src/Pure/library.ML
author wenzelm
Tue Dec 02 12:41:02 1997 +0100 (1997-12-02)
changeset 4343 9849fb57c395
parent 4326 7211ea5f29e2
child 4363 b449831f03f4
permissions -rw-r--r--
added prod_ord, dict_ord, list_ord;
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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
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trees, orders, diagnostics, timing, misc functions.
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*)
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infix |> ~~ \ \\ ins ins_string ins_int orf andf prefix upto downto
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  mem mem_int mem_string union union_int union_string inter inter_int
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  inter_string subset subset_int subset_string;
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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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(*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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(*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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(** stamps **)
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type stamp = unit ref;
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val stamp: unit -> stamp = ref;
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(** options **)
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datatype 'a option = None | Some of 'a;
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exception OPTION;
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fun the (Some x) = x
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  | the None = raise OPTION;
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(*strict!*)
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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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(*handle partial functions*)
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fun can f x = (f x; true) handle _ => false;
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fun try f x = Some (f x) handle _ => 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 function to components*)
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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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fun pairself f (x, y) = (f 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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(* predicates on lists *)
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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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(*temporarily set flag, handling errors*)
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fun setmp flag value f x =
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  let
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    val orig_value = ! flag;
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    fun return y = (flag := orig_value; y);
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  in
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    flag := value;
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    return (f x handle exn => (return (); raise exn))
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  end;
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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
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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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(*rear decomposition*)
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fun split_last [] = raise LIST "split_last"
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  | split_last [x] = ([], x)
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  | split_last (x :: xs) = apfst (cons x) (split_last xs);
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(*find the position of an element in a list*)
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fun find_index pred =
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  let fun find _ [] = ~1
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        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
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  in find 0 end;
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fun find_index_eq x = find_index (equal x);
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(*find first element satisfying predicate*)
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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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(*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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(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
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fun multiply ([], _) = []
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  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
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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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(* 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; ! i);
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fun dec i = (i := ! i - 1; ! i);
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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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val string_of_int = Int.toString;
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paulson@3407
   369
fun string_of_indexname (a,0) = a
paulson@3407
   370
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   371
wenzelm@233
   372
wenzelm@4212
   373
wenzelm@233
   374
(** strings **)
wenzelm@233
   375
wenzelm@233
   376
fun is_letter ch =
wenzelm@233
   377
  ord "A" <= ord ch andalso ord ch <= ord "Z" orelse
wenzelm@233
   378
  ord "a" <= ord ch andalso ord ch <= ord "z";
wenzelm@233
   379
wenzelm@233
   380
fun is_digit ch =
wenzelm@233
   381
  ord "0" <= ord ch andalso ord ch <= ord "9";
wenzelm@233
   382
wenzelm@233
   383
(*letter or _ or prime (')*)
wenzelm@233
   384
fun is_quasi_letter "_" = true
wenzelm@233
   385
  | is_quasi_letter "'" = true
wenzelm@233
   386
  | is_quasi_letter ch = is_letter ch;
wenzelm@233
   387
lcp@512
   388
(*white space: blanks, tabs, newlines, formfeeds*)
wenzelm@233
   389
val is_blank : string -> bool =
wenzelm@3393
   390
  fn " " => true | "\t" => true | "\n" => true | "\^L" => true | "\160" => true
wenzelm@3063
   391
    | _ => false;
wenzelm@233
   392
wenzelm@233
   393
val is_letdig = is_quasi_letter orf is_digit;
wenzelm@233
   394
wenzelm@2196
   395
(*printable chars*)
wenzelm@2196
   396
fun is_printable c = ord c > ord " " andalso ord c <= ord "~";
wenzelm@2196
   397
wenzelm@233
   398
(*lower all chars of string*)
wenzelm@233
   399
val to_lower =
wenzelm@233
   400
  let
wenzelm@233
   401
    fun lower ch =
wenzelm@233
   402
      if ch >= "A" andalso ch <= "Z" then
wenzelm@233
   403
        chr (ord ch - ord "A" + ord "a")
wenzelm@233
   404
      else ch;
wenzelm@233
   405
  in implode o (map lower) o explode end;
wenzelm@233
   406
lcp@512
   407
(*enclose in brackets*)
lcp@512
   408
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@255
   409
wenzelm@233
   410
(*simple quoting (does not escape special chars)*)
lcp@512
   411
val quote = enclose "\"" "\"";
wenzelm@233
   412
wenzelm@4212
   413
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   414
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   415
wenzelm@255
   416
val commas = space_implode ", ";
wenzelm@380
   417
val commas_quote = commas o map quote;
wenzelm@255
   418
wenzelm@233
   419
(*concatenate messages, one per line, into a string*)
wenzelm@255
   420
val cat_lines = space_implode "\n";
wenzelm@233
   421
wenzelm@4212
   422
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   423
fun space_explode _ "" = []
wenzelm@3832
   424
  | space_explode sep str =
wenzelm@3832
   425
      let
wenzelm@3832
   426
        fun expl chs =
wenzelm@3832
   427
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   428
            (cs, []) => [implode cs]
wenzelm@3832
   429
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   430
      in expl (explode str) end;
wenzelm@3832
   431
wenzelm@3832
   432
val split_lines = space_explode "\n";
wenzelm@3832
   433
wenzelm@3832
   434
wenzelm@233
   435
wenzelm@233
   436
(** lists as sets **)
wenzelm@233
   437
wenzelm@233
   438
(*membership in a list*)
wenzelm@233
   439
fun x mem [] = false
wenzelm@233
   440
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   441
paulson@2175
   442
(*membership in a list, optimized version for ints*)
berghofe@1576
   443
fun (x:int) mem_int [] = false
berghofe@1576
   444
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   445
paulson@2175
   446
(*membership in a list, optimized version for strings*)
berghofe@1576
   447
fun (x:string) mem_string [] = false
berghofe@1576
   448
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   449
clasohm@0
   450
(*generalized membership test*)
wenzelm@233
   451
fun gen_mem eq (x, []) = false
wenzelm@233
   452
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   453
wenzelm@233
   454
wenzelm@233
   455
(*insertion into list if not already there*)
paulson@2175
   456
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   457
paulson@2175
   458
(*insertion into list, optimized version for ints*)
paulson@2175
   459
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   460
paulson@2175
   461
(*insertion into list, optimized version for strings*)
paulson@2175
   462
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   463
clasohm@0
   464
(*generalized insertion*)
wenzelm@233
   465
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   466
wenzelm@233
   467
wenzelm@233
   468
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   469
fun xs union [] = xs
wenzelm@233
   470
  | [] union ys = ys
wenzelm@233
   471
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   472
paulson@2175
   473
(*union of sets, optimized version for ints*)
berghofe@1576
   474
fun (xs:int list) union_int [] = xs
berghofe@1576
   475
  | [] union_int ys = ys
berghofe@1576
   476
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   477
paulson@2175
   478
(*union of sets, optimized version for strings*)
berghofe@1576
   479
fun (xs:string list) union_string [] = xs
berghofe@1576
   480
  | [] union_string ys = ys
berghofe@1576
   481
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   482
clasohm@0
   483
(*generalized union*)
wenzelm@233
   484
fun gen_union eq (xs, []) = xs
wenzelm@233
   485
  | gen_union eq ([], ys) = ys
wenzelm@233
   486
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   487
wenzelm@233
   488
wenzelm@233
   489
(*intersection*)
wenzelm@233
   490
fun [] inter ys = []
wenzelm@233
   491
  | (x :: xs) inter ys =
wenzelm@233
   492
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   493
paulson@2175
   494
(*intersection, optimized version for ints*)
berghofe@1576
   495
fun ([]:int list) inter_int ys = []
berghofe@1576
   496
  | (x :: xs) inter_int ys =
berghofe@1576
   497
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   498
paulson@2175
   499
(*intersection, optimized version for strings *)
berghofe@1576
   500
fun ([]:string list) inter_string ys = []
berghofe@1576
   501
  | (x :: xs) inter_string ys =
berghofe@1576
   502
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   503
wenzelm@233
   504
wenzelm@233
   505
(*subset*)
wenzelm@233
   506
fun [] subset ys = true
wenzelm@233
   507
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   508
paulson@2175
   509
(*subset, optimized version for ints*)
berghofe@1576
   510
fun ([]:int list) subset_int ys = true
berghofe@1576
   511
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   512
paulson@2175
   513
(*subset, optimized version for strings*)
berghofe@1576
   514
fun ([]:string list) subset_string ys = true
berghofe@1576
   515
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   516
paulson@2182
   517
(*set equality for strings*)
berghofe@1576
   518
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   519
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   520
paulson@2182
   521
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   522
wenzelm@265
   523
wenzelm@233
   524
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   525
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   526
  | [] \ x = [];
wenzelm@233
   527
paulson@2243
   528
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   529
wenzelm@233
   530
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   531
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   532
paulson@2243
   533
fun gen_rems eq = foldl (gen_rem eq);
wenzelm@233
   534
wenzelm@233
   535
wenzelm@233
   536
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   537
  first of equal elements*)
wenzelm@233
   538
fun gen_distinct eq lst =
wenzelm@233
   539
  let
wenzelm@233
   540
    val memb = gen_mem eq;
clasohm@0
   541
wenzelm@233
   542
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   543
      | dist (rev_seen, x :: xs) =
wenzelm@233
   544
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   545
          else dist (x :: rev_seen, xs);
wenzelm@233
   546
  in
wenzelm@233
   547
    dist ([], lst)
wenzelm@233
   548
  end;
wenzelm@233
   549
paulson@2243
   550
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   551
wenzelm@4102
   552
(*tuned version of distinct -- eq wrt. strings in fst component*)
wenzelm@4102
   553
fun distinct_fst_string lst =
wenzelm@4102
   554
  let
wenzelm@4102
   555
    fun mem_str ((_:string, _), []) = false
wenzelm@4102
   556
      | mem_str (p as (x, _), ((y, _) :: qs)) = x = y orelse mem_str (p, qs);
wenzelm@4102
   557
wenzelm@4102
   558
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@4102
   559
      | dist (rev_seen, p :: ps) =
wenzelm@4102
   560
          if mem_str (p, rev_seen) then dist (rev_seen, ps)
wenzelm@4102
   561
          else dist (p :: rev_seen, ps);
wenzelm@4102
   562
  in
wenzelm@4102
   563
    dist ([], lst)
wenzelm@4102
   564
  end;
wenzelm@4102
   565
wenzelm@233
   566
wenzelm@233
   567
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   568
fun findrep [] = []
wenzelm@233
   569
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   570
wenzelm@233
   571
wenzelm@255
   572
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   573
  order, takes first of equal elements*)
wenzelm@255
   574
fun gen_duplicates eq lst =
wenzelm@255
   575
  let
wenzelm@255
   576
    val memb = gen_mem eq;
wenzelm@255
   577
wenzelm@255
   578
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   579
      | dups (rev_dups, x :: xs) =
wenzelm@255
   580
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   581
            dups (rev_dups, xs)
wenzelm@255
   582
          else dups (x :: rev_dups, xs);
wenzelm@255
   583
  in
wenzelm@255
   584
    dups ([], lst)
wenzelm@255
   585
  end;
wenzelm@255
   586
paulson@2243
   587
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   588
wenzelm@255
   589
wenzelm@233
   590
wenzelm@233
   591
(** association lists **)
clasohm@0
   592
wenzelm@233
   593
(*association list lookup*)
wenzelm@233
   594
fun assoc ([], key) = None
wenzelm@233
   595
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   596
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   597
paulson@2175
   598
(*association list lookup, optimized version for ints*)
berghofe@1576
   599
fun assoc_int ([], (key:int)) = None
berghofe@1576
   600
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   601
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   602
paulson@2175
   603
(*association list lookup, optimized version for strings*)
berghofe@1576
   604
fun assoc_string ([], (key:string)) = None
berghofe@1576
   605
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   606
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   607
paulson@2175
   608
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   609
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   610
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   611
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   612
wenzelm@233
   613
fun assocs ps x =
wenzelm@233
   614
  (case assoc (ps, x) of
wenzelm@233
   615
    None => []
wenzelm@233
   616
  | Some ys => ys);
wenzelm@233
   617
wenzelm@255
   618
(*two-fold association list lookup*)
wenzelm@255
   619
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   620
  (case assoc (aal, key1) of
wenzelm@255
   621
    Some al => assoc (al, key2)
wenzelm@255
   622
  | None => None);
wenzelm@255
   623
wenzelm@233
   624
(*generalized association list lookup*)
wenzelm@233
   625
fun gen_assoc eq ([], key) = None
wenzelm@233
   626
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   627
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   628
wenzelm@233
   629
(*association list update*)
wenzelm@233
   630
fun overwrite (al, p as (key, _)) =
wenzelm@233
   631
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   632
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   633
        | over [] = [p]
wenzelm@233
   634
  in over al end;
wenzelm@233
   635
wenzelm@2522
   636
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
   637
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
   638
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
   639
        | over [] = [p]
wenzelm@2522
   640
  in over al end;
wenzelm@2522
   641
wenzelm@233
   642
wenzelm@233
   643
wenzelm@233
   644
(** generic tables **)
clasohm@0
   645
wenzelm@233
   646
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   647
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   648
  for long-term space efficiency.*)
wenzelm@233
   649
wenzelm@233
   650
(*append (new) elements to a table*)
wenzelm@233
   651
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   652
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   653
      let
wenzelm@233
   654
        val lst1 = dest_tab tab1;
wenzelm@233
   655
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   656
      in
wenzelm@233
   657
        if null new_lst2 then tab1
wenzelm@233
   658
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
   659
      end;
clasohm@0
   660
wenzelm@233
   661
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
   662
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
   663
  let
wenzelm@233
   664
    val lst1 = dest_tab tab1;
wenzelm@233
   665
    val lst2 = dest_tab tab2;
wenzelm@233
   666
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   667
  in
wenzelm@233
   668
    if null new_lst2 then tab1
wenzelm@233
   669
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
   670
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
   671
  end;
clasohm@0
   672
wenzelm@233
   673
wenzelm@233
   674
(*lists as tables*)
paulson@2243
   675
fun extend_list tab = generic_extend (op =) I I tab;
paulson@2243
   676
fun merge_lists tab = generic_merge (op =) I I tab;
wenzelm@233
   677
wenzelm@380
   678
fun merge_rev_lists xs [] = xs
wenzelm@380
   679
  | merge_rev_lists [] ys = ys
wenzelm@380
   680
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
   681
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
   682
clasohm@0
   683
clasohm@0
   684
wenzelm@233
   685
(** balanced trees **)
wenzelm@233
   686
wenzelm@233
   687
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   688
wenzelm@233
   689
(*balanced folding; avoids deep nesting*)
wenzelm@233
   690
fun fold_bal f [x] = x
wenzelm@233
   691
  | fold_bal f [] = raise Balance
wenzelm@233
   692
  | fold_bal f xs =
wenzelm@233
   693
      let val k = length xs div 2
wenzelm@233
   694
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
   695
             fold_bal f (drop(k, xs)))
wenzelm@233
   696
      end;
wenzelm@233
   697
wenzelm@233
   698
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   699
fun access_bal (f, g, x) n i =
wenzelm@233
   700
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   701
          if n=1 then x else
wenzelm@233
   702
          let val n2 = n div 2
wenzelm@233
   703
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   704
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   705
          end
wenzelm@233
   706
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   707
wenzelm@233
   708
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   709
fun accesses_bal (f, g, x) n =
wenzelm@233
   710
  let fun acc n =
wenzelm@233
   711
          if n=1 then [x] else
wenzelm@233
   712
          let val n2 = n div 2
wenzelm@233
   713
              val acc2 = acc n2
wenzelm@233
   714
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   715
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   716
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   717
wenzelm@233
   718
wenzelm@233
   719
wenzelm@2506
   720
(** orders **)
wenzelm@2506
   721
wenzelm@2506
   722
datatype order = LESS | EQUAL | GREATER;
wenzelm@2506
   723
wenzelm@4343
   724
fun int_ord (i, j: int) =
wenzelm@2506
   725
  if i < j then LESS
wenzelm@2506
   726
  else if i = j then EQUAL
wenzelm@2506
   727
  else GREATER;
wenzelm@2506
   728
wenzelm@4343
   729
fun string_ord (a, b: string) =
wenzelm@2506
   730
  if a < b then LESS
wenzelm@2506
   731
  else if a = b then EQUAL
wenzelm@2506
   732
  else GREATER;
wenzelm@2506
   733
wenzelm@4343
   734
(*lexicographic product*)
wenzelm@4343
   735
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   736
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   737
wenzelm@4343
   738
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
   739
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
   740
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
   741
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
   742
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
   743
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   744
wenzelm@4343
   745
(*lexicographic product of lists*)
wenzelm@4343
   746
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
   747
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
   748
wenzelm@2506
   749
wenzelm@2506
   750
wenzelm@3525
   751
(** input / output and diagnostics **)
wenzelm@233
   752
paulson@2243
   753
val cd = OS.FileSys.chDir;
wenzelm@2317
   754
val pwd = OS.FileSys.getDir;
paulson@2243
   755
wenzelm@3525
   756
wenzelm@3525
   757
local
wenzelm@3525
   758
  fun out s =
wenzelm@3525
   759
    (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
wenzelm@3525
   760
wenzelm@3525
   761
  fun prefix_lines prfx txt =
wenzelm@3832
   762
    txt |> split_lines |> map (fn s => prfx ^ s ^ "\n") |> implode;
wenzelm@3525
   763
in
wenzelm@3525
   764
wenzelm@3525
   765
(*hooks for output channels: normal, warning, error*)
wenzelm@3525
   766
val prs_fn = ref (fn s => out s);
wenzelm@3525
   767
val warning_fn = ref (fn s => out (prefix_lines "### " s));
wenzelm@3525
   768
val error_fn = ref (fn s => out (prefix_lines "*** " s));
wenzelm@3525
   769
wenzelm@3525
   770
end;
berghofe@1580
   771
berghofe@1580
   772
fun prs s = !prs_fn s;
wenzelm@233
   773
fun writeln s = prs (s ^ "\n");
wenzelm@233
   774
wenzelm@3525
   775
fun warning s = !warning_fn s;
wenzelm@233
   776
wenzelm@233
   777
(*print error message and abort to top level*)
wenzelm@233
   778
exception ERROR;
wenzelm@4212
   779
fun error_msg s = !error_fn s;	  (*promise to raise ERROR later!*)
wenzelm@3553
   780
fun error s = (error_msg s; raise ERROR);
wenzelm@3553
   781
fun sys_error msg = (error_msg " !! SYSTEM ERROR !!\n"; error msg);
wenzelm@233
   782
wenzelm@233
   783
fun assert p msg = if p then () else error msg;
wenzelm@233
   784
fun deny p msg = if p then error msg else ();
wenzelm@233
   785
lcp@544
   786
(*Assert pred for every member of l, generating a message if pred fails*)
wenzelm@4212
   787
fun assert_all pred l msg_fn =
lcp@544
   788
  let fun asl [] = ()
wenzelm@4212
   789
        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)
wenzelm@4212
   790
  in asl l end;
wenzelm@233
   791
wenzelm@3624
   792
wenzelm@4212
   793
(* handle errors capturing messages *)
wenzelm@3699
   794
wenzelm@3699
   795
datatype 'a error =
wenzelm@3699
   796
  Error of string |
wenzelm@3699
   797
  OK of 'a;
wenzelm@3699
   798
wenzelm@4248
   799
fun get_error (Error msg) = Some msg
wenzelm@4248
   800
  | get_error _ = None;
wenzelm@4248
   801
wenzelm@4248
   802
fun get_ok (OK x) = Some x
wenzelm@4248
   803
  | get_ok _ = None;
wenzelm@4248
   804
wenzelm@3699
   805
fun handle_error f x =
wenzelm@3699
   806
  let
wenzelm@3699
   807
    val buffer = ref "";
wenzelm@3699
   808
    fun capture s = buffer := ! buffer ^ s ^ "\n";
wenzelm@3699
   809
    val result = Some (setmp error_fn capture f x) handle ERROR => None;
wenzelm@3699
   810
  in
wenzelm@4212
   811
    (case result of
wenzelm@3699
   812
      None => Error (! buffer)
wenzelm@4212
   813
    | Some y => OK y)
wenzelm@3624
   814
  end;
wenzelm@3624
   815
wenzelm@3624
   816
wenzelm@233
   817
wenzelm@233
   818
(** timing **)
wenzelm@233
   819
paulson@4326
   820
(*a conditional timing function: applies f to () and, if the flag is true,
paulson@4326
   821
  prints its runtime*)
paulson@4326
   822
fun cond_timeit flag f =
paulson@4326
   823
  if flag then
paulson@4326
   824
    let val start = startTiming()
paulson@4326
   825
        val result = f ()
paulson@4326
   826
    in
paulson@4326
   827
	writeln (endTiming start);  result
paulson@4326
   828
    end
paulson@4326
   829
  else f ();
paulson@4326
   830
wenzelm@233
   831
(*unconditional timing function*)
paulson@2243
   832
fun timeit x = cond_timeit true x;
wenzelm@233
   833
wenzelm@233
   834
(*timed application function*)
wenzelm@233
   835
fun timeap f x = timeit (fn () => f x);
wenzelm@233
   836
berghofe@3606
   837
wenzelm@233
   838
wenzelm@233
   839
(** misc functions **)
wenzelm@233
   840
wenzelm@233
   841
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
   842
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
   843
  let fun keypair x = (x, keyfun x)
wenzelm@233
   844
  in map keypair end;
clasohm@0
   845
wenzelm@233
   846
(*given a list of (x, key) pairs and a searchkey
clasohm@0
   847
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
   848
fun keyfilter [] searchkey = []
wenzelm@233
   849
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
   850
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
   851
      else keyfilter pairs searchkey;
clasohm@0
   852
clasohm@0
   853
clasohm@0
   854
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
   855
  Preserves order of elements in both lists.*)
clasohm@0
   856
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
   857
    let fun part ([], answer) = answer
wenzelm@233
   858
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
   859
            then  part (xs, (x::ys, ns))
wenzelm@233
   860
            else  part (xs, (ys, x::ns))
wenzelm@233
   861
    in  part (rev ys, ([], []))  end;
clasohm@0
   862
clasohm@0
   863
clasohm@0
   864
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
   865
    let fun part [] = []
wenzelm@233
   866
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
   867
                           in (x::xs)::(part xs') end
clasohm@0
   868
    in part end;
clasohm@0
   869
clasohm@0
   870
wenzelm@233
   871
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
   872
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
   873
fun partition_list p i j =
wenzelm@233
   874
  let fun part k xs =
wenzelm@233
   875
            if k>j then
clasohm@0
   876
              (case xs of [] => []
clasohm@0
   877
                         | _ => raise LIST "partition_list")
clasohm@0
   878
            else
wenzelm@233
   879
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
   880
            in  ns :: part(k+1)rest  end
clasohm@0
   881
  in  part i end;
clasohm@0
   882
clasohm@0
   883
wenzelm@233
   884
(* sorting *)
wenzelm@233
   885
wenzelm@233
   886
(*insertion sort; stable (does not reorder equal elements)
wenzelm@233
   887
  'less' is less-than test on type 'a*)
wenzelm@233
   888
fun sort (less: 'a*'a -> bool) =
clasohm@0
   889
  let fun insert (x, []) = [x]
wenzelm@233
   890
        | insert (x, y::ys) =
wenzelm@233
   891
              if less(y, x) then y :: insert (x, ys) else x::y::ys;
clasohm@0
   892
      fun sort1 [] = []
clasohm@0
   893
        | sort1 (x::xs) = insert (x, sort1 xs)
clasohm@0
   894
  in  sort1  end;
clasohm@0
   895
wenzelm@41
   896
(*sort strings*)
wenzelm@3973
   897
fun sort_wrt sel xs = sort (op <= o pairself (sel: 'a -> string)) xs;
wenzelm@3973
   898
val sort_strings = sort_wrt I;
wenzelm@41
   899
wenzelm@41
   900
wenzelm@233
   901
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
   902
wenzelm@233
   903
fun transitive_closure [] = []
wenzelm@233
   904
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
   905
      let val qs = transitive_closure ps
paulson@2182
   906
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
paulson@2182
   907
          fun step(u, us) = (u, if x mem_string us then zs union_string us 
paulson@2243
   908
                                else us)
wenzelm@233
   909
      in (x, zs) :: map step qs end;
clasohm@0
   910
clasohm@0
   911
wenzelm@233
   912
(* generating identifiers *)
clasohm@0
   913
paulson@4063
   914
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
   915
local
paulson@4063
   916
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
   917
fun char i =      if i<26 then chr (ord "A" + i)
paulson@4063
   918
	     else if i<52 then chr (ord "a" + i - 26)
paulson@4063
   919
	     else if i<62 then chr (ord"0" + i - 52)
paulson@4063
   920
	     else if i=62 then "_"
paulson@4063
   921
	     else  (*i=63*)    "'";
paulson@4063
   922
paulson@4063
   923
val charVec = Vector.tabulate (64, char);
paulson@4063
   924
paulson@4063
   925
fun newid n = 
paulson@4063
   926
  let 
wenzelm@4284
   927
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
   928
wenzelm@4284
   929
val seedr = ref 0;
clasohm@0
   930
paulson@4063
   931
in
wenzelm@4284
   932
paulson@4063
   933
fun init_gensym() = (seedr := 0);
paulson@2003
   934
wenzelm@4284
   935
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@4063
   936
end;
paulson@4063
   937
paulson@4063
   938
paulson@4063
   939
local
paulson@4063
   940
(*Identifies those character codes legal in identifiers.
paulson@4063
   941
  chould use Basis Library character functions if Poly/ML provided characters*)
paulson@4063
   942
fun idCode k = (ord "a" <= k andalso k < ord "z") orelse 
paulson@4063
   943
               (ord "A" <= k andalso k < ord "Z") orelse
paulson@4063
   944
               (ord "0" <= k andalso k < ord "9");
paulson@4063
   945
paulson@4063
   946
val idCodeVec = Vector.tabulate (256, idCode);
paulson@4063
   947
paulson@4063
   948
in
paulson@2003
   949
clasohm@0
   950
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
   951
  If head is "z", bumps chars in tail.
clasohm@0
   952
  Digits are incremented as if they were integers.
clasohm@0
   953
  "_" and "'" are not changed.
wenzelm@233
   954
  For making variants of identifiers.*)
clasohm@0
   955
paulson@4063
   956
fun bump_int_list(c::cs) = 
paulson@4063
   957
	if c="9" then "0" :: bump_int_list cs 
paulson@4063
   958
	else
paulson@4063
   959
        if "0" <= c andalso c < "9" then chr(ord(c)+1) :: cs
wenzelm@233
   960
        else "1" :: c :: cs
clasohm@0
   961
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
   962
wenzelm@233
   963
fun bump_list([], d) = [d]
wenzelm@233
   964
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
   965
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
   966
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
   967
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
paulson@4063
   968
  | bump_list(c::cs, _) = 
paulson@4063
   969
        let val k = ord(c)
paulson@4063
   970
        in if Vector.sub(idCodeVec,k) then chr(k+1) :: cs 
paulson@4063
   971
	   else
paulson@4063
   972
           if c="'" orelse c="_" then c :: bump_list(cs, "") 
paulson@4063
   973
	   else error("bump_list: not legal in identifier: " ^
paulson@4063
   974
		      implode(rev(c::cs)))
wenzelm@233
   975
        end;
clasohm@0
   976
clasohm@0
   977
end;
clasohm@0
   978
wenzelm@233
   979
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
   980
wenzelm@41
   981
wenzelm@233
   982
(* lexical scanning *)
clasohm@0
   983
wenzelm@233
   984
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
   985
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
   986
fun scanwords is_let cs =
clasohm@0
   987
  let fun scan1 [] = []
wenzelm@233
   988
        | scan1 cs =
wenzelm@233
   989
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
   990
            in implode lets :: scanwords is_let rest end;
wenzelm@233
   991
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
   992
wenzelm@4212
   993
wenzelm@4212
   994
wenzelm@4212
   995
(* Variable-branching trees: for proof terms etc. *)
wenzelm@4212
   996
datatype 'a mtree = Join of 'a * 'a mtree list;
wenzelm@4212
   997
wenzelm@4212
   998
wenzelm@4255
   999
(* generic objects -- fool the ML type system via exception constructors *)
wenzelm@4255
  1000
type object = exn;
wenzelm@4255
  1001
wenzelm@4255
  1002
clasohm@1364
  1003
end;
clasohm@1364
  1004
clasohm@1364
  1005
open Library;