# Calc Mini Tutorial¶

TatSu users have suggested that a simple calculator, like the one in the documentation for PLY would be useful.

Here it is.

## The initial grammar¶

This is the original PLY grammar for arithmetic expressions:

```expression : expression + term
| expression - term
| term

term       : term * factor
| term / factor
| factor

factor     : NUMBER
| ( expression )
```

And this is the input expression for testing:

```3 + 5 * ( 10 - 20 )
```

## The Tatsu grammar¶

The first step is to convert the grammar to 竜 TatSu syntax and style, add rules for lexical elements (`number` in this case), add a `start` rule that checks for end of input, and a directive to name the generated classes:

```@@grammar::CALC

start
=
expression \$
;

expression
=
| expression '+' term
| expression '-' term
| term
;

term
=
| term '*' factor
| term '/' factor
| factor
;

factor
=
| '(' expression ')'
| number
;

number
=
/\d+/
;
```

Cut expressions make a parser commit to a particular option after certain tokens have been seen. They make parsing more efficient, because other options are not tried. They also make error messages more precise, because errors will be reported closest to the point of failure in the input.

```@@grammar::CALC

start
=
expression \$
;

expression
=
| expression '+' ~ term
| expression '-' ~ term
| term
;

term
=
| term '*' ~ factor
| term '/' ~ factor
| factor
;

factor
=
| '(' ~ expression ')'
| number
;

number
=
/\d+/
;
```

Let’s save the above grammar in a file called `calc_cut.ebnf`. We can now compile the grammar, and test the parser:

```import json
from pprint import pprint

import tatsu

def simple_parse():
with open('calc_cut.ebnf') as f:

parser = tatsu.compile(grammar)
ast = parser.parse('3 + 5 * ( 10 - 20 )')

print('# SIMPLE PARSE')
print('# AST')
pprint(ast, width=20, indent=4)

print()

print('# JSON')
print(json.dumps(ast, indent=4))

if __name__ == '__main__':
simple_parse()
```

Save the above in `calc.py`. This is the output:

```\$ python calc.py
```
```# SIMPLE PARSE
# AST
[   '3',
'+',
[   '5',
'*',
[   '(',
[   '10',
'-',
'20'],
')']]]

# JSON
[
"3",
"+",
[
"5",
"*",
[
"(",
[
"10",
"-",
"20"
],
")"
]
]
]
```

## Annotating the grammar¶

Dealing with ASTs that are lists of lists leads to code that is difficult to read, and error-prone. 竜 TatSu allows naming the elements in a rule to produce more humanly-readable ASTs and to allow for clearer semantics code. This is an annotated version of the grammar:

```@@grammar::CALC

start
=
expression \$
;

expression
=
| left:expression op:'+' ~ right:term
| left:expression op:'-' ~ right:term
| term
;

term
=
| left:term op:'*' ~ right:factor
| left:term '/' ~ right:factor
| factor
;

factor
=
| '(' ~ @:expression ')'
| number
;

number
=
/\d+/
;
```

Save the annotated grammar in `calc_annotated.ebnf`, change the grammar filename in `calc.py` and re-execute it to get the resulting AST:

```# ANNOTATED AST
{   'left': '3',
'op': '+',
'right': {   'left': '5',
'op': '*',
'right': {   'left': '10',
'op': '-',
'right': '20'}}}
```

## Semantics¶

Semantic actions for 竜 TatSu parsers are not specified in the grammar, but in a separate semantics class.

```from pprint import pprint

import tatsu
from tatsu.ast import AST

class CalcBasicSemantics:
def number(self, ast):
return int(ast)

def term(self, ast):
if not isinstance(ast, AST):
return ast
elif ast.op == '*':
return ast.left * ast.right
elif ast.op == '/':
return ast.left / ast.right
else:
raise Exception('Unknown operator', ast.op)

def expression(self, ast):
if not isinstance(ast, AST):
return ast
elif ast.op == '+':
return ast.left + ast.right
elif ast.op == '-':
return ast.left - ast.right
else:
raise Exception('Unknown operator', ast.op)

def parse_with_basic_semantics():
with open('calc_annotated.ebnf') as f:

parser = tatsu.compile(grammar)
ast = parser.parse(
'3 + 5 * ( 10 - 20 )',
semantics=CalcBasicSemantics()
)

print('# BASIC SEMANTICS RESULT')
pprint(ast, width=20, indent=4)

if __name__ == '__main__':
parse_with_basic_semantics()
```

Save the above in `calc_semantics.py` and execute it with `python calc_semantics.py`. The result is:

```# BASIC SEMANTICS RESULT
-47
```

## One rule per expression type¶

Having semantic actions determine what was parsed with `isinstance()` or querying the AST for operators is not very pythonic, nor object oriented, and it leads to code that’s more difficult to maintain. It’s preferable to have one rule per expression kind, something that will be necessary if we want to build object models to use walkers and code generation.

```@@grammar::CALC

start
=
expression \$
;

expression
=
| subtraction
| term
;

=
left:expression op:'+' ~ right:term
;

subtraction
=
left:expression op:'-' ~ right:term
;

term
=
| multiplication
| division
| factor
;

multiplication
=
left:term op:'*' ~ right:factor
;

division
=
left:term '/' ~ right:factor
;

factor
=
| '(' ~ @:expression ')'
| number
;

number
=
/\d+/
;
```

Save the above in `calc_refactored.ebnf`.

```from pprint import pprint

import tatsu

class CalcSemantics:
def number(self, ast):
return int(ast)

return ast.left + ast.right

def subtraction(self, ast):
return ast.left - ast.right

def multiplication(self, ast):
return ast.left * ast.right

def division(self, ast):
return ast.left / ast.right

def parse_refactored():
with open('calc_refactored.ebnf') as f:

parser = tatsu.compile(grammar)
ast = parser.parse(
'3 + 5 * ( 10 - 20 )',
semantics=CalcSemantics()
)

print('# REFACTORED SEMANTICS RESULT')
pprint(ast, width=20, indent=4)
print()

if __name__ == '__main__':
parse_refactored()
```

The semantics implementation is simpler, and the results are the same:

```# REFACTORED SEMANTICS RESULT
-47
```

## Object models¶

Binding semantics to grammar rules is powerful and versatile, but this approach risks tying the semantics to the parsing process, rather than to the parsed objects.

That is not a problem for simple languages, like the arithmetic expression language in this tutorial. But as the complexity of the parsed language increases, the number of grammar rules quickly becomes larger than the types of objects parsed.

TatSu can create typed object models directly from the parsing process which can be navigated (walked) and transformed (with code generation) in later passes.

The first step to create an object model is to annotate the rule names with the desired class names:

```@@grammar::Calc

start
=
expression \$
;

expression
=
| subtraction
| term
;

=
left:term op:'+' ~ right:expression
;

subtraction::Subtract
=
left:term op:'-' ~ right:expression
;

term
=
| multiplication
| division
| factor
;

multiplication::Multiply
=
left:factor op:'*' ~ right:term
;

division::Divide
=
left:factor '/' ~ right:term
;

factor
=
| subexpression
| number
;

subexpression
=
'(' ~ @:expression ')'
;

number::int
=
/\d+/
;
```

Save the grammar in a file name `calc_model.ebnf`.

The `tatsu.objectmodel.Node` descendants are synthetized at runtime using `tatsu.semantics.ModelBuilderSemantics`.

This is how the model looks like when generated with the `tatsu.to_python_model()` function or from the command line with `tatsu --object-model calc_model.ebnf -G calc_semantics_model.py`:

```from tatsu.objectmodel import Node
from tatsu.semantics import ModelBuilderSemantics

class ModelBase(Node):
pass

class CalcModelBuilderSemantics(ModelBuilderSemantics):
def __init__(self, context=None, types=None):
types = [
t for t in globals().values()
if type(t) is type and issubclass(t, ModelBase)
] + (types or [])
super(CalcModelBuilderSemantics, self).__init__(context=context, types=types)

left = None
op = None
right = None

class Subtract(ModelBase):
left = None
op = None
right = None

class Multiply(ModelBase):
left = None
op = None
right = None

class Divide(ModelBase):
left = None
right = None
```

The model that results from a parse can be printed, and walked:

```import tatsu
from tatsu.walkers import NodeWalker

class CalcWalker(NodeWalker):
def walk_object(self, node):
return node

return self.walk(node.left) + self.walk(node.right)

def walk__subtract(self, node):
return self.walk(node.left) - self.walk(node.right)

def walk__multiply(self, node):
return self.walk(node.left) * self.walk(node.right)

def walk__divide(self, node):
return self.walk(node.left) / self.walk(node.right)

def parse_and_walk_model():
with open('calc_model.ebnf') as f:

parser = tatsu.compile(grammar, asmodel=True)
model = parser.parse('3 + 5 * ( 10 - 20 )')

print('# WALKER RESULT IS:')
print(CalcWalker().walk(model))
print()

if __name__ == '__main__':
parse_and_walk_model()
```

Save the above program in `calc_model.py` and execute it to get this result:

```# WALKER RESULT IS:
-47
```

## Code Generation¶

Translation is one of the most common tasks in language processing. Analysis often sumarizes the parsed input, and walkers are good for that. In translation, the output can often be as verbose as the input, so a systematic approach that avoids bookkeeping as much as possible is convenient.

TatSu provides support for template-based code generation (translation) in the `tatsu.codegen` module. Code generation works by defining a translation class for each class in the model specified by the grammar.

Adjust our previous `calc_model.ebnf` grammar and annotate the number rule like so:

```number::Number
=
value:/\d+/
;
```

The following code generator translates input expressions to the postfix instructions of a stack-based processor:

```import sys

from tatsu.codegen import ModelRenderer
from tatsu.codegen import CodeGenerator

THIS_MODULE =  sys.modules[__name__]

class PostfixCodeGenerator(CodeGenerator):
def __init__(self):
super().__init__(modules=[THIS_MODULE])

class Number(ModelRenderer):
template = '''\
PUSH {value}'''

template = '''\
{left}
{right}

class Subtract(ModelRenderer):
template = '''\
{left}
{right}
SUB'''

class Multiply(ModelRenderer):
template = '''\
{left}
{right}
MUL'''

class Divide(ModelRenderer):
template = '''\
{left}
{right}
DIV'''
```

Save the above in `codegen.py`. The code generator can be used as follows:

```from codegen import PostfixCodeGenerator

def parse_and_translate():
with open('calc_model.ebnf') as f:

parser = tatsu.compile(grammar, asmodel=True)
model = parser.parse('3 + 5 * ( 10 - 20 )')

postfix = PostfixCodeGenerator().render(model)

print('# TRANSLATED TO POSTFIX')
print(postfix)

if __name__ == '__main__':
parse_and_translate()
```

Save the above program in `calc_translate.py` and execute it to get this result:

```# TRANSLATED TO POSTFIX
PUSH 3
PUSH 5
PUSH 10
PUSH 20
SUB
MUL