--- a/src/Pure/library.ML Tue Jan 18 16:58:41 1994 +0100
+++ b/src/Pure/library.ML Wed Jan 19 14:10:54 1994 +0100
@@ -1,354 +1,42 @@
(* Title: Pure/library.ML
ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1992 University of Cambridge
-Basic library: booleans, lists, pairs, input/output, etc.
+Basic library: functions, options, pairs, booleans, lists, integers,
+strings, lists as sets, association lists, generic tables, balanced trees,
+input / output, timing, filenames, misc functions.
*)
-(**** Booleans: operators for combining predicates ****)
-
-infix orf;
-fun p orf q = fn x => p x orelse q x ;
-
-infix andf;
-fun p andf q = fn x => p x andalso q x ;
+(** functions **)
-fun notf p x = not (p x) ;
+(*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;
-fun orl [] = false
- | orl (x::l) = x orelse orl l;
-
-fun andl [] = true
- | andl (x::l) = x andalso andl l;
+(*combine two functions forming the union of their domains*)
+infix orelf;
+fun f orelf g = fn x => f x handle Match => g x;
-(*exists pred [x1,...,xn] ======> pred(x1) orelse ... orelse pred(xn)*)
-fun exists (pred: 'a -> bool) : 'a list -> bool =
- let fun boolf [] = false
- | boolf (x::l) = (pred x) orelse boolf l
- in boolf end;
+(*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);
-(*forall pred [x1,...,xn] ======> pred(x1) andalso ... andalso pred(xn)*)
-fun forall (pred: 'a -> bool) : 'a list -> bool =
- let fun boolf [] = true
- | boolf (x::l) = (pred x) andalso (boolf l)
- in boolf end;
+(*functional for pairs*)
+fun pairself f (x, y) = (f x, f y);
-
-(** curried equality **)
-
-fun equal x y = (x = y);
-
-fun not_equal x y = 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;
-(*** Lists ***)
-
-exception LIST of string;
-
-(*discriminator and selectors for lists. *)
-fun null [] = true
- | null (_::_) = false;
-
-fun hd [] = raise LIST "hd"
- | hd (a::_) = a;
-
-fun tl [] = raise LIST "tl"
- | tl (_::l) = l;
-
-
-(*curried cons and reverse cons*)
-
-fun cons x xs = x :: xs;
-
-fun rcons xs x = x :: xs;
-
-
-(*curried functions for pairing and reversed pairing*)
-fun pair x y = (x,y);
-fun rpair x y = (y,x);
-
-fun fst(x,y) = x and snd(x,y) = y;
-
-(*Handy combinators*)
-fun curry f x y = f(x,y);
-fun uncurry f(x,y) = f x y;
-fun I x = x and K x y = x;
-
-(*Combine two functions forming the union of their domains*)
-infix orelf;
-fun f orelf g = fn x => f x handle Match=> g 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);
-
-
-(*functional for pairs*)
-fun pairself f (x,y) = (f x, f y);
-
-(*Apply the function to a component of a pair*)
-fun apfst f (x, y) = (f x, y);
-fun apsnd f (x, y) = (x, f y);
-
-fun square (n: int) = n*n;
-
-fun fact 0 = 1
- | fact n = n * fact(n-1);
-
-
-(*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;
-
-
-(*Length of a list. Should unquestionably be a standard function*)
-local fun length1 (n, [ ]) = n (*TAIL RECURSIVE*)
- | length1 (n, x::l) = length1 (n+1, l)
-in fun length l = length1 (0,l) end;
-
-
-(*Take the first n elements from l.*)
-fun take (n, []) = []
- | take (n, x::xs) = if n>0 then x::take(n-1,xs)
- else [];
-
-(*Drop the first n elements from l.*)
-fun drop (_, []) = []
- | drop (n, x::xs) = if n>0 then drop (n-1, xs)
- else x::xs;
-
-(*Return nth element of l, 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::l => x;
-
-
-(*Last element of a list*)
-fun last_elem [] = raise LIST "last_elem"
- | last_elem [x] = x
- | last_elem (_ :: xs) = last_elem xs;
-
-
-(*make the list [from, from+1, ..., to]*)
-infix upto;
-fun from upto to =
- if from>to then [] else from :: ((from+1) upto to);
-
-(*make the list [from, from-1, ..., to]*)
-infix downto;
-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;
-
-(*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::l) = (proc x; seqf l)
- in seqf end;
-
-
-(*** Balanced folding; access to 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;
-
-
-(*** Input/Output ***)
-
-fun prs s = output(std_out,s);
-fun writeln s = prs (s ^ "\n");
-
-(*Print error message and abort to top level*)
-exception ERROR;
-fun error msg = (writeln msg; raise ERROR);
-fun sys_error msg = (writeln "-- System Error --"; error msg);
-
-fun assert p msg = if p then () else error msg;
-fun deny p msg = if p then error msg else ();
-
-(*For the "test" target in Makefiles -- signifies successful termination*)
-fun maketest msg =
- (writeln msg;
- output(open_out "test", "Test examples ran successfully\n"));
-
-(*print a list surrounded by the brackets lpar and rpar, with comma separator
- print nothing for empty list*)
-fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
- let fun prec(x) = (prs","; pre(x))
- in case l of
- [] => ()
- | x::l => (prs lpar; pre x; seq prec l; prs rpar)
- end;
-
-(*print a list of items separated by newlines*)
-fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
- seq (fn x => (pre x; writeln""));
-
-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*)
-val is_blank : string -> bool = fn
- " " => true | "\t" => true | "\n" => true | _ => false;
-
-val is_letdig = is_quasi_letter orf is_digit;
-
-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;
-
-
-(*** Timing ***)
-
-(*Unconditional timing function*)
-val timeit = cond_timeit true;
-
-(*Timed application function*)
-fun timeap f x = timeit(fn()=> f x);
-
-(*Timed "use" function, printing filenames*)
-fun time_use fname = timeit(fn()=>
- (writeln("\n**** Starting " ^ fname ^ " ****"); use fname;
- writeln("\n**** Finished " ^ fname ^ " ****")));
-
-
-(*** Misc functions ***)
-
-(*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;
-
-(*Combine two lists forming a list of pairs:
- [x1,...,xn] ~~ [y1,...,yn] ======> [(x1,y1), ..., (xn,yn)] *)
-infix ~~;
-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);
-
-(*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;
-
-(*Flatten a list of lists to a list.*)
-fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls,[]);
-
-
-(*** polymorphic set operations ***)
-
-(*membership in a list*)
-infix mem;
-fun x mem [] = false
- | x mem (y::l) = (x=y) orelse (x mem l);
-
-(*insertion into list if not already there*)
-infix ins;
-fun x ins xs = if x mem xs then xs else x::xs;
-
-(*union of sets represented as lists: no repetitions*)
-infix union;
-fun xs union [] = xs
- | [] union ys = ys
- | (x::xs) union ys = xs union (x ins ys);
-
-infix inter;
-fun [] inter ys = []
- | (x::xs) inter ys = if x mem ys then x::(xs inter ys)
- else xs inter ys;
-
-infix subset;
-fun [] subset ys = true
- | (x::xs) subset ys = x mem ys andalso xs subset ys;
-
-(*removing an element from a list WITHOUT duplicates*)
-infix \;
-fun (y::ys) \ x = if x=y then ys else y::(ys \ x)
- | [] \ x = [];
-
-infix \\;
-val op \\ = foldl (op \);
-
-(*** option stuff ***)
+(** options **)
datatype 'a option = None | Some of 'a;
@@ -363,131 +51,656 @@
fun is_none (Some _) = false
| is_none None = true;
+fun apsome f (Some x) = Some (f x)
+ | apsome _ None = None;
-(*** Association lists ***)
+
+
+(** 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 the function to a component of a pair*)
+fun apfst f (x, y) = (f x, y);
+fun apsnd f (x, y) = (x, f y);
+
+
+
+(** booleans **)
+
+(* equality *)
+
+fun equal x y = x = y;
+fun not_equal x y = x <> y;
+
+
+(* operators for combining predicates *)
+
+infix orf;
+fun p orf q = fn x => p x orelse q x;
+
+infix andf;
+fun p andf q = fn x => p x andalso q x;
+
+fun notf p x = not (p x);
-(*Association list lookup*)
-fun assoc ([], key) = None
- | assoc ((keyi,xi)::pairs, key) =
- if key=keyi then Some xi else assoc (pairs,key);
+
+(* predicates on lists *)
+
+fun orl [] = false
+ | orl (x :: xs) = x orelse orl xs;
+
+fun andl [] = true
+ | andl (x :: xs) = x andalso andl xs;
+
+(*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;
-fun assocs ps x = case assoc(ps,x) of None => [] | Some(ys) => ys;
+
+
+(** 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*)
-(*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;
+(* (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 (* FIXME [] case: elim warn (?) *)
+ | 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;
-(*Copy the list preserving elements that satisfy the predicate*)
-fun filter (pred: 'a->bool) : 'a list -> 'a list =
+(*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;
+
+(*find the position of an element in a list*)
+fun find (x, ys) =
+ let fun f (y :: ys, i) = if x = y then i else f (ys, i + 1)
+ | f (_, _) = raise LIST "find"
+ in f (ys, 0) end;
+
+(*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;
+
+
+(* 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;
+ | filt (x :: xs) = if pred x then x :: filt xs else filt xs
+ in filt end;
fun filter_out f = filter (not o f);
-(*** List operations, generalized to an arbitrary equality function "eq"
- -- so what good are equality types?? ***)
+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 *)
+
+(*combine two lists forming a list of pairs:
+ [x1, ..., xn] ~~ [y1, ..., yn] ===> [(x1, y1), ..., (xn, yn)]*)
+infix ~~;
+fun [] ~~ [] = []
+ | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
+ | _ ~~ _ = raise LIST "~~";
+
+(*combine two lists*)
+fun map2 _ ([], []) = []
+ | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
+ | map2 _ _ = raise LIST "map2";
+
+(*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 *)
+
+infix prefix;
+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;
+fun dec i = i := ! i - 1;
+
+
+fun square (n:int) = n * n;
+
+fun fact 0 = 1
+ | fact n = n * fact (n - 1);
+
+
+(* lists of integers *)
+
+(*make the list [from, from + 1, ..., to]*)
+infix upto;
+fun from upto to =
+ if from > to then [] else from :: ((from + 1) upto to);
+
+(*make the list [from, from - 1, ..., to]*)
+infix downto;
+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;
+
+
+(* operations on integer lists *)
-(*removing an element from a list -- possibly WITH duplicates*)
-fun gen_rem eq (xs,y) = filter_out (fn x => eq(x,y)) xs;
+fun sum [] = 0
+ | sum (n :: ns) = n + sum ns;
+
+fun max [m:int] = m
+ | max (m :: n :: ns) = if m > n then max (m :: ns) else max (n :: ns)
+ | max [] = raise LIST "max";
+
+fun min [m:int] = m
+ | min (m :: n :: ns) = if m < n then min (m :: ns) else min (n :: ns)
+ | min [] = raise LIST "min";
+
+
+(* 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;
+
+
+fun string_of_int n =
+ if n < 0 then "~" ^ radixstring (10, "0", ~n) else radixstring (10, "0", n);
+
+
+
+(** 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*)
+val is_blank : string -> bool =
+ fn " " => true | "\t" => true | "\n" => true | _ => false;
+
+val is_letdig = is_quasi_letter orf is_digit;
+
+
+(*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;
+
+
+(*simple quoting (does not escape special chars)*)
+fun quote s = "\"" ^ s ^ "\"";
+
+(*space_implode "..." (explode "hello"); gives "h...e...l...l...o"*)
+fun space_implode a bs = implode (separate a bs);
+
+(*concatenate messages, one per line, into a string*)
+val cat_lines = implode o (map (apr (op ^, "\n")));
+
+
+
+(** lists as sets **)
+
+(*membership in a list*)
+infix mem;
+fun x mem [] = false
+ | x mem (y :: ys) = x = y orelse x mem 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);
+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*)
+infix ins;
+fun x ins xs = if x mem 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;
+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*)
+infix union;
+fun xs union [] = xs
+ | [] union ys = ys
+ | (x :: xs) union ys = xs union (x ins 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));
+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*)
+infix inter;
+fun [] inter ys = []
+ | (x :: xs) inter ys =
+ if x mem ys then x :: (xs inter ys) else xs inter ys;
+
+
+(*subset*)
+infix subset;
+fun [] subset ys = true
+ | (x :: xs) subset ys = x mem ys andalso xs subset ys;
+
+fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
+
+
+(*removing an element from a list WITHOUT duplicates*)
+infix \;
+fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
+ | [] \ x = [];
+
+infix \\;
+val op \\ = foldl (op \);
-(*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);
+(*removing an element from a list -- possibly WITH duplicates*)
+fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
+
+val gen_rems = foldl o gen_rem;
+
+
+(*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;
-(** Finding list elements and duplicates **)
+ 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;
+
+val distinct = gen_distinct (op =);
+
+
+(*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;
+
+
+
+(** association lists **)
-(* find the position of an element in a list *)
-fun find(x,ys) =
- let fun f(y::ys,i) = if x=y then i else f(ys,i+1)
- | f(_,_) = raise LIST "find"
- in f(ys,0) end;
+(*association list lookup*)
+fun assoc ([], key) = None
+ | assoc ((keyi, xi) :: pairs, key) =
+ if key = keyi then Some xi else assoc (pairs, key);
+
+fun assocs ps x =
+ (case assoc (ps, x) of
+ None => []
+ | Some ys => ys);
+
+(*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;
+
+
+
+(** generic tables **)
-(*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;
+(*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;
-fun distinct1 (seen, []) = rev seen
- | distinct1 (seen, x::xs) =
- if x mem seen then distinct1 (seen, xs)
- else distinct1 (x::seen, xs);
+(*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;
-(*Makes a list of the distinct members of the input*)
-fun distinct xs = distinct1([],xs);
+
+(*lists as tables*)
+val extend_list = generic_extend (op =) I I;
+val merge_lists = generic_merge (op =) I I;
+
-(*Use the keyfun to make a list of (x,key) pairs.*)
+(** 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;
+
+
+
+(** input / output **)
+
+fun prs s = output (std_out, s);
+fun writeln s = prs (s ^ "\n");
+
+
+(*print error message and abort to top level*)
+exception ERROR;
+fun error msg = (writeln msg; raise ERROR);
+fun sys_error msg = (writeln "*** System Error ***"; error msg);
+
+fun assert p msg = if p then () else error msg;
+fun deny p msg = if p then error msg else ();
+
+
+(* FIXME close file (?) *)
+(*for the "test" target in Makefiles -- signifies successful termination*)
+fun maketest msg =
+ (writeln msg; output (open_out "test", "Test examples ran successfully\n"));
+
+
+(*print a list surrounded by the brackets lpar and rpar, with comma separator
+ print nothing for empty list*)
+fun print_list (lpar, rpar, pre: 'a -> unit) (l : 'a list) =
+ let fun prec x = (prs ","; pre x)
+ in
+ (case l of
+ [] => ()
+ | x::l => (prs lpar; pre x; seq prec l; prs rpar))
+ end;
+
+(*print a list of items separated by newlines*)
+fun print_list_ln (pre: 'a -> unit) : 'a list -> unit =
+ seq (fn x => (pre x; writeln ""));
+
+
+val print_int = prs o string_of_int;
+
+
+
+(** timing **)
+
+(*unconditional timing function*)
+val timeit = cond_timeit true;
+
+(*timed application function*)
+fun timeap f x = timeit (fn () => f x);
+
+(*timed "use" function, printing filenames*)
+fun time_use fname = timeit (fn () =>
+ (writeln ("\n**** Starting " ^ fname ^ " ****"); use fname;
+ writeln ("\n**** Finished " ^ fname ^ " ****")));
+
+
+
+(** filenames **)
+
+(*convert UNIX filename of the form "path/file" to "path/" and "file";
+ if filename contains no slash, then it returns "" and "file"*)
+val split_filename =
+ (pairself implode) o take_suffix (not_equal "/") o explode;
+
+val base_name = #2 o split_filename;
+
+(*merge splitted filename (path and file);
+ if path does not end with one a slash is appended*)
+fun tack_on "" name = name
+ | tack_on path name =
+ if last_elem (explode path) = "/" then path ^ name
+ else path ^ "/" ^ name;
+
+(*remove the extension of a filename, i.e. the part after the last '.'*)
+val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;
+
+
+
+(** 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;
+ let fun keypair x = (x, keyfun x)
+ in map keypair end;
-(*Given a list of (x,key) pairs and a searchkey
+(*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;
-
-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;
+ | 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. *)
+ 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;
+ | 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
+ | 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 ]
+(*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
+ 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
+ let val (ns, rest) = partition (p k) xs;
+ in ns :: part(k+1)rest end
in part i end;
-(*Insertion sort. Stable (does not reorder equal elements)
- 'less' is less-than test on type 'a. *)
-fun sort (less: 'a*'a -> bool) =
+(* sorting *)
+
+(*insertion sort; stable (does not reorder equal elements)
+ 'less' is less-than test on type 'a*)
+fun sort (less: 'a*'a -> bool) =
let fun insert (x, []) = [x]
- | insert (x, y::ys) =
- if less(y,x) then y :: insert (x,ys) else x::y::ys;
+ | insert (x, y::ys) =
+ if less(y, x) then y :: insert (x, ys) else x::y::ys;
fun sort1 [] = []
| sort1 (x::xs) = insert (x, sort1 xs)
in sort1 end;
@@ -496,146 +709,60 @@
val sort_strings = sort (op <= : string * string -> bool);
-(*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 zs) (ys,ys)
- fun step(u,us) = (u, if x mem us then zs union us else us)
- in (x,zs) :: map step qs end;
-
-(*** Converting integers to strings, generating identifiers, etc. ***)
+(* transitive closure (not Warshall's algorithm) *)
-(*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;
+fun transitive_closure [] = []
+ | transitive_closure ((x, ys)::ps) =
+ let val qs = transitive_closure ps
+ val zs = foldl (fn (zs, y) => assocs qs y union zs) (ys, ys)
+ fun step(u, us) = (u, if x mem us then zs union us else us)
+ in (x, zs) :: map step qs 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;
-fun string_of_int n =
- if n < 0 then "~" ^ radixstring(10,"0",~n) else radixstring(10,"0",n);
-
-val print_int = prs o string_of_int;
+(* generating identifiers *)
local
-val a = ord("a") and z = ord("z") and A = ord("A") and Z = ord("Z")
-and k0 = ord("0") and k9 = ord("9")
+ val a = ord "a" and z = ord "z" and A = ord "A" and Z = ord "Z"
+ and k0 = ord "0" and k9 = ord "9"
in
(*Increment a list of letters like a reversed base 26 number.
- If head is "z", bumps chars in tail.
+ 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. *)
+ For making variants of identifiers.*)
fun bump_int_list(c::cs) = if c="9" then "0" :: bump_int_list cs else
- if k0 <= ord(c) andalso ord(c) < k9 then chr(ord(c)+1) :: cs
- else "1" :: c :: cs
+ if k0 <= ord(c) andalso ord(c) < k9 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 (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
- (k0 <= k andalso k < k9) 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;
+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 (a <= k andalso k < z) orelse (A <= k andalso k < Z) orelse
+ (k0 <= k andalso k < k9) 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),"")));
-
-
-(*** Operations on integer lists ***)
-
-fun sum [] = 0
- | sum (n::ns) = n + sum ns;
-
-fun max[m : int] = m
- | max(m::n::ns) = if m>n then max(m::ns) else max(n::ns)
- | max [] = raise LIST "max";
-
-fun min[m : int] = m
- | min(m::n::ns) = if m<n then min(m::ns) else min(n::ns)
- | min [] = raise LIST "min";
-
-
-(*** Lexical scanning ***)
-
-(* [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));
+fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
-infix prefix;
-fun [] prefix _ = true
- | (x::xs) prefix (y::ys) = (x=y) andalso (xs prefix ys)
- | _ prefix _ = false;
-
-(* [x1, x2, ..., xn] ---> [x1, s, x2, s, ..., s, xn] *)
-fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
- | separate _ xs = xs;
+(* lexical scanning *)
-(*space_implode "..." (explode "hello"); gives "h...e...l...l...o" *)
-fun space_implode a bs = implode (separate a bs);
-
-(*simple quoting (does not escape special chars) *)
-fun quote s = "\"" ^ s ^ "\"";
-
-(*Concatenate messages, one per line, into a string*)
-val cat_lines = implode o (map (apr(op^,"\n")));
-
-(*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 =
+(*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 =
let fun scan1 [] = []
- | scan1 cs =
- let val (lets, rest) = take_prefix is_let cs
- in implode lets :: scanwords is_let rest end;
- in scan1 (#2 (take_prefix (not o is_let) cs)) end;
-
-
-(*** Operations on filenames ***)
+ | scan1 cs =
+ let val (lets, rest) = take_prefix is_let cs
+ in implode lets :: scanwords is_let rest end;
+ in scan1 (#2 (take_prefix (not o is_let) cs)) end;
-(*Convert Unix filename of the form path/file to "path/" and "file" ;
- if filename contains no slash, then it returns "" and "file" *)
-val split_filename =
- (pairself implode) o take_suffix (not_equal "/") o explode;
-
-val base_name = #2 o split_filename;
-
-(*Merge splitted filename (path and file);
- if path does not end with one a slash is appended *)
-fun tack_on "" name = name
- | tack_on path name =
- if last_elem (explode path) = "/" then path ^ name
- else path ^ "/" ^ name;
-
-(*Remove the extension of a filename, i.e. the part after the last '.' *)
-val remove_ext = implode o #1 o take_suffix (not_equal ".") o explode;