Parsing expressions from Token Stream - parsing

I'm trying to parse expressions for a simple scripting language, but I'm confused. Right now, only numbers and string literals can be parsed as an expression:
int x = 5;
double y = 3.4;
str t = "this is a string";
However, I am confused on parsing more complex expressions:
int a = 5 + 9;
int x = (5 + a) - (a ^ 2);
I'm thinking I would implement it like:
do {
// no clue what I would do here?
if (current token is a semi colon) break;
}
while (true);
Any help would be great, I have no clue where to start. Thanks.
EDIT:
My parser is a Recursive Descent Parser
My expression "class" is as follows:
typedef struct s_Expression {
char type;
Token *value;
struct s_Expression *leftHand;
char operand;
struct s_Expression *rightHand;
} ExpressionNode;
Someone mentioned that a Recursive Descent Parser is capable of parsing expressions without doing infix, to postfix. Preferably, I would like an Expression like this:
For example this:
int x = (5 + 5) - (a / b);
Would be parsed into this:
Note: this isn't valid C, this is just some pseudo ish code to get my point across simply :)
ExpressionNode lh;
lh.leftHand = new ExpressionNode(5);
lh.operand = '+'
lh.rightHand = new ExpressionNode(5);
ExpressionNode rh;
rh.leftHand = new ExpressionNode(a);
rh.operand = '/';
rh.rightHand = new ExpressionNode(b);
ExpressionNode res;
res.leftHand = lh;
res.operand = '-';
res.rightHand = rh;
I asked the question pretty late at night, so sorry if I wasn't clear and that I completely forgot what my original goal was.

There are multiple methods to do this. One I've used in the past is to read the input string (that is, the programming language code) and convert expressions from infix to reverse-polish notation. Here's a really good post about doing just that:
http://andreinc.net/2010/10/05/converting-infix-to-rpn-shunting-yard-algorithm/
Note that = is an operator also, so your parsing should really include the whole file of code, and not just certain expressions.
Once in reverse-polish, expressions are super-easy to evaluate. You just pop the stack, storing operands as you go, until you hit an operator. Pop as many operands from the stack as required by the operator and perform your operation.

The method I ended up using is Operator precedence parsing.
parse_expression_1 (lhs, min_precedence)
lookahead := peek next token
while lookahead is a binary operator whose precedence is >= min_precedence
op := lookahead
advance to next token
rhs := parse_primary ()
lookahead := peek next token
while lookahead is a binary operator whose precedence is greater
than op's, or a right-associative operator
whose precedence is equal to op's
rhs := parse_expression_1 (rhs, lookahead's precedence)
lookahead := peek next token
lhs := the result of applying op with operands lhs and rhs
return lhs

If you are building a recursive descent parser, implementing a shunting yard is a lot of unnecessary work because recursive descent is perfectly capable of evaluating expressions or outputting RPN by itself.
You haven't told us anything about your programming language, your Token structs, or even what you are trying to achieve, so it is really hard to give you sample code. Take a look at Eric White's implementation of a recursive descent parser in C#. If you provide more details we will be able to help more.

Related

Does a priority declaration disambiguate between alternative lexicals?

In my previous question, there was a priority > declaration in the example. It turned out not to matter because the solution there did not actually invoke priority but rather avoided it by making the alternatives disjoint. In this question, I'm asking whether priority can be used to select one lexical production over another. In the example below, the language of the production WordInitialDigit is intentionally a subset of that of WordAny. The production Word looks like it should disambiguate between the two properly, but the resulting parse tree has an ambiguity node at the top. Is a priority declaration able to decide between different lexical reductions, or does it require there to be a basis of common lexical elements? Or something else?
The example is contrived (there are no actions in the grammar), but the situations it arises from are not. For example, I'd like to use something like this for error recovery, where I can recognize a natural boundary for a unit of syntax and write a production for it. This generic production would be the last element in a priority chain; if it reduces, it means that there was no valid parse. More generally, I need to be able to select lexical elements based on syntactic context. I had hoped, since Rascal is scannerless, that this would be seamless. Perhaps it is, though I don't see it at the moment.
I'm on the unstable branch, version 0.10.0.201807050853.
EDIT: This question is not about > for defining an expression grammar. The documentation for priority declarations talks mostly about expressions, but the very first sentence provides what looks like a perfectly clear definition:
Priority declarations define a partial ordering between the productions within a single non-terminal.
So the example has two productions, an ordering declared between them, and yet the parser is still generating an ambiguity node in the clear presence of a disambiguation rule. So to put a finer point on my question, it looks like I don't know which of two situations pertains. Either (1) if this isn't supposed to work, then there's a defect in the language definition as documented, a deficiency in error reporting of the compiler, and a language design decision that's somewhere between counter-intuitive and user-hostile. Or (2) if this is supposed to work, there's a defect in the compiler and/or parser (presumably because the focus was initially on expressions) and at some point the example will pass its tests.
module ssce
import analysis::grammars::Ambiguity;
import ParseTree;
import IO;
import String;
lexical WordChar = [0-9A-Za-z] ;
lexical Digit = [0-9] ;
lexical WordInitialDigit = Digit WordChar* !>> WordChar;
lexical WordAny = WordChar+ !>> WordChar;
syntax Word =
WordInitialDigit
> WordAny
;
test bool WordInitialDigit_0() = parseAccept( #Word, "4foo" );
test bool WordInitialDigit_1() = parseAccept( #WordInitialDigit, "4foo" );
test bool WordInitialDigit_2() = parseAccept( #WordAny, "4foo" );
bool verbose = false;
bool parseAccept( type[&T<:Tree] begin, str input )
{
try
{
parse(begin, input, allowAmbiguity=false);
}
catch ParseError(loc _):
{
return false;
}
catch Ambiguity(loc l, str a, str b):
{
if (verbose)
{
println("[Ambiguity] #<a>, \"<b>\"");
Tree tt = parse(begin, input, allowAmbiguity=true) ;
iprintln(tt);
list[Message] m = diagnose(tt) ;
println( ToString(m) );
}
fail;
}
return true;
}
bool parseReject( type[&T<:Tree] begin, str input )
{
try
{
parse(begin, input, allowAmbiguity=false);
}
catch ParseError(loc _):
{
return true;
}
return false;
}
str ToString( list[Message] msgs ) =
( ToString( msgs[0] ) | it + "\n" + ToString(m) | m <- msgs[1..] );
str ToString( Message msg)
{
switch(msg)
{
case error(str s, loc _): return "error: " + s;
case warning(str s, loc _): return "warning: " + s;
case info(str s, loc _): return "info: " + s;
}
return "";
}
Excellent questions.
TL;DR:
the rule priority mechanism is not capable of an algorithmic ordering of a non-terminal's alternatives. Although some kind of partial order is involved in the additional grammatical constraints that a priority declaration generates, there is no "trying" one rule first, before the other. So it simply can't do that. The good news is that the priority mechanism has a formal semantics independent of any parsing algorithm, it's just defined in terms of context-free grammar rules and reduction traces.
using ambiguous rules for error recovery or "robust parsing", is a good idea. However, if there are too many such rules, the parser will eventually start showing quadratic or even cubic behavior, and tree building after parsing might even have higher polynomials. I believe the generated parser algorithm should have a (parameterized) mode for error recovery rather then expressing this at the grammar level.
Accepting ambiguity at parse time, and filtering/choosing trees after parsing is the recommended way to go.
All this talk of "ordering" in the documentation is misleading. Disambiguation is minefield of confusing terminology. For now, I recommend this SLE paper which has some definitions: https://homepages.cwi.nl/~jurgenv/papers/SLE2013-1.pdf
Details
priority mechanism not capable of choosing among alternatives
The use of the > operator and left, right generates a partial order between mutually recursive rules, such as found in expression languages, and limited to specific item positions in each rule: namely the left-most and right-most recursive positions which overlap. Rules which are lower in the hierarchy are not allowed to be grammatically expanded as "children" of rules which are higher in the hierarchy. So in E "*" E, neither E may be expaned to E "+" E if E "*" E > E "+" E.
The additional constraints do not choose for any E which alternative to try first. No they simply disallow certain expansions, assuming the other expansion is still valid and thus the ambiguity is solved.
The reason for the limitation at specific positions is that for these positions the parser generator can "prove" that they will generate ambiguity, and thus filtering one of the two alternatives by disallowing certain nestings will not result in additional parse errors. (consider a rule for array indexing: E "[" E "]" which should not have additional constraints for the second E. This is a so-called "syntax-safe" disambiguation mechanism.
All and all it is a pretty weak mechanism algorithmically, and specifically tailored for mutually recursive combinator/expression-like languages. The end-goal of the mechanism is to make sure we use have to use only 1 non-terminal for the entire expression language, and the parse trees looking very much akin in shape to abstract syntax trees. Rascal inherited all these considerations from SDF, via SDF2, by the way.
Current implementations actually "factor" the grammar or the parse table in some fashion invisibly to get the same effect, as-if somebody would have factored the grammar completely; however these implementations under-the-hood are very specific to the parsing algorithm in question. the GLR version is quite different from the GLL version, which again is quite different from the DataDependent version.
Post-parse filtering
Of course any tree, including ambiguous parse forests produced by the parser, can be manipulated by Rascal programs using pattern matching, visit, etc. You could write any algorithm to remove the trees you want. However, this requires the entire forest to be constructed first. It's possible and often fast enough, but there is a faster alternative.
Since the tree is built in a bottom-up fashion from the parse graph after parsing, we can also apply "rewrite rules" during the construction of the tree, and remove certain alternatives.
For example:
Tree amb({Tree a, *Tree others}) = amb(others) when weDoNotWant(a);
Tree amb({Tree a}) = a;
This first rule would match on the ambiguity cluster for all trees, and remove all alternatives which weDoNotWant. The second rule removes the cluster if only one alternative is left and let's the last tree "win".
If you want to choose among alternatives:
Tree amb({Tree a, Tree b, *Tree others}) = amb({a, others} when weFindPeferable(a, b);
If you don't want to use Tree but a more specific non-terminal like Statement that should also work.
This example module uses #prefer tags in syntax definitions to "prefer" rules which have been tagged over the other rules, as post-parse rewrite rules:
https://github.com/usethesource/rascal/blob/master/src/org/rascalmpl/library/lang/sdf2/filters/PreferAvoid.rsc
Hacking around with additional lexical constraints
Next to priority disambiguation and post-parse rewriting, we still have the lexical level disambiguation mechanisms in the toolkit:
`NT \ Keywords" - rejecting finite (keyword) languages from a non-terminals
CC << NT, NT >> CC, CC !<< NT, NT !>> CC follow and preceede restrictions (where CC stands for character-class and NT for non-terminal)
Solving other kinds of ambiguity apart from the operator precedence stuff can be tried with these, in particular if the length of different sub-sentences is shorter/longer between the different alternatives, !>> can do the "maximal munch" or "longest match" thing. So I was thinking out loud:
lexical C = A? B?;
where A is one lexical alternative and B is the other. With the proper !>> restrictions on A and !<< restrictions on B the grammar might be tricked into always wanting to put all characters in A, unless they don't fit into A as a language, in which case they would default to B.
The obvious/annoying advice
Think harder about an unambiguous and simpler grammar.
Sometimes this means to abstract and allow more sentences in the grammar, avoiding use of the grammar for "type checking" the tree. It's often better to over-approximate the syntax of the language and then use (static) semantic analysis (over simpler trees) to get what you want, rather then staring at a complex ambiguous grammar.
A typical example: C blocks with declarations only at the start are much harder to define unambiguously then C blocks where declarations are allowed everywhere. And for a C90 mode, all you have to do is flag declarations which are not at the start of a block.
This particular example
lexical WordChar = [0-9A-Za-z] ;
lexical Digit = [0-9] ;
lexical WordInitialDigit = Digit WordChar* !>> WordChar;
lexical WordAny = WordChar+ !>> WordChar;
syntax Word =
WordInitialDigit
| [0-9] !<< WordAny // this would help!
;
wrap up
Great question, thanks for the patience. Hope this helps!
The > disambiguation mechanism is for recursive definitions, like for example a expression grammar.
So it's to solve the following ambiguity:
syntax E
= [0-9]+
| E "+" E
| E "-" E
;
The string 1 + 3 - 4 can not be parsed as 1 + (3 - 4) or (1 + 3) - 4.
The > gives an order to this grammar, which production should be at the top of the tree.
layout L = " "*;
syntax E
= [0-9]+
| E "+" E
> E "-" E
;
this now only allows the (1 + 3) - 4 tree.
To finish this story, how about 1 + 1 + 1? That could be 1 + (1 + 1) or (1 + 1) + 1.
This is what we have left, right, and non-assoc for. They define how recursion in the same production should be handled.
syntax E
= [0-9]+
| left E "+" E
> left E "-" E
;
will now enforce: 1 + (1 + 1).
When you take an operator precendence table, like for example this c operator precedance table you can almost literally copy them.
note that these two disambiguation features are not exactly opposite to each other. the first ambiguitity could also have been solved by putting both productions in a left group like this:
syntax E
= [0-9]+
| left (
E "+" E
| E "-" E
)
;
As the left side of the tree is favored, you will now get a different tree 1 + (3 - 4). So it makes a difference, but it all depends on what you want.
More details can be found in the tutor pages on disambiguation

Using midaction rules in Lemon to interpret "let" expression

I'm trying to write a "toy" interpreter using Flex + Lemon that supports a very basic "let" syntax where a variable X is temporarily bound to an expression. For example, "letx 3 + 4 in x + 8" should evaluate to 15.
In essence, what I'd "like" the rule to say is:
expr(E) ::= LETX expr(N) IN expr(O). {
environment->X = N;
E = O;
}
But that won't work since O is evaluated before the X = N assignment is made.
I understand that the usual solution for this would be a mid-rule action. Lemon doesn't explicitly support this, but I've read elsewhere that would just be syntactic sugar in any event.
So I've tried to put together a mid-rule action that would do my assignment of X = N before interpreting O:
midruleaction ::= /* mid rule */. { environment->X = N; }
expr(E) ::= LETX expr(N) IN midruleaction expr(O). { E = O; }
But that won't work because there's no way for the midruleaction rule to access N, or at least none I can see in the lemon docs/examples.
I think I'm missing something here. I know I could build up a tree and then walk it in a second pass. And I might end up doing that, but I'd like to understand how to solve this more directly first.
Any suggestions?
It's really not a very scalable solution to evaluate immediately in a parser. See below.
It is true that mid-rule actions are (mostly) syntactic sugar. However, in most cases they are not syntactic sugar for "markers" (non-terminals with empty right-hand sides) but rather for non-terminals representing production prefixes. For example, you could write your letx rule like this:
expr(E) ::= letx_prefix IN expr(O). { E = O; }
letx_prefix ::= LETX expr(N). { environment->X = N; }
Or you could do this:
expr(E) ::= LETX assigned_expr IN expr(O). { E = O; }
assigned_expr ::= expr(N). { environment->X = N; }
The first one is the prefix desugaring; the second one is the one I'd use because I feel that it separates concerns better. The important point is that the environment->X = N; action requires access to the semantic values of the prefix of the RHS, so it must be part of a prefix rule (which includes at least the symbols whose semantic values are requires), rather than a marker, which has access to no semantic values at all.
Having said all that, immediate evaluation during parsing is a very limited strategy. It cannot cope with a large range of constructs which require deferred evaluation, such as loops and function definitions. It cannot cleanly cope with constructs which may suppress evaluation, such as conditionals and short-circuit operators. (These can be handled using MRAs and a stateful environment which contains an evaluation-suppressed flag, but that's very ugly.)
Another problem is that syntactically incorrect expressions may be partially evaluated before the syntax error is discovered, and it may not be immediately obvious to the user which parts of the expression have and have not been evaluated.
On the whole, you're better off building an easily-evaluated AST during the parse, and evaluating the AST when the parse successfully completes.

How to adapt this LL(1) parser to a LL(k) parser?

In the appendices of the Dragon-book, a LL(1) front end was given as a example. I think it is very helpful. However, I find out that for the context free grammar below, a at least LL(2) parser was needed instead.
statement : variable ':=' expression
| functionCall
functionCall : ID'(' (expression ( ',' expression )*)? ')'
;
variable : ID
| ID'.'variable
| ID '[' expression ']'
;
How could I adapt the lexer for LL(1) parser to support k look ahead tokens?
Are there some elegant ways?
I know I can add some buffers for tokens. I'd like to discuss some details of programming.
this is the Parser:
class Parser
{
private Lexer lex;
private Token look;
public Parser(Lexer l)
{
lex = l;
move();
}
private void move()
{
look = lex.scan();
}
}
and the Lexer.scan() returns the next token from the stream.
In effect, you need to buffer k lookahead tokens in order to do LL(k) parsing. If k is 2, then you just need to extend your current method, which buffers one token in look, using another private member look2 or some such. For larger k, you could use a ring buffer.
In practice, you don't need the full lookahead all the time. Most of the time, one-token lookahead is sufficient. You should structure the code as a decision tree, where future tokens are only consulted if necessary to resolve ambiguity. (It's often useful to provide a special token type, "unknown", which can be assigned to the buffered token list to indicate that the lookahead hasn't reached that point yet. Alternatively, you can just always maintain k tokens of lookahead; for handbuilt parsers, that can be simpler.)
Alternatively, you can use a fallback structure where you simply try one alternative and if that doesn't work, instead of reporting a syntax error, restore the state of the parser and lexer to the next alternative. In this model, the lexer takes as an explicit argument the current input buffer position, and the input buffer needs to be rewindable. However, you can use a lookahead buffer to effectively memoize the lexer function, which can avoid rewinding and rescanning. (Scanning is usually fast enough that occasional rescans don't matter, so you might want to put off adding code complexity until your profiling indicates that it would be useful.)
Two notes:
1) I'm skeptical about the rule:
functionCall : ID'(' (expression ( ',' expression )*)* ')'
;
That would allow, for example:
function(a[3], b[2] c[x] d[y], e.foo)
which doesn't look right to me. Normally, you'd mark the contents of the () as optional instead of repeatable, eg. using an optional marker ? instead of the second Kleene star *:
functionCall : ID'(' (expression ( ',' expression )*)? ')'
;
2) In my opinion, you really should consider using bottom-up parsing for an expression language, either a generated LR(1) parser or a hand-built Pratt parser. LL(1) is rarely adequate. Of course, if you're using a parser generator, you can use tools like ANTLR which effectively implement LL(∞); that will take care of the lookahead for you.

Bison: how to fix reduce/reduce conflict

Below is a a Bison grammar which illustrates my problem. The actual grammar that I'm using is more complicated.
%glr-parser
%%
s : e | p '=' s;
p : fp | p ',' fp;
fp : 'x';
e : te | e ';' te;
te : fe | te ',' fe;
fe : 'x';
Some examples of input would be:
x
x = x
x,x = x,x
x,x = x;x
x,x,x = x,x;x,x
x = x,x = x;x
What I'm after is for the x's on the left side of an '=' to be parsed differently than those on the right. However, the set of legal "expressions" which may appear on the right of an '='-sign is larger than those on the left (because of the ';').
Bison prints the message (input file was test.y):
test.y: conflicts: 1 reduce/reduce.
There must be some way around this problem. In C, you have a similar situation. The program below passes through gcc with no errors.
int main(void) {
int x;
int *px;
x;
*px;
*px = x = 1;
}
In this case, the 'px' and 'x' get treated differently depending on whether they appear to the left or right of an '='-sign.
You're using %glr-parser, so there's no need to "fix" the reduce/reduce conflict. Bison just tells you there is one, so that you know you grammar might be ambiguous, so you might need to add ambiguity resolution with %dprec or %merge directives. But in your case, the grammar is not ambiguous, so you don't need to do anything.
A conflict is NOT an error, its just an indication that your grammar is not LALR(1).
The reduce-reduce conflict in your grammar comes from the context:
... = ... x ,
At this point, the parser has to decide whether x is an fe or an fp, and it cannot know with one symbol lookahead. Indeed, it cannot know with any finite lookahead, you could have any number of repetitions of x , following that point without encountering a =, ; or the end of the input, any of which would reveal the answer.
This is not quite the same as the C issue, which can be resolved with single symbol lookahead. However, the C example is a classic illustration of why SLR(1) grammars are less powerful than LALR(1) grammars -- it's used for that purpose in the dragon book -- and a similarly problematic grammar is an example of the difference between LALR(1) and LR(1); it can be found in the bison manual (here):
def: param_spec return_spec ',';
param_spec: type | name_list ':' type;
return_spec: type | name ':' type;
type: "id";
name: "id";
name_list: name | name ',' name_list;
(The bison manual explains how to resolve this issue for LALR(1) grammars, although using a GLR grammar is always a possibility.)
The key to resolving such conflicts without using a GLR grammar is to avoid forcing the parser to make premature decisions.
For example, it is traditional to distinguish syntactically between lvalues and rvalues, and some languages continue to do so. C and C++ do not, however; and this turns out to be an extremely powerful feature in C++ because it allows the definition of functions which can act as lvalues.
In C, I think it's just to simplify the grammar a bit: the C grammar allows the result of any unary operator to appear on the left hand side of an assignment operator, but unary operators are actually a mix of lvalues (*v, v[expr]) and rvalues (sizeof v, f(expr)). The grammar could have distinguished between the two kinds of unary operators, but it could not resolve the actual restriction, which is that only modifiable lvalues may appears on the left side of an assignment operator.
C++ allows an arbitrary expression to appear on the left-hand side of an assignment operator (although some need to be parenthesized); consequently, the following is totally legal:
(predicate(x) ? *some_pointer : some_variable) = 42;
In your case, you could resolve the conflict syntactically by replacing te with p, since both non-terminals produce the same set of derivations. That's probably not the general solution, unless it is really the case in your full grammar that left-side expressions are a strict subset of right-side expressions. In a full grammar, you might end up with three types of expression (left-only, right-only, common), which could considerably complicated the grammar, and leaving the resolution for semantic analysis might prove to be easier (and even, as in the case of C++, surprisingly useful).

Parsers and Compilers for Dummies. Where to start? [duplicate]

This question already has answers here:
Learning to write a compiler [closed]
(38 answers)
Closed 8 years ago.
This is a good listing, but what is the best one for a complete newb in this area. One for someone coming from a higher level background (VB6,C#,Java,Python) - not to familiar with C or C++. I'm much more interested in hand-written parsing versus Lex/Yacc at this stage.
If I had just majored in Computer Science instead of Psychology I might have taken a class on this in college. Oh well.
Please have a look at: learning to write a compiler
Also interesting:
how to write a programming language
parsing where can i learn about it
learning resources on parsers interpreters and compilers (ok you already mentioned this one.
And there are more on the topic. But I can give a short introduction:
The first step is the lexical analysis. A stream of characters is translated into a stream of tokens. Tokens can be simple like == <= + - (etc) and they can be complex like identifiers and numbers. If you like I can elaborate on this.
The next step is to translate the tokenstream into a syntaxtree or an other representation. This is called the parsing step.
Before you can create a parser, you need to write the grammar. For example we create an expression parser:
Tokens
addOp = '+' | '-';
mulOp = '*' | '/';
parLeft = '(';
parRight = ')';
number = digit, {digit};
digit = '0'..'9';
Each token can have different representations: + and = are both addOp and
23 6643 and 223322 are all numbers.
The language
exp = term | exp, addOp, term;
// an expression is a series of terms separated by addOps.
term = factor | term, mulOp, factor;
// a term is a series of factors separated by mulOps
factor = addOp, factor | parLeft, exp, parRight | number;
// a factor can be an addOp followed by another factor,
// an expression enclosed in parentheses or a number.
The lexer
We create a state engine that walks through the char stream, creating a token
s00
'+', '-' -> s01 // if a + or - is found, read it and go to state s01.
'*', '/' -> s02
'(' -> s03
')' -> s04
'0'..'9' -> s05
whitespace -> ignore and retry // if a whitespace is found ignore it
else ERROR // sorry but we don't recognize this character in this state.
s01
found TOKEN addOp // ok we have found an addOp, stop reading and return token
s02
found TOKEN mulOp
s03
found TOKEN parLeft
s04
found TOKEN parRight
s05
'0'..'9' -> s05 // as long as we find digits, keep collecting them
else found number // last digit read, we have a number
Parser
It is now time to create a simple parser/evaluator. This is complete in code. Normally they are created using tables. But we keep it simple. Read the tokens and calculate the result.
ParseExp
temp = ParseTerm // start by reading a term
while token = addOp do
// as long as we read an addop keep reading terms
if token('+') then temp = temp + ParseTerm // + so we add the term
if token('-') then temp = temp - ParseTerm // - so we subtract the term
od
return temp // we are done with the expression
ParseTerm
temp = ParseFactor
while token = mulOp do
if token('*') then temp = temp * ParseFactor
if token('/') then temp = temp / ParseFactor
od
return temp
ParseFactor
if token = addOp then
if token('-') then return - ParseFactor // yes we can have a lot of these
if token('+') then return ParseFactor
else if token = parLeft then
return ParseExpression
if not token = parRight then ERROR
else if token = number then
return EvaluateNumber // use magic to translate a string into a number
This was a simple example. In real examples you will see that error handling is a big part of the parser.
I hope this clarified a bit ;-).
If you're a complete n00b, the most accessible resource (in both senses of the term) is probably Jack Crenshaw's tutorial. It's nowhere near comprehensive but for getting started, I can't think of anything close except for books that are long out of print.
I'd like to suggest an article that I wrote called Implementing Programming Languages using C# 4.0. I've tried to make it accessible for newcomers. It isn't comprehensive, but afterwards it should be easier to understand other more advanced texts.

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