Introduction

The parser’s job is to figure out the relationship(grammar) among the input tokens. Those tokens come from the scanner (flex).
A grammar is a series of rules that the parser uses to recognize syntactically valid input.

Bison only deal with the syntax no the semantic, for instance the code bellow has a valid syntax but is invalid, bison will think that this is fine

int var = "Leo"

Consider the following grammar on bison. NAME, NUMBER, '+', '-', are tokens that flex gives to us.

statement: NAME '=' expression
expression: NUMBER '+' NUMBER
 | NUMBER '−' NUMBER

Every line here is a rule, so the rule for a statement is the pattern "NAME = expression". And the rule for expression is the pattern "NUMBER+NUMBER" OR "NUMBER-NUMBER"

Every grammar includes a start symbol, the one that has to be at the root of the parse tree. In this grammar, statement is the start symbol.

So the following source code line:

fred = 12 + 13

Would produce from the scanner the following tokens:
NAME,'=',NUMBER,'+',NUMBER

This AST tree would be created:

Where "fred =" is a statement. And "12+13" is an expression.

Now what would happen if we would want to parse a longer instruction

fred = 14 + 23 − 11 + 7

To solve this can use a Recursive rule, where the rule call itself.

statement: NAME '=' expression
expression: NUMBER
 | expression '+' NUMBER
 | expression '−' NUMBER

Now the tree would grow to this:

To start use our token inputs, starting from a simple example.

function result = justSum(a,b)
  result = a + b; # Simple comment
end

Tokens generated with out scanner

FUNCTION: function
Identifier: result
ASSIGN: =
Identifier: justSum
Open Parenthesis: (
Identifier: a
Comma: ,
Identifier: b
Close Parenthesis: )

Identifier: result
ASSIGN: =
Identifier: a
Plus: +
Identifier: b
EndLine: ;

END: end

And build an AST tree

Class diagram for parser Nodes

Considering the class diagram bellow, we need to create a rule for every class that inherites from Node.

References

• https://www.youtube.com/watch?v=oOFfVZrvhMA
• https://www.youtube.com/watch?v=yTXCPGAD3SQ
• http://aquamentus.com/flex_bison.html
• https://github.com/meyerd/flex-bison-example
• https://www.usna.edu/Users/cs/lmcdowel/courses/si413/F10/labs/L04/calc1/ex1.html
• https://learn.yancyparedes.net/2013/03/writing-a-calculator-program-using-bison-and-flex/
• calculator.pdf
• http://www.progtools.org/compilers/tutorials/cxx_and_bison/cxx_and_bison.html
• http://stackoverflow.com/questions/2993658/creating-simple-calculator-with-bison-flex-in-c-not-c
• https://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form
• https://vinaytech.wordpress.com/2008/10/04/abstract-syntax-tree/
• Matlab parser and scanner on matlab
• Matlab Parser final project.pdf
• http://stackoverflow.com/questions/9583307/where-can-i-find-a-formal-grammar-for-matlab
• Language Implementation Patterns.pdf