(* Title: Pure/library.ML ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Author: Markus Wenzel, TU Muenchen Basic library: functions, options, pairs, booleans, lists, integers, strings, lists as sets, balanced trees, orders, current directory, misc. See also General/basics.ML for the most fundamental concepts. *) infix 1 |>>> infix 2 ? infix 3 o oo ooo oooo infix 4 ~~ upto downto infix orf andf \ \\ mem mem_int mem_string union union_int union_string inter inter_int inter_string subset subset_int subset_string signature BASIC_LIBRARY = sig (*functions*) val I: 'a -> 'a val K: 'a -> 'b -> 'a val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c val |>>> : ('a * 'c) * ('a -> 'b * 'd) -> 'b * ('c * 'd) val ? : bool * ('a -> 'a) -> 'a -> 'a val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b val funpow: int -> ('a -> 'a) -> 'a -> 'a (*exceptions*) exception EXCEPTION of exn * string val do_transform_failure: bool ref val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b datatype 'a result = Result of 'a | Exn of exn val capture: ('a -> 'b) -> 'a -> 'b result val release: 'a result -> 'a val get_result: 'a result -> 'a option val get_exn: 'a result -> exn option (*errors*) exception SYS_ERROR of string val sys_error: string -> 'a exception ERROR of string val error: string -> 'a val cat_error: string -> string -> 'a val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit (*pairs*) val pair: 'a -> 'b -> 'a * 'b val rpair: 'a -> 'b -> 'b * 'a val fst: 'a * 'b -> 'a val snd: 'a * 'b -> 'b val eq_fst: ('a * 'c -> bool) -> ('a * 'b) * ('c * 'd) -> bool val eq_snd: ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool val eq_pair: ('a * 'c -> bool) -> ('b * 'd -> bool) -> ('a * 'b) * ('c * 'd) -> bool val swap: 'a * 'b -> 'b * 'a val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b (*booleans*) val equal: ''a -> ''a -> bool val not_equal: ''a -> ''a -> bool val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool val exists: ('a -> bool) -> 'a list -> bool val forall: ('a -> bool) -> 'a list -> bool val set: bool ref -> bool val reset: bool ref -> bool val toggle: bool ref -> bool val change: 'a ref -> ('a -> 'a) -> unit val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c (*lists*) exception UnequalLengths val single: 'a -> 'a list val the_single: 'a list -> 'a val singleton: ('a list -> 'b list) -> 'a -> 'b val apply: ('a -> 'a) list -> 'a -> 'a val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list val flat: 'a list list -> 'a list val unflat: 'a list list -> 'b list -> 'b list list val burrow: ('a list -> 'b list) -> 'a list list -> 'b list list val fold_burrow: ('a list -> 'c -> 'b list * 'd) -> 'a list list -> 'c -> 'b list list * 'd val maps: ('a -> 'b list) -> 'a list -> 'b list val chop: int -> 'a list -> 'a list * 'a list val dropwhile: ('a -> bool) -> 'a list -> 'a list val nth: 'a list -> int -> 'a val nth_map: int -> ('a -> 'a) -> 'a list -> 'a list val nth_list: 'a list list -> int -> 'a list val map_index: (int * 'a -> 'b) -> 'a list -> 'b list val fold_index: (int * 'a -> 'b -> 'b) -> 'a list -> 'b -> 'b val split_last: 'a list -> 'a list * 'a val find_index: ('a -> bool) -> 'a list -> int val find_index_eq: ''a -> ''a list -> int val find_first: ('a -> bool) -> 'a list -> 'a option val get_index: ('a -> 'b option) -> 'a list -> (int * 'b) option val get_first: ('a -> 'b option) -> 'a list -> 'b option val eq_list: ('a * 'b -> bool) -> 'a list * 'b list -> bool val map2: ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list val fold2: ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c val zip_options: 'a list -> 'b option list -> ('a * 'b) list val ~~ : 'a list * 'b list -> ('a * 'b) list val split_list: ('a * 'b) list -> 'a list * 'b list val separate: 'a -> 'a list -> 'a list val replicate: int -> 'a -> 'a list val multiply: 'a list -> 'a list list -> 'a list list val product: 'a list -> 'b list -> ('a * 'b) list val filter: ('a -> bool) -> 'a list -> 'a list val filter_out: ('a -> bool) -> 'a list -> 'a list val map_filter: ('a -> 'b option) -> 'a list -> 'b list val is_prefix: ('a * 'a -> bool) -> 'a list -> 'a list -> bool val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list val chop_prefix: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list * ('a list * 'b list) val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list val prefixes1: 'a list -> 'a list list val prefixes: 'a list -> 'a list list val suffixes1: 'a list -> 'a list list val suffixes: 'a list -> 'a list list (*integers*) val gcd: IntInf.int * IntInf.int -> IntInf.int val lcm: IntInf.int * IntInf.int -> IntInf.int val inc: int ref -> int val dec: int ref -> int val upto: int * int -> int list val downto: int * int -> int list val downto0: int list * int -> bool val radixpand: int * int -> int list val radixstring: int * string * int -> string val string_of_int: int -> string val signed_string_of_int: int -> string val string_of_indexname: string * int -> string val read_intinf: int -> string list -> IntInf.int * string list val read_int: string list -> int * string list val oct_char: string -> string (*strings*) val nth_string: string -> int -> string val fold_string: (string -> 'a -> 'a) -> string -> 'a -> 'a val exists_string: (string -> bool) -> string -> bool val forall_string: (string -> bool) -> string -> bool val enclose: string -> string -> string -> string val unenclose: string -> string val quote: string -> string val space_implode: string -> string list -> string val commas: string list -> string val commas_quote: string list -> string val cat_lines: string list -> string val space_explode: string -> string -> string list val split_lines: string -> string list val prefix_lines: string -> string -> string val untabify: string list -> string list val prefix: string -> string -> string val suffix: string -> string -> string val unprefix: string -> string -> string val unsuffix: string -> string -> string val replicate_string: int -> string -> string val translate_string: (string -> string) -> string -> string (*lists as sets -- see also Pure/General/ord_list.ML*) val member: ('b * 'a -> bool) -> 'a list -> 'b -> bool val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list val subtract: ('b * 'a -> bool) -> 'b list -> 'a list -> 'a list val merge: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list val mem: ''a * ''a list -> bool val mem_int: int * int list -> bool val mem_string: string * string list -> bool val union: ''a list * ''a list -> ''a list val union_int: int list * int list -> int list val union_string: string list * string list -> string list val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list val gen_inter: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list val inter: ''a list * ''a list -> ''a list val inter_int: int list * int list -> int list val inter_string: string list * string list -> string list val subset: ''a list * ''a list -> bool val subset_int: int list * int list -> bool val subset_string: string list * string list -> bool val eq_set: ''a list * ''a list -> bool val eq_set_string: string list * string list -> bool val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool val gen_eq_set: ('a * 'b -> bool) -> 'a list * 'b list -> bool val \ : ''a list * ''a -> ''a list val \\ : ''a list * ''a list -> ''a list val distinct: ('a * 'a -> bool) -> 'a list -> 'a list val duplicates: ('a * 'a -> bool) -> 'a list -> 'a list val has_duplicates: ('a * 'a -> bool) -> 'a list -> bool (* lists as multisets *) val remove1: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list val gen_submultiset: ('a * 'b -> bool) -> 'a list * 'b list -> bool (*lists as tables -- see also Pure/General/alist.ML*) val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list val merge_lists: ''a list -> ''a list -> ''a list val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list (*balanced trees*) exception Balance val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list (*orders*) val is_equal: order -> bool val rev_order: order -> order val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order val int_ord: int * int -> order val string_ord: string * string -> order val fast_string_ord: string * string -> order val option_ord: ('a * 'b -> order) -> 'a option * 'b option -> order val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order val sort: ('a * 'a -> order) -> 'a list -> 'a list val sort_distinct: ('a * 'a -> order) -> 'a list -> 'a list val sort_strings: string list -> string list val sort_wrt: ('a -> string) -> 'a list -> 'a list (*random numbers*) exception RANDOM val random: unit -> real val random_range: int -> int -> int val one_of: 'a list -> 'a val frequency: (int * 'a) list -> 'a (*current directory*) val cd: string -> unit val pwd: unit -> string (*misc*) val divide_and_conquer: ('a -> 'a list * ('b list -> 'b)) -> 'a -> 'b val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list val gensym: string -> string type stamp val stamp: unit -> stamp type serial val serial: unit -> serial val serial_string: unit -> string structure Object: sig type T end end; signature LIBRARY = sig include BASIC_LIBRARY val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b val take: int * 'a list -> 'a list val drop: int * 'a list -> 'a list val last_elem: 'a list -> 'a val seq: ('a -> unit) -> 'a list -> unit end; structure Library: LIBRARY = struct (* functions *) fun I x = x; fun K x = fn _ => x; fun curry f x y = f (x, y); fun uncurry f (x, y) = f x y; (*application and structured results -- old version*) fun (x, y) |>>> f = let val (x', z) = f x in (x', (y, z)) end; (*conditional application*) fun b ? f = fn x => if b then f x else x; (*composition with multiple args*) fun (f oo g) x y = f (g x y); fun (f ooo g) x y z = f (g x y z); fun (f oooo g) x y z w = f (g x y z w); (*function exponentiation: f(...(f x)...) with n applications of f*) fun funpow n f x = let fun rep (0, x) = x | rep (n, x) = rep (n - 1, f x) in rep (n, x) end; (* exceptions *) val do_transform_failure = ref true; fun transform_failure exn f x = if ! do_transform_failure then f x handle Interrupt => raise Interrupt | e => raise exn e else f x; exception EXCEPTION of exn * string; datatype 'a result = Result of 'a | Exn of exn; fun capture f x = Result (f x) handle e => Exn e; fun release (Result y) = y | release (Exn e) = raise e; fun get_result (Result x) = SOME x | get_result _ = NONE; fun get_exn (Exn exn) = SOME exn | get_exn _ = NONE; (* errors *) exception SYS_ERROR of string; fun sys_error msg = raise SYS_ERROR msg; exception ERROR of string; fun error msg = raise ERROR msg; fun cat_error "" msg = error msg | cat_error msg1 msg2 = error (msg1 ^ "\n" ^ msg2); fun assert_all pred list msg = let fun ass [] = () | ass (x :: xs) = if pred x then ass xs else error (msg x); in ass list end; (* pairs *) fun pair x y = (x, y); fun rpair x y = (y, x); fun fst (x, y) = x; fun snd (x, y) = y; fun eq_fst eq ((x1, _), (x2, _)) = eq (x1, x2); fun eq_snd eq ((_, y1), (_, y2)) = eq (y1, y2); fun eq_pair eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2); fun swap (x, y) = (y, x); (*apply function to components*) fun apfst f (x, y) = (f x, y); fun apsnd f (x, y) = (x, f y); fun pairself f (x, y) = (f x, f y); (* booleans *) (*polymorphic equality*) fun equal x y = x = y; fun not_equal x y = x <> y; (*combining predicates*) fun p orf q = fn x => p x orelse q x; fun p andf q = fn x => p x andalso q x; (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) fun exists (pred: 'a -> bool) : 'a list -> bool = let fun boolf [] = false | boolf (x :: xs) = pred x orelse boolf xs in boolf end; (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) fun forall (pred: 'a -> bool) : 'a list -> bool = let fun boolf [] = true | boolf (x :: xs) = pred x andalso boolf xs in boolf end; (* flags *) fun set flag = (flag := true; true); fun reset flag = (flag := false; false); fun toggle flag = (flag := not (! flag); ! flag); fun change r f = r := f (! r); (*temporarily set flag during execution*) fun setmp flag value f x = let val orig_value = ! flag; val _ = flag := value; val result = capture f x; val _ = flag := orig_value; in release result end; (** lists **) exception UnequalLengths; fun single x = [x]; fun the_single [x] = x | the_single _ = raise Empty; fun singleton f x = the_single (f [x]); fun apply [] x = x | apply (f :: fs) x = apply fs (f x); (* fold -- old versions *) (*the following versions of fold are designed to fit nicely with infixes*) (* (op @) (e, [x1, ..., xn]) ===> ((e @ x1) @ x2) ... @ xn for operators that associate to the left (TAIL RECURSIVE)*) fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a = let fun itl (e, []) = e | itl (e, a::l) = itl (f(e, a), l) in itl end; (* (op @) ([x1, ..., xn], e) ===> x1 @ (x2 ... @ (xn @ e)) for operators that associate to the right (not tail recursive)*) fun foldr f (l, e) = let fun itr [] = e | itr (a::l) = f(a, itr l) in itr l end; (* (op @) [x1, ..., xn] ===> x1 @ (x2 ... @ (x[n-1] @ xn)) for n > 0, operators that associate to the right (not tail recursive)*) fun foldr1 f [] = raise Empty | foldr1 f l = let fun itr [x] = x | itr (x::l) = f(x, itr l) in itr l end; fun foldl_map f = let fun fold_aux (x, []) = (x, []) | fold_aux (x, y :: ys) = let val (x', y') = f (x, y); val (x'', ys') = fold_aux (x', ys); in (x'', y' :: ys') end; in fold_aux end; (* basic list functions *) fun eq_list eq (list1, list2) = let fun eq_lst (x :: xs, y :: ys) = eq (x, y) andalso eq_lst (xs, ys) | eq_lst _ = true; in length list1 = length list2 andalso eq_lst (list1, list2) end; fun maps f [] = [] | maps f (x :: xs) = f x @ maps f xs; fun chop n xs = unfold_rev n dest xs; (*take the first n elements from a list*) fun take (n, []) = [] | take (n, x :: xs) = if n > 0 then x :: take (n - 1, xs) else []; (*drop the first n elements from a list*) fun drop (n, []) = [] | drop (n, x :: xs) = if n > 0 then drop (n - 1, xs) else x :: xs; fun dropwhile P [] = [] | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys; (*return nth element of a list, where 0 designates the first element; raise Subscript if list too short*) fun nth xs i = List.nth (xs, i); fun nth_list xss i = nth xss i handle Subscript => []; fun nth_map 0 f (x :: xs) = f x :: xs | nth_map n f (x :: xs) = x :: nth_map (n - 1) f xs | nth_map _ _ [] = raise Subscript; fun map_index f = let fun mapp _ [] = [] | mapp i (x :: xs) = f (i, x) :: mapp (i+1) xs in mapp 0 end; fun fold_index f = let fun fold_aux _ [] y = y | fold_aux i (x :: xs) y = fold_aux (i+1) xs (f (i, x) y); in fold_aux 0 end; val last_elem = List.last; (*rear decomposition*) fun split_last [] = raise Empty | split_last [x] = ([], x) | split_last (x :: xs) = apfst (cons x) (split_last xs); (*find the position of an element in a list*) fun find_index pred = let fun find _ [] = ~1 | find n (x :: xs) = if pred x then n else find (n + 1) xs; in find 0 end; fun find_index_eq x = find_index (equal x); (*find first element satisfying predicate*) fun find_first _ [] = NONE | find_first pred (x :: xs) = if pred x then SOME x else find_first pred xs; (*get first element by lookup function*) fun get_first _ [] = NONE | get_first f (x :: xs) = (case f x of NONE => get_first f xs | some => some); fun get_index f = let fun get _ [] = NONE | get i (x :: xs) = case f x of NONE => get (i + 1) xs | SOME y => SOME (i, y) in get 0 end; val flat = List.concat; fun unflat (xs :: xss) ys = let val (ps, qs) = chop (length xs) ys in ps :: unflat xss qs end | unflat [] [] = [] | unflat _ _ = raise UnequalLengths; fun burrow f xss = unflat xss (f (flat xss)); fun fold_burrow f xss s = apfst (unflat xss) (f (flat xss) s); (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates (proc x1; ...; proc xn) for side effects*) val seq = List.app; (*separate s [x1, x2, ..., xn] ===> [x1, s, x2, s, ..., s, xn]*) fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs | separate _ xs = xs; (*make the list [x, x, ..., x] of length n*) fun replicate n (x: 'a) : 'a list = let fun rep (0, xs) = xs | rep (n, xs) = rep (n - 1, x :: xs) in if n < 0 then raise Subscript else rep (n, []) end; fun translate_string f = String.translate (f o String.str); (*multiply [a, b, c, ...] * [xs, ys, zs, ...]*) fun multiply [] _ = [] | multiply (x :: xs) yss = map (cons x) yss @ multiply xs yss; (*direct product*) fun product _ [] = [] | product [] _ = [] | product (x :: xs) ys = map (pair x) ys @ product xs ys; (* filter *) (*copy the list preserving elements that satisfy the predicate*) val filter = List.filter; fun filter_out f = filter (not o f); val map_filter = List.mapPartial; (* lists of pairs *) exception UnequalLengths; fun map2 _ [] [] = [] | map2 f (x :: xs) (y :: ys) = f x y :: map2 f xs ys | map2 _ _ _ = raise UnequalLengths; fun fold2 f = let fun fold_aux [] [] z = z | fold_aux (x :: xs) (y :: ys) z = fold_aux xs ys (f x y z) | fold_aux _ _ _ = raise UnequalLengths; in fold_aux end; fun zip_options (x :: xs) (SOME y :: ys) = (x, y) :: zip_options xs ys | zip_options (_ :: xs) (NONE :: ys) = zip_options xs ys | zip_options _ [] = [] | zip_options [] _ = raise UnequalLengths; (*combine two lists forming a list of pairs: [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*) fun [] ~~ [] = [] | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys) | _ ~~ _ = raise UnequalLengths; (*inverse of ~~; the old 'split': [(x1, y1), ..., (xn, yn)] ===> ([x1, ..., xn], [y1, ..., yn])*) val split_list = ListPair.unzip; (* prefixes, suffixes *) fun is_prefix _ [] _ = true | is_prefix eq (x :: xs) (y :: ys) = eq (x, y) andalso is_prefix eq xs ys | is_prefix eq _ _ = false; (* [x1, ..., xi, ..., xn] ---> ([x1, ..., x(i-1)], [xi, ..., xn]) where xi is the first element that does not satisfy the predicate*) fun take_prefix (pred : 'a -> bool) (xs: 'a list) : 'a list * 'a list = let fun take (rxs, []) = (rev rxs, []) | take (rxs, x :: xs) = if pred x then take(x :: rxs, xs) else (rev rxs, x :: xs) in take([], xs) end; fun chop_prefix eq ([], ys) = ([], ([], ys)) | chop_prefix eq (xs, []) = ([], (xs, [])) | chop_prefix eq (xs as x::xs', ys as y::ys') = if eq (x, y) then let val (ps', xys'') = chop_prefix eq (xs', ys') in (x::ps', xys'') end else ([], (xs, ys)); (* [x1, ..., xi, ..., xn] ---> ([x1, ..., xi], [x(i+1), ..., xn]) where xi is the last element that does not satisfy the predicate*) fun take_suffix _ [] = ([], []) | take_suffix pred (x :: xs) = (case take_suffix pred xs of ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx) | (prfx, sffx) => (x :: prfx, sffx)); fun prefixes1 [] = [] | prefixes1 (x :: xs) = map (cons x) ([] :: prefixes1 xs); fun prefixes xs = [] :: prefixes1 xs; fun suffixes1 xs = map rev (prefixes1 (rev xs)); fun suffixes xs = [] :: suffixes1 xs; (** integers **) fun gcd (x, y) = let fun gxd x y : IntInf.int = if y = IntInf.fromInt 0 then x else gxd y (x mod y) in if x < y then gxd y x else gxd x y end; fun lcm (x, y) = (x * y) div gcd (x, y); fun inc i = (i := ! i + 1; ! i); fun dec i = (i := ! i - 1; ! i); (* lists of integers *) (*make the list [from, from + 1, ..., to]*) fun (i upto j) = if i > j then [] else i :: (i + 1 upto j); (*make the list [from, from - 1, ..., to]*) fun (i downto j) = if i < j then [] else i :: (i - 1 downto j); (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*) fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1) | downto0 ([], n) = n = ~1; (* convert integers to strings *) (*expand the number in the given base; example: radixpand (2, 8) gives [1, 0, 0, 0]*) fun radixpand (base, num) : int list = let fun radix (n, tail) = if n < base then n :: tail else radix (n div base, (n mod base) :: tail) in radix (num, []) end; (*expands a number into a string of characters starting from "zerochar"; example: radixstring (2, "0", 8) gives "1000"*) fun radixstring (base, zerochar, num) = let val offset = ord zerochar; fun chrof n = chr (offset + n) in implode (map chrof (radixpand (base, num))) end; val string_of_int = Int.toString; fun signed_string_of_int i = if i < 0 then "-" ^ string_of_int (~ i) else string_of_int i; fun string_of_indexname (a,0) = a | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i; (* read integers *) fun read_intinf radix cs = let val zero = ord "0"; val limit = zero + radix; fun scan (num, []) = (num, []) | scan (num, c :: cs) = if zero <= ord c andalso ord c < limit then scan (IntInf.fromInt radix * num + IntInf.fromInt (ord c - zero), cs) else (num, c :: cs); in scan (IntInf.fromInt 0, cs) end; fun read_int cs = apfst IntInf.toInt (read_intinf 10 cs); fun oct_char s = chr (IntInf.toInt (#1 (read_intinf 8 (explode s)))); (** strings **) (* functions tuned for strings, avoiding explode *) fun nth_string str i = (case try String.substring (str, i, 1) of SOME s => s | NONE => raise Subscript); fun fold_string f str x0 = let val n = size str; fun iter (x, i) = if i < n then iter (f (String.substring (str, i, 1)) x, i + 1) else x; in iter (x0, 0) end; fun exists_string pred str = let val n = size str; fun ex i = i < n andalso (pred (String.substring (str, i, 1)) orelse ex (i + 1)); in ex 0 end; fun forall_string pred = not o exists_string (not o pred); (*enclose in brackets*) fun enclose lpar rpar str = lpar ^ str ^ rpar; fun unenclose str = String.substring (str, 1, size str - 2); (*simple quoting (does not escape special chars)*) val quote = enclose "\"" "\""; (*space_implode "..." (explode "hello") = "h...e...l...l...o"*) fun space_implode a bs = implode (separate a bs); val commas = space_implode ", "; val commas_quote = commas o map quote; (*concatenate messages, one per line, into a string*) val cat_lines = space_implode "\n"; (*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*) fun space_explode _ "" = [] | space_explode sep s = String.fields (fn c => str c = sep) s; val split_lines = space_explode "\n"; fun prefix_lines "" txt = txt | prefix_lines prfx txt = txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines; fun untabify chs = let val tab_width = 8; fun untab pos [] ys = rev ys | untab pos ("\n" :: xs) ys = untab 0 xs ("\n" :: ys) | untab pos ("\t" :: xs) ys = let val d = tab_width - (pos mod tab_width) in untab (pos + d) xs (replicate d " " @ ys) end | untab pos (c :: xs) ys = untab (pos + 1) xs (c :: ys); in if not (exists (fn c => c = "\t") chs) then chs else untab 0 chs [] end; fun prefix prfx s = prfx ^ s; fun suffix sffx s = s ^ sffx; fun unprefix prfx s = if String.isPrefix prfx s then String.substring (s, size prfx, size s - size prfx) else raise Fail "unprefix"; fun unsuffix sffx s = if String.isSuffix sffx s then String.substring (s, 0, size s - size sffx) else raise Fail "unsuffix"; fun replicate_string 0 _ = "" | replicate_string 1 a = a | replicate_string k a = if k mod 2 = 0 then replicate_string (k div 2) (a ^ a) else replicate_string (k div 2) (a ^ a) ^ a; (** lists as sets -- see also Pure/General/ord_list.ML **) (*canonical member, insert, remove*) fun member eq list x = let fun memb [] = false | memb (y :: ys) = eq (x, y) orelse memb ys; in memb list end; fun insert eq x xs = if member eq xs x then xs else x :: xs; fun remove eq x xs = if member eq xs x then filter_out (fn y => eq (x, y)) xs else xs; fun subtract eq = fold (remove eq); fun merge _ ([], ys) = ys | merge eq (xs, ys) = fold_rev (insert eq) ys xs; (*old-style infixes*) fun x mem xs = member (op =) xs x; fun (x: int) mem_int xs = member (op =) xs x; fun (x: string) mem_string xs = member (op =) xs x; (*union of sets represented as lists: no repetitions*) fun xs union [] = xs | [] union ys = ys | (x :: xs) union ys = xs union (insert (op =) x ys); (*union of sets, optimized version for ints*) fun (xs:int list) union_int [] = xs | [] union_int ys = ys | (x :: xs) union_int ys = xs union_int (insert (op =) x ys); (*union of sets, optimized version for strings*) fun (xs:string list) union_string [] = xs | [] union_string ys = ys | (x :: xs) union_string ys = xs union_string (insert (op =) x ys); (*generalized union*) fun gen_union eq (xs, []) = xs | gen_union eq ([], ys) = ys | gen_union eq (x :: xs, ys) = gen_union eq (xs, insert eq x ys); (*intersection*) fun [] inter ys = [] | (x :: xs) inter ys = if x mem ys then x :: (xs inter ys) else xs inter ys; (*intersection, optimized version for ints*) fun ([]:int list) inter_int ys = [] | (x :: xs) inter_int ys = if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys; (*intersection, optimized version for strings *) fun ([]:string list) inter_string ys = [] | (x :: xs) inter_string ys = if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys; (*generalized intersection*) fun gen_inter eq ([], ys) = [] | gen_inter eq (x::xs, ys) = if member eq ys x then x :: gen_inter eq (xs, ys) else gen_inter eq (xs, ys); (*subset*) fun [] subset ys = true | (x :: xs) subset ys = x mem ys andalso xs subset ys; (*subset, optimized version for ints*) fun ([]: int list) subset_int ys = true | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys; (*subset, optimized version for strings*) fun ([]: string list) subset_string ys = true | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys; (*set equality*) fun eq_set (xs, ys) = xs = ys orelse (xs subset ys andalso ys subset xs); (*set equality for strings*) fun eq_set_string ((xs: string list), ys) = xs = ys orelse (xs subset_string ys andalso ys subset_string xs); fun gen_subset eq (xs, ys) = forall (member eq ys) xs; fun gen_eq_set eq (xs, ys) = eq_list eq (xs, ys) orelse (gen_subset eq (xs, ys) andalso gen_subset (eq o swap) (ys, xs)); (*removing an element from a list WITHOUT duplicates*) fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x) | [] \ x = []; fun ys \\ xs = foldl (op \) (ys,xs); (*makes a list of the distinct members of the input; preserves order, takes first of equal elements*) fun distinct eq lst = let fun dist (rev_seen, []) = rev rev_seen | dist (rev_seen, x :: xs) = if member eq rev_seen x then dist (rev_seen, xs) else dist (x :: rev_seen, xs); in dist ([], lst) end; (*returns a list containing all repeated elements exactly once; preserves order, takes first of equal elements*) fun duplicates eq lst = let fun dups (rev_dups, []) = rev rev_dups | dups (rev_dups, x :: xs) = if member eq rev_dups x orelse not (member eq xs x) then dups (rev_dups, xs) else dups (x :: rev_dups, xs); in dups ([], lst) end; fun has_duplicates eq = let fun dups [] = false | dups (x :: xs) = member eq xs x orelse dups xs; in dups end; (** lists as multisets **) fun remove1 _ _ [] = raise Empty | remove1 eq y (x::xs) = if eq(y,x) then xs else x :: remove1 eq y xs; fun gen_submultiset _ ([], _) = true | gen_submultiset eq (x::xs, ys) = member eq ys x andalso gen_submultiset eq (xs, remove1 eq x ys); (** association lists -- legacy operations **) fun gen_merge_lists _ xs [] = xs | gen_merge_lists _ [] ys = ys | gen_merge_lists eq xs ys = xs @ filter_out (member eq xs) ys; fun merge_lists xs ys = gen_merge_lists (op =) xs ys; fun merge_alists xs = gen_merge_lists (eq_fst (op =)) xs; (** balanced trees **) exception Balance; (*indicates non-positive argument to balancing fun*) (*balanced folding; avoids deep nesting*) fun fold_bal f [x] = x | fold_bal f [] = raise Balance | fold_bal f xs = let val (ps, qs) = chop (length xs div 2) xs in f (fold_bal f ps, fold_bal f qs) end; (*construct something of the form f(...g(...(x)...)) for balanced access*) fun access_bal (f, g, x) n i = let fun acc n i = (*1<=i<=n*) if n=1 then x else let val n2 = n div 2 in if i<=n2 then f (acc n2 i) else g (acc (n-n2) (i-n2)) end in if 1<=i andalso i<=n then acc n i else raise Balance end; (*construct ALL such accesses; could try harder to share recursive calls!*) fun accesses_bal (f, g, x) n = let fun acc n = if n=1 then [x] else let val n2 = n div 2 val acc2 = acc n2 in if n-n2=n2 then map f acc2 @ map g acc2 else map f acc2 @ map g (acc (n-n2)) end in if 1<=n then acc n else raise Balance end; (** orders **) fun is_equal EQUAL = true | is_equal _ = false; fun rev_order LESS = GREATER | rev_order EQUAL = EQUAL | rev_order GREATER = LESS; (*assume rel is a linear strict order*) fun make_ord rel (x, y) = if rel (x, y) then LESS else if rel (y, x) then GREATER else EQUAL; val int_ord = Int.compare; val string_ord = String.compare; fun fast_string_ord (s1, s2) = (case int_ord (size s1, size s2) of EQUAL => string_ord (s1, s2) | ord => ord); fun option_ord ord (SOME x, SOME y) = ord (x, y) | option_ord _ (NONE, NONE) = EQUAL | option_ord _ (NONE, SOME _) = LESS | option_ord _ (SOME _, NONE) = GREATER; (*lexicographic product*) fun prod_ord a_ord b_ord ((x, y), (x', y')) = (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord); (*dictionary order -- in general NOT well-founded!*) fun dict_ord elem_ord (x :: xs, y :: ys) = (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord) | dict_ord _ ([], []) = EQUAL | dict_ord _ ([], _ :: _) = LESS | dict_ord _ (_ :: _, []) = GREATER; (*lexicographic product of lists*) fun list_ord elem_ord (xs, ys) = (case int_ord (length xs, length ys) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord); (* sorting *) (*quicksort -- stable, i.e. does not reorder equal elements*) fun quicksort unique ord = let fun qsort [] = [] | qsort (xs as [_]) = xs | qsort (xs as [x, y]) = (case ord (x, y) of LESS => xs | EQUAL => if unique then [x] else xs | GREATER => [y, x]) | qsort xs = let val (lts, eqs, gts) = part (nth xs (length xs div 2)) xs in qsort lts @ eqs @ qsort gts end and part _ [] = ([], [], []) | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs) and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts) | add EQUAL x (lts, [], gts) = (lts, [x], gts) | add EQUAL x (res as (lts, eqs, gts)) = if unique then res else (lts, x :: eqs, gts) | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); in qsort end; fun sort ord = quicksort false ord; fun sort_distinct ord = quicksort true ord; val sort_strings = sort string_ord; fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; (** random numbers **) exception RANDOM; fun rmod x y = x - y * Real.realFloor (x / y); local val a = 16807.0; val m = 2147483647.0; val random_seed = ref 1.0; in fun random () = let val r = rmod (a * !random_seed) m in (random_seed := r; r) end; end; fun random_range l h = if h < l orelse l < 0 then raise RANDOM else l + Real.floor (rmod (random ()) (real (h - l + 1))); fun one_of xs = nth xs (random_range 0 (length xs - 1)); fun frequency xs = let val sum = foldl op + (0, map fst xs); fun pick n ((k: int, x) :: xs) = if n <= k then x else pick (n - k) xs in pick (random_range 1 sum) xs end; (** current directory **) val cd = OS.FileSys.chDir; val pwd = OS.FileSys.getDir; (** misc **) fun divide_and_conquer decomp x = let val (ys, recomb) = decomp x in recomb (map (divide_and_conquer decomp) ys) end; (*Partition a list into buckets [ bi, b(i+1), ..., bj ] putting x in bk if p(k)(x) holds. Preserve order of elements if possible.*) fun partition_list p i j = let fun part k xs = if k>j then (case xs of [] => [] | _ => raise Fail "partition_list") else let val (ns, rest) = List.partition (p k) xs; in ns :: part(k+1)rest end in part i end; fun partition_eq (eq:'a * 'a -> bool) = let fun part [] = [] | part (x :: ys) = let val (xs, xs') = List.partition (fn y => eq (x, y)) ys in (x::xs)::(part xs') end in part end; (* generating identifiers *) (** Freshly generated identifiers; supplied prefix MUST start with a letter **) local (*Maps 0-61 to A-Z, a-z, 0-9; exclude _ or ' to avoid clash with internal/unusual indentifiers*) fun gensym_char i = if i<26 then chr (ord "A" + i) else if i<52 then chr (ord "a" + i - 26) else chr (ord "0" + i - 52); val char_vec = Vector.tabulate (62, gensym_char); fun newid n = implode (map (fn i => Vector.sub (char_vec, i)) (radixpand (62, n))); val gensym_seed = ref 0; in fun gensym pre = pre ^ newid (inc gensym_seed); end; (* stamps and serial numbers *) type stamp = unit ref; val stamp: unit -> stamp = ref; type serial = int; local val count = ref 0 in fun serial () = inc count end; val serial_string = string_of_int o serial; (* generic objects *) (*note that the builtin exception datatype may be extended by new constructors at any time*) structure Object = struct type T = exn end; end; structure BasicLibrary: BASIC_LIBRARY = Library; open BasicLibrary;