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@14826: rational numbers, strings, lists as sets, association lists, generic wenzelm@14826: tables, balanced trees, orders, current directory, misc. clasohm@0: *) clasohm@0: wenzelm@8418: infix |> |>> |>>> ~~ \ \\ ins ins_string ins_int orf andf prefix upto downto wenzelm@4212: mem mem_int mem_string union union_int union_string inter inter_int wenzelm@4212: inter_string subset subset_int subset_string; clasohm@1364: wenzelm@6510: infix 3 oo ooo oooo; wenzelm@5893: wenzelm@15745: signature BASIC_LIBRARY = wenzelm@4621: sig wenzelm@4621: (*functions*) wenzelm@4621: val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c wenzelm@4621: val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c wenzelm@4621: val I: 'a -> 'a wenzelm@4621: val K: 'a -> 'b -> 'a wenzelm@4621: val |> : 'a * ('a -> 'b) -> 'b wenzelm@8418: val |>> : ('a * 'b) * ('a -> 'c) -> 'c * 'b wenzelm@8418: val |>>> : ('a * 'b) * ('a -> 'c * 'd) -> 'c * ('b * 'd) wenzelm@4621: val apl: 'a * ('a * 'b -> 'c) -> 'b -> 'c wenzelm@4621: val apr: ('a * 'b -> 'c) * 'b -> 'a -> 'c wenzelm@4621: val funpow: int -> ('a -> 'a) -> 'a -> 'a wenzelm@5893: val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b wenzelm@5893: val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b wenzelm@6510: val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b clasohm@1364: wenzelm@4621: (*stamps*) wenzelm@4621: type stamp wenzelm@4621: val stamp: unit -> stamp wenzelm@4621: wenzelm@15670: (*old options -- invalidated*) wenzelm@15670: datatype invalid = None of invalid wenzelm@15670: exception OPTION of invalid wenzelm@15670: wenzelm@15970: (*options*) wenzelm@15970: val the: 'a option -> 'a wenzelm@15970: val if_none: 'a option -> 'a -> 'a wenzelm@15970: val is_some: 'a option -> bool wenzelm@15970: val is_none: 'a option -> bool wenzelm@15970: wenzelm@14826: exception ERROR wenzelm@6959: val try: ('a -> 'b) -> 'a -> 'b option wenzelm@4621: val can: ('a -> 'b) -> 'a -> bool wenzelm@14868: datatype 'a result = Result of 'a | Exn of exn wenzelm@14868: val capture: ('a -> 'b) -> 'a -> 'b result wenzelm@14868: val release: 'a result -> 'a wenzelm@14868: val get_result: 'a result -> 'a option wenzelm@14868: val get_exn: 'a result -> exn option wenzelm@4621: 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 wenzelm@4621: val eq_fst: (''a * 'b) * (''a * 'c) -> bool wenzelm@4621: val eq_snd: ('a * ''b) * ('c * ''b) -> 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@4621: val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c wenzelm@11853: val conditional: bool -> (unit -> unit) -> unit wenzelm@4621: wenzelm@4621: (*lists*) skalberg@15570: exception UnequalLengths wenzelm@4621: val cons: 'a -> 'a list -> 'a list wenzelm@5285: val single: 'a -> 'a list wenzelm@4629: val append: 'a list -> 'a list -> 'a list wenzelm@5904: val apply: ('a -> 'a) list -> 'a -> 'a wenzelm@14792: val fold: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b wenzelm@15035: val fold_rev: ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b wenzelm@4956: val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list wenzelm@15760: val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a oheimb@11002: val foldln: ('a * int -> 'b -> 'b) -> 'a list -> 'b -> 'b skalberg@15570: val unflat: 'a list list -> 'b list -> 'b list list nipkow@13629: val splitAt: int * 'a list -> 'a list * 'a list nipkow@4713: val dropwhile: ('a -> bool) -> 'a list -> 'a list wenzelm@11773: val map_nth_elem: int -> ('a -> 'a) -> 'a list -> 'a list wenzelm@4621: val split_last: 'a list -> 'a list * 'a wenzelm@4893: val nth_update: 'a -> int * 'a list -> 'a list 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 wenzelm@4916: val get_first: ('a -> 'b option) -> 'a list -> 'b option wenzelm@4621: val separate: 'a -> 'a list -> 'a list wenzelm@4621: val replicate: int -> 'a -> 'a list wenzelm@4621: val multiply: 'a list * 'a list list -> 'a list list wenzelm@14792: val product: 'a list -> 'b list -> ('a * 'b) list wenzelm@16129: val filter: ('a -> bool) -> 'a list -> 'a list wenzelm@4621: val filter_out: ('a -> bool) -> 'a list -> 'a list wenzelm@4621: val map2: ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list wenzelm@4621: val exists2: ('a * 'b -> bool) -> 'a list * 'b list -> bool wenzelm@4621: val forall2: ('a * 'b -> bool) -> 'a list * 'b list -> bool wenzelm@4956: val seq2: ('a * 'b -> unit) -> 'a list * 'b list -> unit wenzelm@4621: val ~~ : 'a list * 'b list -> ('a * 'b) list wenzelm@4621: val split_list: ('a * 'b) list -> 'a list * 'b list wenzelm@7468: val equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool wenzelm@4621: val prefix: ''a list * ''a list -> bool wenzelm@4621: val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list wenzelm@4621: val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list wenzelm@12249: val prefixes1: 'a list -> 'a list list wenzelm@12249: val suffixes1: 'a list -> 'a list list wenzelm@4621: wenzelm@4621: (*integers*) paulson@15965: val gcd: IntInf.int * IntInf.int -> IntInf.int paulson@15965: val lcm: IntInf.int * IntInf.int -> IntInf.int 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 downto0: int list * int -> bool 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@4621: val string_of_indexname: string * int -> string wenzelm@14826: val read_radixint: 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: nipkow@10692: (*rational numbers*) nipkow@10692: type rat wenzelm@14826: exception RAT of string paulson@15965: val rep_rat: rat -> IntInf.int * IntInf.int nipkow@10692: val ratadd: rat * rat -> rat nipkow@10692: val ratmul: rat * rat -> rat nipkow@10692: val ratinv: rat -> rat paulson@15965: val int_ratdiv: IntInf.int * IntInf.int -> rat nipkow@10692: val ratneg: rat -> rat nipkow@10692: val rat_of_int: int -> rat paulson@15965: val rat_of_intinf: IntInf.int -> rat nipkow@10692: wenzelm@4621: (*strings*) wenzelm@6312: val nth_elem_string: int * string -> 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@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@7712: val untabify: string list -> string list wenzelm@5285: val suffix: string -> string -> string wenzelm@5285: val unsuffix: string -> string -> string berghofe@15060: val unprefix: string -> string -> string wenzelm@10951: val replicate_string: int -> string -> string wenzelm@14926: val translate_string: (string -> string) -> string -> string wenzelm@4621: wenzelm@4621: (*lists as sets*) 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 gen_mem: ('a * 'b -> bool) -> 'a * 'b list -> bool wenzelm@4621: val ins: ''a * ''a list -> ''a list wenzelm@4621: val ins_int: int * int list -> int list wenzelm@4621: val ins_string: string * string list -> string list wenzelm@4621: val gen_ins: ('a * 'a -> bool) -> 'a * 'a list -> 'a list wenzelm@15760: val insert: ('a * 'a -> bool) -> 'a -> 'a list -> 'a list wenzelm@16129: val remove: ('b * 'a -> bool) -> 'b -> 'a list -> 'a list 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@4621: val \ : ''a list * ''a -> ''a list wenzelm@4621: val \\ : ''a list * ''a list -> ''a list wenzelm@4621: val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list wenzelm@4621: val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list wenzelm@4621: val gen_distinct: ('a * 'a -> bool) -> 'a list -> 'a list wenzelm@4621: val distinct: ''a list -> ''a list wenzelm@4621: val findrep: ''a list -> ''a list wenzelm@4621: val gen_duplicates: ('a * 'a -> bool) -> 'a list -> 'a list wenzelm@4621: val duplicates: ''a list -> ''a list wenzelm@4621: wenzelm@4621: (*association lists*) wenzelm@4621: val assoc: (''a * 'b) list * ''a -> 'b option wenzelm@4621: val assoc_int: (int * 'a) list * int -> 'a option wenzelm@4621: val assoc_string: (string * 'a) list * string -> 'a option wenzelm@4621: val assoc_string_int: ((string * int) * 'a) list * (string * int) -> 'a option wenzelm@4621: val assocs: (''a * 'b list) list -> ''a -> 'b list wenzelm@4621: val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) -> 'c option wenzelm@4621: val gen_assoc: ('a * 'b -> bool) -> ('b * 'c) list * 'a -> 'c option wenzelm@4621: val overwrite: (''a * 'b) list * (''a * 'b) -> (''a * 'b) list wenzelm@4621: val gen_overwrite: ('a * 'a -> bool) -> ('a * 'b) list * ('a * 'b) -> ('a * 'b) list wenzelm@4621: wenzelm@12284: (*lists as tables*) wenzelm@12284: val gen_merge_lists: ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list wenzelm@12284: val gen_merge_lists': ('a * 'a -> bool) -> 'a list -> 'a list -> 'a list wenzelm@4621: val merge_lists: ''a list -> ''a list -> ''a list wenzelm@12284: val merge_lists': ''a list -> ''a list -> ''a list wenzelm@4692: val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list berghofe@15263: val merge_alists': (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list wenzelm@4621: wenzelm@4621: (*balanced trees*) wenzelm@4621: exception Balance wenzelm@4621: val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a wenzelm@4621: val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a wenzelm@4621: val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list wenzelm@4621: wenzelm@4621: (*orders*) wenzelm@4621: val rev_order: order -> order wenzelm@4621: val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order wenzelm@4621: val int_ord: int * int -> order wenzelm@4621: val string_ord: string * string -> 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@4621: val sort_strings: string list -> string list wenzelm@4621: val sort_wrt: ('a -> string) -> 'a list -> 'a list berghofe@11514: val unique_strings: string list -> string 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@14826: (*current directory*) wenzelm@4621: val cd: string -> unit wenzelm@4621: val pwd: unit -> string wenzelm@4621: wenzelm@4621: (*misc*) wenzelm@4621: val make_keylist: ('a -> 'b) -> 'a list -> ('a * 'b) list wenzelm@4621: val keyfilter: ('a * ''b) list -> ''b -> 'a list 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@4621: val scanwords: (string -> bool) -> string list -> string list 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 nth_elem: int * 'a list -> 'a skalberg@15570: val last_elem: 'a list -> 'a skalberg@15570: val flat: 'a list list -> 'a list skalberg@15570: val seq: ('a -> unit) -> 'a list -> unit skalberg@15570: val partition: ('a -> bool) -> 'a list -> 'a list * 'a list skalberg@15570: val mapfilter: ('a -> 'b option) -> 'a list -> 'b list skalberg@15570: end; skalberg@15570: wenzelm@15745: structure Library: LIBRARY = clasohm@1364: struct clasohm@0: wenzelm@4995: wenzelm@233: (** functions **) clasohm@0: wenzelm@233: (*handy combinators*) wenzelm@233: fun curry f x y = f (x, y); wenzelm@233: fun uncurry f (x, y) = f x y; wenzelm@233: fun I x = x; wenzelm@233: fun K x y = x; clasohm@0: wenzelm@380: (*reverse apply*) wenzelm@410: fun (x |> f) = f x; wenzelm@8418: fun ((x, y) |>> f) = (f x, y); wenzelm@8418: fun ((x, y) |>>> f) = let val (x', z) = f x in (x', (y, z)) end; wenzelm@380: wenzelm@233: (*application of (infix) operator to its left or right argument*) wenzelm@233: fun apl (x, f) y = f (x, y); wenzelm@233: fun apr (f, y) x = f (x, y); clasohm@0: wenzelm@233: (*function exponentiation: f(...(f x)...) with n applications of f*) wenzelm@233: fun funpow n f x = wenzelm@233: let fun rep (0, x) = x wenzelm@233: | rep (n, x) = rep (n - 1, f x) wenzelm@233: in rep (n, x) end; wenzelm@160: wenzelm@5893: (*concatenation: 2 and 3 args*) wenzelm@5893: fun (f oo g) x y = f (g x y); wenzelm@5893: fun (f ooo g) x y z = f (g x y z); wenzelm@6510: fun (f oooo g) x y z w = f (g x y z w); wenzelm@6510: wenzelm@160: wenzelm@160: wenzelm@2471: (** stamps **) wenzelm@2471: wenzelm@2471: type stamp = unit ref; wenzelm@2471: val stamp: unit -> stamp = ref; wenzelm@2471: wenzelm@2471: wenzelm@2471: wenzelm@233: (** options **) clasohm@0: wenzelm@15670: (*invalidate former constructors to prevent accidental use as match-all patterns!*) wenzelm@15670: datatype invalid = None of invalid; wenzelm@15670: exception OPTION of invalid; clasohm@0: wenzelm@15970: val the = Option.valOf; wenzelm@15970: wenzelm@15970: (*strict!*) wenzelm@15970: fun if_none NONE y = y wenzelm@15970: | if_none (SOME x) _ = x; wenzelm@15970: wenzelm@15970: fun is_some (SOME _) = true wenzelm@15970: | is_some NONE = false; wenzelm@15970: wenzelm@15970: fun is_none (SOME _) = false wenzelm@15970: | is_none NONE = true; wenzelm@15970: wenzelm@6959: wenzelm@6959: (* exception handling *) wenzelm@6959: wenzelm@6959: exception ERROR; wenzelm@6959: skalberg@15531: fun try f x = SOME (f x) skalberg@15531: handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => NONE; wenzelm@6959: wenzelm@6959: fun can f x = is_some (try f x); wenzelm@4139: wenzelm@4139: wenzelm@14868: datatype 'a result = wenzelm@14868: Result of 'a | wenzelm@14868: Exn of exn; wenzelm@14868: wenzelm@14868: fun capture f x = Result (f x) handle e => Exn e; wenzelm@14868: wenzelm@14868: fun release (Result y) = y wenzelm@14868: | release (Exn e) = raise e; wenzelm@14868: skalberg@15531: fun get_result (Result x) = SOME x skalberg@15531: | get_result _ = NONE; wenzelm@14868: skalberg@15531: fun get_exn (Exn exn) = SOME exn skalberg@15531: | get_exn _ = NONE; wenzelm@14868: wenzelm@14868: wenzelm@4139: wenzelm@233: (** 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: wenzelm@233: fun eq_fst ((x1, _), (x2, _)) = x1 = x2; wenzelm@233: fun eq_snd ((_, y1), (_, y2)) = y1 = y2; wenzelm@233: wenzelm@233: fun swap (x, y) = (y, x); wenzelm@233: wenzelm@4212: (*apply function to components*) 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@233: wenzelm@233: (** booleans **) wenzelm@233: wenzelm@233: (* equality *) wenzelm@233: wenzelm@233: fun equal x y = x = y; wenzelm@233: fun not_equal x y = x <> y; wenzelm@233: wenzelm@233: wenzelm@233: (* operators for combining predicates *) wenzelm@233: paulson@2175: fun (p orf q) = fn x => p x orelse q x; paulson@2175: fun (p andf q) = fn x => p x andalso q x; wenzelm@233: wenzelm@233: wenzelm@233: (* predicates on lists *) wenzelm@233: wenzelm@233: (*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*) wenzelm@233: fun exists (pred: 'a -> bool) : 'a list -> bool = wenzelm@233: let fun boolf [] = false wenzelm@233: | boolf (x :: xs) = pred x orelse boolf xs wenzelm@233: in boolf end; wenzelm@233: wenzelm@233: (*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*) wenzelm@233: fun forall (pred: 'a -> bool) : 'a list -> bool = wenzelm@233: let fun boolf [] = true wenzelm@233: | boolf (x :: xs) = pred x andalso boolf xs wenzelm@233: in boolf end; clasohm@0: wenzelm@233: 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@9118: wenzelm@14826: (*temporarily set flag, handling exceptions*) wenzelm@2978: fun setmp flag value f x = wenzelm@2958: let wenzelm@2958: val orig_value = ! flag; wenzelm@2958: fun return y = (flag := orig_value; y); wenzelm@2958: in wenzelm@2958: flag := value; wenzelm@2958: return (f x handle exn => (return (); raise exn)) wenzelm@2958: end; wenzelm@2958: wenzelm@380: wenzelm@11853: (* conditional execution *) wenzelm@11853: wenzelm@11853: fun conditional b f = if b then f () else (); wenzelm@11853: wenzelm@11853: wenzelm@233: wenzelm@233: (** lists **) wenzelm@233: skalberg@15570: exception UnequalLengths; wenzelm@233: wenzelm@233: fun cons x xs = x :: xs; wenzelm@5285: fun single x = [x]; wenzelm@233: wenzelm@4629: fun append xs ys = xs @ ys; wenzelm@4629: wenzelm@5904: fun apply [] x = x wenzelm@5904: | apply (f :: fs) x = apply fs (f x); wenzelm@5904: wenzelm@233: wenzelm@233: (* fold *) wenzelm@233: wenzelm@15760: fun fold _ [] y = y wenzelm@15760: | fold f (x :: xs) y = fold f xs (f x y); wenzelm@15760: wenzelm@15760: fun fold_rev _ [] y = y wenzelm@15760: | fold_rev f (x :: xs) y = f x (fold_rev f xs y); wenzelm@15760: wenzelm@15760: fun foldl_map _ (x, []) = (x, []) wenzelm@15760: | foldl_map f (x, y :: ys) = wenzelm@15760: let wenzelm@15760: val (x', y') = f (x, y); wenzelm@15760: val (x'', ys') = foldl_map f (x', ys); wenzelm@15760: in (x'', y' :: ys') end; wenzelm@15760: 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: 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@233: fun foldr1 f l = wenzelm@4181: let fun itr [x] = x wenzelm@233: | itr (x::l) = f(x, itr l) wenzelm@233: in itr l end; wenzelm@233: wenzelm@15760: fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs)); wenzelm@14792: wenzelm@233: wenzelm@233: (* basic list functions *) wenzelm@233: wenzelm@233: (*take the first n elements from a list*) wenzelm@233: fun take (n, []) = [] 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@233: fun drop (n, []) = [] wenzelm@233: | drop (n, x :: xs) = wenzelm@233: if n > 0 then drop (n - 1, xs) else x :: xs; clasohm@0: nipkow@13629: fun splitAt(n,[]) = ([],[]) nipkow@13629: | splitAt(n,xs as x::ys) = nipkow@13629: if n>0 then let val (ps,qs) = splitAt(n-1,ys) in (x::ps,qs) end nipkow@13629: else ([],xs) nipkow@13629: 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@233: raise EXCEPTION if list too short*) skalberg@15570: fun nth_elem (i,xs) = List.nth(xs,i); wenzelm@233: wenzelm@11773: fun map_nth_elem 0 f (x :: xs) = f x :: xs wenzelm@11773: | map_nth_elem n f (x :: xs) = x :: map_nth_elem (n - 1) f xs skalberg@15570: | map_nth_elem _ _ [] = raise Subscript; wenzelm@11773: wenzelm@233: (*last element of a list*) 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@4893: (*update nth element*) nipkow@13629: fun nth_update x n_xs = nipkow@13629: (case splitAt n_xs of skalberg@15570: (_,[]) => raise Subscript nipkow@13629: | (prfx, _ :: sffx') => prfx @ (x :: sffx')) wenzelm@4893: wenzelm@4212: (*find the position of an element in a list*) wenzelm@4212: fun find_index pred = wenzelm@4212: let fun find _ [] = ~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*) skalberg@15531: fun find_first _ [] = NONE wenzelm@4212: | find_first pred (x :: xs) = skalberg@15531: if pred x then SOME x else find_first pred xs; 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: wenzelm@233: (*flatten a list of lists to a list*) skalberg@15531: val flat = List.concat; wenzelm@233: wenzelm@12136: fun unflat (xs :: xss) ys = nipkow@13629: let val (ps,qs) = splitAt(length xs,ys) nipkow@13629: in ps :: unflat xss qs end wenzelm@12136: | unflat [] [] = [] skalberg@15570: | unflat _ _ = raise UnequalLengths; wenzelm@12136: wenzelm@233: (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates wenzelm@233: (proc x1; ...; proc xn) for side effects*) skalberg@15570: val seq = List.app; wenzelm@233: 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@233: (*make the list [x, x, ..., x] of length n*) wenzelm@233: fun replicate n (x: 'a) : 'a list = 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@4248: fun multiply ([], _) = [] wenzelm@4248: | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss); wenzelm@4248: wenzelm@14792: (*direct product*) wenzelm@14792: fun product _ [] = [] wenzelm@14792: | product [] _ = [] wenzelm@14792: | product (x :: xs) ys = map (pair x) ys @ product xs ys; wenzelm@14792: wenzelm@233: wenzelm@233: (* filter *) wenzelm@233: wenzelm@233: (*copy the list preserving elements that satisfy the predicate*) skalberg@15531: val filter = List.filter; clasohm@0: fun filter_out f = filter (not o f); skalberg@15570: val mapfilter = List.mapPartial; wenzelm@233: wenzelm@233: wenzelm@233: (* lists of pairs *) wenzelm@233: skalberg@15570: exception UnequalLengths; skalberg@15570: wenzelm@380: fun map2 _ ([], []) = [] wenzelm@380: | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys)) skalberg@15570: | map2 _ _ = raise UnequalLengths; wenzelm@380: wenzelm@380: fun exists2 _ ([], []) = false wenzelm@380: | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys) skalberg@15570: | exists2 _ _ = raise UnequalLengths; wenzelm@380: wenzelm@380: fun forall2 _ ([], []) = true wenzelm@380: | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys) skalberg@15570: | forall2 _ _ = raise UnequalLengths; wenzelm@380: wenzelm@4956: fun seq2 _ ([], []) = () wenzelm@4956: | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys)) skalberg@15570: | seq2 _ _ = 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@7468: fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys); wenzelm@7468: wenzelm@233: wenzelm@233: (* prefixes, suffixes *) wenzelm@233: wenzelm@233: fun [] prefix _ = true wenzelm@233: | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys) wenzelm@233: | _ prefix _ = 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: 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@12249: fun suffixes1 xs = map rev (prefixes1 (rev xs)); wenzelm@12249: wenzelm@233: wenzelm@233: wenzelm@233: (** integers **) wenzelm@233: nipkow@10692: fun gcd(x,y) = paulson@15965: let fun gxd x y : IntInf.int = nipkow@10692: if y = 0 then x else gxd y (x mod y) nipkow@10692: in if x < y then gxd y x else gxd x y end; nipkow@10692: nipkow@10692: fun lcm(x,y) = (x * y) div gcd(x,y); nipkow@10692: wenzelm@2958: fun inc i = (i := ! i + 1; ! i); wenzelm@2958: fun dec i = (i := ! i - 1; ! i); wenzelm@233: wenzelm@233: wenzelm@233: (* lists of integers *) wenzelm@233: wenzelm@233: (*make the list [from, from + 1, ..., to]*) paulson@2175: fun (from upto to) = wenzelm@233: if from > to then [] else from :: ((from + 1) upto to); wenzelm@233: wenzelm@233: (*make the list [from, from - 1, ..., to]*) paulson@2175: fun (from downto to) = wenzelm@233: if from < to then [] else from :: ((from - 1) downto to); wenzelm@233: wenzelm@233: (*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*) wenzelm@233: fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1) wenzelm@233: | downto0 ([], n) = n = ~1; 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: paulson@3407: fun string_of_indexname (a,0) = a paulson@3407: | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i; wenzelm@233: wenzelm@233: wenzelm@14826: (* read integers *) wenzelm@14826: wenzelm@14826: fun read_radixint (radix: int, cs) : int * string list = wenzelm@14826: let val zero = ord"0" wenzelm@14826: val limit = zero+radix wenzelm@14826: fun scan (num,[]) = (num,[]) wenzelm@14826: | scan (num, c::cs) = wenzelm@14826: if zero <= ord c andalso ord c < limit wenzelm@14826: then scan(radix*num + ord c - zero, cs) wenzelm@14826: else (num, c::cs) wenzelm@14826: in scan(0,cs) end; wenzelm@14826: wenzelm@14826: fun read_int cs = read_radixint (10, cs); wenzelm@14826: wenzelm@14826: fun oct_char s = chr (#1 (read_radixint (8, explode s))); wenzelm@14826: wenzelm@14826: wenzelm@14826: wenzelm@233: (** strings **) wenzelm@233: wenzelm@16188: (* functions tuned for strings, avoiding explode *) wenzelm@6312: wenzelm@6312: fun nth_elem_string (i, str) = 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: 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 _ "" = [] wenzelm@3832: | space_explode sep str = wenzelm@3832: let wenzelm@3832: fun expl chs = wenzelm@3832: (case take_prefix (not_equal sep) chs of wenzelm@3832: (cs, []) => [implode cs] wenzelm@3832: | (cs, _ :: cs') => implode cs :: expl cs'); wenzelm@3832: in expl (explode str) end; 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@7712: fun untabify chs = wenzelm@7712: let wenzelm@7712: val tab_width = 8; wenzelm@7712: wenzelm@7712: fun untab (_, "\n") = (0, ["\n"]) wenzelm@9118: | untab (pos, "\t") = wenzelm@9118: let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end wenzelm@7712: | untab (pos, c) = (pos + 1, [c]); wenzelm@7712: in wenzelm@7712: if not (exists (equal "\t") chs) then chs wenzelm@7712: else flat (#2 (foldl_map untab (0, chs))) wenzelm@7712: end; wenzelm@7712: wenzelm@16188: fun suffix sffx s = s ^ sffx; wenzelm@5285: wenzelm@16188: fun unsuffix sffx s = wenzelm@16188: let val m = size sffx; val n = size s - m in wenzelm@16188: if n >= 0 andalso String.substring (s, n, m) = sffx then String.substring (s, 0, n) skalberg@15570: else raise Fail "unsuffix" wenzelm@5285: end; wenzelm@5285: berghofe@15060: fun unprefix prfx s = wenzelm@16188: let val m = size prfx; val n = size s - m in wenzelm@16188: if String.isPrefix prfx s then String.substring (s, m, n) skalberg@15570: else raise Fail "unprefix" berghofe@15060: end; berghofe@15060: wenzelm@10951: fun replicate_string 0 _ = "" 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@3832: wenzelm@233: wenzelm@233: (** lists as sets **) wenzelm@233: wenzelm@233: (*membership in a list*) wenzelm@233: fun x mem [] = false wenzelm@233: | x mem (y :: ys) = x = y orelse x mem ys; clasohm@0: paulson@2175: (*membership in a list, optimized version for ints*) berghofe@1576: fun (x:int) mem_int [] = false berghofe@1576: | x mem_int (y :: ys) = x = y orelse x mem_int ys; berghofe@1576: paulson@2175: (*membership in a list, optimized version for strings*) berghofe@1576: fun (x:string) mem_string [] = false berghofe@1576: | x mem_string (y :: ys) = x = y orelse x mem_string ys; berghofe@1576: clasohm@0: (*generalized membership test*) wenzelm@233: fun gen_mem eq (x, []) = false wenzelm@233: | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys); wenzelm@233: wenzelm@15760: (*insert and remove*) wenzelm@15760: fun insert eq x xs = if gen_mem eq (x, xs) then xs else x :: xs; wenzelm@15760: fun remove eq x xs = if gen_mem eq (x, xs) then filter_out (fn y => eq (x, y)) xs else xs; wenzelm@233: wenzelm@233: (*insertion into list if not already there*) paulson@2175: fun (x ins xs) = if x mem xs then xs else x :: xs; clasohm@0: paulson@2175: (*insertion into list, optimized version for ints*) paulson@2175: fun (x ins_int xs) = if x mem_int xs then xs else x :: xs; berghofe@1576: paulson@2175: (*insertion into list, optimized version for strings*) paulson@2175: fun (x ins_string xs) = if x mem_string xs then xs else x :: xs; berghofe@1576: clasohm@0: (*generalized insertion*) wenzelm@15760: fun gen_ins eq (x, xs) = insert eq x xs; wenzelm@233: wenzelm@233: (*union of sets represented as lists: no repetitions*) wenzelm@233: fun xs union [] = xs wenzelm@233: | [] union ys = ys wenzelm@233: | (x :: xs) union ys = xs union (x ins 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 berghofe@1576: | (x :: xs) union_int ys = xs union_int (x ins_int 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 berghofe@1576: | (x :: xs) union_string ys = xs union_string (x ins_string ys); berghofe@1576: clasohm@0: (*generalized union*) wenzelm@233: fun gen_union eq (xs, []) = xs wenzelm@233: | gen_union eq ([], ys) = ys wenzelm@233: | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins 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) = paulson@7090: if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys) wenzelm@12284: 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*) berghofe@1576: 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*) berghofe@1576: 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*) berghofe@1576: fun eq_set_string ((xs:string list), ys) = berghofe@1576: xs = ys orelse (xs subset_string ys andalso ys subset_string xs); berghofe@1576: paulson@2182: fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs; paulson@2182: 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 = []; wenzelm@233: paulson@2243: fun ys \\ xs = foldl (op \) (ys,xs); clasohm@0: wenzelm@233: (*removing an element from a list -- possibly WITH duplicates*) wenzelm@233: fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs; wenzelm@12295: fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs; wenzelm@233: wenzelm@233: (*makes a list of the distinct members of the input; preserves order, takes wenzelm@233: first of equal elements*) wenzelm@233: fun gen_distinct eq lst = wenzelm@233: let wenzelm@233: val memb = gen_mem eq; clasohm@0: wenzelm@233: fun dist (rev_seen, []) = rev rev_seen wenzelm@233: | dist (rev_seen, x :: xs) = wenzelm@233: if memb (x, rev_seen) then dist (rev_seen, xs) wenzelm@233: else dist (x :: rev_seen, xs); wenzelm@233: in wenzelm@233: dist ([], lst) wenzelm@233: end; wenzelm@233: paulson@2243: fun distinct l = gen_distinct (op =) l; wenzelm@233: wenzelm@233: wenzelm@233: (*returns the tail beginning with the first repeated element, or []*) wenzelm@233: fun findrep [] = [] wenzelm@233: | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs; wenzelm@233: wenzelm@233: wenzelm@255: (*returns a list containing all repeated elements exactly once; preserves wenzelm@255: order, takes first of equal elements*) wenzelm@255: fun gen_duplicates eq lst = wenzelm@255: let wenzelm@255: val memb = gen_mem eq; wenzelm@255: wenzelm@255: fun dups (rev_dups, []) = rev rev_dups wenzelm@255: | dups (rev_dups, x :: xs) = wenzelm@255: if memb (x, rev_dups) orelse not (memb (x, xs)) then wenzelm@255: dups (rev_dups, xs) wenzelm@255: else dups (x :: rev_dups, xs); wenzelm@255: in wenzelm@255: dups ([], lst) wenzelm@255: end; wenzelm@255: paulson@2243: fun duplicates l = gen_duplicates (op =) l; wenzelm@255: wenzelm@255: wenzelm@233: wenzelm@233: (** association lists **) clasohm@0: wenzelm@233: (*association list lookup*) skalberg@15531: fun assoc ([], key) = NONE wenzelm@233: | assoc ((keyi, xi) :: pairs, key) = skalberg@15531: if key = keyi then SOME xi else assoc (pairs, key); wenzelm@233: paulson@2175: (*association list lookup, optimized version for ints*) skalberg@15531: fun assoc_int ([], (key:int)) = NONE berghofe@1576: | assoc_int ((keyi, xi) :: pairs, key) = skalberg@15531: if key = keyi then SOME xi else assoc_int (pairs, key); berghofe@1576: paulson@2175: (*association list lookup, optimized version for strings*) skalberg@15531: fun assoc_string ([], (key:string)) = NONE berghofe@1576: | assoc_string ((keyi, xi) :: pairs, key) = skalberg@15531: if key = keyi then SOME xi else assoc_string (pairs, key); berghofe@1576: paulson@2175: (*association list lookup, optimized version for string*ints*) skalberg@15531: fun assoc_string_int ([], (key:string*int)) = NONE berghofe@1576: | assoc_string_int ((keyi, xi) :: pairs, key) = skalberg@15531: if key = keyi then SOME xi else assoc_string_int (pairs, key); berghofe@1576: wenzelm@233: fun assocs ps x = wenzelm@233: (case assoc (ps, x) of skalberg@15531: NONE => [] skalberg@15531: | SOME ys => ys); wenzelm@233: wenzelm@255: (*two-fold association list lookup*) wenzelm@255: fun assoc2 (aal, (key1, key2)) = wenzelm@255: (case assoc (aal, key1) of skalberg@15531: SOME al => assoc (al, key2) skalberg@15531: | NONE => NONE); wenzelm@255: wenzelm@233: (*generalized association list lookup*) skalberg@15531: fun gen_assoc eq ([], key) = NONE wenzelm@233: | gen_assoc eq ((keyi, xi) :: pairs, key) = skalberg@15531: if eq (key, keyi) then SOME xi else gen_assoc eq (pairs, key); wenzelm@233: wenzelm@233: (*association list update*) wenzelm@233: fun overwrite (al, p as (key, _)) = wenzelm@233: let fun over ((q as (keyi, _)) :: pairs) = wenzelm@233: if keyi = key then p :: pairs else q :: (over pairs) wenzelm@233: | over [] = [p] wenzelm@233: in over al end; wenzelm@233: wenzelm@2522: fun gen_overwrite eq (al, p as (key, _)) = wenzelm@2522: let fun over ((q as (keyi, _)) :: pairs) = wenzelm@2522: if eq (keyi, key) then p :: pairs else q :: (over pairs) wenzelm@2522: | over [] = [p] wenzelm@2522: in over al end; wenzelm@2522: wenzelm@233: wenzelm@12284: (* lists as tables *) wenzelm@233: wenzelm@12284: fun gen_merge_lists _ xs [] = xs wenzelm@12284: | gen_merge_lists _ [] ys = ys wenzelm@12284: | gen_merge_lists eq xs ys = xs @ gen_rems eq (ys, xs); clasohm@0: wenzelm@12284: fun gen_merge_lists' _ xs [] = xs wenzelm@12284: | gen_merge_lists' _ [] ys = ys wenzelm@12295: | gen_merge_lists' eq xs ys = gen_rems eq (ys, xs) @ xs; clasohm@0: wenzelm@12284: fun merge_lists xs ys = gen_merge_lists (op =) xs ys; wenzelm@12284: fun merge_lists' xs ys = gen_merge_lists' (op =) xs ys; wenzelm@12284: fun merge_alists al = gen_merge_lists eq_fst al; berghofe@15263: fun merge_alists' al = gen_merge_lists' eq_fst al; wenzelm@380: clasohm@0: clasohm@0: wenzelm@233: (** balanced trees **) wenzelm@233: wenzelm@233: exception Balance; (*indicates non-positive argument to balancing fun*) wenzelm@233: wenzelm@233: (*balanced folding; avoids deep nesting*) wenzelm@233: fun fold_bal f [x] = x wenzelm@233: | fold_bal f [] = raise Balance wenzelm@233: | fold_bal f xs = nipkow@13629: let val (ps,qs) = splitAt(length xs div 2, xs) nipkow@13629: in f (fold_bal f ps, fold_bal f qs) end; wenzelm@233: wenzelm@233: (*construct something of the form f(...g(...(x)...)) for balanced access*) wenzelm@233: fun access_bal (f, g, x) n i = wenzelm@233: let fun acc n i = (*1<=i<=n*) wenzelm@233: if n=1 then x else wenzelm@233: let val n2 = n div 2 wenzelm@233: in if i<=n2 then f (acc n2 i) wenzelm@233: else g (acc (n-n2) (i-n2)) wenzelm@233: end wenzelm@233: in if 1<=i andalso i<=n then acc n i else raise Balance end; wenzelm@233: wenzelm@233: (*construct ALL such accesses; could try harder to share recursive calls!*) wenzelm@233: fun accesses_bal (f, g, x) n = wenzelm@233: let fun acc n = wenzelm@233: if n=1 then [x] else wenzelm@233: let val n2 = n div 2 wenzelm@233: val acc2 = acc n2 wenzelm@233: in if n-n2=n2 then map f acc2 @ map g acc2 wenzelm@233: else map f acc2 @ map g (acc (n-n2)) end wenzelm@233: in if 1<=n then acc n else raise Balance end; wenzelm@233: wenzelm@233: wenzelm@233: wenzelm@2506: (** orders **) wenzelm@2506: 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@15051: val int_ord = Int.compare; wenzelm@15051: val string_ord = String.compare; wenzelm@2506: 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@4343: fun dict_ord _ ([], []) = EQUAL wenzelm@4343: | dict_ord _ ([], _ :: _) = LESS wenzelm@4343: | dict_ord _ (_ :: _, []) = GREATER wenzelm@4343: | dict_ord elem_ord (x :: xs, y :: ys) = wenzelm@4343: (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord); wenzelm@4343: wenzelm@4343: (*lexicographic product of lists*) wenzelm@4343: fun list_ord elem_ord (xs, ys) = wenzelm@4343: prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys)); wenzelm@4343: wenzelm@2506: wenzelm@4621: (* sorting *) wenzelm@4621: wenzelm@4621: (*quicksort (stable, i.e. does not reorder equal elements)*) wenzelm@4621: fun sort ord = wenzelm@4621: let wenzelm@4621: fun qsort xs = wenzelm@4621: let val len = length xs in wenzelm@4621: if len <= 1 then xs wenzelm@4621: else wenzelm@4621: let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in wenzelm@4621: qsort lts @ eqs @ qsort gts wenzelm@4621: end wenzelm@4621: 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@4621: | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts) wenzelm@4621: | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts); wenzelm@4621: in qsort end; wenzelm@4621: wenzelm@4621: (*sort strings*) wenzelm@4621: val sort_strings = sort string_ord; wenzelm@4621: fun sort_wrt sel xs = sort (string_ord o pairself sel) xs; wenzelm@4621: berghofe@11514: fun unique_strings ([]: string list) = [] berghofe@11514: | unique_strings [x] = [x] berghofe@11514: | unique_strings (x :: y :: ys) = berghofe@11514: if x = y then unique_strings (y :: ys) berghofe@11514: else x :: unique_strings (y :: ys); 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: berghofe@14106: fun random () = berghofe@14106: let val r = rmod (a * !random_seed) m berghofe@14106: 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: berghofe@14106: fun one_of xs = nth_elem (random_range 0 (length xs - 1), xs); berghofe@14106: berghofe@14106: fun frequency xs = berghofe@14106: let berghofe@14106: val sum = foldl op + (0, map fst xs); berghofe@14106: fun pick n ((k, 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@14826: (** current directory **) wenzelm@233: paulson@2243: val cd = OS.FileSys.chDir; wenzelm@2317: val pwd = OS.FileSys.getDir; paulson@2243: berghofe@3606: wenzelm@233: nipkow@10692: (** rational numbers **) nipkow@10692: paulson@15965: datatype rat = Rat of bool * IntInf.int * IntInf.int nipkow@10692: wenzelm@14826: exception RAT of string; wenzelm@14826: nipkow@10692: fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q) nipkow@10692: nipkow@10692: fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else nipkow@10692: let val absp = abs p nipkow@10692: val m = gcd(absp,q) nipkow@10692: in Rat(a = (0 <= p), absp div m, q div m) end; nipkow@10692: nipkow@10692: fun ratadd(Rat(a,p,q),Rat(b,r,s)) = nipkow@10692: let val den = lcm(q,s) nipkow@10692: val p = p*(den div q) and r = r*(den div s) nipkow@10692: val num = (if a then p else ~p) + (if b then r else ~r) nipkow@10692: in ratnorm(true,num,den) end; nipkow@10692: nipkow@10692: fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s) nipkow@10692: wenzelm@14826: fun ratinv(Rat(a,p,q)) = if p=0 then raise RAT "ratinv" else Rat(a,q,p) nipkow@10692: nipkow@10692: fun int_ratdiv(p,q) = wenzelm@14826: if q=0 then raise RAT "int_ratdiv" else ratnorm(0<=q, p, abs q) nipkow@10692: nipkow@10692: fun ratneg(Rat(b,p,q)) = Rat(not b,p,q); nipkow@10692: paulson@15965: fun rat_of_intinf i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1); paulson@15965: paulson@15965: fun rat_of_int i = rat_of_intinf (IntInf.fromInt i); nipkow@10692: nipkow@10692: wenzelm@4621: (** misc **) wenzelm@233: wenzelm@233: (*use the keyfun to make a list of (x, key) pairs*) clasohm@0: fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list = wenzelm@233: let fun keypair x = (x, keyfun x) wenzelm@233: in map keypair end; clasohm@0: wenzelm@233: (*given a list of (x, key) pairs and a searchkey clasohm@0: return the list of xs from each pair whose key equals searchkey*) clasohm@0: fun keyfilter [] searchkey = [] wenzelm@233: | keyfilter ((x, key) :: pairs) searchkey = wenzelm@233: if key = searchkey then x :: keyfilter pairs searchkey wenzelm@233: else keyfilter pairs searchkey; clasohm@0: clasohm@0: clasohm@0: (*Partition list into elements that satisfy predicate and those that don't. wenzelm@233: Preserves order of elements in both lists.*) skalberg@15570: val partition = List.partition; clasohm@0: clasohm@0: clasohm@0: fun partition_eq (eq:'a * 'a -> bool) = clasohm@0: let fun part [] = [] wenzelm@233: | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys wenzelm@233: in (x::xs)::(part xs') end clasohm@0: in part end; clasohm@0: 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@233: let val (ns, rest) = partition (p k) xs; wenzelm@233: in ns :: part(k+1)rest end clasohm@0: in part i end; clasohm@0: clasohm@0: wenzelm@233: (* generating identifiers *) clasohm@0: paulson@4063: (** Freshly generated identifiers; supplied prefix MUST start with a letter **) clasohm@0: local paulson@4063: (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*) paulson@4063: fun char i = if i<26 then chr (ord "A" + i) wenzelm@5904: else if i<52 then chr (ord "a" + i - 26) wenzelm@5904: else if i<62 then chr (ord"0" + i - 52) wenzelm@5904: else if i=62 then "_" wenzelm@5904: else (*i=63*) "'"; paulson@4063: paulson@4063: val charVec = Vector.tabulate (64, char); paulson@4063: wenzelm@5904: fun newid n = wenzelm@5904: let wenzelm@4284: in implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n))) end; paulson@2003: wenzelm@4284: val seedr = ref 0; clasohm@0: paulson@4063: in wenzelm@4284: wenzelm@12346: fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr)); paulson@2003: paulson@4063: end; paulson@4063: paulson@4063: wenzelm@233: (* lexical scanning *) clasohm@0: wenzelm@233: (*scan a list of characters into "words" composed of "letters" (recognized by wenzelm@233: is_let) and separated by any number of non-"letters"*) wenzelm@233: fun scanwords is_let cs = clasohm@0: let fun scan1 [] = [] wenzelm@233: | scan1 cs = wenzelm@233: let val (lets, rest) = take_prefix is_let cs wenzelm@233: in implode lets :: scanwords is_let rest end; wenzelm@233: in scan1 (#2 (take_prefix (not o is_let) cs)) end; clasohm@24: wenzelm@4212: clasohm@1364: end; clasohm@1364: wenzelm@15745: structure BasicLibrary: BASIC_LIBRARY = Library; wenzelm@15745: open BasicLibrary;