src/Pure/library.ML
author wenzelm
Thu May 19 16:12:37 1994 +0200 (1994-05-19)
changeset 380 daca5b594fb3
parent 265 443dc2c37583
child 410 c8171ee32744
permissions -rw-r--r--
added infix op also: 'a * ('a -> 'b) -> 'b;
added set, reset, toggle: bool ref -> bool;
added find_first, exists2, forall2, commas_quote, merge_rev_lists;
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(*  Title:      Pure/library.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1992  University of Cambridge
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Basic library: functions, options, pairs, booleans, lists, integers,
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strings, lists as sets, association lists, generic tables, balanced trees,
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input / output, timing, filenames, misc functions.
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*)
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(** functions **)
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(*handy combinators*)
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fun curry f x y = f (x, y);
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fun uncurry f (x, y) = f x y;
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fun I x = x;
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fun K x y = x;
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(*reverse apply*)
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infix also;
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fun (x also f) = f x;
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(*combine two functions forming the union of their domains*)
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infix orelf;
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fun f orelf g = fn x => f x handle Match => g x;
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(*application of (infix) operator to its left or right argument*)
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fun apl (x, f) y = f (x, y);
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fun apr (f, y) x = f (x, y);
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(*functional for pairs*)
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fun pairself f (x, y) = (f x, f y);
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(*function exponentiation: f(...(f x)...) with n applications of f*)
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fun funpow n f x =
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  let fun rep (0, x) = x
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        | rep (n, x) = rep (n - 1, f x)
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  in rep (n, x) end;
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(** options **)
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datatype 'a option = None | Some of 'a;
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exception OPTION of string;
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fun the (Some x) = x
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  | the None = raise OPTION "the";
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fun if_none None y = y
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  | if_none (Some x) _ = x;
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fun is_some (Some _) = true
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  | is_some None = false;
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fun is_none (Some _) = false
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  | is_none None = true;
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fun apsome f (Some x) = Some (f x)
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  | apsome _ None = None;
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(** pairs **)
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fun pair x y = (x, y);
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fun rpair x y = (y, x);
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fun fst (x, y) = x;
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fun snd (x, y) = y;
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fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
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fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
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fun swap (x, y) = (y, x);
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(*apply the function to a component of a pair*)
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fun apfst f (x, y) = (f x, y);
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fun apsnd f (x, y) = (x, f y);
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(** booleans **)
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(* equality *)
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fun equal x y = x = y;
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fun not_equal x y = x <> y;
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(* operators for combining predicates *)
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infix orf;
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fun p orf q = fn x => p x orelse q x;
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infix andf;
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fun p andf q = fn x => p x andalso q x;
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fun notf p x = not (p x);
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(* predicates on lists *)
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fun orl [] = false
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  | orl (x :: xs) = x orelse orl xs;
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fun andl [] = true
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  | andl (x :: xs) = x andalso andl xs;
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(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
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fun exists (pred: 'a -> bool) : 'a list -> bool =
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  let fun boolf [] = false
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        | boolf (x :: xs) = pred x orelse boolf xs
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  in boolf end;
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(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
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fun forall (pred: 'a -> bool) : 'a list -> bool =
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  let fun boolf [] = true
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        | boolf (x :: xs) = pred x andalso boolf xs
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  in boolf end;
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(* flags *)
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fun set flag = (flag := true; true);
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fun reset flag = (flag := false; false);
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fun toggle flag = (flag := not (! flag); ! flag);
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(** lists **)
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exception LIST of string;
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fun null [] = true
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  | null (_ :: _) = false;
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fun hd [] = raise LIST "hd"
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  | hd (x :: _) = x;
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fun tl [] = raise LIST "tl"
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  | tl (_ :: xs) = xs;
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fun cons x xs = x :: xs;
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(* fold *)
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(*the following versions of fold are designed to fit nicely with infixes*)
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(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
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    for operators that associate to the left (TAIL RECURSIVE)*)
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fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
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  let fun itl (e, [])  = e
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        | itl (e, a::l) = itl (f(e, a), l)
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  in  itl end;
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(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
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    for operators that associate to the right (not tail recursive)*)
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fun foldr f (l, e) =
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  let fun itr [] = e
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        | itr (a::l) = f(a, itr l)
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  in  itr l  end;
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(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
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    for n > 0, operators that associate to the right (not tail recursive)*)
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fun foldr1 f l =
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  let fun itr [x] = x                       (* FIXME [] case: elim warn (?) *)
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        | itr (x::l) = f(x, itr l)
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  in  itr l  end;
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(* basic list functions *)
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(*length of a list, should unquestionably be a standard function*)
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local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
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        | length1 (n, x :: xs) = length1 (n + 1, xs)
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in  fun length l = length1 (0, l) end;
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(*take the first n elements from a list*)
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fun take (n, []) = []
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  | take (n, x :: xs) =
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      if n > 0 then x :: take (n - 1, xs) else [];
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(*drop the first n elements from a list*)
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fun drop (n, []) = []
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  | drop (n, x :: xs) =
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      if n > 0 then drop (n - 1, xs) else x :: xs;
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(*return nth element of a list, where 0 designates the first element;
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  raise EXCEPTION if list too short*)
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fun nth_elem NL =
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  (case drop NL of
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    [] => raise LIST "nth_elem"
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  | x :: _ => x);
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(*last element of a list*)
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fun last_elem [] = raise LIST "last_elem"
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  | last_elem [x] = x
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  | last_elem (_ :: xs) = last_elem xs;
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(*find the position of an element in a list*)
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fun find (x, ys) =
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  let fun f (y :: ys, i) = if x = y then i else f (ys, i + 1)
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        | f (_, _) = raise LIST "find"
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  in f (ys, 0) end;
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(*flatten a list of lists to a list*)
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fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
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(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
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  (proc x1; ...; proc xn) for side effects*)
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fun seq (proc: 'a -> unit) : 'a list -> unit =
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  let fun seqf [] = ()
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        | seqf (x :: xs) = (proc x; seqf xs)
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  in seqf end;
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(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
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fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
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  | separate _ xs = xs;
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(*make the list [x, x, ..., x] of length n*)
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fun replicate n (x: 'a) : 'a list =
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  let fun rep (0, xs) = xs
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        | rep (n, xs) = rep (n - 1, x :: xs)
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  in
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    if n < 0 then raise LIST "replicate"
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    else rep (n, [])
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  end;
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(* filter *)
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(*copy the list preserving elements that satisfy the predicate*)
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fun filter (pred: 'a->bool) : 'a list -> 'a list =
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  let fun filt [] = []
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        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
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  in filt end;
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fun filter_out f = filter (not o f);
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fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
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  | mapfilter f (x :: xs) =
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      (case f x of
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        None => mapfilter f xs
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      | Some y => y :: mapfilter f xs);
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fun find_first _ [] = None
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  | find_first pred (x :: xs) =
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      if pred x then Some x else find_first pred xs;
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(* lists of pairs *)
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fun map2 _ ([], []) = []
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  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
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  | map2 _ _ = raise LIST "map2";
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fun exists2 _ ([], []) = false
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  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
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  | exists2 _ _ = raise LIST "exists2";
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fun forall2 _ ([], []) = true
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  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
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  | forall2 _ _ = raise LIST "forall2";
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(*combine two lists forming a list of pairs:
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  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
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infix ~~;
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fun [] ~~ [] = []
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  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
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  | _ ~~ _ = raise LIST "~~";
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(*inverse of ~~; the old 'split':
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  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
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fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
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(* prefixes, suffixes *)
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infix prefix;
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fun [] prefix _ = true
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  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
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  | _ prefix _ = false;
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(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
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   where xi is the first element that does not satisfy the predicate*)
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fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
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  let fun take (rxs, []) = (rev rxs, [])
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        | take (rxs, x :: xs) =
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            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
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  in  take([], xs)  end;
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(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
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   where xi is the last element that does not satisfy the predicate*)
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fun take_suffix _ [] = ([], [])
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  | take_suffix pred (x :: xs) =
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      (case take_suffix pred xs of
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        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
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      | (prfx, sffx) => (x :: prfx, sffx));
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(** integers **)
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fun inc i = i := ! i + 1;
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fun dec i = i := ! i - 1;
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(* lists of integers *)
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(*make the list [from, from + 1, ..., to]*)
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infix upto;
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fun from upto to =
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  if from > to then [] else from :: ((from + 1) upto to);
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(*make the list [from, from - 1, ..., to]*)
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infix downto;
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fun from downto to =
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  if from < to then [] else from :: ((from - 1) downto to);
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(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
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fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
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  | downto0 ([], n) = n = ~1;
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(* operations on integer lists *)
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fun sum [] = 0
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  | sum (n :: ns) = n + sum ns;
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fun max [m:int] = m
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  | max (m :: n :: ns) = if m > n then max (m :: ns) else max (n :: ns)
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  | max [] = raise LIST "max";
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fun min [m:int] = m
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  | min (m :: n :: ns) = if m < n then min (m :: ns) else min (n :: ns)
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  | min [] = raise LIST "min";
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(* convert integers to strings *)
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(*expand the number in the given base;
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  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
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fun radixpand (base, num) : int list =
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  let
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    fun radix (n, tail) =
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      if n < base then n :: tail
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      else radix (n div base, (n mod base) :: tail)
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  in radix (num, []) end;
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(*expands a number into a string of characters starting from "zerochar";
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  example: radixstring (2, "0", 8) gives "1000"*)
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fun radixstring (base, zerochar, num) =
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  let val offset = ord zerochar;
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      fun chrof n = chr (offset + n)
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  in implode (map chrof (radixpand (base, num))) end;
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fun string_of_int n =
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  if n < 0 then "~" ^ radixstring (10, "0", ~n) else radixstring (10, "0", n);
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(** strings **)
wenzelm@233
   373
wenzelm@233
   374
fun is_letter ch =
wenzelm@233
   375
  ord "A" <= ord ch andalso ord ch <= ord "Z" orelse
wenzelm@233
   376
  ord "a" <= ord ch andalso ord ch <= ord "z";
wenzelm@233
   377
wenzelm@233
   378
fun is_digit ch =
wenzelm@233
   379
  ord "0" <= ord ch andalso ord ch <= ord "9";
wenzelm@233
   380
wenzelm@233
   381
(*letter or _ or prime (')*)
wenzelm@233
   382
fun is_quasi_letter "_" = true
wenzelm@233
   383
  | is_quasi_letter "'" = true
wenzelm@233
   384
  | is_quasi_letter ch = is_letter ch;
wenzelm@233
   385
wenzelm@233
   386
(*white space: blanks, tabs, newlines*)
wenzelm@233
   387
val is_blank : string -> bool =
wenzelm@233
   388
  fn " " => true | "\t" => true | "\n" => true | _ => false;
wenzelm@233
   389
wenzelm@233
   390
val is_letdig = is_quasi_letter orf is_digit;
wenzelm@233
   391
wenzelm@233
   392
wenzelm@233
   393
(*lower all chars of string*)
wenzelm@233
   394
val to_lower =
wenzelm@233
   395
  let
wenzelm@233
   396
    fun lower ch =
wenzelm@233
   397
      if ch >= "A" andalso ch <= "Z" then
wenzelm@233
   398
        chr (ord ch - ord "A" + ord "a")
wenzelm@233
   399
      else ch;
wenzelm@233
   400
  in implode o (map lower) o explode end;
wenzelm@233
   401
wenzelm@233
   402
wenzelm@255
   403
(*parentesize*)
wenzelm@255
   404
fun parents lpar rpar str = lpar ^ str ^ rpar;
wenzelm@255
   405
wenzelm@233
   406
(*simple quoting (does not escape special chars)*)
wenzelm@255
   407
val quote = parents "\"" "\"";
wenzelm@233
   408
wenzelm@233
   409
(*space_implode "..." (explode "hello"); gives "h...e...l...l...o"*)
wenzelm@233
   410
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   411
wenzelm@255
   412
val commas = space_implode ", ";
wenzelm@380
   413
val commas_quote = commas o map quote;
wenzelm@255
   414
wenzelm@233
   415
(*concatenate messages, one per line, into a string*)
wenzelm@255
   416
val cat_lines = space_implode "\n";
wenzelm@233
   417
wenzelm@233
   418
wenzelm@233
   419
wenzelm@233
   420
(** lists as sets **)
wenzelm@233
   421
wenzelm@233
   422
(*membership in a list*)
wenzelm@233
   423
infix mem;
wenzelm@233
   424
fun x mem [] = false
wenzelm@233
   425
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   426
clasohm@0
   427
(*generalized membership test*)
wenzelm@233
   428
fun gen_mem eq (x, []) = false
wenzelm@233
   429
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   430
wenzelm@233
   431
wenzelm@233
   432
(*insertion into list if not already there*)
wenzelm@233
   433
infix ins;
wenzelm@233
   434
fun x ins xs = if x mem xs then xs else x :: xs;
clasohm@0
   435
clasohm@0
   436
(*generalized insertion*)
wenzelm@233
   437
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   438
wenzelm@233
   439
wenzelm@233
   440
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   441
infix union;
wenzelm@233
   442
fun xs union [] = xs
wenzelm@233
   443
  | [] union ys = ys
wenzelm@233
   444
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   445
clasohm@0
   446
(*generalized union*)
wenzelm@233
   447
fun gen_union eq (xs, []) = xs
wenzelm@233
   448
  | gen_union eq ([], ys) = ys
wenzelm@233
   449
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   450
wenzelm@233
   451
wenzelm@233
   452
(*intersection*)
wenzelm@233
   453
infix inter;
wenzelm@233
   454
fun [] inter ys = []
wenzelm@233
   455
  | (x :: xs) inter ys =
wenzelm@233
   456
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   457
wenzelm@233
   458
wenzelm@233
   459
(*subset*)
wenzelm@233
   460
infix subset;
wenzelm@233
   461
fun [] subset ys = true
wenzelm@233
   462
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   463
wenzelm@233
   464
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
wenzelm@233
   465
wenzelm@233
   466
wenzelm@265
   467
(*eq_set*)
wenzelm@265
   468
wenzelm@265
   469
fun eq_set (xs, ys) =
wenzelm@265
   470
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@265
   471
wenzelm@265
   472
wenzelm@233
   473
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   474
infix \;
wenzelm@233
   475
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   476
  | [] \ x = [];
wenzelm@233
   477
wenzelm@233
   478
infix \\;
wenzelm@233
   479
val op \\ = foldl (op \);
clasohm@0
   480
wenzelm@233
   481
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   482
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   483
wenzelm@233
   484
val gen_rems = foldl o gen_rem;
wenzelm@233
   485
wenzelm@233
   486
wenzelm@233
   487
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   488
  first of equal elements*)
wenzelm@233
   489
fun gen_distinct eq lst =
wenzelm@233
   490
  let
wenzelm@233
   491
    val memb = gen_mem eq;
clasohm@0
   492
wenzelm@233
   493
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   494
      | dist (rev_seen, x :: xs) =
wenzelm@233
   495
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   496
          else dist (x :: rev_seen, xs);
wenzelm@233
   497
  in
wenzelm@233
   498
    dist ([], lst)
wenzelm@233
   499
  end;
wenzelm@233
   500
wenzelm@233
   501
val distinct = gen_distinct (op =);
wenzelm@233
   502
wenzelm@233
   503
wenzelm@233
   504
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   505
fun findrep [] = []
wenzelm@233
   506
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   507
wenzelm@233
   508
wenzelm@255
   509
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   510
  order, takes first of equal elements*)
wenzelm@255
   511
fun gen_duplicates eq lst =
wenzelm@255
   512
  let
wenzelm@255
   513
    val memb = gen_mem eq;
wenzelm@255
   514
wenzelm@255
   515
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   516
      | dups (rev_dups, x :: xs) =
wenzelm@255
   517
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   518
            dups (rev_dups, xs)
wenzelm@255
   519
          else dups (x :: rev_dups, xs);
wenzelm@255
   520
  in
wenzelm@255
   521
    dups ([], lst)
wenzelm@255
   522
  end;
wenzelm@255
   523
wenzelm@255
   524
val duplicates = gen_duplicates (op =);
wenzelm@255
   525
wenzelm@255
   526
wenzelm@233
   527
wenzelm@233
   528
(** association lists **)
clasohm@0
   529
wenzelm@233
   530
(*association list lookup*)
wenzelm@233
   531
fun assoc ([], key) = None
wenzelm@233
   532
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   533
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   534
wenzelm@233
   535
fun assocs ps x =
wenzelm@233
   536
  (case assoc (ps, x) of
wenzelm@233
   537
    None => []
wenzelm@233
   538
  | Some ys => ys);
wenzelm@233
   539
wenzelm@255
   540
(*two-fold association list lookup*)
wenzelm@255
   541
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   542
  (case assoc (aal, key1) of
wenzelm@255
   543
    Some al => assoc (al, key2)
wenzelm@255
   544
  | None => None);
wenzelm@255
   545
wenzelm@233
   546
(*generalized association list lookup*)
wenzelm@233
   547
fun gen_assoc eq ([], key) = None
wenzelm@233
   548
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   549
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   550
wenzelm@233
   551
(*association list update*)
wenzelm@233
   552
fun overwrite (al, p as (key, _)) =
wenzelm@233
   553
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   554
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   555
        | over [] = [p]
wenzelm@233
   556
  in over al end;
wenzelm@233
   557
wenzelm@233
   558
wenzelm@233
   559
wenzelm@233
   560
(** generic tables **)
clasohm@0
   561
wenzelm@233
   562
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   563
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   564
  for long-term space efficiency.*)
wenzelm@233
   565
wenzelm@233
   566
(*append (new) elements to a table*)
wenzelm@233
   567
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   568
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   569
      let
wenzelm@233
   570
        val lst1 = dest_tab tab1;
wenzelm@233
   571
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   572
      in
wenzelm@233
   573
        if null new_lst2 then tab1
wenzelm@233
   574
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
   575
      end;
clasohm@0
   576
wenzelm@233
   577
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
   578
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
   579
  let
wenzelm@233
   580
    val lst1 = dest_tab tab1;
wenzelm@233
   581
    val lst2 = dest_tab tab2;
wenzelm@233
   582
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   583
  in
wenzelm@233
   584
    if null new_lst2 then tab1
wenzelm@233
   585
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
   586
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
   587
  end;
clasohm@0
   588
wenzelm@233
   589
wenzelm@233
   590
(*lists as tables*)
wenzelm@233
   591
val extend_list = generic_extend (op =) I I;
wenzelm@233
   592
val merge_lists = generic_merge (op =) I I;
wenzelm@233
   593
wenzelm@380
   594
fun merge_rev_lists xs [] = xs
wenzelm@380
   595
  | merge_rev_lists [] ys = ys
wenzelm@380
   596
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
   597
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
   598
clasohm@0
   599
clasohm@0
   600
wenzelm@233
   601
(** balanced trees **)
wenzelm@233
   602
wenzelm@233
   603
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   604
wenzelm@233
   605
(*balanced folding; avoids deep nesting*)
wenzelm@233
   606
fun fold_bal f [x] = x
wenzelm@233
   607
  | fold_bal f [] = raise Balance
wenzelm@233
   608
  | fold_bal f xs =
wenzelm@233
   609
      let val k = length xs div 2
wenzelm@233
   610
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
   611
             fold_bal f (drop(k, xs)))
wenzelm@233
   612
      end;
wenzelm@233
   613
wenzelm@233
   614
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   615
fun access_bal (f, g, x) n i =
wenzelm@233
   616
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   617
          if n=1 then x else
wenzelm@233
   618
          let val n2 = n div 2
wenzelm@233
   619
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   620
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   621
          end
wenzelm@233
   622
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   623
wenzelm@233
   624
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   625
fun accesses_bal (f, g, x) n =
wenzelm@233
   626
  let fun acc n =
wenzelm@233
   627
          if n=1 then [x] else
wenzelm@233
   628
          let val n2 = n div 2
wenzelm@233
   629
              val acc2 = acc n2
wenzelm@233
   630
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   631
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   632
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   633
wenzelm@233
   634
wenzelm@233
   635
wenzelm@233
   636
(** input / output **)
wenzelm@233
   637
wenzelm@233
   638
fun prs s = output (std_out, s);
wenzelm@233
   639
fun writeln s = prs (s ^ "\n");
wenzelm@233
   640
wenzelm@233
   641
wenzelm@233
   642
(*print error message and abort to top level*)
wenzelm@233
   643
exception ERROR;
wenzelm@233
   644
fun error msg = (writeln msg; raise ERROR);
wenzelm@380
   645
fun sys_error msg = (writeln "*** SYSTEM ERROR ***"; error msg);
wenzelm@233
   646
wenzelm@233
   647
fun assert p msg = if p then () else error msg;
wenzelm@233
   648
fun deny p msg = if p then error msg else ();
wenzelm@233
   649
wenzelm@233
   650
wenzelm@233
   651
(* FIXME close file (?) *)
wenzelm@233
   652
(*for the "test" target in Makefiles -- signifies successful termination*)
wenzelm@233
   653
fun maketest msg =
wenzelm@233
   654
  (writeln msg; output (open_out "test", "Test examples ran successfully\n"));
wenzelm@233
   655
wenzelm@233
   656
wenzelm@233
   657
(*print a list surrounded by the brackets lpar and rpar, with comma separator
wenzelm@233
   658
  print nothing for empty list*)
wenzelm@233
   659
fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
wenzelm@233
   660
  let fun prec x = (prs ","; pre x)
wenzelm@233
   661
  in
wenzelm@233
   662
    (case l of
wenzelm@233
   663
      [] => ()
wenzelm@233
   664
    | x::l => (prs lpar; pre x; seq prec l; prs rpar))
wenzelm@233
   665
  end;
wenzelm@233
   666
wenzelm@233
   667
(*print a list of items separated by newlines*)
wenzelm@233
   668
fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
wenzelm@233
   669
  seq (fn x => (pre x; writeln ""));
wenzelm@233
   670
wenzelm@233
   671
wenzelm@233
   672
val print_int = prs o string_of_int;
wenzelm@233
   673
wenzelm@233
   674
wenzelm@233
   675
wenzelm@233
   676
(** timing **)
wenzelm@233
   677
wenzelm@233
   678
(*unconditional timing function*)
wenzelm@233
   679
val timeit = cond_timeit true;
wenzelm@233
   680
wenzelm@233
   681
(*timed application function*)
wenzelm@233
   682
fun timeap f x = timeit (fn () => f x);
wenzelm@233
   683
wenzelm@233
   684
(*timed "use" function, printing filenames*)
wenzelm@233
   685
fun time_use fname = timeit (fn () =>
wenzelm@233
   686
  (writeln ("\n**** Starting " ^ fname ^ " ****"); use fname;
wenzelm@233
   687
   writeln ("\n**** Finished " ^ fname ^ " ****")));
wenzelm@233
   688
wenzelm@233
   689
wenzelm@233
   690
wenzelm@233
   691
(** filenames **)
wenzelm@233
   692
wenzelm@233
   693
(*convert UNIX filename of the form "path/file" to "path/" and "file";
wenzelm@233
   694
  if filename contains no slash, then it returns "" and "file"*)
wenzelm@233
   695
val split_filename =
wenzelm@233
   696
  (pairself implode) o take_suffix (not_equal "/") o explode;
wenzelm@233
   697
wenzelm@233
   698
val base_name = #2 o split_filename;
wenzelm@233
   699
wenzelm@233
   700
(*merge splitted filename (path and file);
wenzelm@233
   701
  if path does not end with one a slash is appended*)
wenzelm@233
   702
fun tack_on "" name = name
wenzelm@233
   703
  | tack_on path name =
wenzelm@233
   704
      if last_elem (explode path) = "/" then path ^ name
wenzelm@233
   705
      else path ^ "/" ^ name;
wenzelm@233
   706
wenzelm@233
   707
(*remove the extension of a filename, i.e. the part after the last '.'*)
wenzelm@233
   708
val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;
wenzelm@233
   709
wenzelm@233
   710
wenzelm@233
   711
wenzelm@233
   712
(** misc functions **)
wenzelm@233
   713
wenzelm@233
   714
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
   715
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
   716
  let fun keypair x = (x, keyfun x)
wenzelm@233
   717
  in map keypair end;
clasohm@0
   718
wenzelm@233
   719
(*given a list of (x, key) pairs and a searchkey
clasohm@0
   720
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
   721
fun keyfilter [] searchkey = []
wenzelm@233
   722
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
   723
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
   724
      else keyfilter pairs searchkey;
clasohm@0
   725
clasohm@0
   726
clasohm@0
   727
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
   728
  Preserves order of elements in both lists.*)
clasohm@0
   729
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
   730
    let fun part ([], answer) = answer
wenzelm@233
   731
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
   732
            then  part (xs, (x::ys, ns))
wenzelm@233
   733
            else  part (xs, (ys, x::ns))
wenzelm@233
   734
    in  part (rev ys, ([], []))  end;
clasohm@0
   735
clasohm@0
   736
clasohm@0
   737
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
   738
    let fun part [] = []
wenzelm@233
   739
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
   740
                           in (x::xs)::(part xs') end
clasohm@0
   741
    in part end;
clasohm@0
   742
clasohm@0
   743
wenzelm@233
   744
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
   745
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
   746
fun partition_list p i j =
wenzelm@233
   747
  let fun part k xs =
wenzelm@233
   748
            if k>j then
clasohm@0
   749
              (case xs of [] => []
clasohm@0
   750
                         | _ => raise LIST "partition_list")
clasohm@0
   751
            else
wenzelm@233
   752
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
   753
            in  ns :: part(k+1)rest  end
clasohm@0
   754
  in  part i end;
clasohm@0
   755
clasohm@0
   756
wenzelm@233
   757
(* sorting *)
wenzelm@233
   758
wenzelm@233
   759
(*insertion sort; stable (does not reorder equal elements)
wenzelm@233
   760
  'less' is less-than test on type 'a*)
wenzelm@233
   761
fun sort (less: 'a*'a -> bool) =
clasohm@0
   762
  let fun insert (x, []) = [x]
wenzelm@233
   763
        | insert (x, y::ys) =
wenzelm@233
   764
              if less(y, x) then y :: insert (x, ys) else x::y::ys;
clasohm@0
   765
      fun sort1 [] = []
clasohm@0
   766
        | sort1 (x::xs) = insert (x, sort1 xs)
clasohm@0
   767
  in  sort1  end;
clasohm@0
   768
wenzelm@41
   769
(*sort strings*)
wenzelm@41
   770
val sort_strings = sort (op <= : string * string -> bool);
wenzelm@41
   771
wenzelm@41
   772
wenzelm@233
   773
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
   774
wenzelm@233
   775
fun transitive_closure [] = []
wenzelm@233
   776
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
   777
      let val qs = transitive_closure ps
wenzelm@233
   778
          val zs = foldl (fn (zs, y) => assocs qs y union zs) (ys, ys)
wenzelm@233
   779
          fun step(u, us) = (u, if x mem us then zs union us else us)
wenzelm@233
   780
      in (x, zs) :: map step qs end;
clasohm@0
   781
clasohm@0
   782
wenzelm@233
   783
(* generating identifiers *)
clasohm@0
   784
clasohm@0
   785
local
wenzelm@233
   786
  val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z"
wenzelm@233
   787
  and k0 = ord "0" and k9 = ord "9"
clasohm@0
   788
in
clasohm@0
   789
clasohm@0
   790
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
   791
  If head is "z", bumps chars in tail.
clasohm@0
   792
  Digits are incremented as if they were integers.
clasohm@0
   793
  "_" and "'" are not changed.
wenzelm@233
   794
  For making variants of identifiers.*)
clasohm@0
   795
clasohm@0
   796
fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
wenzelm@233
   797
        if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
wenzelm@233
   798
        else "1" :: c :: cs
clasohm@0
   799
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
   800
wenzelm@233
   801
fun bump_list([], d) = [d]
wenzelm@233
   802
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
   803
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
   804
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
   805
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
wenzelm@233
   806
  | bump_list(c::cs, _) = let val k = ord(c)
wenzelm@233
   807
        in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
wenzelm@233
   808
              (k0 <= k andalso k < k9) then chr(k+1) :: cs else
wenzelm@233
   809
           if c="'" orelse c="_" then c :: bump_list(cs, "") else
wenzelm@233
   810
                error("bump_list: not legal in identifier: " ^
wenzelm@233
   811
                        implode(rev(c::cs)))
wenzelm@233
   812
        end;
clasohm@0
   813
clasohm@0
   814
end;
clasohm@0
   815
wenzelm@233
   816
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
   817
wenzelm@41
   818
wenzelm@233
   819
(* lexical scanning *)
clasohm@0
   820
wenzelm@233
   821
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
   822
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
   823
fun scanwords is_let cs =
clasohm@0
   824
  let fun scan1 [] = []
wenzelm@233
   825
        | scan1 cs =
wenzelm@233
   826
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
   827
            in implode lets :: scanwords is_let rest end;
wenzelm@233
   828
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
   829