*
specially, no. But it supports many other features (wildcards don't match a leading dot, curlies, etc) plus it uses a rather Clike approach to converting the pattern (iterating over single characters, state machine) so it would take more than 10 seconds of looking at it to make any major changes to the algorithm.]]>
I don't think your version handles the last case with backslash escapes.
]]>[...]
here.]]>
/
isn't treated specially.
(In one place I use this for matching some HTTP header values, in which case .
is actually [!#$%&'*+\.^`~\w]
.)
?
matches any character and *
matches any string (0 or more characters). You want to convert it to a regex, maybe because you just want to match it (and Perl already supports regexes) or because you want to embed it as part of a bigger regex.
You might start with a naive replacement:
s/\?/./g; # ? > .
s/\*/.*/g; # * > .*
Unfortunately this is broken: It leaves all other characters untouched, including those that have a special meaning in regexes, such as (
, +
, 
, etc.
Let's revise it:
s{(\W)}{
$1 eq '?' ? '.' :
$1 eq '*' ? '.*' :
'\\' . $1
}eg;
Now we match and replace every nonword character. If it's ?
or *
, we turn it into its regex equivalent; otherwise we backslashescape it just like quotemeta
would do.
But what if the input is something like a***b
? This would turn into a.*.*.*b
, which when run on a long target string without b
s by a backtracking engine can be very inefficient (barring extra optimizations). A missing b
would make the match fail at the end, which would cause the engine to go through all possible ways .*.*.*
could subdivide the string amongst themselves before giving up. In general this takes O(n^{k}) time (where n is the length of the target string and k is the number of stars in the pattern).
We can do better than that by realizing **
is equivalent to *
, which means that any sequence of stars is equivalent to a single *
, and preprocessing the pattern:
tr,*,,s; # ***...* > *
This still doesn't fix everything, though: *?*?*
doesn't contain any repeated *
s but still allows for exponential backtracking. One way to work around this is to normalize the pattern even further: Because *?
is equivalent to ?*
, we can move all the ?
s to the front:
# "*?*?*"
1 while s/\*\?/?*/g;
# "?*?**" (after 1 iteration)
# "??***" (after 2 iterations)
tr,*,,s;
# "??*"
s{(\W)}{
$1 eq '?' ? '.' :
$1 eq '*' ? '.*' :
'\\' . $1
}eg;
# "...*"
However, I don't like that the transformation is spread out over two regex substitutions and one transliteration, when there is a way to do it all in a single substitution:
s{
( [?*]+ ) # a run of ? or * characters

(\W) # any other nonword character
}{
defined $1
? '.{' . ($1 =~ tr,?,,) . (index($1, '*') >= 0 ? ',' : '') . '}'
: '\\' . $2
}xeg;
That is, we turn each run of ?
or *
characters into .{N}
(if there was no *
) or .{N,}
(if there was at least one *
) where N
is the number of ?
s in the run.
Given an input of *?*?*
, this would generate .{2,}
("match 2 or more of any character").
And finally, if we wanted the user to be able to escape characters with a backslash to match them literally:
s{
( [?*]+ ) # a run of ? or * characters

\\ (.) # backslash escape

(\W) # any other nonword character
}{
defined $1
? '.{' . ($1 =~ tr,?,,) . (index($1, '*') >= 0 ? ',' : '') . '}'
: quotemeta $+
}xeg;
]]>
$ echo IEabEba  perl try.pl
ORIG: IEabEba
MOD: V~V~V~a~b;~V~~a~~b;;V~V~b~a;~V~~b~~a;;;
...> V~V~V~a~b;~Vab;;V~V~b~a;~Vba;;;
...> V~V~V~a~b;~Vab;;~V~b~a;~Vba;;
Not a tautology
(a equals b) implies (b equals a)
is a tautology but the program
fails to recognize it. With the fixed code below it generates this
output instead:
$ echo IEabEba  perl taut.pl
ORIG: IEabEba
MOD: V~V~V~a~b;~V~~a~~b;;V~V~b~a;~V~~b~~a;;;
...> V~V~V~a~b;~Vab;;V~V~b~a;~Vba;;;
...> V~V~V~a~b;~Vab;;~V~b~a;~Vba;;
...> V~Vba;~V~V~a~b;~Vab;;~V~b~a;;
...> V~Vab;~V~Vab;~V~a~b;;~V~a~b;;
...> V~Vab;~V0~V~a~b;;~V~a~b;;
...> V~Vab;~V~V~a~b;;~V~a~b;;
...> V~Vab;~~V~a~b;~V~a~b;;
...> V~Vab;V~a~b;~V~a~b;;
...> V~Vab;~a~b~V~a~b;;
...> V~Vab;~a~b~V0~b;;
...> V~Vab;~a~b~V~b;;
...> V~Vab;~a~b~~b;
...> V~Vab;~a~bb;
...> V~V1b;~a~bb;
...> V~1~a~bb;
...> V0~a~bb;
...> V~a~bb;
...> V~a~b1;
...> 1
Tautology
The following changes were made to the code:
The "regex libraries" $rawlib
and $modlib
and their named
subpatterns (?&rawexpr)
and (?&exp)
are gone. They were
replaced by $rawexpr
and $exp
, subregexes that directly match
and capture a simplifed and modified expression, respectively.
This change was made in order to make it possible to split a
string into subexpressions using my @expr = $str =~ /$exp/g
(i.e. m//g
in list context).
Two regexes were simplified by using \K
.
The old "final rule" did some duplicate work: It used
index($1, $3) < 0 && index($4, $3) < 0
inside the regex to
search for the subexpression $3
in both $1
and $4
. If
successful, it repeated the search in the replacement part:
s{ \Q$x\E }{$spec}g for $pre, $post;
The new version uses s///
directly in the regex and checks the
return value to see if any match was found/replaced. The
replacement string is assembled directly in the regex and
saved in an outer lexical variable to make it available in the
righthand side.
A new rule was added. If the other rules get stuck, it reorders
V
operands. The canonical order chosen is simply the default
sort
behavior: lexicographically ascending strings.
Due to change #3 and #4 the code no longer works on old perls (before v5.18) because in v5.18 the implementation of embedded code blocks in regexes was rewritten, fixing many bugs.
The new code:
#!/usr/bin/env perl
use v5.18.0;
use warnings;
use re '/xms';
my $rawexpr = qr{
(
(?>
[az]

N (?1)

[CDIE] (?1) (?1)
)
)
};
my $exp = qr{
(
(?>
[01az]

~ (?1)

V (?1)*+ ;
)
)
};
while (readline) {
chomp;
say "ORIG: $_";
1 while s{ E $rawexpr $rawexpr }{DC$1$2CN$1N$2}g;
1 while s{ I $rawexpr $rawexpr }{DN$1$2}g;
1 while s{ C $rawexpr $rawexpr }{NDN$1N$2}g;
1 while s{ D $rawexpr $rawexpr }{V$1$2;}g;
tr/N/~/;
say "MOD: $_";
say "...> $_" while 0
 s{ ~ ~ }{}g
 s{ ~ 0 }{1}g
 s{ ~ 1 }{0}g
 s{ V ; }{0}g
 s{ V $exp ; }{$1}g
 s{ V $exp* \K V ($exp*+) ; }{$2}g
 s{ V $exp* \K 0 }{}g
 s{ V $exp* 1 $exp*+ ; }{1}g
 do {
my $repl;
s{
V ($exp*?) (~??) $exp ($exp*+) ;
(?(?{
my ($pre, $neg, $x, $post) = ($1, $3, $4, $5);
my $spec = $neg ? '1' : '0';
my $n = 0;
$n += s{ \Q$x\E }{$spec}g for $pre, $post;
$repl = "V$pre$neg$x$post;";
!$n
}) (*FAIL) )
}{$repl}g
}
 do {
my $canon;
s{
V ($exp {2,}+) ;
(?(?{
my $orig = $1;
$canon = join '', sort $orig =~ m{ $exp }g;
$orig eq $canon
}) (*FAIL) )
}{V$canon;}g
}
;
say $_ eq '1' ? "Tautology" : "Not a tautology", "\n";
}
__END__
]]>
{# LANGUAGE LambdaCase #}
module Main (main) where
import Control.Applicative (Applicative (..), (<$>))
import Control.Arrow (first)
import Data.Ix (inRange)
import Control.Monad (guard, mplus, msum)
import Data.Maybe (fromMaybe, isJust, listToMaybe)
data RawExpr
= VarR Char
 N RawExpr
 D RawExpr RawExpr
 C RawExpr RawExpr
 I RawExpr RawExpr
 E RawExpr RawExpr
deriving (Eq, Ord, Read, Show)
newtype Parser a = Parser{ unParser :: String > (a, String) }
instance Functor Parser where
fmap f (Parser p) = Parser (first f . p)
instance Applicative Parser where
pure x = Parser (\s > (x, s))
Parser f <*> Parser x = Parser (\s >
let (f', s') = f s
(x', s'') = x s'
in (f' x', s''))
instance Monad Parser where
return = pure
Parser x >>= f = Parser (\s >
let (x', s') = x s
in unParser (f x') s')
anyChar :: Parser Char
anyChar = Parser (\(c : cs) > (c, cs))
parseRaw :: String > RawExpr
parseRaw s = case unParser expr s of
(x, "") > x
(_, rest) > error ("parseRaw: trailing garbage: " ++ show rest)
where
expr = anyChar >>= \case
c  inRange ('a', 'z') c > pure (VarR c)
'N' > N <$> expr
'D' > D <$> expr <*> expr
'C' > C <$> expr <*> expr
'I' > I <$> expr <*> expr
'E' > E <$> expr <*> expr
data ModExpr
= VarM Char
 T
 F
 Not ModExpr
 Or [ModExpr]
deriving (Eq, Ord, Read, Show)
desugar :: RawExpr > ModExpr
desugar = \case
VarR v > VarM v
N x > not (desugar x)
D x y > or (desugar x) (desugar y)
C x y > and (desugar x) (desugar y)
I x y > or (not (desugar x)) (desugar y)
E x y > or (and x' y') (and (not x') (not y'))
where
x' = desugar x
y' = desugar y
where
not = Not
or x y = Or [x, y]
and x y = not (or (not x) (not y))
render :: ModExpr > String
render e = go e "" where
go = \case
VarM c > (c :)
T > ('1' :)
F > ('0' :)
Not x > ('~' :) . go x
Or xs > ('V' :) . foldr (.) id (map go xs) . (';' :)
type Rule = ModExpr > Maybe ModExpr
mkRule :: (Maybe ModExpr > Maybe ModExpr) > Rule
mkRule t = rule
where
rule e = t (Just e) `mplus` rec
where
rec = case e of
Not x > Not <$> rule x
Or xs > do
let ys = map rule xs
guard (any isJust ys)
return (Or (zipWith fromMaybe xs ys))
_ > Nothing
not_not, not_true, not_false :: Rule
not_not = mkRule $ \e > do
Not (Not x) < e
pure x
not_true = mkRule $ \e > do
Not T < e
pure F
not_false = mkRule $ \e > do
Not F < e
pure T
or_true, or_false :: Rule
or_true = mkRule $ \e > do
Or xs < e
guard (T `elem` xs)
pure T
or_false = mkRule $ \e > do
Or xs < e
let ys = filter (F /=) xs
guard (length ys < length xs)
pure $ Or ys
first3 :: (a > r) > (a, b, c) > (r, b, c)
first3 f (x, y, z) = (f x, y, z)
second3 :: (b > r) > (a, b, c) > (a, r, c)
second3 f (x, y, z) = (x, f y, z)
selectSplit :: [a] > [([a], a, [a])]
selectSplit [] = []
selectSplit (x : xs) = ([], x, xs) : map (first3 (x :)) (selectSplit xs)
extract :: (a > Maybe b) > [a] > Maybe ([a], b, [a])
extract f xs = msum (map (evert . second3 f) (selectSplit xs))
where
evert (x, Just y, z) = Just (x, y, z)
evert _ = Nothing
or_none, or_one, or_assoc :: Rule
or_none = mkRule $ \e > do
Or [] < e
pure F
or_one = mkRule $ \e > do
Or [x] < e
pure x
or_assoc = mkRule $ \e > do
Or xs < e
(pre, ys, post) < extractOr xs
pure $ Or (pre ++ ys ++ post)
where
extractOr = extract (\case Or xs > Just xs; _ > Nothing)
isSubExpr :: ModExpr > ModExpr > Bool
isSubExpr e1 e2 =
e1 == e2  case e2 of
Not x > e1 `isSubExpr` x
Or xs > any (e1 `isSubExpr`) xs
_ > False
substitute :: ModExpr > ModExpr > ModExpr > ModExpr
substitute x y = go
where
go = \case
e  e == x > y
Not e > Not (go e)
Or es > Or (map go es)
e > e
or_spec :: Rule
or_spec = mkRule $ \e > do
Or xs < e
listToMaybe $ do
(pre, x_orig, post) < selectSplit xs
(Not x, r) < [(x_orig, T), (Not x_orig, F)]
guard $ any (x `isSubExpr`) (pre ++ post)
let z = Or (map (substitute x r) pre ++ [x_orig] ++ map (substitute x r) post)
pure z
rules :: [Rule]
rules =
[
not_not, not_true, not_false,
or_true, or_false,
or_none, or_one, or_assoc,
or_spec
]
simplify1 :: ModExpr > Maybe ModExpr
simplify1 e = msum (map ($ e) rules)
simplify :: ModExpr > (ModExpr, [String])
simplify e = case simplify1 e of
Nothing > (e, [])
Just e' > (render e' :) <$> simplify e'
process :: String > String
process s = unlines $
("ORIG: " ++ s) :
("MOD: " ++ render e) :
foldr (\x z > ("...> " ++ x) : z) [v, ""] ts
where
e = desugar (parseRaw s)
(r, ts) = simplify e
v  r == T = "Tautology"
 otherwise = "Not a tautology"
main :: IO ()
main = interact (unlines . map process . lines)
]]>
Addendum: I've written a more or less equivalent Haskell version of this program.
Some programmers, when confronted with a boolean expression, think "I know, I'll use regular expressions". Now they have
true
problems.
This post was inspired by the TAUT exercise on SPOJ.
You're given a boolean expression consisting of variables (each being either true
or false
), a unary operator (not
), and several binary operators (and
, or
, implies
, equals
). Your task is to determine whether the expression is a tautology, i.e. whether it evaluates to true
for all possible variable values.
To make parsing easier, we're going to use a very simplified syntax:
a
z
), i.e. an expression can use at most 26 different variablesN
for not
, C
(conjunction) for and
, D
(disjunction) for or
, I
for implies
, E
for equals
x and not y
is written as CxNy
, etc.For example, the expression ((a implies b) and (b implies c)) implies (a implies c)
becomes ICIabIbcIac
.
There is a number of ways to solve this problem, e.g. using brute force to enumerate all possible variable assignments and test the formula, but we're going to use algebraic simplification to determine directly whether a given expression reduces to true
. To make it more fun, we're going to implement it as a string rewriting system using Perl's regex engine.
In the following sections I'm going to take you through the code sections in an order that makes it easier to explain. The full runnable code is at the end.
#!/usr/bin/env perl
use v5.14.0;
use warnings;
use re '/xms', $^V lt v5.18.0 ? 'eval' : ();
The header: The #!
line instructs the system to use whatever perl is in the path. use v5.14.0
requires at least version 14 of perl5 (any earlier version will abort parsing with an error at this point). This enables a few features new in version 14 and also turns on strict
(since v5.12). use warnings
enables warnings  almost always a good idea. use re '/xms'
enables the xms
flags by default for all regexes in the current scope (this feature was introduced in v5.14). Finally, for perls before v5.18, we use re 'eval'
to work around a bug related to parsing of (?{ })
blocks in regexes.
while (readline) {
chomp;
say "ORIG: $_";
We iterate over the lines in ARGV
(formed by the contents of the files listed in @ARGV
or STDIN
if @ARGV
is empty). From each line (stored in $_
) we remove the trailing newline and print it to STDOUT
so we can see what we're working on.
Our next goal is to reduce the number of possible operators in the expression. We do that by rewriting everything in terms of N
(not
) and D
(or
).
The first step is getting rid of E
: What does it mean for two expressions x, y to be equal? Well, either they're both true
or they're both false
, so the first part is simply x and y
. If they're both false
, their negations must be true
, giving us not x and not y
. Putting it all together, X equals Y
can be rewritten as (X and Y) or (not X and not Y)
, which in the simplified syntax is Exy
and DCxyCNxNy
, respectively.
1 while s{ E ((?&rawexpr)) ((?&rawexpr)) $rawlib }{DC$1$2CN$1N$2}g;
I'm going to explain the (?&rawexpr)
and $rawlib
bits in a moment. For now, it suffices to say that (?&rawexpr)
is a regex that matches an expression in the simplified syntax and $rawlib
contains the definition of (?&rawexpr)
.
We have a few spaces in our regex. These are just for readability and ignored because of the /x
flag, which we enabled for all regexes in our main file.
We match E
followed by two subexpressions, which we capture as $1
and $2
. We replace it by DC$1$2CN$1N$2
, which (as explained above) is equivalent. The /g
flag makes s///
replace all occurrences, so what is the outer while
loop for? It's for nested expressions of the form ExEyz
: x
would be matched as $1
and Eyz
as $2
, but we're not recursively replacing E
inside of $1
or $2
, so at the end we still have an instance of E
left. Instead of trying to write some kind of nested recursive substitution, we just wrap the whole thing in a loop that tries again if any match/replacement happened in the previous iteration, until all the E
s are gone.
1 while s{ I ((?&rawexpr)) ((?&rawexpr)) $rawlib }{DN$1$2}g;
Next we get rid of I
. x implies y
is only false
if x
is true
and y
is false
; all other cases are true
. This corresponds to not x or y
, which is DNxy
in the simplified syntax.
1 while s{ C ((?&rawexpr)) ((?&rawexpr)) $rawlib }{NDN$1N$2}g;
Now we get rid of C
using De Morgan's law: not (x and y) = not x or not y
. Adding a not
on both sides gives us not (not (x and y)) = not (not x or not y)
. The two not
s on the left side cancel out, giving x and y = not (not x or not y)
, which is NDNxNy
in the simplified syntax.
Now for the definition of $rawlib
, which makes use of regex features introduced in v5.10:
my $rawlib = qr{
(?(DEFINE)
(?<rawexpr>
(?>
[az]

N (?&rawexpr)

[CDIE] (?&rawexpr) (?&rawexpr)
)
)
)
};
This says the whole regex is in a (?(DEFINE) ... )
block, which has no effect on matching. It merely provides definitions for use in the rest of the regex (i.e. $rawlib
is effectively a regex library). Using (?<rawexpr> ... )
we define a named subpattern called rawexpr
: A rawexpr
is either a character from the range az
, or N followed by a rawexpr
, or one of CDIE
followed by two rawexpr
s. The (?&rawexpr)
syntax lets us invoke named subpatterns recursively.
By including $rawlib
in the regexes above we made the name rawexpr
visible in the surrounding regex, which allowed us to simply write (?&rawexpr)
to match a nontrivial piece of the input.
At this point in the program we've reduced the input expression to nothing but combinations of variables, N
, and D
. To proceed further, we're going to switch from a 2operand or
(D
) to an operator with a variable number of operands (V...;
), i.e. we're going to turn Dxy
into Vxy;
:
1 while s{ D ((?&rawexpr)) ((?&rawexpr)) $rawlib }{V$1$2;}g;
This line works because even though (?&rawexpr)
doesn't match V...;
, regexes always find the leftmost match first, and because we're using prefix notation, the first match will be the outermost expression. This means we're rewriting from the outside in, so any subexpressions are guaranteed to not contain V...;
yet.
tr/N/~/;
Finally (because I think it looks better) we turn all the N
s into ~
s.
say "MOD: $_";
At this point we've completely changed from the raw input form to something using variables, ~
, and V...;
. To confirm everything went well, we output the modified expression.
What follows are the rewrite rules that simplify the expression. We start with another regex library:
my $modlib = qr{
(?(DEFINE)
(?<exp>
(?>
[01az]

~ (?&exp)

V (?&exp)*+ ;
)
)
)
};
A (modified) expression exp
is either 0
or 1
(constants representing false
and true
, respectively), or a variable from the set az
, or ~
followed by an exp
, or V
followed by 0 or more exp
s, followed by ;
.
Now the actual rewrite code:
say "...> $_" while 0
We print the current expression after each substitution step to see what's going on. The 0
after while
lets us start the next line with 
, which makes the substitutions look uniform. We repeatedly try to find matches of our rules until none of the regexes matches anymore. At that point we've finished rewriting (and hopefully simplifying) the expression as much as possible.
 s{ ~ ~ }{}g
All instances of ~~
can be removed (not not
cancels out).
 s{ ~ 0 }{1}g
not false
is true
.
 s{ ~ 1 }{0}g
not true
is false
.
 s{ V ; }{0}g
or []
with no operands is false
(because false
is the neutral element for or
).
 s{ V ((?&exp)) ; $modlib }{$1}g
or [x]
with a single operand is just that operand (x
).
 s{ V ((?&exp)*) V ((?&exp)*) ; $modlib }{V$1$2}g
or [@x, or [@y], @z]
is the same as or [@x, @y, @z]
(using @x
to stand for "a list of expressions called x"). This is essentially an associativity rule that eliminates nested or
s.
 s{ V (?&exp)* 1 (?&exp)*+ ; $modlib }{1}g
or [@x, true, @y]
is true
; i.e. an or
with true
among its operands is itself true
.
 s{ V ((?&exp)*) 0 $modlib }{V$1}g
or [@x, false, @y]
is or [@x, @y]
; i.e. false
can be eliminated if it's an operand of or
.
The final rule is quite a mouthful so I'm going to provide inline commentary:
 s{
V ((?&exp)*?) (~??) ((?&exp)) ((?&exp)*+) ;
We match V
, followed by 0 or more expressions, followed by an (optionally negated) expression, followed by 0 or more expressions, followed by ;
. So far this is really general (it matches all or
s with at least one operand).
(?(?{
index($1, $3) < 0 &&
index($4, $3) < 0
}) (*FAIL) )
This is an instance of the (?(COND)YESPATTERN)
regex syntax, which lets us match a regex conditionally. Our condition has the form (?{ ... })
, which embeds arbitrary Perl code into the regex. If the condition is true, we match the regex (*FAIL)
, which simply fails right away. This is effectively a (negated) assertion: If the condition is false, nothing happens; if it is true, the match fails (and we backtrack).
The whole thing asserts that the subexpression $3
can be found somewhere in either $1
(the list of expressions before $3
) or in $4
(the list of expressions after $3
).
Taken together, we're looking for or [@x, y, @z]
or or [@x, not y, @z]
where y
occurs in @x
or @z
, either directly or nested in a subexpression.
$modlib
}{
my ($pre, $neg, $x, $post) = ($1, $2, $3, $4);
Having found such a match, we can now do a bit of simplification. The basic idea is that in or [@x, y, @z]
, all occurrences of y
in @x
and @z
can be replaced by false
. Why? Because y
is either true
or false
. If it's true
, or [@x, true, @z]
is true
no matter what we do to @x
or @z
. If it's false
, replacing y
by false
is a noop. Therefore replacing y
by false
in @x
and @z
doesn't change the outcome in either case.
Similar reasoning applies to or [@x, not y, @z]
, only we replace y
by true
in @x
and @z
(instead of false
).
my $spec = $neg ? '1' : '0';
If the original match was negated, the replacement is true
, else false
.
s{ \Q$x\E }{$spec}g for $pre, $post;
Replace y
in both @x
and @z
.
"V$pre$neg$x$post;"
Reassemble the expression from the modified pieces.
}ge
;
say $_ eq '1' ? "Tautology" : "Not a tautology", "\n";
}
Finally, if the whole thing was reduced to 1
(i.e. true
), say that it is tautological.
For a practical demonstration, here's the output from the sample input at SPOJ:
ORIG: IIpqDpNp
MOD: V~V~pq;Vp~p;;
...> V~V~pq;p~p;
...> V~V~0q;p~0;
...> V~V1q;p1;
...> 1
Tautology
ORIG: NCNpp
MOD: ~~V~~p~p;
...> Vp~p;
...> Vp~0;
...> Vp1;
...> 1
Tautology
ORIG: Iaz
MOD: V~az;
Not a tautology
ORIG: NNNNNNNp
MOD: ~~~~~~~p
...> ~p
Not a tautology
ORIG: IIqrIIpqIpr
MOD: V~V~qr;V~V~pq;V~pr;;;
...> V~V~qr;~V~pq;V~pr;;
...> V~V~qr;~V~pq;~pr;
...> V~V~qr;~V0q;~pr;
...> V~V~qr;~Vq;~pr;
...> V~V~qr;~q~pr;
...> V~V0r;~q~pr;
...> V~Vr;~q~pr;
...> V~r~q~pr;
...> V~r~q~p1;
...> 1
Tautology
ORIG: Ipp
MOD: V~pp;
...> V~p1;
...> 1
Tautology
ORIG: Ezz
MOD: V~V~z~z;~V~~z~~z;;
...> V~V~z~z;~Vzz;;
...> V~V~z0;~Vz0;;
...> V~V~z;~Vz;;
...> V~~z~z;
...> Vz~z;
...> Vz~0;
...> Vz1;
...> 1
Tautology
The complete program:
#!/usr/bin/env perl
use v5.14.0;
use warnings;
use re '/xms', $^V lt v5.18.0 ? 'eval' : ();
my $rawlib = qr{
(?(DEFINE)
(?<rawexpr>
(?>
[az]

N (?&rawexpr)

[CDIE] (?&rawexpr) (?&rawexpr)
)
)
)
};
my $modlib = qr{
(?(DEFINE)
(?<exp>
(?>
[01az]

~ (?&exp)

V (?&exp)*+ ;
)
)
)
};
while (readline) {
chomp;
say "ORIG: $_";
1 while s{ E ((?&rawexpr)) ((?&rawexpr)) $rawlib }{DC$1$2CN$1N$2}g;
1 while s{ I ((?&rawexpr)) ((?&rawexpr)) $rawlib }{DN$1$2}g;
1 while s{ C ((?&rawexpr)) ((?&rawexpr)) $rawlib }{NDN$1N$2}g;
1 while s{ D ((?&rawexpr)) ((?&rawexpr)) $rawlib }{V$1$2;}g;
tr/N/~/;
say "MOD: $_";
say "...> $_" while 0
 s{ ~ ~ }{}g
 s{ ~ 0 }{1}g
 s{ ~ 1 }{0}g
 s{ V ; }{0}g
 s{ V ((?&exp)) ; $modlib }{$1}g
 s{ V ((?&exp)*) V ((?&exp)*) ; $modlib }{V$1$2}g
 s{ V (?&exp)* 1 (?&exp)*+ ; $modlib }{1}g
 s{ V ((?&exp)*) 0 $modlib }{V$1}g
 s{
V ((?&exp)*?) (~??) ((?&exp)) ((?&exp)*+) ;
(?(?{
index($1, $3) < 0 &&
index($4, $3) < 0
}) (*FAIL) )
$modlib
}{
my ($pre, $neg, $x, $post) = ($1, $2, $3, $4);
my $spec = $neg ? '1' : '0';
s{ \Q$x\E }{$spec}g for $pre, $post;
"V$pre$neg$x$post;"
}ge
;
say $_ eq '1' ? "Tautology" : "Not a tautology", "\n";
}
__END__
]]>
From: Tessel van Leeuwen <tessel@waag.org>
Subject: Invitation: Join the Apps for Europe competition and win 5,000 euro!
To: undisclosedrecipients:;Hello,
I'm writing to you because I found your email address on the website, http://act.useperl.at/apw2014/wiki?node=HackaThon, and I would like to invite you to enter the Apps for Europe competition: ... <snip>
There are a couple of things about this I find interesting:
The following program contains 3 test cases that you need to make pass. To do
that, you should replace XXX
in the assignments to $a
, $b
and $c
by the
right magic values.
<?php
header('ContentType: text/plain');
function t_1($x) {
switch ($x) {
case 'one': return false;
case 0: return !is_string($x);
default: return false;
}
}
function t_2($x) {
$k = array('one thousand', 2000, 'a363b8d13575101a0226e8d0d054f2e', 'php');
return in_array(md5($x), $k);
}
function t_3($x) {
$k = '1020304050607';
$x = (string)$x;
return strlen($x) < strlen($k) && $x == $k;
}
echo "1..3\n";
$a = XXX;
echo t_1($a) ? 'ok 1' : 'not ok 1', "\n";
$b = XXX;
echo t_2($b) ? 'ok 2' : 'not ok 2', "\n";
$c = XXX;
echo t_3($c) ? 'ok 3' : 'not ok 3', "\n";
If you've done everything right, the output should look like this:
1..3
ok 1
ok 2
ok 3
(Thanks to http://www.reddit.com/r/lolphp for inspiration.)
]]>package Foo { method meth($arg) { ... } }
.]]>
OP
trees
manually.
Perl 5.14.0 added many functions to the API that make custom keywords worthwhile (especially the ability to invoke the Perl parser recursively in order to parse a custom syntax with embedded Perl fragments).
So what can this be used for? In the following, I'm going to show you three modules I've written that make heavy use of custom keywords.
]]>Quote::Code
 quoted strings with arbitrary code interpolation
This module adds a new qc
quoting operator similar to
q
and qq
.
It gives you strings (as usual) but with the ability to interpolate arbitrary
expressions (such as method calls!) by wrapping them in { ... }
:
print qc!2 + 2 = {2 + 2}\n!;
It also defines qc_to
for heredocs with Rubyesque #{ ... }
interpolation:
my $msg = qc_to <<'EOF';
\o/ His power level is #{$user>level + 1}! \o/
EOF
Switch::Plain
 a simple switch statement for PerlThis module exists because I wanted something a lot less magical/crazy than
Switch
or
given
/when
.
It provides two keywords, sswitch
and nswitch
, for string and numeric
comparisons, respectively. It doesn't try to do anything "smart" or dynamic, it
just compares strings or numbers:
nswitch ($input) {
case 1: {
foo();
}
case 2: {
bar();
}
case 3: {
baz();
}
default: {
print "What's this, then?\n";
return;
}
}
Function::Parameters
 subroutine definitions with parameter listsThis module is the original reason I started looking into pluggable keywords. It extends Perl with the ability to define functions and methods with parameter lists:
fun foo($x, $y, $z) {
...
}
method bar($x, $y) {
# $self automatically defined here
$self>frobnicate($x, $y);
}
Or at least that's the short version. It optionally also
method new($class: %args) { ... }
)fun foo(:$x, :$y) {}
(callable as foo(y => 1, x => 2)
):method
to all methods)... and a few other things I'm not going to list here.
I think all of the above modules are seriously cool (I know I wrote them, but
still!). If you agree, feel free to go ahead and give them a try. And if you
find any bugs,
please report them at the usual address (report a bug in
Quote::Code
,
report a bug in
Switch::Plain
report a bug in
Function::Parameters
).
If you've been looking for a reason to upgrade to Perl 5.14 or 5.16, maybe these modules can help. ☺
And if this has given you ideas for your own keywords, give it a spin. This is powerful stuff.
]]>sizeof
is purely a compile time operation. It only looks at the types: sizeof EXPR == sizeof (typeof(EXPR))
(if we pretend C had typeof
for a moment).]]>
Neither C nor Perl have array values (that is, values that represent arrays). When you evaluate an array in C, you get a pointer to its first element. When you evaluate an array in Perl, you get a count (in scalar context) or a list of elements (in list context).
Both languages let you avoid this "decay" by taking the address of (&, C) or a reference to (\, Perl) the array.
]]>Why is a raven like a writingdesk?(Lewis Carroll)
This is a copy of an article I wrote a long time ago. I'm putting it here to give it a more permanent home. Sorry for being off topic again!
I'm glad you asked. The answer is surprisingly simple: almost everything. In other words, they have almost nothing in common. To understand why, we'll take a look at what they are and what operations they support.
]]> ArraysAn array is a fixedlength collection of objects, which are stored sequentially in memory. There are only three things you can do with an array:
sizeof
 get its size sizeof
to it. An array x of N elements of type T (T x[N]
)
has the size N * sizeof (T)
, which is what you should expect. For
example, if sizeof (int) == 2
and int arr[5];
, then
sizeof arr == 10 == 5 * 2 == 5 * sizeof (int)
.&
 get its address &
, which results in a pointer to the entire array.That's all. Yes, this means arrays don't provide direct access to their contents. More specifically, there is no array indexing operator.
A pointer is a value that refers to another object (or function). You might say it contains the object's address. Here are the operations that pointers support:
sizeof
 get its size
Like arrays, pointers have a size that can be obtained with sizeof
. Note
that different pointer types can have different sizes.
&
 get its address
Assuming your pointer is an lvalue, you can take its address with &
. The
result is a pointer to a pointer.
*
 dereference it
Assuming the base type of your pointer isn't an incomplete type, you can
dereference it; i.e., you can follow the pointer and get the object it
refers to. Incomplete types include void
and predeclared struct
types
that haven't been defined yet.
+
, 
 pointer arithmetic
If you have a pointer to an array element, you can add an integer amount to
it. This amount can be negative, and ptr  n
is equivalent to ptr + n
(and n + ptr
, since +
is commutative, even with pointers). If ptr
is
a pointer to the i
'th element of an array, then ptr + n
is a pointer to
the (i + n)
'th array element, unless i + n
is negative or greater than
the number of array elements, in which case the results are undefined. If
i + n
is equal to the number of elements, the result is a pointer that
must not be dereferenced.
That's it, really. However, there are a few other pointer operations defined in terms of the above fundamental operations:
>
 struct dereference
p>m
is equivalent to (*p).m
, where .
is the struct/union member
access operator. This means p
must be a pointer to a struct or union.
[]
 indexed dereference
a[b]
is equivalent to *(a + b)
. This means a
and b
must be a pointer
to an array element and an integer; not necessarily respectively, because
a[b] == *(a + b) == *(b + a) == b[a]
. Another important equivalence is
p[0] == 0[p] == *p
.
However, there's one thing that confuses this issue. Whenever you declare a function parameter to have an array type, it gets silently converted to a pointer and any size information is ignored. Thus the following four declarations are equivalent:
void foo(int [42]);
void foo(int []);
typedef int t_array[23];
void foo(t_array);
void foo(int *);
A more common example is int main(int argc, char *argv[])
, which is the same
as int main(int argc, char **argv)
. However,
int main(int argc, char argv[][])
would be an error because the above rule
isn't recursive; the result after conversion would be
int main(int argc, char (*argv)[])
, i.e. argv
would be a pointer to an
array of unknown size, not a pointer to a pointer.
Arrays by themselves are nearly useless in C. Even the fundamental []
operator, which is used for getting at the array's contents, is an illusion:
it's defined on pointers and only happens to work with arrays because of the
rule that any use of an array outside of sizeof
and &
yields a pointer.