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executable file 650 lines (596 sloc) 20.281 kB
## Last modification: 8/3/00 by akp
## Originally written by Daniel Martin, Dept of Math, John Hopkins
## Additions and modifications were made by James Martino, Dept of Math, John Hopkins
## Additions and modifications were made by Arnold Pizer, Dept of Math, Univ of Rochester
#use Data::Dumper;
package AlgParser;
use HTML::Entities;
%close = ();
sub new {
my $package = shift;
my (%ret);
$ret{string} = "";
$ret{posarray} = [];
$ret{parseerror} = "";
$ret{parseresult} = [];
bless \%ret, $package;
return \%ret;
}
sub inittokenizer {
my($self, $string) = @_;
$self->{string} =~ m/\G.*$/g;
$self->{string} = undef;
$self->{string} = $string;
$self->{string} =~ m/\G.*$/g;
$self->{string} =~ m/^/g;
}
$close{'{'} = '}';
$close{'['} = ']';
$close{'('} = ')';
$binoper3 = '(?:\\^|\\*\\*)';
$binoper2 = '[/*_,]';
$binoper1 = '[-+=><%!#]';
$openparen = '[{(\\[]';
$closeparen = '[})\\]]';
$varname = '[A-Za-z](?:_[0-9]+)?';
$specialvalue = '(?:e|pi|da|db|dc|de|df|dg|dh|di|dj|dk|dl|dm|dn|do|dp|dq|dr|ds|dt|du|dv|dw|dx|dy|dz|infty|alpha|bita|gamma|zita|thita|iota|kappa|lambda|mu|nu|xi|rho|sigma|tau|phi|chi|psi|omega|zepslon|zdelta|xeta|zupslon)';
$numberplain = '(?:\d+(?:\.\d*)?|\.\d+)';
$numberE = '(?:' . $numberplain . 'E[-+]?\d+)';
$number = '(?:' . $numberE . '|' . $numberplain . ')';
#
# DPVC -- 2003/03/31
# added missing trig and inverse functions
#
#$trigfname = '(?:cosh|sinh|tanh|cot|(?:a(?:rc)?)?cos|(?:a(?:rc)?)?sin|' .
# '(?:a(?:rc)?)?tan|sech?)';
$trigfname = '(?:(?:a(?:rc)?)?(?:sin|cos|tan|sec|csc|cot)h?)';
#
# End DPVC
#
$otherfunc = '(?:exp|abs|logten|log|ln|sqrt|sgn|step|fact|int|lim|fun[a-zA-Z])';
$funcname = '(?:' . $otherfunc . '|' . $trigfname . ')';
$tokenregexp = "(?:($binoper3)|($binoper2)|($binoper1)|($openparen)|" .
"($closeparen)|($funcname)|($specialvalue)|($varname)|" .
"($numberE)|($number))";
sub nexttoken {
my($self) = shift;
$self->{string} =~ m/\G\s+/gc;
my($p1) = pos($self->{string}) || 0;
if(scalar($self->{string} =~ m/\G$tokenregexp/gc)) {
push @{$self->{posarray}}, [$p1, pos($self->{string})];
if (defined($1)) {return ['binop3', $1];}
if (defined($2)) {return ['binop2', $2];}
if (defined($3)) {return ['binop1', $3];}
if (defined($4)) {return ['openp', $4];}
if (defined($5)) {return ['closep', $5];}
if (defined($6)) {return ['func1', $6];}
if (defined($7)) {return ['special', $7];}
if (defined($8)) {return ['varname', $8];}
if (defined($9)) {return ['numberE', $9];}
if (defined($10)) {return ['number', $10];}
}
else {
push @{$self->{posarray}}, [$p1, undef];
return undef;
}
}
sub parse {
my $self = shift;
$self->{parseerror} = "";
$self->{posarray} = [];
$self->{parseresult} = ['top', undef];
my (@backtrace) = (\$self->{parseresult});
my (@pushback) = ();
my $currentref = \$self->{parseresult}->[1];
my $curenttok;
my $sstring = shift;
$self->inittokenizer($sstring);
$currenttok = $self->nexttoken;
if (!$currenttok) {
if ($self->{string} =~ m/\G$/g) {
return $self->error("empty");
} else {
my($mark) = pop @{$self->{posarray}};
my $position = 1+$mark->[0];
return $self->error("Illegal character at position $position", $mark);
}
}
# so I can assume we got a token
local $_;
while ($currenttok) {
$_ = $currenttok->[0];
/binop1/ && do {
# check if we have a binary or unary operation here.
if (defined(${$currentref})) {
# binary - walk up the tree until we hit an open paren or the top
while (${$currentref}->[0] !~ /^(openp|top)/) {
$currentref = pop @backtrace;
}
my $index = ((${$currentref}->[0] eq 'top')?1:3);
${$currentref}->[$index] = ['binop1', $currenttok->[1],
${$currentref}->[$index], undef];
push @backtrace, $currentref;
push @backtrace, \${$currentref}->[$index];
$currentref = \${$currentref}->[$index]->[3];
} else {
# unary
${$currentref} = ['unop1', $currenttok->[1], undef];
push @backtrace, $currentref;
$currentref = \${$currentref}->[2];
}
};
/binop2/ && do {
if (defined(${$currentref})) {
# walk up the tree until an open paren, the top, binop1 or unop1
# I decide arbitrarily that -3*4 should be parsed as -(3*4)
# instead of as (-3)*4. Not that it makes a difference.
while (${$currentref}->[0] !~ /^(openp|top|binop1)/) {
$currentref = pop @backtrace;
}
my $a = ${$currentref}->[0];
my $index = (($a eq 'top')?1:3);
${$currentref}->[$index] = ['binop2', $currenttok->[1],
${$currentref}->[$index], undef];
push @backtrace, $currentref;
push @backtrace, \${$currentref}->[$index];
$currentref = \${$currentref}->[$index]->[3];
} else {
# Error
my($mark) = pop @{$self->{posarray}};
my $position =1+$mark->[0];
return $self->error("Didn't expect " . $currenttok->[1] .
" at position $position" , $mark);
}
};
/binop3/ && do {
if (defined(${$currentref})) {
# walk up the tree until we need to stop
# Note that the right-associated nature of ^ means we need to
# stop walking backwards when we hit a ^ as well.
while (${$currentref}->[0] !~ /^(openp|top|binop[123]|unop1)/) {
$currentref = pop @backtrace;
}
my $a = ${$currentref}->[0];
my $index = ($a eq 'top')?1:($a eq 'unop1')?2:3;
${$currentref}->[$index] = ['binop3', $currenttok->[1],
${$currentref}->[$index], undef];
push @backtrace, $currentref;
push @backtrace, \${$currentref}->[$index];
$currentref = \${$currentref}->[$index]->[3];
} else {
# Error
my($mark) = pop @{$self->{posarray}};
my $position = 1+$mark->[0];
return $self->error("Didn't expect " . $currenttok->[1] .
" at position $position", $mark);
}
};
/openp/ && do {
if (defined(${$currentref})) {
# we weren't expecting this - must be implicit
# multiplication.
push @pushback, $currenttok;
$currenttok = ['binop2', 'implicit'];
next;
} else {
my($me) = pop @{$self->{posarray}};
${$currentref} = [$currenttok->[0], $currenttok->[1], $me, undef];
push @backtrace, $currentref;
$currentref = \${$currentref}->[3];
}
};
/func1/ && do {
if (defined(${$currentref})) {
# we weren't expecting this - must be implicit
# multiplication.
push @pushback, $currenttok;
$currenttok = ['binop2', 'implicit'];
next;
} else {
# just like a unary operator
${$currentref} = [$currenttok->[0], $currenttok->[1], undef];
push @backtrace, $currentref;
$currentref = \${$currentref}->[2];
}
};
/closep/ && do {
if (defined(${$currentref})) {
# walk up the tree until we need to stop
while (${$currentref}->[0] !~ /^(openp|top)/) {
$currentref = pop @backtrace;
}
my $a = ${$currentref}->[0];
if ($a eq 'top') {
my($mark) = pop @{$self->{posarray}};
my $position = 1+$mark->[0];
return $self->error("Unmatched close " . $currenttok->[1] .
" at position $position", $mark);
} elsif ($close{${$currentref}->[1]} ne $currenttok->[1]) {
my($mark) = pop @{$self->{posarray}};
my $position = 1+$mark->[0];
return $self->error("Mismatched parens at position $position"
, ${$currentref}->[2], $mark);
} else {
${$currentref}->[0] = 'closep';
${$currentref}->[2] = pop @{${$currentref}};
}
} else {
# Error - something like (3+4*)
my($mark) = pop @{$self->{posarray}};
my $position = 1+$mark->[0];
return $self->error("Premature close " . $currenttok->[1] .
" at position $position", $mark);
}
};
/special|varname|numberE?/ && do {
if (defined(${$currentref})) {
# we weren't expecting this - must be implicit
# multiplication.
push @pushback, $currenttok;
$currenttok = ['binop2', 'implicit'];
next;
} else {
${$currentref} = [$currenttok->[0], $currenttok->[1]];
}
};
if (@pushback) {
$currenttok = pop @pushback;
} else {
$currenttok = $self->nexttoken;
}
}
# ok, we stopped parsing. Now we need to see why.
if ($self->{parseresult}->[0] eq 'top') {
$self->{parseresult} = $self->arraytoexpr($self->{parseresult}->[1]);
} else {
return $self->error("Internal consistency error; not at top when done");
}
if ($self->{string} =~ m/\G\s*$/g) {
if (!defined(${$currentref})) {
$self->{string} .= " ";
return $self->error("I was expecting more at the end of the line",
[length($self->{string})-1, length($self->{string})]);
} else {
# check that all the parens were closed
while (@backtrace) {
$currentref = pop @backtrace;
if (${$currentref}->[0] eq 'openp') {
my($mark) = ${$currentref}->[2];
my $position = 1+$mark->[0];
return $self->error("Unclosed parentheses beginning at position $position"
, $mark);
}
}
# Ok, we must really have parsed something
return $self->{parseresult};
}
} else {
my($mark) = pop @{$self->{posarray}};
my $position = 1+$mark->[0];
return $self->error("Illegal character at position $position",$mark);
}
}
sub arraytoexpr {
my ($self) = shift;
return Expr->fromarray(@_);
}
sub error {
my($self, $errstr, @markers) = @_;
# print STDERR Data::Dumper->Dump([\@markers],
# ['$markers']);
$self->{parseerror} = $errstr;
my($htmledstring) = '<tt class="parseinput">';
my($str) = $self->{string};
# print STDERR Data::Dumper->Dump([$str], ['$str']);
my($lastpos) = 0;
$str =~ s/ /\240/g;
while(@markers) {
my($ref) = shift @markers;
my($pos1) = $ref->[0];
my($pos2) = $ref->[1];
if (!defined($pos2)) {$pos2 = $pos1+1;}
$htmledstring .= encode_entities(substr($str,$lastpos,$pos1-$lastpos)) .
'<b class="parsehilight">' .
encode_entities(substr($str,$pos1,$pos2-$pos1)) .
'</b>';
$lastpos = $pos2;
}
# print STDERR Data::Dumper->Dump([$str, $htmledstring, $lastpos],
# ['$str', '$htmledstring', '$lastpos']);
$htmledstring .= encode_entities(substr($str,$lastpos));
$htmledstring .= '</tt>';
# $self->{htmlerror} = '<p class="parseerr">' . "\n" .
# '<span class="parsedesc">' .
# encode_entities($errstr) . '</span><br>' . "\n" .
# $htmledstring . "\n" . '</p>' . "\n";
$self->{htmlerror} = $htmledstring ;
$self->{htmlerror} = 'empty' if $errstr eq 'empty';
$self->{error_msg} = $errstr;
# warn $errstr . "\n";
return undef;
}
sub tostring {
my ($self) = shift;
return $self->{parseresult}->tostring(@_);
}
sub tolatex {
my ($self) = shift;
return $self->{parseresult}->tolatex(@_);
}
sub tolatexstring { return tolatex(@_);}
sub exprtolatexstr {
return exprtolatex(@_);
}
sub exprtolatex {
my($expr) = shift;
my($exprobj);
if ((ref $expr) eq 'ARRAY') {
$exprobj = Expr->new(@$expr);
} else {
$exprobj = $expr;
}
return $exprobj->tolatex();
}
sub exprtostr {
my($expr) = shift;
my($exprobj);
if ((ref $expr) eq 'ARRAY') {
$exprobj = Expr->new(@$expr);
} else {
$exprobj = $expr;
}
return $exprobj->tostring();
}
sub normalize {
my ($self, $degree) = @_;
$self->{parseresult} = $self->{parseresult}->normalize($degree);
}
sub normalize_expr {
my($expr, $degree) = @_;
my($exprobj);
if ((ref $expr) eq 'ARRAY') {
$exprobj = Expr->new(@$expr);
} else {
$exprobj = $expr;
}
return $exprobj->normalize($degree);
}
package AlgParserWithImplicitExpand;
@ISA=qw(AlgParser);
sub arraytoexpr {
my ($self) = shift;
my ($foo) = ExprWithImplicitExpand->fromarray(@_);
# print STDERR Data::Dumper->Dump([$foo],['retval']);
return $foo;
}
package Expr;
sub new {
my($class) = shift;
my(@args) = @_;
my($ret) = [@args];
return (bless $ret, $class);
}
sub head {
my($self) = shift;
return ($self->[0]);
}
sub normalize {
#print STDERR "normalize\n";
#print STDERR Data::Dumper->Dump([@_]);
my($self, $degree) = @_;
my($class) = ref $self;
$degree = $degree || 0;
my($type, @args) = @$self;
local $_;
$_ = $type;
my ($ret) = [$type, @args];
if(/closep/) {
$ret = $args[1]->normalize($degree);
} elsif (/unop1/) {
$ret = $class->new($type, $args[0], $args[1]->normalize($degree));
} elsif (/binop/) {
$ret = $class->new($type, $args[0], $args[1]->normalize($degree),
$args[2]->normalize($degree));
} elsif (/func1/) {
$args[0] =~ s/^arc/a/;
$ret = $class->new($type, $args[0], $args[1]->normalize($degree));
}
if ($degree < 0) {return $ret;}
($type, @args) = @$ret;
$ret = $class->new($type, @args);
$_ = $type;
if (/binop1/ && ($args[2]->[0] =~ 'unop1')) {
my($h1, $h2) = ($args[0], $args[2]->[1]);
my($s1, $s2) = ($h1 eq '-', $h2 eq '-');
my($eventual) = ($s1==$s2);
if ($eventual) {
$ret = $class->new('binop1', '+', $args[1], $args[2]->[2] );
} else {
$ret = $class->new('binop1', '-', $args[1], $args[2]->[2] );
}
} elsif (/binop2/ && ($args[1]->[0] =~ 'unop1')) {
$ret = $class->new('unop1', '-',
$class->new($type, $args[0], $args[1]->[2],
$args[2])->normalize($degree) );
} elsif (/binop[12]/ && ($args[2]->[0] eq $type) &&
($args[0] =~ /[+*]/)) {
# Remove frivolous right-association
# For example, fix 3+(4-5) or 3*(4x)
$ret = $class->new($type, $args[2]->[1],
$class->new($type, $args[0], $args[1],
$args[2]->[2])->normalize($degree),
$args[2]->[3]);
} elsif (/unop1/ && ($args[0] eq '+')) {
$ret = $args[1];
} elsif (/unop1/ && ($args[1]->[0] =~ 'unop1')) {
$ret = $args[1]->[2];
}
if ($degree > 0) {
}
return $ret;
}
sub tostring {
# print STDERR "Expr::tostring\n";
# print STDERR Data::Dumper->Dump([@_]);
my($self) = shift;
my($type, @args) = @$self;
local $_;
$_ = $type;
/binop1/ && do {
my ($p1, $p2) = ('','');
if ($args[2]->[0] eq 'binop1') {($p1,$p2)=qw{ ( ) };}
return ($args[1]->tostring() . $args[0] . $p1 .
$args[2]->tostring() . $p2);
};
/unop1/ && do {
my ($p1, $p2) = ('','');
if ($args[1]->[0] =~ /binop1/) {($p1,$p2)=qw{ ( ) };}
return ($args[0] . $p1 . $args[1]->tostring() . $p2);
};
/binop2/ && do {
my ($p1, $p2, $p3, $p4)=('','','','');
if ($args[0] =~ /implicit/) {$args[0] = ' ';}
if ($args[1]->[0] =~ /binop1/) {($p1,$p2)=qw{ ( ) };}
# if ($args[2]->[0] =~ /binop[12]/) {($p3,$p4)=qw{ ( ) };}
if ($args[2]->[0] =~ /binop[12]|unop1/) {($p3,$p4)=qw{ ( ) };}
return ($p1 . $args[1]->tostring() . $p2 . $args[0] . $p3 .
$args[2]->tostring() . $p4);
};
/binop3/ && do {
my ($p1, $p2, $p3, $p4)=('','','','');
# if ($args[1]->[0] =~ /binop[123]|numberE/) {($p1,$p2)=qw{ ( ) };}
if ($args[1]->[0] =~ /binop[123]|unop1|numberE/) {($p1,$p2)=qw{ ( ) };}
# if ($args[2]->[0] =~ /binop[12]|numberE/) {($p3,$p4)=qw{ ( ) };}
if ($args[2]->[0] =~ /binop[12]|unop1|numberE/) {($p3,$p4)=qw{ ( ) };}
return ($p1 . $args[1]->tostring() . $p2 . $args[0] . $p3 .
$args[2]->tostring() . $p4);
};
/func1/ && do {
return ($args[0] . '(' . $args[1]->tostring() . ')');
};
/special|varname|numberE?/ && return $args[0];
/closep/ && do {
my(%close) = %AlgParser::close;
return ($args[0] . $args[1]->tostring() . $close{$args[0]});
};
}
sub tolatex {
my($self) = shift;
my($type, @args) = @$self;
local $_;
$_ = $type;
/binop1/ && do {
my ($p1, $p2) = ('','');
if ($args[2]->[0] eq 'binop1') {($p1,$p2)=qw{ \left( \right) };}
return ($args[1]->tolatex() . $args[0] . $p1 .
$args[2]->tolatex() . $p2);
};
/unop1/ && do {
my ($p1, $p2) = ('','');
if ($args[1]->[0] =~ /binop1/) {($p1,$p2)=qw{ \left( \right) };}
return ($args[0] . $p1 . $args[1]->tolatex() . $p2);
};
/binop2/ && do {
my ($p1, $p2, $p3, $p4) = ('','','','');
if ($args[0] =~ /implicit/) {
if ( (($args[1]->head eq qq(number)) &&
($args[2]->head eq qq(number))) ||
(($args[1]->head eq qq(binop2)) &&
($args[1]->[2]->head eq qq(number))) ) {
$args[0] = '\\,';
} else {
$args[0] = ' ';
}
}
if ($args[1]->[0] =~ /binop1|numberE/)
{($p1,$p2)=qw{ \left( \right) };}
# if ($args[2]->[0] =~ /binop[12]|numberE/)
if ($args[2]->[0] =~ /binop[12]|numberE|unop1/)
{($p3,$p4)=qw{ \left( \right) };}
if ($args[0] eq '/'){
return('\frac{' . $p1 . $args[1]->tolatex() . $p2 . '}'.
'{' . $p3 . $args[2]->tolatex() . $p4 . '}' );
}
else{
return ($p1 . $args[1]->tolatex() . $p2 . $args[0] . $p3 .
$args[2]->tolatex() . $p4);
}
};
/binop3/ && do {
my ($p1, $p2, $p3, $p4)=('','','','');
# if ($args[1]->[0] =~ /binop[123]|numberE/) {($p1,$p2)=qw{ \left( \right) };}
if ($args[1]->[0] =~ /binop[123]|unop1|numberE/) {($p1,$p2)=qw{ \left( \right) };}
# Not necessary in latex
# if ($args[2]->[0] =~ /binop[12]/) {($p3,$p4)=qw{ \left( \right) };}
return ($p1 . $args[1]->tolatex() . $p2 . "^{" . $p3 .
$args[2]->tolatex() . $p4 . "}");
};
/func1/ && do {
my($p1,$p2);
if($args[0] eq "sqrt"){($p1,$p2)=qw{ \left{ \right} };}
else {($p1,$p2)=qw{ \left( \right) };}
#
# DPVC -- 2003/03/31
# added missing trig functions
#
#$specialfunc = '(?:abs|logten|asin|acos|atan|sech|sgn|step|fact)';
$specialfunc = '(?:abs|logten|a(?:sin|cos|tan|sec|csc|cot)h?|sgn|step|fact)';
#
# End DPVC
#
if ($args[0] =~ /$specialfunc/) {
return ('\mbox{' . $args[0] .'}'. $p1 . $args[1]->tolatex() . $p2);
}
else {
return ('\\' . $args[0] . $p1 . $args[1]->tolatex() . $p2);
}
};
/special/ && do {
if ($args[0] eq 'pi') {return '\pi';} else {return $args[0];}
};
/varname|(:?number$)/ && return $args[0];
/numberE/ && do {
$args[0] =~ m/($AlgParser::numberplain)E([-+]?\d+)/;
return ($1 . '\times 10^{' . $2 . '}');
};
/closep/ && do {
my($backslash) = '';
my(%close) = %AlgParser::close;
if ($args[0] eq '{') {$backslash = '\\';}
#This is for editors to match: }
return ('\left' . $backslash . $args[0] . $args[1]->tolatex() .
'\right' . $backslash . $close{$args[0]});
};
}
sub fromarray {
my($class) = shift;
my($expr) = shift;
if ((ref $expr) ne qq{ARRAY}) {
die "Program error; fromarray not passed an array ref.";
}
my($type, @args) = @$expr;
foreach my $i (@args) {
if (ref $i) {
$i = $class->fromarray($i);
}
}
return $class->new($type, @args);
}
package ExprWithImplicitExpand;
@ISA=qw(Expr);
sub tostring {
# print STDERR "ExprWIE::tostring\n";
# print STDERR Data::Dumper->Dump([@_]);
my ($self) = shift;
my($type, @args) = @$self;
if (($type eq qq(binop2)) && ($args[0] eq qq(implicit))) {
my ($p1, $p2, $p3, $p4)=('','','','');
if ($args[1]->head =~ /binop1/) {($p1,$p2)=qw{ ( ) };}
# if ($args[2]->head =~ /binop[12]/) {($p3,$p4)=qw{ ( ) };}
if ($args[2]->head =~ /binop[12]|unop1/) {($p3,$p4)=qw{ ( ) };}
return ($p1 . $args[1]->tostring() . $p2 . '*' . $p3 .
$args[2]->tostring() . $p4);
} else {
return $self->SUPER::tostring(@_);
}
}
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