Object: sig type T end 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: val take: int * 'a list -> 'a list skalberg@15570: val drop: int * 'a list -> 'a list skalberg@15570: val last_elem: 'a list -> 'a 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: wenzelm@21395: (*application and structured results -- old version*) wenzelm@16705: fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end; wenzelm@16842: 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: wenzelm@233: (*function exponentiation: f(...(f x)...) with n applications of f*) wenzelm@24593: fun funpow (0: int) _ x = x wenzelm@23718: | funpow n f x = funpow (n - 1) f (f x); wenzelm@160: wenzelm@160: wenzelm@18681: (* errors *) wenzelm@18681: wenzelm@19542: exception SYS_ERROR of string; wenzelm@19542: fun sys_error msg = raise SYS_ERROR msg; wenzelm@19542: wenzelm@18681: exception ERROR of string; wenzelm@18681: fun error msg = raise ERROR msg; wenzelm@18681: wenzelm@18681: fun cat_error "" msg = error msg wenzelm@18681: | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2); wenzelm@18681: wenzelm@18681: fun assert_all pred list msg = wenzelm@18681: let wenzelm@18681: fun ass [] = () wenzelm@18681: | ass (x :: xs) = if pred x then ass xs else error (msg x); wenzelm@18681: in ass list end; wenzelm@18681: wenzelm@18681: 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@4212: fun pairself 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@380: (* flags *) wenzelm@380: wenzelm@380: fun set flag = (flag := true; true); wenzelm@380: fun reset flag = (flag := false; false); wenzelm@380: fun toggle flag = (flag := not (! flag); ! flag); wenzelm@380: wenzelm@9118: fun change r f = r := f (! r); wenzelm@28157: fun change_result r f = let val (x, y) = f (! r) in r := y; x end; wenzelm@9118: wenzelm@18712: (*temporarily set flag during execution*) wenzelm@23932: fun setmp_noncritical flag value f x = wenzelm@26079: uninterruptible (fn restore_attributes => fn () => wenzelm@26079: let wenzelm@26079: val orig_value = ! flag; wenzelm@26079: val _ = flag := value; wenzelm@26079: val result = Exn.capture (restore_attributes f) x; wenzelm@26079: val _ = flag := orig_value; wenzelm@26079: in Exn.release result end) (); wenzelm@2958: wenzelm@26079: fun setmp flag value f x = wenzelm@26079: NAMED_CRITICAL "setmp" (fn () => setmp_noncritical flag value f x); wenzelm@23932: wenzelm@25797: fun setmp_thread_data tag orig_data data f x = wenzelm@26079: uninterruptible (fn restore_attributes => fn () => wenzelm@26079: let wenzelm@28122: val _ = Thread.setLocal (tag, data); wenzelm@26079: val result = Exn.capture (restore_attributes f) x; wenzelm@28122: val _ = Thread.setLocal (tag, orig_data); wenzelm@26079: in Exn.release result end) (); wenzelm@25797: wenzelm@19644: wenzelm@21395: wenzelm@233: (** lists **) wenzelm@233: skalberg@15570: exception UnequalLengths; wenzelm@233: wenzelm@5285: fun single x = [x]; wenzelm@233: wenzelm@20882: fun the_single [x] = x wenzelm@20882: | the_single _ = raise 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@5904: fun apply [] x = x wenzelm@5904: | apply (f :: fs) x = apply fs (f x); wenzelm@5904: 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)*) berghofe@25681: fun foldl1 f [] = raise 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)*) paulson@20443: fun foldr1 f [] = raise 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@16705: fun foldl_map f = wenzelm@16705: let wenzelm@16705: fun fold_aux (x, []) = (x, []) wenzelm@16705: | fold_aux (x, y :: ys) = wenzelm@16705: let wenzelm@16705: val (x', y') = f (x, y); wenzelm@16705: val (x'', ys') = fold_aux (x', ys); wenzelm@16705: in (x'', y' :: ys') end; wenzelm@16705: in fold_aux end; wenzelm@16705: wenzelm@233: wenzelm@233: (* basic list functions *) wenzelm@233: wenzelm@20510: fun eq_list eq (list1, list2) = haftmann@20348: let wenzelm@20510: fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys) wenzelm@20510: | eq_lst _ = true; wenzelm@20510: 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: 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@233: (*take the first n elements from a list*) wenzelm@24593: fun take (n: int, []) = [] wenzelm@233: | take (n, x :: xs) = wenzelm@233: if n > 0 then x :: take (n - 1, xs) else []; wenzelm@233: wenzelm@233: (*drop the first n elements from a list*) wenzelm@24593: fun drop (n: int, []) = [] wenzelm@233: | drop (n, x :: xs) = wenzelm@233: if n > 0 then drop (n - 1, xs) else x :: xs; clasohm@0: nipkow@4713: fun dropwhile P [] = [] nipkow@4713: | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; nipkow@4713: 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@18461: fun nth_list xss i = nth xss i handle 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 wenzelm@24593: fun mapp (_: int) [] = [] wenzelm@24593: | mapp i (x :: xs) = f (i, x) :: mapp (i + 1) xs haftmann@18514: in mapp 0 end; haftmann@18514: haftmann@21118: fun fold_index f = haftmann@21118: let wenzelm@24593: fun fold_aux (_: int) [] y = y wenzelm@24593: | fold_aux i (x :: xs) y = fold_aux (i + 1) xs (f (i, x) y); haftmann@21118: in fold_aux 0 end; haftmann@21118: skalberg@15570: val last_elem = List.last; wenzelm@233: wenzelm@3762: (*rear decomposition*) skalberg@15570: fun split_last [] = raise Empty wenzelm@3762: | split_last [x] = ([], x) wenzelm@3762: | split_last (x :: xs) = apfst (cons x) (split_last xs); wenzelm@3762: wenzelm@4212: (*find the position of an element in a list*) 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@4224: fun find_index_eq x = find_index (equal x); wenzelm@4212: wenzelm@4212: (*find first element satisfying predicate*) paulson@22593: val find_first = List.find; wenzelm@233: 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@24593: fun get (_: int) [] = NONE wenzelm@19461: | get i (x :: xs) = haftmann@19233: case f x wenzelm@19461: of NONE => get (i + 1) xs haftmann@19233: | SOME y => SOME (i, y) haftmann@19233: in get 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 [] [] = [] skalberg@15570: | unflat _ _ = raise UnequalLengths; wenzelm@12136: 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@14926: fun translate_string f = String.translate (f o String.str); wenzelm@14926: wenzelm@4248: (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*) wenzelm@18148: fun multiply [] _ = [] wenzelm@18148: | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss; wenzelm@4248: wenzelm@25549: 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: skalberg@15570: exception UnequalLengths; skalberg@15570: haftmann@18330: fun map2 _ [] [] = [] haftmann@18330: | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys haftmann@18330: | map2 _ _ _ = raise UnequalLengths; wenzelm@380: wenzelm@23220: fun fold2 f [] [] z = z wenzelm@23220: | fold2 f (x :: xs) (y :: ys) z = fold2 f xs ys (f x y z) wenzelm@23220: | fold2 f _ _ _ = raise UnequalLengths; wenzelm@380: haftmann@25943: fun map_split f [] = ([], []) 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@19799: | zip_options [] _ = raise 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) skalberg@15570: | _ ~~ _ = raise 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: wenzelm@233: 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@233: (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn]) wenzelm@233: where xi is the first element that does not satisfy the predicate*) wenzelm@233: fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list = wenzelm@233: let fun take (rxs, []) = (rev rxs, []) wenzelm@255: | take (rxs, x :: xs) = wenzelm@255: if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) wenzelm@233: in take([], xs) end; wenzelm@233: haftmann@20108: fun chop_prefix eq ([], ys) = ([], ([], ys)) haftmann@20108: | chop_prefix eq (xs, []) = ([], (xs, [])) wenzelm@23220: | chop_prefix eq (xs as x :: xs', ys as y :: ys') = haftmann@20108: if eq (x, y) then haftmann@20108: let val (ps', xys'') = chop_prefix eq (xs', ys') wenzelm@23220: in (x :: ps', xys'') end haftmann@20108: else ([], (xs, ys)); haftmann@20108: wenzelm@233: (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn]) wenzelm@233: where xi is the last element that does not satisfy the predicate*) wenzelm@233: fun take_suffix _ [] = ([], []) wenzelm@233: | take_suffix pred (x :: xs) = wenzelm@233: (case take_suffix pred xs of wenzelm@233: ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) wenzelm@233: | (prfx, sffx) => (x :: prfx, sffx)); wenzelm@233: 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@23220: wenzelm@233: (** integers **) wenzelm@233: wenzelm@24593: fun inc i = (i := ! i + (1: int); ! i); wenzelm@24593: fun dec i = (i := ! i - (1: int); ! i); wenzelm@233: 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@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: paulson@3407: val string_of_int = Int.toString; 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@20095: val zero = ord "0"; wenzelm@20095: val limit = zero + radix; wenzelm@20095: fun scan (num, []) = (num, []) wenzelm@20095: | scan (num, c :: cs) = wenzelm@20095: if zero <= ord c andalso ord c < limit then wenzelm@24630: scan (radix * num + (ord c - zero), cs) wenzelm@20095: 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@24630: fun oct_char s = chr (#1 (read_radix_int 8 (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@4212: (*space_implode "..." (explode "hello") = "h...e...l...l...o"*) wenzelm@233: fun space_implode a bs = implode (separate a bs); wenzelm@233: wenzelm@255: val commas = space_implode ", "; wenzelm@380: val commas_quote = commas o map quote; wenzelm@255: wenzelm@233: (*concatenate messages, one per line, into a string*) 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@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@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: wenzelm@233: wenzelm@23220: 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: wenzelm@19301: fun subtract eq = fold (remove eq); wenzelm@19301: wenzelm@18923: fun merge _ ([], ys) = ys wenzelm@18923: | merge eq (xs, ys) = fold_rev (insert eq) ys xs; clasohm@0: wenzelm@26439: wenzelm@26439: (* old-style infixes *) wenzelm@26439: wenzelm@18923: fun x mem xs = member (op =) xs x; wenzelm@18923: fun (x: int) mem_int xs = member (op =) xs x; wenzelm@18923: fun (x: string) mem_string xs = member (op =) xs x; berghofe@1576: wenzelm@233: (*union of sets represented as lists: no repetitions*) wenzelm@233: fun xs union [] = xs wenzelm@233: | [] union ys = ys haftmann@20854: | (x :: xs) union ys = xs union (insert (op =) x ys); clasohm@0: paulson@2175: (*union of sets, optimized version for ints*) berghofe@1576: fun (xs:int list) union_int [] = xs berghofe@1576: | [] union_int ys = ys haftmann@20854: | (x :: xs) union_int ys = xs union_int (insert (op =) x ys); berghofe@1576: paulson@2175: (*union of sets, optimized version for strings*) berghofe@1576: fun (xs:string list) union_string [] = xs berghofe@1576: | [] union_string ys = ys haftmann@20854: | (x :: xs) union_string ys = xs union_string (insert (op =) x ys); berghofe@1576: clasohm@0: (*generalized union*) wenzelm@233: fun gen_union eq (xs, []) = xs wenzelm@233: | gen_union eq ([], ys) = ys wenzelm@18923: | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys); wenzelm@233: wenzelm@233: wenzelm@233: (*intersection*) wenzelm@233: fun [] inter ys = [] wenzelm@233: | (x :: xs) inter ys = wenzelm@233: if x mem ys then x :: (xs inter ys) else xs inter ys; wenzelm@233: paulson@2175: (*intersection, optimized version for ints*) berghofe@1576: fun ([]:int list) inter_int ys = [] berghofe@1576: | (x :: xs) inter_int ys = berghofe@1576: if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys; berghofe@1576: paulson@2175: (*intersection, optimized version for strings *) berghofe@1576: fun ([]:string list) inter_string ys = [] berghofe@1576: | (x :: xs) inter_string ys = berghofe@1576: if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys; berghofe@1576: paulson@7090: (*generalized intersection*) paulson@7090: fun gen_inter eq ([], ys) = [] wenzelm@12284: | gen_inter eq (x::xs, ys) = wenzelm@18923: if member eq ys x then x :: gen_inter eq (xs, ys) wenzelm@18923: else gen_inter eq (xs, ys); paulson@7090: wenzelm@233: wenzelm@233: (*subset*) wenzelm@233: fun [] subset ys = true wenzelm@233: | (x :: xs) subset ys = x mem ys andalso xs subset ys; wenzelm@233: paulson@2175: (*subset, optimized version for ints*) wenzelm@16439: fun ([]: int list) subset_int ys = true berghofe@1576: | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys; berghofe@1576: paulson@2175: (*subset, optimized version for strings*) wenzelm@16439: fun ([]: string list) subset_string ys = true berghofe@1576: | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys; berghofe@1576: wenzelm@4363: (*set equality*) wenzelm@4363: fun eq_set (xs, ys) = wenzelm@4363: xs = ys orelse (xs subset ys andalso ys subset xs); wenzelm@4363: paulson@2182: (*set equality for strings*) wenzelm@16439: fun eq_set_string ((xs: string list), ys) = berghofe@1576: xs = ys orelse (xs subset_string ys andalso ys subset_string xs); berghofe@1576: wenzelm@18923: fun gen_subset eq (xs, ys) = forall (member eq ys) xs; paulson@2182: wenzelm@19301: fun gen_eq_set eq (xs, ys) = haftmann@20348: eq_list eq (xs, ys) orelse wenzelm@19301: (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs)); wenzelm@19301: wenzelm@265: wenzelm@233: (*removing an element from a list WITHOUT duplicates*) wenzelm@233: fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) wenzelm@233: | [] \ x = []; paulson@2243: fun ys \\ xs = foldl (op \) (ys,xs); clasohm@0: wenzelm@233: 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: wenzelm@23220: nipkow@22142: (** lists as multisets **) nipkow@22142: nipkow@22142: fun remove1 _ _ [] = raise Empty wenzelm@23220: | remove1 eq y (x::xs) = if eq (y, x) then xs else x :: remove1 eq y xs; nipkow@22142: wenzelm@23220: fun submultiset _ ([], _) = true wenzelm@23220: | submultiset eq (x :: xs, ys) = member eq ys x andalso submultiset eq (xs, remove1 eq x ys); wenzelm@233: clasohm@0: clasohm@0: wenzelm@2506: (** orders **) wenzelm@2506: wenzelm@18966: fun is_equal EQUAL = true wenzelm@18966: | is_equal _ = false; 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@16676: (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@18427: (*quicksort -- stable, i.e. does not reorder equal elements*) wenzelm@18427: fun quicksort unique ord = wenzelm@4621: let wenzelm@16878: fun qsort [] = [] wenzelm@16878: | qsort (xs as [_]) = xs wenzelm@18427: | qsort (xs as [x, y]) = wenzelm@18427: (case ord (x, y) of wenzelm@18427: LESS => xs wenzelm@18427: | EQUAL => if unique then [x] else xs wenzelm@18427: | GREATER => [y, x]) wenzelm@16878: | qsort xs = haftmann@18011: let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs wenzelm@16878: in qsort lts @ eqs @ qsort gts end wenzelm@4621: and part _ [] = ([], [], []) wenzelm@4621: | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) wenzelm@4621: and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) wenzelm@18427: | add EQUAL x (lts, [], gts) = (lts, [x], gts) wenzelm@18427: | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts) wenzelm@4621: | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); wenzelm@4621: in qsort end; wenzelm@4621: wenzelm@18427: fun sort ord = quicksort false ord; wenzelm@18427: fun sort_distinct ord = quicksort true ord; wenzelm@18427: wenzelm@4621: val sort_strings = sort string_ord; wenzelm@4621: fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; wenzelm@4621: wenzelm@4621: wenzelm@2506: berghofe@14106: (** random numbers **) berghofe@14106: berghofe@14106: exception RANDOM; berghofe@14106: berghofe@14618: fun rmod x y = x - y * Real.realFloor (x / y); berghofe@14106: berghofe@14106: local berghofe@14106: val a = 16807.0; berghofe@14106: val m = 2147483647.0; berghofe@14106: val random_seed = ref 1.0; berghofe@14106: in berghofe@14106: wenzelm@23922: fun random () = CRITICAL (fn () => wenzelm@23922: let val r = rmod (a * ! random_seed) m wenzelm@23922: in (random_seed := r; r) end); berghofe@14106: berghofe@14106: end; berghofe@14106: berghofe@14106: fun random_range l h = berghofe@14106: if h < l orelse l < 0 then raise RANDOM berghofe@14106: else l + Real.floor (rmod (random ()) (real (h - l + 1))); berghofe@14106: haftmann@18011: fun one_of xs = nth xs (random_range 0 (length xs - 1)); berghofe@14106: berghofe@14106: fun frequency xs = berghofe@14106: let berghofe@14106: val sum = foldl op + (0, map fst xs); wenzelm@17756: fun pick n ((k: int, x) :: xs) = berghofe@14106: if n <= k then x else pick (n - k) xs berghofe@14106: in pick (random_range 1 sum) xs end; berghofe@14106: berghofe@14106: wenzelm@23220: 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: 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@233: let fun part k xs = wenzelm@233: if k>j then clasohm@0: (case xs of [] => [] skalberg@15570: | _ => raise Fail "partition_list") clasohm@0: else wenzelm@19691: let val (ns, rest) = List.partition (p k) xs; wenzelm@233: in ns :: part(k+1)rest end wenzelm@24593: in part (i: int) end; clasohm@0: wenzelm@19691: 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@19691: in (x::xs)::(part xs') end wenzelm@19691: in part end; wenzelm@19691: wenzelm@19691: clasohm@0: wenzelm@233: (* generating identifiers *) clasohm@0: paulson@4063: (** Freshly generated identifiers; supplied prefix MUST start with a letter **) wenzelm@22369: local wenzelm@22369: (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*) wenzelm@22582: fun gensym_char i = paulson@22368: if i<26 then chr (ord "A" + i) paulson@22368: else if i<52 then chr (ord "a" + i - 26) wenzelm@22369: else chr (ord "0" + i - 52); paulson@4063: wenzelm@22369: val char_vec = Vector.tabulate (62, gensym_char); wenzelm@22369: fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n))); wenzelm@4284: wenzelm@24593: val gensym_seed = ref (0: int); paulson@2003: wenzelm@22369: in wenzelm@24148: fun gensym pre = pre ^ newid (NAMED_CRITICAL "gensym" (fn () => inc gensym_seed)); wenzelm@22369: end; paulson@4063: paulson@4063: wenzelm@16439: (* stamps and serial numbers *) wenzelm@16439: wenzelm@16439: type stamp = unit ref; wenzelm@16439: val stamp: unit -> stamp = ref; wenzelm@16439: wenzelm@16439: type serial = int; wenzelm@25702: val serial = Multithreading.serial; wenzelm@19512: val serial_string = string_of_int o serial; wenzelm@19512: wenzelm@16535: wenzelm@16535: (* generic objects *) wenzelm@16535: wenzelm@16535: (*note that the builtin exception datatype may be extended by new wenzelm@16535: constructors at any time*) wenzelm@16535: structure Object = struct type T = exn end; wenzelm@16535: clasohm@1364: end; clasohm@1364: wenzelm@15745: structure BasicLibrary: BASIC_LIBRARY = Library; wenzelm@15745: open BasicLibrary;