wenzelm@41: (*  Title:      Pure/library.ML
clasohm@0:     ID:         $Id$
wenzelm@233:     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0:     Copyright   1992  University of Cambridge
clasohm@0: 
wenzelm@233: Basic library: functions, options, pairs, booleans, lists, integers,
wenzelm@233: strings, lists as sets, association lists, generic tables, balanced trees,
wenzelm@233: input / output, timing, filenames, misc functions.
clasohm@0: *)
clasohm@0: 
berghofe@1576: infix |> ~~ \ \\ orelf ins ins_string ins_int orf andf prefix upto downto
berghofe@1576:       mem mem_int mem_string union union_string union_int inter inter_int
berghofe@1576:       inter_string subset subset_int subset_string subdir_of;
clasohm@1364: 
clasohm@1364: 
clasohm@1364: structure Library =
clasohm@1364: struct
clasohm@0: 
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@380: 
wenzelm@233: (*combine two functions forming the union of their domains*)
wenzelm@233: fun f orelf g = fn x => f x handle Match => g x;
clasohm@0: 
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: (*functional for pairs*)
wenzelm@233: fun pairself f (x, y) = (f x, f 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@160: 
wenzelm@160: 
wenzelm@233: (** options **)
clasohm@0: 
clasohm@0: datatype 'a option = None | Some of 'a;
clasohm@0: 
clasohm@0: exception OPTION of string;
clasohm@0: 
clasohm@0: fun the (Some x) = x
clasohm@0:   | the None = raise OPTION "the";
clasohm@0: 
wenzelm@255: fun if_none None y = y
wenzelm@255:   | if_none (Some x) _ = x;
wenzelm@255: 
clasohm@0: fun is_some (Some _) = true
clasohm@0:   | is_some None = false;
clasohm@0: 
clasohm@0: fun is_none (Some _) = false
clasohm@0:   | is_none None = true;
clasohm@0: 
wenzelm@233: fun apsome f (Some x) = Some (f x)
wenzelm@233:   | apsome _ None = None;
clasohm@0: 
wenzelm@233: 
wenzelm@233: 
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@233: (*apply the function to a component of a pair*)
wenzelm@233: fun apfst f (x, y) = (f x, y);
wenzelm@233: fun apsnd f (x, y) = (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: 
wenzelm@233: fun p orf q = fn x => p x orelse q x;
wenzelm@233: 
wenzelm@233: fun p andf q = fn x => p x andalso q x;
wenzelm@233: 
wenzelm@233: fun notf p x = not (p x);
clasohm@0: 
wenzelm@233: 
wenzelm@233: (* predicates on lists *)
wenzelm@233: 
wenzelm@233: fun orl [] = false
wenzelm@233:   | orl (x :: xs) = x orelse orl xs;
wenzelm@233: 
wenzelm@233: fun andl [] = true
wenzelm@233:   | andl (x :: xs) = x andalso andl xs;
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@380: 
wenzelm@233: 
wenzelm@233: (** lists **)
wenzelm@233: 
wenzelm@233: exception LIST of string;
wenzelm@233: 
wenzelm@233: fun null [] = true
wenzelm@233:   | null (_ :: _) = false;
wenzelm@233: 
wenzelm@233: fun hd [] = raise LIST "hd"
wenzelm@233:   | hd (x :: _) = x;
wenzelm@233: 
wenzelm@233: fun tl [] = raise LIST "tl"
wenzelm@233:   | tl (_ :: xs) = xs;
wenzelm@233: 
wenzelm@233: fun cons x xs = x :: xs;
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (* fold *)
wenzelm@233: 
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@233:   let fun itr [x] = x                       (* FIXME [] case: elim warn (?) *)
wenzelm@233:         | itr (x::l) = f(x, itr l)
wenzelm@233:   in  itr l  end;
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (* basic list functions *)
wenzelm@233: 
wenzelm@233: (*length of a list, should unquestionably be a standard function*)
wenzelm@233: local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233:         | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233: in  fun length l = length1 (0, l) end;
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: 
wenzelm@233: (*return nth element of a list, where 0 designates the first element;
wenzelm@233:   raise EXCEPTION if list too short*)
wenzelm@233: fun nth_elem NL =
wenzelm@233:   (case drop NL of
wenzelm@233:     [] => raise LIST "nth_elem"
wenzelm@233:   | x :: _ => x);
wenzelm@233: 
wenzelm@233: (*last element of a list*)
wenzelm@233: fun last_elem [] = raise LIST "last_elem"
wenzelm@233:   | last_elem [x] = x
wenzelm@233:   | last_elem (_ :: xs) = last_elem xs;
wenzelm@233: 
wenzelm@233: (*find the position of an element in a list*)
wenzelm@233: fun find (x, ys) =
wenzelm@233:   let fun f (y :: ys, i) = if x = y then i else f (ys, i + 1)
wenzelm@233:         | f (_, _) = raise LIST "find"
wenzelm@233:   in f (ys, 0) end;
wenzelm@233: 
wenzelm@233: (*flatten a list of lists to a list*)
wenzelm@233: fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233:   (proc x1; ...; proc xn) for side effects*)
wenzelm@233: fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233:   let fun seqf [] = ()
wenzelm@233:         | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233:   in seqf end;
wenzelm@233: 
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
wenzelm@233:     if n < 0 then raise LIST "replicate"
wenzelm@233:     else rep (n, [])
wenzelm@233:   end;
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (* filter *)
wenzelm@233: 
wenzelm@233: (*copy the list preserving elements that satisfy the predicate*)
wenzelm@233: fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0:   let fun filt [] = []
wenzelm@233:         | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233:   in filt end;
clasohm@0: 
clasohm@0: fun filter_out f = filter (not o f);
clasohm@0: 
clasohm@0: 
wenzelm@233: fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233:   | mapfilter f (x :: xs) =
wenzelm@233:       (case f x of
wenzelm@233:         None => mapfilter f xs
wenzelm@233:       | Some y => y :: mapfilter f xs);
wenzelm@233: 
wenzelm@233: 
wenzelm@380: fun find_first _ [] = None
wenzelm@380:   | find_first pred (x :: xs) =
wenzelm@380:       if pred x then Some x else find_first pred xs;
wenzelm@380: 
wenzelm@380: 
wenzelm@233: (* lists of pairs *)
wenzelm@233: 
wenzelm@380: fun map2 _ ([], []) = []
wenzelm@380:   | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380:   | map2 _ _ = raise LIST "map2";
wenzelm@380: 
wenzelm@380: fun exists2 _ ([], []) = false
wenzelm@380:   | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380:   | exists2 _ _ = raise LIST "exists2";
wenzelm@380: 
wenzelm@380: fun forall2 _ ([], []) = true
wenzelm@380:   | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380:   | forall2 _ _ = raise LIST "forall2";
wenzelm@380: 
wenzelm@233: (*combine two lists forming a list of pairs:
wenzelm@233:   [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233: fun [] ~~ [] = []
wenzelm@233:   | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233:   | _ ~~ _ = raise LIST "~~";
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (*inverse of ~~; the old 'split':
wenzelm@233:   [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233: fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233: 
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@233: 
wenzelm@233: 
wenzelm@233: (** integers **)
wenzelm@233: 
wenzelm@233: fun inc i = i := ! i + 1;
wenzelm@233: fun dec i = i := ! i - 1;
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (* lists of integers *)
wenzelm@233: 
wenzelm@233: (*make the list [from, from + 1, ..., to]*)
wenzelm@233: 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]*)
wenzelm@233: 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: 
wenzelm@233: fun string_of_int n =
wenzelm@233:   if n < 0 then "~" ^ radixstring (10, "0", ~n) else radixstring (10, "0", n);
wenzelm@233: 
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (** strings **)
wenzelm@233: 
wenzelm@233: fun is_letter ch =
wenzelm@233:   ord "A" <= ord ch andalso ord ch <= ord "Z" orelse
wenzelm@233:   ord "a" <= ord ch andalso ord ch <= ord "z";
wenzelm@233: 
wenzelm@233: fun is_digit ch =
wenzelm@233:   ord "0" <= ord ch andalso ord ch <= ord "9";
wenzelm@233: 
wenzelm@233: (*letter or _ or prime (')*)
wenzelm@233: fun is_quasi_letter "_" = true
wenzelm@233:   | is_quasi_letter "'" = true
wenzelm@233:   | is_quasi_letter ch = is_letter ch;
wenzelm@233: 
lcp@512: (*white space: blanks, tabs, newlines, formfeeds*)
wenzelm@233: val is_blank : string -> bool =
lcp@512:   fn " " => true | "\t" => true | "\n" => true | "\^L" => true | _ => false;
wenzelm@233: 
wenzelm@233: val is_letdig = is_quasi_letter orf is_digit;
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (*lower all chars of string*)
wenzelm@233: val to_lower =
wenzelm@233:   let
wenzelm@233:     fun lower ch =
wenzelm@233:       if ch >= "A" andalso ch <= "Z" then
wenzelm@233:         chr (ord ch - ord "A" + ord "a")
wenzelm@233:       else ch;
wenzelm@233:   in implode o (map lower) o explode end;
wenzelm@233: 
wenzelm@233: 
lcp@512: (*enclose in brackets*)
lcp@512: fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@255: 
wenzelm@233: (*simple quoting (does not escape special chars)*)
lcp@512: val quote = enclose "\"" "\"";
wenzelm@233: 
wenzelm@233: (*space_implode "..." (explode "hello"); gives "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: 
clasohm@1290: (*space_explode "." "h.e..l.lo"; gives ["h", "e", "l", "lo"]*)
clasohm@1290: fun space_explode sep s =
clasohm@1290:   let fun divide [] "" = []
clasohm@1290:         | divide [] part = [part]
clasohm@1290:         | divide (c::s) part =
clasohm@1290:             if c = sep then
clasohm@1290:               (if part = "" then divide s "" else part :: divide s "")
clasohm@1290:             else divide s (part ^ c)
clasohm@1290:   in divide (explode s) "" end;
wenzelm@233: 
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: 
berghofe@1576: (*membership in a list, optimized version for int lists*)
berghofe@1576: fun (x:int) mem_int [] = false
berghofe@1576:   | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576: 
berghofe@1576: (*membership in a list, optimized version for string lists*)
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@233: 
wenzelm@233: (*insertion into list if not already there*)
wenzelm@233: fun x ins xs = if x mem xs then xs else x :: xs;
clasohm@0: 
berghofe@1576: (*insertion into list if not already there, optimized version for int lists*)
berghofe@1576: fun (x:int) ins_int xs = if x mem_int xs then xs else x :: xs;
berghofe@1576: 
berghofe@1576: (*insertion into list if not already there, optimized version for string lists*)
berghofe@1576: fun (x:string) ins_string xs = if x mem_string xs then xs else x :: xs;
berghofe@1576: 
clasohm@0: (*generalized insertion*)
wenzelm@233: fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233: 
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: 
berghofe@1576: (*union of sets represented as lists: no repetitions, optimized version for int lists*)
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: 
berghofe@1576: (*union of sets represented as lists: no repetitions, optimized version for string lists*)
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: 
berghofe@1576: (*intersection, optimized version for int lists*)
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: 
berghofe@1576: (*intersection, optimized version for string lists *)
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: 
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: 
berghofe@1576: (*subset, optimized version for int lists*)
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: 
berghofe@1576: (*subset, optimized version for string lists*)
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@233: fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233: 
wenzelm@233: 
wenzelm@265: (*eq_set*)
wenzelm@265: 
wenzelm@265: fun eq_set (xs, ys) =
wenzelm@265:   xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@265: 
berghofe@1576: (*eq_set, optimized version for int lists*)
berghofe@1576: 
berghofe@1576: fun eq_set_int ((xs:int list), ys) =
berghofe@1576:   xs = ys orelse (xs subset_int ys andalso ys subset_int xs);
berghofe@1576: 
berghofe@1576: (*eq_set, optimized version for string lists*)
berghofe@1576: 
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: 
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: 
wenzelm@233: val op \\ = foldl (op \);
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@233: 
wenzelm@233: val gen_rems = foldl o gen_rem;
wenzelm@233: 
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: 
wenzelm@233: val distinct = gen_distinct (op =);
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: 
wenzelm@255: val duplicates = gen_duplicates (op =);
wenzelm@255: 
wenzelm@255: 
wenzelm@233: 
wenzelm@233: (** association lists **)
clasohm@0: 
wenzelm@233: (*association list lookup*)
wenzelm@233: fun assoc ([], key) = None
wenzelm@233:   | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233:       if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233: 
berghofe@1576: (*association list lookup, optimized version for int lists*)
berghofe@1576: fun assoc_int ([], (key:int)) = None
berghofe@1576:   | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576:       if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576: 
berghofe@1576: (*association list lookup, optimized version for string lists*)
berghofe@1576: fun assoc_string ([], (key:string)) = None
berghofe@1576:   | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576:       if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576: 
berghofe@1576: (*association list lookup, optimized version for string*int lists*)
berghofe@1576: fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576:   | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576:       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
wenzelm@233:     None => []
wenzelm@233:   | 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
wenzelm@255:     Some al => assoc (al, key2)
wenzelm@255:   | None => None);
wenzelm@255: 
wenzelm@233: (*generalized association list lookup*)
wenzelm@233: fun gen_assoc eq ([], key) = None
wenzelm@233:   | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233:       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@233: 
wenzelm@233: 
wenzelm@233: (** generic tables **)
clasohm@0: 
wenzelm@233: (*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233:   wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233:   for long-term space efficiency.*)
wenzelm@233: 
wenzelm@233: (*append (new) elements to a table*)
wenzelm@233: fun generic_extend _ _ _ tab [] = tab
wenzelm@233:   | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233:       let
wenzelm@233:         val lst1 = dest_tab tab1;
wenzelm@233:         val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233:       in
wenzelm@233:         if null new_lst2 then tab1
wenzelm@233:         else mk_tab (lst1 @ new_lst2)
wenzelm@233:       end;
clasohm@0: 
wenzelm@233: (*append (new) elements of 2nd table to 1st table*)
wenzelm@233: fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233:   let
wenzelm@233:     val lst1 = dest_tab tab1;
wenzelm@233:     val lst2 = dest_tab tab2;
wenzelm@233:     val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233:   in
wenzelm@233:     if null new_lst2 then tab1
wenzelm@233:     else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233:     else mk_tab (lst1 @ new_lst2)
wenzelm@233:   end;
clasohm@0: 
wenzelm@233: 
wenzelm@233: (*lists as tables*)
wenzelm@233: val extend_list = generic_extend (op =) I I;
wenzelm@233: val merge_lists = generic_merge (op =) I I;
wenzelm@233: 
wenzelm@380: fun merge_rev_lists xs [] = xs
wenzelm@380:   | merge_rev_lists [] ys = ys
wenzelm@380:   | merge_rev_lists xs (y :: ys) =
wenzelm@380:       (if y mem xs then I else cons y) (merge_rev_lists xs ys);
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 =
wenzelm@233:       let val k = length xs div 2
wenzelm@233:       in  f (fold_bal f (take(k, xs)),
wenzelm@233:              fold_bal f (drop(k, xs)))
wenzelm@233:       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@233: (** input / output **)
wenzelm@233: 
berghofe@1580: val prs_fn = ref(fn s => output (std_out, s));
berghofe@1580: 
berghofe@1580: fun prs s = !prs_fn s;
wenzelm@233: fun writeln s = prs (s ^ "\n");
wenzelm@233: 
berghofe@1628: (* output to LaTeX / xdvi *)
berghofe@1628: fun latex s = 
berghofe@1628: 	execute ( "( cd /tmp ; echo \"" ^ s ^
berghofe@1628: 	"\" | isa2latex -s > $$.tex ; latex $$.tex ; xdvi $$.dvi ; rm $$.* ) > /dev/null &" ) ;
berghofe@1628: 
berghofe@1580: (*print warning*)
berghofe@1580: val warning_fn = ref(fn s => output (std_out, s ^ "\n"));
berghofe@1580: fun warning s = !warning_fn ("Warning: " ^ s);
wenzelm@233: 
wenzelm@233: (*print error message and abort to top level*)
berghofe@1580: 
berghofe@1580: val error_fn = ref(fn s => output (std_out, s ^ "\n"));
berghofe@1580: 
wenzelm@233: exception ERROR;
berghofe@1580: fun error msg = (!error_fn msg; raise ERROR);
berghofe@1580: fun sys_error msg = (!error_fn "*** SYSTEM ERROR ***"; error msg);
wenzelm@233: 
wenzelm@233: fun assert p msg = if p then () else error msg;
wenzelm@233: fun deny p msg = if p then error msg else ();
wenzelm@233: 
lcp@544: (*Assert pred for every member of l, generating a message if pred fails*)
lcp@544: fun assert_all pred l msg_fn = 
lcp@544:   let fun asl [] = ()
clasohm@1460: 	| asl (x::xs) = if pred x then asl xs
clasohm@1460: 	                else error (msg_fn x)
lcp@544:   in  asl l  end;
wenzelm@233: 
wenzelm@233: (*for the "test" target in Makefiles -- signifies successful termination*)
wenzelm@233: fun maketest msg =
paulson@1592:   (writeln msg; 
paulson@1592:    let val os = open_out "test" 
paulson@1592:    in  output (os, "Test examples ran successfully\n");
paulson@1592:        close_out os
paulson@1592:    end);
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (*print a list surrounded by the brackets lpar and rpar, with comma separator
wenzelm@233:   print nothing for empty list*)
wenzelm@233: fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
wenzelm@233:   let fun prec x = (prs ","; pre x)
wenzelm@233:   in
wenzelm@233:     (case l of
wenzelm@233:       [] => ()
wenzelm@233:     | x::l => (prs lpar; pre x; seq prec l; prs rpar))
wenzelm@233:   end;
wenzelm@233: 
wenzelm@233: (*print a list of items separated by newlines*)
wenzelm@233: fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
wenzelm@233:   seq (fn x => (pre x; writeln ""));
wenzelm@233: 
wenzelm@233: 
wenzelm@233: val print_int = prs o string_of_int;
wenzelm@233: 
wenzelm@233: 
wenzelm@233: 
wenzelm@233: (** timing **)
wenzelm@233: 
wenzelm@233: (*unconditional timing function*)
wenzelm@233: val timeit = cond_timeit true;
wenzelm@233: 
wenzelm@233: (*timed application function*)
wenzelm@233: fun timeap f x = timeit (fn () => f x);
wenzelm@233: 
wenzelm@233: (*timed "use" function, printing filenames*)
wenzelm@233: fun time_use fname = timeit (fn () =>
wenzelm@233:   (writeln ("\n**** Starting " ^ fname ^ " ****"); use fname;
wenzelm@233:    writeln ("\n**** Finished " ^ fname ^ " ****")));
wenzelm@233: 
lcp@955: (*For Makefiles: use the file, but exit with error code if errors found.*)
lcp@955: fun exit_use fname = use fname handle _ => exit 1;
wenzelm@233: 
wenzelm@233: 
clasohm@1407: (** filenames and paths **)
wenzelm@233: 
clasohm@1290: (*Convert UNIX filename of the form "path/file" to "path/" and "file";
wenzelm@233:   if filename contains no slash, then it returns "" and "file"*)
wenzelm@233: val split_filename =
wenzelm@233:   (pairself implode) o take_suffix (not_equal "/") o explode;
wenzelm@233: 
wenzelm@233: val base_name = #2 o split_filename;
wenzelm@233: 
clasohm@1290: (*Merge splitted filename (path and file);
wenzelm@233:   if path does not end with one a slash is appended*)
wenzelm@233: fun tack_on "" name = name
wenzelm@233:   | tack_on path name =
wenzelm@233:       if last_elem (explode path) = "/" then path ^ name
wenzelm@233:       else path ^ "/" ^ name;
wenzelm@233: 
clasohm@1290: (*Remove the extension of a filename, i.e. the part after the last '.'*)
wenzelm@233: val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;
wenzelm@233: 
clasohm@1290: (*Make relative path to reach an absolute location from a different one*)
clasohm@1290: fun relative_path cur_path dest_path =
clasohm@1290:   let (*Remove common beginning of both paths and make relative path*)
clasohm@1290:       fun mk_relative [] [] = []
clasohm@1290:         | mk_relative [] ds = ds
clasohm@1290:         | mk_relative cs [] = map (fn _ => "..") cs
clasohm@1290:         | mk_relative (c::cs) (d::ds) =
clasohm@1290:             if c = d then mk_relative cs ds
clasohm@1290:             else ".." :: map (fn _ => "..") cs @ (d::ds);
clasohm@1290:   in if cur_path = "" orelse hd (explode cur_path) <> "/" orelse
clasohm@1290:         dest_path = "" orelse hd (explode dest_path) <> "/" then
clasohm@1290:        error "Relative or empty path passed to relative_path"
clasohm@1290:      else ();
clasohm@1290:      space_implode "/" (mk_relative (space_explode "/" cur_path)
clasohm@1290:                                     (space_explode "/" dest_path))
clasohm@1290:   end;
wenzelm@233: 
clasohm@1407: (*Determine if absolute path1 is a subdirectory of absolute path2*)
clasohm@1407: fun path1 subdir_of path2 =
clasohm@1407:   if hd (explode path1) <> "/" orelse hd (explode path2) <> "/" then
clasohm@1407:     error "Relative or empty path passed to subdir_of"
clasohm@1407:   else (space_explode "/" path2) prefix (space_explode "/" path1);
clasohm@1407: 
clasohm@1456: fun absolute_path cwd file =
clasohm@1456:   let fun rm_points [] result = rev result
clasohm@1456:         | rm_points (".."::ds) result = rm_points ds (tl result)
clasohm@1456:         | rm_points ("."::ds) result = rm_points ds result
clasohm@1456:         | rm_points (d::ds) result = rm_points ds (d::result);
clasohm@1456:   in if file = "" then ""
clasohm@1456:      else if hd (explode file) = "/" then file
clasohm@1456:      else "/" ^ space_implode "/"
clasohm@1456:                   (rm_points (space_explode "/" (tack_on cwd file)) [])
clasohm@1456:   end;
clasohm@1456: 
wenzelm@233: 
wenzelm@233: (** misc functions **)
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.*)
clasohm@0: fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0:     let fun part ([], answer) = answer
wenzelm@233:           | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233:             then  part (xs, (x::ys, ns))
wenzelm@233:             else  part (xs, (ys, x::ns))
wenzelm@233:     in  part (rev ys, ([], []))  end;
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 [] => []
clasohm@0:                          | _ => raise LIST "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: (* sorting *)
wenzelm@233: 
wenzelm@233: (*insertion sort; stable (does not reorder equal elements)
wenzelm@233:   'less' is less-than test on type 'a*)
wenzelm@233: fun sort (less: 'a*'a -> bool) =
clasohm@0:   let fun insert (x, []) = [x]
wenzelm@233:         | insert (x, y::ys) =
wenzelm@233:               if less(y, x) then y :: insert (x, ys) else x::y::ys;
clasohm@0:       fun sort1 [] = []
clasohm@0:         | sort1 (x::xs) = insert (x, sort1 xs)
clasohm@0:   in  sort1  end;
clasohm@0: 
wenzelm@41: (*sort strings*)
wenzelm@41: val sort_strings = sort (op <= : string * string -> bool);
wenzelm@41: 
wenzelm@41: 
wenzelm@233: (* transitive closure (not Warshall's algorithm) *)
clasohm@0: 
wenzelm@233: fun transitive_closure [] = []
wenzelm@233:   | transitive_closure ((x, ys)::ps) =
wenzelm@233:       let val qs = transitive_closure ps
wenzelm@233:           val zs = foldl (fn (zs, y) => assocs qs y union zs) (ys, ys)
wenzelm@233:           fun step(u, us) = (u, if x mem us then zs union us else us)
wenzelm@233:       in (x, zs) :: map step qs end;
clasohm@0: 
clasohm@0: 
paulson@2003: (** Recommended by Stephen K. Park and Keith W. Miller, 
paulson@2003:       Random number generators: good ones are hard to find,
paulson@2003:       CACM 31 (1988), 1192-1201. 
paulson@2003:     Real number version for systems with 46-bit mantissae
paulson@2003:     Computes  (a*seed) mod m ;  should be applied to integers only! **)
paulson@2025: local val a = 16807.0  and  m = 2147483647.0  (* 2^31 - 1 *)
paulson@2003: in  fun nextrandom seed =
paulson@2003:           let val t = a*seed
paulson@2003:           in  t - m * real(floor(t/m))  end
paulson@2003: end;
paulson@2003: 
wenzelm@233: (* generating identifiers *)
clasohm@0: 
clasohm@0: local
wenzelm@233:   val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z"
wenzelm@233:   and k0 = ord "0" and k9 = ord "9"
paulson@2003: 
paulson@2003:   val seedr = ref 10000.0;
clasohm@0: in
clasohm@0: 
paulson@2003: (*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@2003: fun newid n = 
paulson@2003:   let fun char i =
paulson@2003:                if i<26 then chr (A+i)
paulson@2003:           else if i<52 then chr (a+i-26)
paulson@2003:           else if i<62 then chr (k0+i-52)
paulson@2003:           else if i=62 then "_"
paulson@2003:           else  (*i=63*)    "'"
paulson@2003:   in  implode (map char (radixpand (64,n)))  end;
paulson@2003: 
paulson@2025: (*Randomly generated identifiers with given prefix; MUST start with a letter
paulson@2025:     [division by two avoids overflow for ML systems whose maxint is 2^30 - 1 *)
paulson@2003: fun gensym pre = pre ^ 
paulson@2025:                  (#1(newid (floor (!seedr/2.0)), 
paulson@2025: 		     seedr := nextrandom (!seedr)))
paulson@2003: 
clasohm@0: (*Increment a list of letters like a reversed base 26 number.
wenzelm@233:   If head is "z", bumps chars in tail.
clasohm@0:   Digits are incremented as if they were integers.
clasohm@0:   "_" and "'" are not changed.
wenzelm@233:   For making variants of identifiers.*)
clasohm@0: 
clasohm@0: fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
wenzelm@233:         if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
wenzelm@233:         else "1" :: c :: cs
clasohm@0:   | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0: 
wenzelm@233: fun bump_list([], d) = [d]
wenzelm@233:   | bump_list(["'"], d) = [d, "'"]
wenzelm@233:   | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233:   | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233:   | bump_list("9"::cs, _) = "0" :: bump_int_list cs
wenzelm@233:   | bump_list(c::cs, _) = let val k = ord(c)
wenzelm@233:         in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
wenzelm@233:               (k0 <= k andalso k < k9) then chr(k+1) :: cs else
wenzelm@233:            if c="'" orelse c="_" then c :: bump_list(cs, "") else
wenzelm@233:                 error("bump_list: not legal in identifier: " ^
wenzelm@233:                         implode(rev(c::cs)))
wenzelm@233:         end;
clasohm@0: 
clasohm@0: end;
clasohm@0: 
wenzelm@233: fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41: 
wenzelm@41: 
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: 
clasohm@1364: end;
clasohm@1364: 
paulson@1592: (*Variable-branching trees: for proof terms*)
paulson@1592: datatype 'a mtree = Join of 'a * 'a mtree list;
paulson@1592: 
clasohm@1364: open Library;