Provided by: libparser-mgc-perl_0.21-1_all 
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
perl v5.34.0 2022-03Parser::MGC::Examples::EvaluateExpression(3pm)