src/Pure/library.ML
author paulson
Thu Nov 28 12:36:31 1996 +0100 (1996-11-28)
changeset 2271 7c4744ed8fc3
parent 2243 3ebeaaacfbd1
child 2303 84ed9e0d7c50
permissions -rw-r--r--
Declares List_ as a synonym for List
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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 / TextIO.output, timing, filenames, misc functions.
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*)
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infix |> ~~ \ \\ orelf ins ins_string ins_int orf andf prefix upto downto
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      mem mem_int mem_string union union_int union_string  
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      inter inter_int inter_string subset subset_int subset_string subdir_of;
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structure Library =
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struct
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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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fun (x |> f) = f x;
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(*combine two functions forming the union of their domains*)
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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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fun (p orf q) = fn x => p x orelse q x;
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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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(*Needed because several object-logics declare the theory, therefore structure,
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  List.*)
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structure List_ = List;
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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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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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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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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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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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(* 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 **)
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fun is_letter ch =
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  ord "A" <= ord ch andalso ord ch <= ord "Z" orelse
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  ord "a" <= ord ch andalso ord ch <= ord "z";
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fun is_digit ch =
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  ord "0" <= ord ch andalso ord ch <= ord "9";
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(*letter or _ or prime (')*)
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fun is_quasi_letter "_" = true
wenzelm@233
   372
  | is_quasi_letter "'" = true
wenzelm@233
   373
  | is_quasi_letter ch = is_letter ch;
wenzelm@233
   374
lcp@512
   375
(*white space: blanks, tabs, newlines, formfeeds*)
wenzelm@233
   376
val is_blank : string -> bool =
lcp@512
   377
  fn " " => true | "\t" => true | "\n" => true | "\^L" => true | _ => false;
wenzelm@233
   378
wenzelm@233
   379
val is_letdig = is_quasi_letter orf is_digit;
wenzelm@233
   380
wenzelm@2196
   381
(*printable chars*)
wenzelm@2196
   382
fun is_printable c = ord c > ord " " andalso ord c <= ord "~";
wenzelm@2196
   383
wenzelm@233
   384
wenzelm@233
   385
(*lower all chars of string*)
wenzelm@233
   386
val to_lower =
wenzelm@233
   387
  let
wenzelm@233
   388
    fun lower ch =
wenzelm@233
   389
      if ch >= "A" andalso ch <= "Z" then
wenzelm@233
   390
        chr (ord ch - ord "A" + ord "a")
wenzelm@233
   391
      else ch;
wenzelm@233
   392
  in implode o (map lower) o explode end;
wenzelm@233
   393
wenzelm@233
   394
lcp@512
   395
(*enclose in brackets*)
lcp@512
   396
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@255
   397
wenzelm@233
   398
(*simple quoting (does not escape special chars)*)
lcp@512
   399
val quote = enclose "\"" "\"";
wenzelm@233
   400
wenzelm@233
   401
(*space_implode "..." (explode "hello"); gives "h...e...l...l...o"*)
wenzelm@233
   402
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   403
wenzelm@255
   404
val commas = space_implode ", ";
wenzelm@380
   405
val commas_quote = commas o map quote;
wenzelm@255
   406
wenzelm@233
   407
(*concatenate messages, one per line, into a string*)
wenzelm@255
   408
val cat_lines = space_implode "\n";
wenzelm@233
   409
clasohm@1290
   410
(*space_explode "." "h.e..l.lo"; gives ["h", "e", "l", "lo"]*)
clasohm@1290
   411
fun space_explode sep s =
clasohm@1290
   412
  let fun divide [] "" = []
clasohm@1290
   413
        | divide [] part = [part]
clasohm@1290
   414
        | divide (c::s) part =
clasohm@1290
   415
            if c = sep then
clasohm@1290
   416
              (if part = "" then divide s "" else part :: divide s "")
clasohm@1290
   417
            else divide s (part ^ c)
clasohm@1290
   418
  in divide (explode s) "" end;
wenzelm@233
   419
wenzelm@233
   420
wenzelm@233
   421
(** lists as sets **)
wenzelm@233
   422
wenzelm@233
   423
(*membership in a list*)
wenzelm@233
   424
fun x mem [] = false
wenzelm@233
   425
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   426
paulson@2175
   427
(*membership in a list, optimized version for ints*)
berghofe@1576
   428
fun (x:int) mem_int [] = false
berghofe@1576
   429
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   430
paulson@2175
   431
(*membership in a list, optimized version for strings*)
berghofe@1576
   432
fun (x:string) mem_string [] = false
berghofe@1576
   433
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   434
clasohm@0
   435
(*generalized membership test*)
wenzelm@233
   436
fun gen_mem eq (x, []) = false
wenzelm@233
   437
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   438
wenzelm@233
   439
wenzelm@233
   440
(*insertion into list if not already there*)
paulson@2175
   441
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   442
paulson@2175
   443
(*insertion into list, optimized version for ints*)
paulson@2175
   444
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   445
paulson@2175
   446
(*insertion into list, optimized version for strings*)
paulson@2175
   447
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   448
clasohm@0
   449
(*generalized insertion*)
wenzelm@233
   450
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   451
wenzelm@233
   452
wenzelm@233
   453
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   454
fun xs union [] = xs
wenzelm@233
   455
  | [] union ys = ys
wenzelm@233
   456
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   457
paulson@2175
   458
(*union of sets, optimized version for ints*)
berghofe@1576
   459
fun (xs:int list) union_int [] = xs
berghofe@1576
   460
  | [] union_int ys = ys
berghofe@1576
   461
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   462
paulson@2175
   463
(*union of sets, optimized version for strings*)
berghofe@1576
   464
fun (xs:string list) union_string [] = xs
berghofe@1576
   465
  | [] union_string ys = ys
berghofe@1576
   466
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   467
clasohm@0
   468
(*generalized union*)
wenzelm@233
   469
fun gen_union eq (xs, []) = xs
wenzelm@233
   470
  | gen_union eq ([], ys) = ys
wenzelm@233
   471
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   472
wenzelm@233
   473
wenzelm@233
   474
(*intersection*)
wenzelm@233
   475
fun [] inter ys = []
wenzelm@233
   476
  | (x :: xs) inter ys =
wenzelm@233
   477
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   478
paulson@2175
   479
(*intersection, optimized version for ints*)
berghofe@1576
   480
fun ([]:int list) inter_int ys = []
berghofe@1576
   481
  | (x :: xs) inter_int ys =
berghofe@1576
   482
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   483
paulson@2175
   484
(*intersection, optimized version for strings *)
berghofe@1576
   485
fun ([]:string list) inter_string ys = []
berghofe@1576
   486
  | (x :: xs) inter_string ys =
berghofe@1576
   487
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   488
wenzelm@233
   489
wenzelm@233
   490
(*subset*)
wenzelm@233
   491
fun [] subset ys = true
wenzelm@233
   492
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   493
paulson@2175
   494
(*subset, optimized version for ints*)
berghofe@1576
   495
fun ([]:int list) subset_int ys = true
berghofe@1576
   496
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   497
paulson@2175
   498
(*subset, optimized version for strings*)
berghofe@1576
   499
fun ([]:string list) subset_string ys = true
berghofe@1576
   500
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   501
paulson@2182
   502
(*set equality for strings*)
berghofe@1576
   503
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   504
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   505
paulson@2182
   506
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   507
wenzelm@265
   508
wenzelm@233
   509
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   510
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   511
  | [] \ x = [];
wenzelm@233
   512
paulson@2243
   513
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   514
wenzelm@233
   515
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   516
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   517
paulson@2243
   518
fun gen_rems eq = foldl (gen_rem eq);
wenzelm@233
   519
wenzelm@233
   520
wenzelm@233
   521
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   522
  first of equal elements*)
wenzelm@233
   523
fun gen_distinct eq lst =
wenzelm@233
   524
  let
wenzelm@233
   525
    val memb = gen_mem eq;
clasohm@0
   526
wenzelm@233
   527
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   528
      | dist (rev_seen, x :: xs) =
wenzelm@233
   529
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   530
          else dist (x :: rev_seen, xs);
wenzelm@233
   531
  in
wenzelm@233
   532
    dist ([], lst)
wenzelm@233
   533
  end;
wenzelm@233
   534
paulson@2243
   535
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   536
wenzelm@233
   537
wenzelm@233
   538
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   539
fun findrep [] = []
wenzelm@233
   540
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   541
wenzelm@233
   542
wenzelm@255
   543
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   544
  order, takes first of equal elements*)
wenzelm@255
   545
fun gen_duplicates eq lst =
wenzelm@255
   546
  let
wenzelm@255
   547
    val memb = gen_mem eq;
wenzelm@255
   548
wenzelm@255
   549
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   550
      | dups (rev_dups, x :: xs) =
wenzelm@255
   551
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   552
            dups (rev_dups, xs)
wenzelm@255
   553
          else dups (x :: rev_dups, xs);
wenzelm@255
   554
  in
wenzelm@255
   555
    dups ([], lst)
wenzelm@255
   556
  end;
wenzelm@255
   557
paulson@2243
   558
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   559
wenzelm@255
   560
wenzelm@233
   561
wenzelm@233
   562
(** association lists **)
clasohm@0
   563
wenzelm@233
   564
(*association list lookup*)
wenzelm@233
   565
fun assoc ([], key) = None
wenzelm@233
   566
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   567
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   568
paulson@2175
   569
(*association list lookup, optimized version for ints*)
berghofe@1576
   570
fun assoc_int ([], (key:int)) = None
berghofe@1576
   571
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   572
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   573
paulson@2175
   574
(*association list lookup, optimized version for strings*)
berghofe@1576
   575
fun assoc_string ([], (key:string)) = None
berghofe@1576
   576
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   577
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   578
paulson@2175
   579
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   580
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   581
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   582
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   583
wenzelm@233
   584
fun assocs ps x =
wenzelm@233
   585
  (case assoc (ps, x) of
wenzelm@233
   586
    None => []
wenzelm@233
   587
  | Some ys => ys);
wenzelm@233
   588
wenzelm@255
   589
(*two-fold association list lookup*)
wenzelm@255
   590
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   591
  (case assoc (aal, key1) of
wenzelm@255
   592
    Some al => assoc (al, key2)
wenzelm@255
   593
  | None => None);
wenzelm@255
   594
wenzelm@233
   595
(*generalized association list lookup*)
wenzelm@233
   596
fun gen_assoc eq ([], key) = None
wenzelm@233
   597
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   598
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   599
wenzelm@233
   600
(*association list update*)
wenzelm@233
   601
fun overwrite (al, p as (key, _)) =
wenzelm@233
   602
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   603
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   604
        | over [] = [p]
wenzelm@233
   605
  in over al end;
wenzelm@233
   606
wenzelm@233
   607
wenzelm@233
   608
wenzelm@233
   609
(** generic tables **)
clasohm@0
   610
wenzelm@233
   611
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   612
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   613
  for long-term space efficiency.*)
wenzelm@233
   614
wenzelm@233
   615
(*append (new) elements to a table*)
wenzelm@233
   616
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   617
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   618
      let
wenzelm@233
   619
        val lst1 = dest_tab tab1;
wenzelm@233
   620
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   621
      in
wenzelm@233
   622
        if null new_lst2 then tab1
wenzelm@233
   623
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
   624
      end;
clasohm@0
   625
wenzelm@233
   626
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
   627
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
   628
  let
wenzelm@233
   629
    val lst1 = dest_tab tab1;
wenzelm@233
   630
    val lst2 = dest_tab tab2;
wenzelm@233
   631
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   632
  in
wenzelm@233
   633
    if null new_lst2 then tab1
wenzelm@233
   634
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
   635
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
   636
  end;
clasohm@0
   637
wenzelm@233
   638
wenzelm@233
   639
(*lists as tables*)
paulson@2243
   640
fun extend_list tab = generic_extend (op =) I I tab;
paulson@2243
   641
fun merge_lists tab = generic_merge (op =) I I tab;
wenzelm@233
   642
wenzelm@380
   643
fun merge_rev_lists xs [] = xs
wenzelm@380
   644
  | merge_rev_lists [] ys = ys
wenzelm@380
   645
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
   646
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
   647
clasohm@0
   648
clasohm@0
   649
wenzelm@233
   650
(** balanced trees **)
wenzelm@233
   651
wenzelm@233
   652
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   653
wenzelm@233
   654
(*balanced folding; avoids deep nesting*)
wenzelm@233
   655
fun fold_bal f [x] = x
wenzelm@233
   656
  | fold_bal f [] = raise Balance
wenzelm@233
   657
  | fold_bal f xs =
wenzelm@233
   658
      let val k = length xs div 2
wenzelm@233
   659
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
   660
             fold_bal f (drop(k, xs)))
wenzelm@233
   661
      end;
wenzelm@233
   662
wenzelm@233
   663
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   664
fun access_bal (f, g, x) n i =
wenzelm@233
   665
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   666
          if n=1 then x else
wenzelm@233
   667
          let val n2 = n div 2
wenzelm@233
   668
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   669
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   670
          end
wenzelm@233
   671
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   672
wenzelm@233
   673
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   674
fun accesses_bal (f, g, x) n =
wenzelm@233
   675
  let fun acc n =
wenzelm@233
   676
          if n=1 then [x] else
wenzelm@233
   677
          let val n2 = n div 2
wenzelm@233
   678
              val acc2 = acc n2
wenzelm@233
   679
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   680
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   681
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   682
wenzelm@233
   683
wenzelm@233
   684
wenzelm@233
   685
(** input / output **)
wenzelm@233
   686
paulson@2243
   687
val cd = OS.FileSys.chDir;
paulson@2243
   688
paulson@2243
   689
val prs_fn = ref(fn s => TextIO.output (TextIO.stdOut, s));
berghofe@1580
   690
berghofe@1580
   691
fun prs s = !prs_fn s;
wenzelm@233
   692
fun writeln s = prs (s ^ "\n");
wenzelm@233
   693
paulson@2243
   694
(* TextIO.output to LaTeX / xdvi *)
berghofe@1628
   695
fun latex s = 
paulson@2243
   696
        execute ( "( cd /tmp ; echo \"" ^ s ^
paulson@2243
   697
        "\" | isa2latex -s > $$.tex ; latex $$.tex ; xdvi $$.dvi ; rm $$.* ) > /dev/null &" ) ;
berghofe@1628
   698
berghofe@1580
   699
(*print warning*)
paulson@2243
   700
val warning_fn = ref(fn s => TextIO.output (TextIO.stdOut, s ^ "\n"));
berghofe@1580
   701
fun warning s = !warning_fn ("Warning: " ^ s);
wenzelm@233
   702
wenzelm@233
   703
(*print error message and abort to top level*)
berghofe@1580
   704
paulson@2243
   705
val error_fn = ref(fn s => TextIO.output (TextIO.stdOut, s ^ "\n"));
berghofe@1580
   706
wenzelm@233
   707
exception ERROR;
berghofe@1580
   708
fun error msg = (!error_fn msg; raise ERROR);
berghofe@1580
   709
fun sys_error msg = (!error_fn "*** SYSTEM ERROR ***"; error msg);
wenzelm@233
   710
wenzelm@233
   711
fun assert p msg = if p then () else error msg;
wenzelm@233
   712
fun deny p msg = if p then error msg else ();
wenzelm@233
   713
lcp@544
   714
(*Assert pred for every member of l, generating a message if pred fails*)
lcp@544
   715
fun assert_all pred l msg_fn = 
lcp@544
   716
  let fun asl [] = ()
paulson@2243
   717
        | asl (x::xs) = if pred x then asl xs
paulson@2243
   718
                        else error (msg_fn x)
lcp@544
   719
  in  asl l  end;
wenzelm@233
   720
wenzelm@233
   721
(*for the "test" target in Makefiles -- signifies successful termination*)
wenzelm@233
   722
fun maketest msg =
paulson@1592
   723
  (writeln msg; 
paulson@2243
   724
   let val os = TextIO.openOut "test" 
paulson@2243
   725
   in  TextIO.output (os, "Test examples ran successfully\n");
paulson@2243
   726
       TextIO.closeOut os
paulson@1592
   727
   end);
wenzelm@233
   728
wenzelm@233
   729
wenzelm@233
   730
(*print a list surrounded by the brackets lpar and rpar, with comma separator
wenzelm@233
   731
  print nothing for empty list*)
wenzelm@233
   732
fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
wenzelm@233
   733
  let fun prec x = (prs ","; pre x)
wenzelm@233
   734
  in
wenzelm@233
   735
    (case l of
wenzelm@233
   736
      [] => ()
wenzelm@233
   737
    | x::l => (prs lpar; pre x; seq prec l; prs rpar))
wenzelm@233
   738
  end;
wenzelm@233
   739
wenzelm@233
   740
(*print a list of items separated by newlines*)
wenzelm@233
   741
fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
wenzelm@233
   742
  seq (fn x => (pre x; writeln ""));
wenzelm@233
   743
wenzelm@233
   744
wenzelm@233
   745
val print_int = prs o string_of_int;
wenzelm@233
   746
wenzelm@233
   747
wenzelm@233
   748
wenzelm@233
   749
(** timing **)
wenzelm@233
   750
wenzelm@233
   751
(*unconditional timing function*)
paulson@2243
   752
fun timeit x = cond_timeit true x;
wenzelm@233
   753
wenzelm@233
   754
(*timed application function*)
wenzelm@233
   755
fun timeap f x = timeit (fn () => f x);
wenzelm@233
   756
wenzelm@233
   757
(*timed "use" function, printing filenames*)
wenzelm@233
   758
fun time_use fname = timeit (fn () =>
wenzelm@233
   759
  (writeln ("\n**** Starting " ^ fname ^ " ****"); use fname;
wenzelm@233
   760
   writeln ("\n**** Finished " ^ fname ^ " ****")));
wenzelm@233
   761
lcp@955
   762
(*For Makefiles: use the file, but exit with error code if errors found.*)
lcp@955
   763
fun exit_use fname = use fname handle _ => exit 1;
wenzelm@233
   764
wenzelm@233
   765
clasohm@1407
   766
(** filenames and paths **)
wenzelm@233
   767
clasohm@1290
   768
(*Convert UNIX filename of the form "path/file" to "path/" and "file";
wenzelm@233
   769
  if filename contains no slash, then it returns "" and "file"*)
wenzelm@233
   770
val split_filename =
wenzelm@233
   771
  (pairself implode) o take_suffix (not_equal "/") o explode;
wenzelm@233
   772
wenzelm@233
   773
val base_name = #2 o split_filename;
wenzelm@233
   774
clasohm@1290
   775
(*Merge splitted filename (path and file);
wenzelm@233
   776
  if path does not end with one a slash is appended*)
wenzelm@233
   777
fun tack_on "" name = name
wenzelm@233
   778
  | tack_on path name =
wenzelm@233
   779
      if last_elem (explode path) = "/" then path ^ name
wenzelm@233
   780
      else path ^ "/" ^ name;
wenzelm@233
   781
clasohm@1290
   782
(*Remove the extension of a filename, i.e. the part after the last '.'*)
wenzelm@233
   783
val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;
wenzelm@233
   784
clasohm@1290
   785
(*Make relative path to reach an absolute location from a different one*)
clasohm@1290
   786
fun relative_path cur_path dest_path =
clasohm@1290
   787
  let (*Remove common beginning of both paths and make relative path*)
clasohm@1290
   788
      fun mk_relative [] [] = []
clasohm@1290
   789
        | mk_relative [] ds = ds
clasohm@1290
   790
        | mk_relative cs [] = map (fn _ => "..") cs
clasohm@1290
   791
        | mk_relative (c::cs) (d::ds) =
clasohm@1290
   792
            if c = d then mk_relative cs ds
clasohm@1290
   793
            else ".." :: map (fn _ => "..") cs @ (d::ds);
clasohm@1290
   794
  in if cur_path = "" orelse hd (explode cur_path) <> "/" orelse
clasohm@1290
   795
        dest_path = "" orelse hd (explode dest_path) <> "/" then
clasohm@1290
   796
       error "Relative or empty path passed to relative_path"
clasohm@1290
   797
     else ();
clasohm@1290
   798
     space_implode "/" (mk_relative (space_explode "/" cur_path)
clasohm@1290
   799
                                    (space_explode "/" dest_path))
clasohm@1290
   800
  end;
wenzelm@233
   801
clasohm@1407
   802
(*Determine if absolute path1 is a subdirectory of absolute path2*)
clasohm@1407
   803
fun path1 subdir_of path2 =
clasohm@1407
   804
  if hd (explode path1) <> "/" orelse hd (explode path2) <> "/" then
clasohm@1407
   805
    error "Relative or empty path passed to subdir_of"
clasohm@1407
   806
  else (space_explode "/" path2) prefix (space_explode "/" path1);
clasohm@1407
   807
clasohm@1456
   808
fun absolute_path cwd file =
clasohm@1456
   809
  let fun rm_points [] result = rev result
clasohm@1456
   810
        | rm_points (".."::ds) result = rm_points ds (tl result)
clasohm@1456
   811
        | rm_points ("."::ds) result = rm_points ds result
clasohm@1456
   812
        | rm_points (d::ds) result = rm_points ds (d::result);
clasohm@1456
   813
  in if file = "" then ""
clasohm@1456
   814
     else if hd (explode file) = "/" then file
clasohm@1456
   815
     else "/" ^ space_implode "/"
clasohm@1456
   816
                  (rm_points (space_explode "/" (tack_on cwd file)) [])
clasohm@1456
   817
  end;
clasohm@1456
   818
wenzelm@233
   819
wenzelm@233
   820
(** misc functions **)
wenzelm@233
   821
wenzelm@233
   822
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
   823
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
   824
  let fun keypair x = (x, keyfun x)
wenzelm@233
   825
  in map keypair end;
clasohm@0
   826
wenzelm@233
   827
(*given a list of (x, key) pairs and a searchkey
clasohm@0
   828
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
   829
fun keyfilter [] searchkey = []
wenzelm@233
   830
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
   831
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
   832
      else keyfilter pairs searchkey;
clasohm@0
   833
clasohm@0
   834
clasohm@0
   835
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
   836
  Preserves order of elements in both lists.*)
clasohm@0
   837
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
   838
    let fun part ([], answer) = answer
wenzelm@233
   839
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
   840
            then  part (xs, (x::ys, ns))
wenzelm@233
   841
            else  part (xs, (ys, x::ns))
wenzelm@233
   842
    in  part (rev ys, ([], []))  end;
clasohm@0
   843
clasohm@0
   844
clasohm@0
   845
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
   846
    let fun part [] = []
wenzelm@233
   847
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
   848
                           in (x::xs)::(part xs') end
clasohm@0
   849
    in part end;
clasohm@0
   850
clasohm@0
   851
wenzelm@233
   852
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
   853
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
   854
fun partition_list p i j =
wenzelm@233
   855
  let fun part k xs =
wenzelm@233
   856
            if k>j then
clasohm@0
   857
              (case xs of [] => []
clasohm@0
   858
                         | _ => raise LIST "partition_list")
clasohm@0
   859
            else
wenzelm@233
   860
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
   861
            in  ns :: part(k+1)rest  end
clasohm@0
   862
  in  part i end;
clasohm@0
   863
clasohm@0
   864
wenzelm@233
   865
(* sorting *)
wenzelm@233
   866
wenzelm@233
   867
(*insertion sort; stable (does not reorder equal elements)
wenzelm@233
   868
  'less' is less-than test on type 'a*)
wenzelm@233
   869
fun sort (less: 'a*'a -> bool) =
clasohm@0
   870
  let fun insert (x, []) = [x]
wenzelm@233
   871
        | insert (x, y::ys) =
wenzelm@233
   872
              if less(y, x) then y :: insert (x, ys) else x::y::ys;
clasohm@0
   873
      fun sort1 [] = []
clasohm@0
   874
        | sort1 (x::xs) = insert (x, sort1 xs)
clasohm@0
   875
  in  sort1  end;
clasohm@0
   876
wenzelm@41
   877
(*sort strings*)
wenzelm@41
   878
val sort_strings = sort (op <= : string * string -> bool);
wenzelm@41
   879
wenzelm@41
   880
wenzelm@233
   881
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
   882
wenzelm@233
   883
fun transitive_closure [] = []
wenzelm@233
   884
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
   885
      let val qs = transitive_closure ps
paulson@2182
   886
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
paulson@2182
   887
          fun step(u, us) = (u, if x mem_string us then zs union_string us 
paulson@2243
   888
                                else us)
wenzelm@233
   889
      in (x, zs) :: map step qs end;
clasohm@0
   890
clasohm@0
   891
paulson@2003
   892
(** Recommended by Stephen K. Park and Keith W. Miller, 
paulson@2003
   893
      Random number generators: good ones are hard to find,
paulson@2003
   894
      CACM 31 (1988), 1192-1201. 
paulson@2003
   895
    Real number version for systems with 46-bit mantissae
paulson@2003
   896
    Computes  (a*seed) mod m ;  should be applied to integers only! **)
paulson@2025
   897
local val a = 16807.0  and  m = 2147483647.0  (* 2^31 - 1 *)
paulson@2003
   898
in  fun nextrandom seed =
paulson@2003
   899
          let val t = a*seed
paulson@2003
   900
          in  t - m * real(floor(t/m))  end
paulson@2003
   901
end;
paulson@2003
   902
wenzelm@233
   903
(* generating identifiers *)
clasohm@0
   904
clasohm@0
   905
local
wenzelm@233
   906
  val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z"
wenzelm@233
   907
  and k0 = ord "0" and k9 = ord "9"
paulson@2003
   908
paulson@2003
   909
  val seedr = ref 10000.0;
clasohm@0
   910
in
clasohm@0
   911
paulson@2003
   912
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@2003
   913
fun newid n = 
paulson@2003
   914
  let fun char i =
paulson@2003
   915
               if i<26 then chr (A+i)
paulson@2003
   916
          else if i<52 then chr (a+i-26)
paulson@2003
   917
          else if i<62 then chr (k0+i-52)
paulson@2003
   918
          else if i=62 then "_"
paulson@2003
   919
          else  (*i=63*)    "'"
paulson@2003
   920
  in  implode (map char (radixpand (64,n)))  end;
paulson@2003
   921
paulson@2025
   922
(*Randomly generated identifiers with given prefix; MUST start with a letter
paulson@2025
   923
    [division by two avoids overflow for ML systems whose maxint is 2^30 - 1 *)
paulson@2003
   924
fun gensym pre = pre ^ 
paulson@2025
   925
                 (#1(newid (floor (!seedr/2.0)), 
paulson@2243
   926
                     seedr := nextrandom (!seedr)))
paulson@2003
   927
clasohm@0
   928
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
   929
  If head is "z", bumps chars in tail.
clasohm@0
   930
  Digits are incremented as if they were integers.
clasohm@0
   931
  "_" and "'" are not changed.
wenzelm@233
   932
  For making variants of identifiers.*)
clasohm@0
   933
clasohm@0
   934
fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
wenzelm@233
   935
        if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
wenzelm@233
   936
        else "1" :: c :: cs
clasohm@0
   937
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
   938
wenzelm@233
   939
fun bump_list([], d) = [d]
wenzelm@233
   940
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
   941
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
   942
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
   943
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
wenzelm@233
   944
  | bump_list(c::cs, _) = let val k = ord(c)
wenzelm@233
   945
        in if (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
wenzelm@233
   946
              (k0 <= k andalso k < k9) then chr(k+1) :: cs else
wenzelm@233
   947
           if c="'" orelse c="_" then c :: bump_list(cs, "") else
wenzelm@233
   948
                error("bump_list: not legal in identifier: " ^
wenzelm@233
   949
                        implode(rev(c::cs)))
wenzelm@233
   950
        end;
clasohm@0
   951
clasohm@0
   952
end;
clasohm@0
   953
wenzelm@233
   954
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
   955
wenzelm@41
   956
wenzelm@233
   957
(* lexical scanning *)
clasohm@0
   958
wenzelm@233
   959
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
   960
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
   961
fun scanwords is_let cs =
clasohm@0
   962
  let fun scan1 [] = []
wenzelm@233
   963
        | scan1 cs =
wenzelm@233
   964
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
   965
            in implode lets :: scanwords is_let rest end;
wenzelm@233
   966
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
   967
clasohm@1364
   968
end;
clasohm@1364
   969
paulson@1592
   970
(*Variable-branching trees: for proof terms*)
paulson@1592
   971
datatype 'a mtree = Join of 'a * 'a mtree list;
paulson@1592
   972
clasohm@1364
   973
open Library;