noble (3) Parser::MGC::Examples::EvaluateExpression.3pm.gz
NAME
"Parser::MGC::Examples::EvaluateExpression" - an example parser to evaluate simple numerical expressions
DESCRIPTION
This evaluator-parser takes simple mathematical expressions involving the four basic arithmetic operators
(+, -, *, /) applied to integers, and returns the numerical result. It handles operator precedence, with
* and / having a higher level than + and -, and copes with parentheses.
Operator precedence is implemented by using two different parsing functions to handle the two different
precedence levels.
Boilerplate
We start off by declaring a package and subclassing Parser::MGC.
package ExprParser;
use base qw( Parser::MGC );
use strict;
use warnings;
parse
The topmost parsing function, "parse", handles the outermost level of operator precedence, the + and -
operators. It first parses a single term from the input by callling "parse_term" to obtain its value.
It then uses the "any_of" structure-forming method to look for either a + or - operator which would
indicate another term will follow it. If it finds either of these, it parses the next term from after the
operator by another call to "parse_term" and then adds or subtracts the value of it from the running
total.
The "any_of" call itself is used as the conditional expression of a "while" loop, to ensure it gets
called multiple times. Whenever another term has been parsed, the body function returns a true value, to
indicate that the while loop should be invoked again. Only when there are no more + or - operators,
indicating no more terms, does the body return false, causing the while loop to stop.
This continues until there are no more + or - operators, when the overall total value is returned to the
caller.
sub parse
{
my $self = shift;
my $val = $self->parse_term
1 while $self->any_of(
sub { $self->expect( "+" ); $val += $self->parse_term; 1 },
sub { $self->expect( "-" ); $val -= $self->parse_term; 1 },
sub { 0 },
);
return $val;
}
This function recognises input matching the following EBNF grammar:
EXPR = TERM { ( '+' | '-' ) TERM };
parse_term
Called by "parse", the next function is "parse_term" which has a similar structure. This function
implements the next level of operator precedence, of the * and / operators. In a similar fashion to the
previous function, this one parses a single factor from the input by calling "parse_factor", and then
looks for * or / operators, multiplying or dividing the value by the next factor it expects to find after
those. This continues until there are no more * or / operators, when the overall product is returned.
sub parse_term
{
my $self = shift;
my $val = $self->parse_factor;
1 while $self->any_of(
sub { $self->expect( "*" ); $val *= $self->parse_factor; 1 },
sub { $self->expect( "/" ); $val /= $self->parse_factor; 1 },
sub { 0 },
);
return $val;
}
This function recognises input matching the following EBNF grammar:
TERM = FACTOR { ( '*' | '/' ) FACTOR };
parse_factor
Finally, the innermost "parse_factor" function is called by "parse_term" to parse out the actual
numerical values. This is also the point at which the grammar can recurse, recognising a parenthesized
expression. It uses an "any_of" with two alternative function bodies, to cover these two cases.
The first case, to handle a parenthesized sub-expression, consists of a call to "scope_of". This call
would expect to find a "(" symbol to indicate the parenthesized expression. If it finds one, it will
recurse back to the toplevel "parse" method to obtain its value, then expects the final ")" symbol. The
value of this factor is then the value of the sub-expression contained within the parentheses.
If the first case fails, because it does not find that leading "(" symbol, the second case is attempted
instead. This handles an actual integer constant. This case is simply a call to the "token_int" method
of the underlying class, which recognises various string forms of integer constants, returning their
numerical value.
sub parse_factor
{
my $self = shift;
$self->any_of(
sub { $self->scope_of( "(", sub { $self->parse }, ")" ) },
sub { $self->token_int },
);
}
This function recognises input matching the following EBNF grammar:
FACTOR = '(' EXPR ')'
| integer
EXAMPLES OF OPERATION
A single integer
The simplest form of operation of this parser is when it is given a single integer value as its input;
for example "15".
INPUT: 15
POSITION: ^
The outermost call to "parse" will call "parse_term", which in turn calls "parse_factor".
INPUT: 15
POSITION ^
CALLS: parse
=> parse_term
=> parse_factor
The "any_of" inside "parse_factor" will first attempt to find a parenthesized sub-expression by using
"scope_of", but this will fail because it does not start with an open parenthesis symbol. The "any_of"
will then attempt the second case, calling "token_int" which will succeed at obtaining an integer value
from the input stream, consuming it by advancing the stream position. The value of 15 is then returned by
"parse_factor" back to "parse_term" where it is stored in the $val lexical.
INPUT: 15
POSITION: ^
CALLS: parse
=> parse_term -- $val = 15
At this point, the "any_of" inside "parse_term" will attempt to find a * or / operator, but both will
fail because there is none, causing the final alternative function to be invoked, which stops the "while"
loop executing. The value of 15 is then returned to the outer caller, "parse". A similar process happens
there, where it fails to find a + or - operator, and thus the final value of 15 is returned as the result
of the entire parsing operation.
INPUT: 15
OUTPUT: 15
A simple sum of two integers
Next lets consider a case that actually requires some real parsing, such as an expression requesting the
sum of two values; "6 + 9".
INPUT: 6 + 9
POSITION: ^
This parsing operation starts the same as the previous; with "parse" calling "parse_term" which in turn
calls "parse_factor".
INPUT: 6 + 9
POSITION: ^
CALLS: parse
=> parse_term
=> parse_factor
As before, the "any_of" inside "parse_factor" first attempts and fails to find a parenthesized sub-
expression and so tries "token_int" instead. As before this obtains an integer value from the stream and
advances the position. This value is again returned to "parse_term". As before, the "any_of" attempts but
fails to find a * or / operator so the value gets returned to "parse" to be stored in $val.
INPUT: 6 + 9
POSITION: ^
CALLS: parse -- $val = 6
This time, the "any_of" in the outer "parse" method attempts to find a + operator and succeeds, because
there is one at the next position in the stream. This causes the first case to continue, making another
call to "parse_term".
INPUT: 6 + 9
POSITION: ^
CALLS: parse -- $val = 6
=> parse_term
This call to "parse_term" proceeds much like the first, eventually returning the value 9 by consuming it
from the input stream. This value is added to $val by the code inside the "any_of" call.
INPUT: 6 + 9
POSITION: ^
CALLS: parse -- $val = 15
"parse" then calls "any_of" a second time, which attempts to find another operator. This time there is
none, so it returns false, which stops the "while" loop and the value is returned as the final result of
the operation.
INPUT: 6 + 9
OUTPUT: 15
Operator precedence
The two kinds of operators (+ and - vs * and /) are split across two different method calls to allow them
to implement precedence; to say that some of the operators bind more tightly than others. Those operators
that are implemented in more inwardly-nested functions bind tighter than the ones implemented further
out.
To see this in operation consider an expression that mixes the two kinds of operators, such as "15 - 2 *
3"
INPUT: 15 - 2 * 3
POSITION: ^
The parsing operation starts by calling down from "parse" all the way to "token_int" which extracts the
first integer, 15, from the stream and returns it all the way up to "parse" as before:
INPUT: 15 - 2 * 3
POSITION: ^
CALLS: parse -- $val = 15
As before, the "parse" function looks for a * or - operator by its "any_of" test, and finds this time the
- operator, which then causes it to call "parse_term" to parse its value:
INPUT: 15 - 2 * 3
POSITION: ^
CALLS: parse -- $val = 15
=> parse_term
Again, "parse_term" starts by calling "parse_factor" which extracts the next integer from the stream and
returns it. "parse_factor" temporarily stores that in its own $val lexical (which remember, is a lexical
variable local to that call, so is distinct from the one in "parse").
INPUT: 15 - 2 * 3
POSITION: ^
CALLS: parse -- $val = 15
=> parse_term -- $val = 2
This time, when "parse_term" attempts its own "any_of" test to look for a * or / operator, it manages to
find one. By a process similar to the way that the outer "parse" method forms a sum of terms,
"parse_term" forms a product of factors by calling down to "parse_factor" and accumulating the result.
Here it will call "parse_factor" again, which returns the value 3. This gets multiplied into $var.
INPUT: 15 - 2 * 3
POSITION: ^
CALLS: parse -- $val = 15
=> parse_term -- $val = 6
"parse_term" will try again to look for a * or / operator, but this time fails to find one, and so
returns its final result, 6, back to "parse", which then subtracts it from its own $val.
INPUT: 15 - 2 * 3
POSITION: ^
CALLS: parse -- $val = 9
The outer "parse" call similarly fails to find any more + or - operators and so returns the final result
of the parsing operation.
INPUT: 15 - 2 * 3
OUTPUT: 9
By implementing the * and / operators separately in a different piece of logic inside the one that
implements the + and - operators, we have ensured that they operate more greedily. That is, that they
bind tighter, consuming their values first, before the outer + and - operators. This is the way that
operator precedence is implemented.
Parentheses
This grammar, like many others, provides a way for expressions to override the usual operator precedence
by supplying a sub-expression in parentheses. The expression inside those parentheses is parsed in the
usual way, and then its result stands in place of the entire parenthesized part, overriding whatever
rules might have governed the order between those operators inside it and those outside.
In this parser we implement this as a recursive call, where one possibility of the innermost part (the
"parse_factor" function or the "FACTOR" EBNF rule) is to recurse back to the outermost thing, inside
parentheses. This example examines what happens to the input string "(15 - 2) * 3".
INPUT: (15 - 2) * 3
POSITION: ^
As with all the other examples the parsing operation starts by "parse" calling "parse_term" which calls
"parse_factor". This time, the first case within the "any_of" in "parse_factor" does successfully manage
to find an open parenthesis, so consumes it. It then stores the close parenthesis pattern as the end-of-
scope marker, and makes a recursive call back to the parse method again.
INPUT: (15 - 2) * 3
POSITION: ^
CALLS: parse
=> parse_term
=> parse_factor
=> parse EOS = ")"
The operation of the inner call to "parse" proceeds much like the first few examples, calling down
through "parse_term" to "parse_factor" to obtain the 15.
INPUT: (15 - 2) * 3
POSITION: ^
CALLS: parse
=> parse_term
=> parse_factor
=> parse -- $val = 15 EOS = ")"
Similar to previous examples, this then finds the - operator, and parses another term to subtract from
it.
INPUT: (15 - 2) * 3
POSITION: ^
CALLS: parse
=> parse_term
=> parse_factor
=> parse -- $val = 13 EOS = ")"
At this point, the "any_of" test in the inner call to "parse" tries again to look for a + or - operator,
and this time fails because it believes it is at the end of the input. It isn't really at the end of the
string, of course, but it believes it to be at the end because of the "end-of-scope" pattern that the
call to "scope_of" established. This pretends that the input has finished whenever the next part of the
input matches the end-of-scope pattern.
Because this inner call to "parse" now believes it has got to the end of its input, it returns its final
answer back to the caller, which in this case was the "scope_of" call that "parse_factor" made. As the
"scope_of" call returns, it consumes the input matching the end-of-scope pattern. This return value is
then stored by "parse_term".
INPUT: (15 - 2) * 3
POSITION: ^
CALLS: parse
=> parse_term -- $val = 13
At this point, "parse_term" proceeds as before, finding and extracting the * operator and calling
"parse_factor" a second time, multiplying them together and returning that to the outer "parse" call.
INPUT: (15 - 2) * 3
POSITION: ^
CALLS: parse -- $val = 39
At this point "parse" fails to extract any more operators because it is at the (real) end of input, so
returns the final answer.
INPUT: (15 - 2) * 3
OUTPUT: 39