(*  Title:      Pure/library.ML

    ID:         $Id$

    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

    Copyright   1992  University of Cambridge

Basic library: functions, options, pairs, booleans, lists, integers,

strings, lists as sets, association lists, generic tables, balanced

trees, orders, diagnostics, timing, misc functions.

*)

infix |> ~~ \ \\ ins ins_string ins_int orf andf prefix upto downto

  mem mem_int mem_string union union_int union_string inter inter_int

  inter_string subset subset_int subset_string;

structure Library =

struct

(** functions **)

(*handy combinators*)

fun curry f x y = f (x, y);

fun uncurry f (x, y) = f x y;

fun I x = x;

fun K x y = x;

(*reverse apply*)

fun (x |> f) = f x;

(*application of (infix) operator to its left or right argument*)

fun apl (x, f) y = f (x, y);

fun apr (f, y) x = f (x, y);

(*function exponentiation: f(...(f x)...) with n applications of f*)

fun funpow n f x =

  let fun rep (0, x) = x

        | rep (n, x) = rep (n - 1, f x)

  in rep (n, x) end;

(** stamps **)

type stamp = unit ref;

val stamp: unit -> stamp = ref;

(** options **)

datatype 'a option = None | Some of 'a;

exception OPTION;

fun the (Some x) = x

  | the None = raise OPTION;

(*strict!*)

fun if_none None y = y

  | if_none (Some x) _ = x;

fun is_some (Some _) = true

  | is_some None = false;

fun is_none (Some _) = false

  | is_none None = true;

fun apsome f (Some x) = Some (f x)

  | apsome _ None = None;

(*handle partial functions*)

fun can f x = (f x; true) handle _ => false;

fun try f x = Some (f x) handle _ => None;

(** pairs **)

fun pair x y = (x, y);

fun rpair x y = (y, x);

fun fst (x, y) = x;

fun snd (x, y) = y;

fun eq_fst ((x1, _), (x2, _)) = x1 = x2;

fun eq_snd ((_, y1), (_, y2)) = y1 = y2;

fun swap (x, y) = (y, x);

(*apply function to components*)

fun apfst f (x, y) = (f x, y);

fun apsnd f (x, y) = (x, f y);

fun pairself f (x, y) = (f x, f y);

(** booleans **)

(* equality *)

fun equal x y = x = y;

fun not_equal x y = x <> y;

(* operators for combining predicates *)

fun (p orf q) = fn x => p x orelse q x;

fun (p andf q) = fn x => p x andalso q x;

(* predicates on lists *)

(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)

fun exists (pred: 'a -> bool) : 'a list -> bool =

  let fun boolf [] = false

        | boolf (x :: xs) = pred x orelse boolf xs

  in boolf end;

(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)

fun forall (pred: 'a -> bool) : 'a list -> bool =

  let fun boolf [] = true

        | boolf (x :: xs) = pred x andalso boolf xs

  in boolf end;

(* flags *)

fun set flag = (flag := true; true);

fun reset flag = (flag := false; false);

fun toggle flag = (flag := not (! flag); ! flag);

(*temporarily set flag, handling errors*)

fun setmp flag value f x =

  let

    val orig_value = ! flag;

    fun return y = (flag := orig_value; y);

  in

    flag := value;

    return (f x handle exn => (return (); raise exn))

  end;

(** lists **)

exception LIST of string;

fun null [] = true

  | null (_ :: _) = false;

fun hd [] = raise LIST "hd"

  | hd (x :: _) = x;

fun tl [] = raise LIST "tl"

  | tl (_ :: xs) = xs;

fun cons x xs = x :: xs;

(* fold *)

(*the following versions of fold are designed to fit nicely with infixes*)

(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn

    for operators that associate to the left (TAIL RECURSIVE)*)

fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =

  let fun itl (e, [])  = e

        | itl (e, a::l) = itl (f(e, a), l)

  in  itl end;

(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))

    for operators that associate to the right (not tail recursive)*)

fun foldr f (l, e) =

  let fun itr [] = e

        | itr (a::l) = f(a, itr l)

  in  itr l  end;

(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))

    for n > 0, operators that associate to the right (not tail recursive)*)

fun foldr1 f l =

  let fun itr [x] = x

        | itr (x::l) = f(x, itr l)

  in  itr l  end;

(* basic list functions *)

(*length of a list, should unquestionably be a standard function*)

local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)

        | length1 (n, x :: xs) = length1 (n + 1, xs)

in  fun length l = length1 (0, l) end;

(*take the first n elements from a list*)

fun take (n, []) = []

  | take (n, x :: xs) =

      if n > 0 then x :: take (n - 1, xs) else [];

(*drop the first n elements from a list*)

fun drop (n, []) = []

  | drop (n, x :: xs) =

      if n > 0 then drop (n - 1, xs) else x :: xs;

(*return nth element of a list, where 0 designates the first element;

  raise EXCEPTION if list too short*)

fun nth_elem NL =

  (case drop NL of

    [] => raise LIST "nth_elem"

  | x :: _ => x);

(*last element of a list*)

fun last_elem [] = raise LIST "last_elem"

  | last_elem [x] = x

  | last_elem (_ :: xs) = last_elem xs;

(*rear decomposition*)

fun split_last [] = raise LIST "split_last"

  | split_last [x] = ([], x)

  | split_last (x :: xs) = apfst (cons x) (split_last xs);

(*find the position of an element in a list*)

fun find_index pred =

  let fun find _ [] = ~1

        | find n (x :: xs) = if pred x then n else find (n + 1) xs;

  in find 0 end;

fun find_index_eq x = find_index (equal x);

(*find first element satisfying predicate*)

fun find_first _ [] = None

  | find_first pred (x :: xs) =

      if pred x then Some x else find_first pred xs;

(*flatten a list of lists to a list*)

fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);

(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates

  (proc x1; ...; proc xn) for side effects*)

fun seq (proc: 'a -> unit) : 'a list -> unit =

  let fun seqf [] = ()

        | seqf (x :: xs) = (proc x; seqf xs)

  in seqf end;

(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)

fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs

  | separate _ xs = xs;

(*make the list [x, x, ..., x] of length n*)

fun replicate n (x: 'a) : 'a list =

  let fun rep (0, xs) = xs

        | rep (n, xs) = rep (n - 1, x :: xs)

  in

    if n < 0 then raise LIST "replicate"

    else rep (n, [])

  end;

(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)

fun multiply ([], _) = []

  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);

(* filter *)

(*copy the list preserving elements that satisfy the predicate*)

fun filter (pred: 'a->bool) : 'a list -> 'a list =

  let fun filt [] = []

        | filt (x :: xs) = if pred x then x :: filt xs else filt xs

  in filt end;

fun filter_out f = filter (not o f);

fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list

  | mapfilter f (x :: xs) =

      (case f x of

        None => mapfilter f xs

      | Some y => y :: mapfilter f xs);

(* lists of pairs *)

fun map2 _ ([], []) = []

  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))

  | map2 _ _ = raise LIST "map2";

fun exists2 _ ([], []) = false

  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)

  | exists2 _ _ = raise LIST "exists2";

fun forall2 _ ([], []) = true

  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)

  | forall2 _ _ = raise LIST "forall2";

(*combine two lists forming a list of pairs:

  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)

fun [] ~~ [] = []

  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)

  | _ ~~ _ = raise LIST "~~";

(*inverse of ~~; the old 'split':

  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)

fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);

(* prefixes, suffixes *)

fun [] prefix _ = true

  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)

  | _ prefix _ = false;

(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])

   where xi is the first element that does not satisfy the predicate*)

fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =

  let fun take (rxs, []) = (rev rxs, [])

        | take (rxs, x :: xs) =

            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)

  in  take([], xs)  end;

(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])

   where xi is the last element that does not satisfy the predicate*)

fun take_suffix _ [] = ([], [])

  | take_suffix pred (x :: xs) =

      (case take_suffix pred xs of

        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)

      | (prfx, sffx) => (x :: prfx, sffx));

(** integers **)

fun inc i = (i := ! i + 1; ! i);

fun dec i = (i := ! i - 1; ! i);

(* lists of integers *)

(*make the list [from, from + 1, ..., to]*)

fun (from upto to) =

  if from > to then [] else from :: ((from + 1) upto to);

(*make the list [from, from - 1, ..., to]*)

fun (from downto to) =

  if from < to then [] else from :: ((from - 1) downto to);

(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)

fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)

  | downto0 ([], n) = n = ~1;

(* convert integers to strings *)

(*expand the number in the given base;

  example: radixpand (2, 8) gives [1, 0, 0, 0]*)

fun radixpand (base, num) : int list =

  let

    fun radix (n, tail) =

      if n < base then n :: tail

      else radix (n div base, (n mod base) :: tail)

  in radix (num, []) end;

(*expands a number into a string of characters starting from "zerochar";

  example: radixstring (2, "0", 8) gives "1000"*)

fun radixstring (base, zerochar, num) =

  let val offset = ord zerochar;

      fun chrof n = chr (offset + n)

  in implode (map chrof (radixpand (base, num))) end;

val string_of_int = Int.toString;

fun string_of_indexname (a,0) = a

  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;

(** strings **)

fun is_letter ch =

  ord "A" <= ord ch andalso ord ch <= ord "Z" orelse

  ord "a" <= ord ch andalso ord ch <= ord "z";

fun is_digit ch =

  ord "0" <= ord ch andalso ord ch <= ord "9";

(*letter or _ or prime (')*)

fun is_quasi_letter "_" = true

  | is_quasi_letter "'" = true

  | is_quasi_letter ch = is_letter ch;

(*white space: blanks, tabs, newlines, formfeeds*)

val is_blank : string -> bool =

  fn " " => true | "\t" => true | "\n" => true | "\^L" => true | "\160" => true

    | _ => false;

val is_letdig = is_quasi_letter orf is_digit;

(*printable chars*)

fun is_printable c = ord c > ord " " andalso ord c <= ord "~";

(*lower all chars of string*)

val to_lower =

  let

    fun lower ch =

      if ch >= "A" andalso ch <= "Z" then

        chr (ord ch - ord "A" + ord "a")

      else ch;

  in implode o (map lower) o explode end;

(*enclose in brackets*)

fun enclose lpar rpar str = lpar ^ str ^ rpar;

(*simple quoting (does not escape special chars)*)

val quote = enclose "\"" "\"";

(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)

fun space_implode a bs = implode (separate a bs);

val commas = space_implode ", ";

val commas_quote = commas o map quote;

(*concatenate messages, one per line, into a string*)

val cat_lines = space_implode "\n";

(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)

fun space_explode _ "" = []

  | space_explode sep str =

      let

        fun expl chs =

          (case take_prefix (not_equal sep) chs of

            (cs, []) => [implode cs]

          | (cs, _ :: cs') => implode cs :: expl cs');

      in expl (explode str) end;

val split_lines = space_explode "\n";

(** lists as sets **)

(*membership in a list*)

fun x mem [] = false

  | x mem (y :: ys) = x = y orelse x mem ys;

(*membership in a list, optimized version for ints*)

fun (x:int) mem_int [] = false

  | x mem_int (y :: ys) = x = y orelse x mem_int ys;

(*membership in a list, optimized version for strings*)

fun (x:string) mem_string [] = false

  | x mem_string (y :: ys) = x = y orelse x mem_string ys;

(*generalized membership test*)

fun gen_mem eq (x, []) = false

  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);

(*insertion into list if not already there*)

fun (x ins xs) = if x mem xs then xs else x :: xs;

(*insertion into list, optimized version for ints*)

fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;

(*insertion into list, optimized version for strings*)

fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;

(*generalized insertion*)

fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;

(*union of sets represented as lists: no repetitions*)

fun xs union [] = xs

  | [] union ys = ys

  | (x :: xs) union ys = xs union (x ins ys);

(*union of sets, optimized version for ints*)

fun (xs:int list) union_int [] = xs

  | [] union_int ys = ys

  | (x :: xs) union_int ys = xs union_int (x ins_int ys);

(*union of sets, optimized version for strings*)

fun (xs:string list) union_string [] = xs

  | [] union_string ys = ys

  | (x :: xs) union_string ys = xs union_string (x ins_string ys);

(*generalized union*)

fun gen_union eq (xs, []) = xs

  | gen_union eq ([], ys) = ys

  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));

(*intersection*)

fun [] inter ys = []

  | (x :: xs) inter ys =

      if x mem ys then x :: (xs inter ys) else xs inter ys;

(*intersection, optimized version for ints*)

fun ([]:int list) inter_int ys = []

  | (x :: xs) inter_int ys =

      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;

(*intersection, optimized version for strings *)

fun ([]:string list) inter_string ys = []

  | (x :: xs) inter_string ys =

      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;

(*subset*)

fun [] subset ys = true

  | (x :: xs) subset ys = x mem ys andalso xs subset ys;

(*subset, optimized version for ints*)

fun ([]:int list) subset_int ys = true

  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;

(*subset, optimized version for strings*)

fun ([]:string list) subset_string ys = true

  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;

(*set equality*)

fun eq_set (xs, ys) =

  xs = ys orelse (xs subset ys andalso ys subset xs);

(*set equality for strings*)

fun eq_set_string ((xs:string list), ys) =

  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);

fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;

(*removing an element from a list WITHOUT duplicates*)

fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)

  | [] \ x = [];

fun ys \\ xs = foldl (op \) (ys,xs);

(*removing an element from a list -- possibly WITH duplicates*)

fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;

fun gen_rems eq = foldl (gen_rem eq);

(*makes a list of the distinct members of the input; preserves order, takes

  first of equal elements*)

fun gen_distinct eq lst =

  let

    val memb = gen_mem eq;

    fun dist (rev_seen, []) = rev rev_seen

      | dist (rev_seen, x :: xs) =

          if memb (x, rev_seen) then dist (rev_seen, xs)

          else dist (x :: rev_seen, xs);

  in

    dist ([], lst)

  end;

fun distinct l = gen_distinct (op =) l;

(*returns the tail beginning with the first repeated element, or []*)

fun findrep [] = []

  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;

(*returns a list containing all repeated elements exactly once; preserves

  order, takes first of equal elements*)

fun gen_duplicates eq lst =

  let

    val memb = gen_mem eq;

    fun dups (rev_dups, []) = rev rev_dups

      | dups (rev_dups, x :: xs) =

          if memb (x, rev_dups) orelse not (memb (x, xs)) then

            dups (rev_dups, xs)

          else dups (x :: rev_dups, xs);

  in

    dups ([], lst)

  end;

fun duplicates l = gen_duplicates (op =) l;

(** association lists **)

(*association list lookup*)

fun assoc ([], key) = None

  | assoc ((keyi, xi) :: pairs, key) =

      if key = keyi then Some xi else assoc (pairs, key);

(*association list lookup, optimized version for ints*)

fun assoc_int ([], (key:int)) = None

  | assoc_int ((keyi, xi) :: pairs, key) =

      if key = keyi then Some xi else assoc_int (pairs, key);

(*association list lookup, optimized version for strings*)

fun assoc_string ([], (key:string)) = None

  | assoc_string ((keyi, xi) :: pairs, key) =

      if key = keyi then Some xi else assoc_string (pairs, key);

(*association list lookup, optimized version for string*ints*)

fun assoc_string_int ([], (key:string*int)) = None

  | assoc_string_int ((keyi, xi) :: pairs, key) =

      if key = keyi then Some xi else assoc_string_int (pairs, key);

fun assocs ps x =

  (case assoc (ps, x) of

    None => []

  | Some ys => ys);

(*two-fold association list lookup*)

fun assoc2 (aal, (key1, key2)) =

  (case assoc (aal, key1) of

    Some al => assoc (al, key2)

  | None => None);

(*generalized association list lookup*)

fun gen_assoc eq ([], key) = None

  | gen_assoc eq ((keyi, xi) :: pairs, key) =

      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);

(*association list update*)

fun overwrite (al, p as (key, _)) =

  let fun over ((q as (keyi, _)) :: pairs) =

            if keyi = key then p :: pairs else q :: (over pairs)

        | over [] = [p]

  in over al end;

fun gen_overwrite eq (al, p as (key, _)) =

  let fun over ((q as (keyi, _)) :: pairs) =

            if eq (keyi, key) then p :: pairs else q :: (over pairs)

        | over [] = [p]

  in over al end;

(** generic tables **)

(*Tables are supposed to be 'efficient' encodings of lists of elements distinct

  wrt. an equality "eq". The extend and merge operations below are optimized

  for long-term space efficiency.*)

(*append (new) elements to a table*)

fun generic_extend _ _ _ tab [] = tab

  | generic_extend eq dest_tab mk_tab tab1 lst2 =

      let

        val lst1 = dest_tab tab1;

        val new_lst2 = gen_rems eq (lst2, lst1);

      in

        if null new_lst2 then tab1

        else mk_tab (lst1 @ new_lst2)

      end;

(*append (new) elements of 2nd table to 1st table*)

fun generic_merge eq dest_tab mk_tab tab1 tab2 =

  let

    val lst1 = dest_tab tab1;

    val lst2 = dest_tab tab2;

    val new_lst2 = gen_rems eq (lst2, lst1);

  in

    if null new_lst2 then tab1

    else if gen_subset eq (lst1, lst2) then tab2

    else mk_tab (lst1 @ new_lst2)

  end;

(*lists as tables*)

fun extend_list tab = generic_extend (op =) I I tab;

fun merge_lists tab = generic_merge (op =) I I tab;

fun merge_rev_lists xs [] = xs

  | merge_rev_lists [] ys = ys

  | merge_rev_lists xs (y :: ys) =

      (if y mem xs then I else cons y) (merge_rev_lists xs ys);

(** balanced trees **)

exception Balance;      (*indicates non-positive argument to balancing fun*)

(*balanced folding; avoids deep nesting*)

fun fold_bal f [x] = x

  | fold_bal f [] = raise Balance

  | fold_bal f xs =

      let val k = length xs div 2

      in  f (fold_bal f (take(k, xs)),

             fold_bal f (drop(k, xs)))

      end;

(*construct something of the form f(...g(...(x)...)) for balanced access*)

fun access_bal (f, g, x) n i =

  let fun acc n i =     (*1<=i<=n*)

          if n=1 then x else

          let val n2 = n div 2

          in  if i<=n2 then f (acc n2 i)

                       else g (acc (n-n2) (i-n2))

          end

  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;

(*construct ALL such accesses; could try harder to share recursive calls!*)

fun accesses_bal (f, g, x) n =

  let fun acc n =

          if n=1 then [x] else

          let val n2 = n div 2

              val acc2 = acc n2

          in  if n-n2=n2 then map f acc2 @ map g acc2

                         else map f acc2 @ map g (acc (n-n2)) end

  in  if 1<=n then acc n else raise Balance  end;

(** orders **)

datatype order = LESS | EQUAL | GREATER;

fun rev_order LESS = GREATER

  | rev_order EQUAL = EQUAL

  | rev_order GREATER = LESS;

(*assume rel is a linear strict order*)

fun make_ord rel (x, y) =

  if rel (x, y) then LESS

  else if rel (y, x) then GREATER

  else EQUAL;

fun int_ord (i, j: int) =

  if i < j then LESS

  else if i = j then EQUAL

  else GREATER;

fun string_ord (a, b: string) =

  if a < b then LESS

  else if a = b then EQUAL

  else GREATER;

(*lexicographic product*)

fun prod_ord a_ord b_ord ((x, y), (x', y')) =

  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);

(*dictionary order -- in general NOT well-founded!*)

fun dict_ord _ ([], []) = EQUAL

  | dict_ord _ ([], _ :: _) = LESS

  | dict_ord _ (_ :: _, []) = GREATER

  | dict_ord elem_ord (x :: xs, y :: ys) =

      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);

(*lexicographic product of lists*)

fun list_ord elem_ord (xs, ys) =

  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));

(** input / output and diagnostics **)

val cd = OS.FileSys.chDir;

val pwd = OS.FileSys.getDir;

local

  fun out s =

    (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);

  fun prefix_lines prfx txt =

    txt |> split_lines |> map (fn s => prfx ^ s ^ "\n") |> implode;

in

(*hooks for output channels: normal, warning, error*)

val prs_fn = ref (fn s => out s);

val warning_fn = ref (fn s => out (prefix_lines "### " s));

val error_fn = ref (fn s => out (prefix_lines "*** " s));

end;

fun prs s = !prs_fn s;

fun writeln s = prs (s ^ "\n");

fun warning s = !warning_fn s;

(*print error message and abort to top level*)

exception ERROR;

fun error_msg s = !error_fn s;	  (*promise to raise ERROR later!*)

fun error s = (error_msg s; raise ERROR);

fun sys_error msg = (error_msg " !! SYSTEM ERROR !!\n"; error msg);

fun assert p msg = if p then () else error msg;

fun deny p msg = if p then error msg else ();

(*Assert pred for every member of l, generating a message if pred fails*)

fun assert_all pred l msg_fn =

  let fun asl [] = ()

        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)

  in asl l end;

(* handle errors capturing messages *)

datatype 'a error =

  Error of string |

  OK of 'a;

fun get_error (Error msg) = Some msg

  | get_error _ = None;

fun get_ok (OK x) = Some x

  | get_ok _ = None;

fun handle_error f x =

  let

    val buffer = ref "";

    fun capture s = buffer := ! buffer ^ s ^ "\n";

    val result = Some (setmp error_fn capture f x) handle ERROR => None;

  in

    (case result of

      None => Error (! buffer)

    | Some y => OK y)

  end;

(** timing **)

(*a conditional timing function: applies f to () and, if the flag is true,

  prints its runtime*)

fun cond_timeit flag f =

  if flag then

    let val start = startTiming()

        val result = f ()

    in

	writeln (endTiming start);  result

    end

  else f ();

(*unconditional timing function*)

fun timeit x = cond_timeit true x;

(*timed application function*)

fun timeap f x = timeit (fn () => f x);

(** misc functions **)

(*use the keyfun to make a list of (x, key) pairs*)

fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =

  let fun keypair x = (x, keyfun x)

  in map keypair end;

(*given a list of (x, key) pairs and a searchkey

  return the list of xs from each pair whose key equals searchkey*)

fun keyfilter [] searchkey = []

  | keyfilter ((x, key) :: pairs) searchkey =

      if key = searchkey then x :: keyfilter pairs searchkey

      else keyfilter pairs searchkey;

(*Partition list into elements that satisfy predicate and those that don't.

  Preserves order of elements in both lists.*)

fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =

    let fun part ([], answer) = answer

          | part (x::xs, (ys, ns)) = if pred(x)

            then  part (xs, (x::ys, ns))

            else  part (xs, (ys, x::ns))

    in  part (rev ys, ([], []))  end;

fun partition_eq (eq:'a * 'a -> bool) =

    let fun part [] = []

          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys

                           in (x::xs)::(part xs') end

    in part end;

(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]

   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)

fun partition_list p i j =

  let fun part k xs =

            if k>j then

              (case xs of [] => []

                         | _ => raise LIST "partition_list")

            else

            let val (ns, rest) = partition (p k) xs;

            in  ns :: part(k+1)rest  end

  in  part i end;

(* sorting *)

(*quicksort (stable, i.e. does not reorder equal elements)*)

fun sort ord =

  let

    fun qsort xs =

      let val len = length xs in

        if len <= 1 then xs

        else

          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in

            qsort lts @ eqs @ qsort gts

          end

      end

    and part _ [] = ([], [], [])

      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)

    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)

      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)

      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);

  in qsort end;

(*sort strings*)

val sort_strings = sort string_ord;

fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;

(* transitive closure (not Warshall's algorithm) *)

fun transitive_closure [] = []

  | transitive_closure ((x, ys)::ps) =

      let val qs = transitive_closure ps

          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)

          fun step(u, us) = (u, if x mem_string us then zs union_string us 

                                else us)

      in (x, zs) :: map step qs end;

(* generating identifiers *)

(** Freshly generated identifiers; supplied prefix MUST start with a letter **)

local

(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)

fun char i =      if i<26 then chr (ord "A" + i)

	     else if i<52 then chr (ord "a" + i - 26)

	     else if i<62 then chr (ord"0" + i - 52)

	     else if i=62 then "_"

	     else  (*i=63*)    "'";

val charVec = Vector.tabulate (64, char);

fun newid n = 

  let 

  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;

val seedr = ref 0;

in

fun init_gensym() = (seedr := 0);

fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));

end;

local

(*Identifies those character codes legal in identifiers.

  chould use Basis Library character functions if Poly/ML provided characters*)

fun idCode k = (ord "a" <= k andalso k < ord "z") orelse 

               (ord "A" <= k andalso k < ord "Z") orelse

               (ord "0" <= k andalso k < ord "9");

val idCodeVec = Vector.tabulate (256, idCode);

in

(*Increment a list of letters like a reversed base 26 number.

  If head is "z", bumps chars in tail.

  Digits are incremented as if they were integers.

  "_" and "'" are not changed.

  For making variants of identifiers.*)

fun bump_int_list(c::cs) = 

	if c="9" then "0" :: bump_int_list cs 

	else

        if "0" <= c andalso c < "9" then chr(ord(c)+1) :: cs

        else "1" :: c :: cs

  | bump_int_list([]) = error("bump_int_list: not an identifier");

fun bump_list([], d) = [d]

  | bump_list(["'"], d) = [d, "'"]

  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")

  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")

  | bump_list("9"::cs, _) = "0" :: bump_int_list cs

  | bump_list(c::cs, _) = 

        let val k = ord(c)

        in if Vector.sub(idCodeVec,k) then chr(k+1) :: cs 

	   else

           if c="'" orelse c="_" then c :: bump_list(cs, "") 

	   else error("bump_list: not legal in identifier: " ^

		      implode(rev(c::cs)))

        end;

end;

fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));

(* lexical scanning *)

(*scan a list of characters into "words" composed of "letters" (recognized by

  is_let) and separated by any number of non-"letters"*)

fun scanwords is_let cs =