# (bison.info)Algorithm

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The Bison Parser Algorithm
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As Bison reads tokens, it pushes them onto a stack along with their
semantic values.  The stack is called the "parser stack".  Pushing a

For example, suppose the infix calculator has read `1 + 5 *', with a
`3' to come.  The stack will have four elements, one for each token
that was shifted.

But the stack does not always have an element for each token read.
When the last N tokens and groupings shifted match the components of a
grammar rule, they can be combined according to that rule.  This is
called "reduction".  Those tokens and groupings are replaced on the
stack by a single grouping whose symbol is the result (left hand side)
of that rule.  Running the rule's action is part of the process of
reduction, because this is what computes the semantic value of the
resulting grouping.

For example, if the infix calculator's parser stack contains this:

1 + 5 * 3

and the next input token is a newline character, then the last three
elements can be reduced to 15 via the rule:

expr: expr '*' expr;

Then the stack contains just these three elements:

1 + 15

At this point, another reduction can be made, resulting in the single
value 16.  Then the newline token can be shifted.

The parser tries, by shifts and reductions, to reduce the entire
input down to a single grouping whose symbol is the grammar's
start-symbol (Note: Languages and Context-Free Grammars
Grammar.).

This kind of parser is known in the literature as a bottom-up parser.

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Parser looks one token ahead when deciding what to do.
Shift/Reduce
Conflicts: when either shifting or reduction is valid.
Precedence
Operator precedence works by resolving conflicts.
Contextual Precedence
When an operator's precedence depends on context.
Parser States
The parser is a finite-state-machine with stack.
Reduce/Reduce
When two rules are applicable in the same situation.
Mystery Conflicts
Reduce/reduce conflicts that look unjustified.
Stack Overflow
What happens when stack gets full. How to avoid it.

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