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22 August 2010

- Author
Christophe Delord

- Web site
- Date
- License
This software is released under the LGPL license.

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Table of Contents

SP (Simple Parser) is a Python^{1} parser generator. It is aimed at easy usage rather than performance. SP produces Top-Down Recursive descent parsers. SP also uses memoization to optimize parsers' speed when dealing with ambiguous grammars.

SP is available under the GNU Lesser General Public:

```
Simple Parser: A Python parser generator
Copyright (C) 2009-2016 Christophe Delord
Simple Parser is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Simple Parser is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with Simple Parser. If not, see <http://www.gnu.org/licenses/>.
```

- Introduction and tutorial
starts smoothly with a gentle tutorial as an introduction. I think this tutorial may be sufficient to start with SP.

- SP reference
is a reference documentation. It will detail SP as much as possible.

- Some examples to illustrate SP
gives the reader some examples to illustrate SP.

SP is freely available on its web page (http://cdelord.fr/sp).

SP is a *pure Python* package. It may run on *any platform* supported by Python. The only requirement of SP is *Python 2.6*, *Python 3.1* or newer^{2}. Python can be downloaded at http://www.python.org.

This short tutorial presents how to make a simple calculator. The calculator will compute basic mathematical expressions (`+`

, `-`

, `*`

, `/`

) possibly nested in parenthesis. We assume the reader is familiar with regular expressions.

Expressions are defined with a grammar. For example an expression is a sum of terms and a term is a product of factors. A factor is either a number or a complete expression in parenthesis.

We describe such grammars with rules. A rule describes the composition of an item of the language. In our grammar we have 3 items (expr, term, factor). We will call these items *symbols* or *non terminal symbols*. The decomposition of a symbol is symbolized with `->`

.

Grammar for expressions:

Grammar rule | Description |
---|---|

`expr -> term (('+'|'-') term)*` |
An expression is a term eventually followed with a plus (`+` ) or a minus (`-` ) sign and an other term any number of times (`*` is a repetition of an expression 0 or more times). |

`term -> fact (('*'|'/') fact)*` |
A term is a factor eventually followed with a `*` or `/` sign and an other factor any number of times. |

`fact -> ('+'|'-') fact | number | '(' expr ')'` |
A factor is either a factor preceded by a sign, a number or an expression in parenthesis. |

We have defined here the grammar rules (i.e.Â the sentences of the language). We now need to describe the lexical items (i.e.Â the words of the language). These words - also called *terminal symbols* - are described using regular expressions. In the rules we have written some of these terminal symbols (`+`

, `-`

, `*`

, `/`

, `(`

, `)`

). We have to define `number`

. For sake of simplicity numbers are integers composed of digits (the corresponding regular expression can be `[0-9]+`

). To simplify the grammar and then the Python script we define two terminal symbols to group the operators (additive and multiplicative operators). We can also define a special symbol that is ignored by SP. This symbol is used as a separator. This is generally useful for white spaces and comments.

Terminal symbol definition for expressions:

Terminal symbol | Regular expression | Comment |
---|---|---|

`number` |
`[0-9]+ or \d+` |
One or more digits |

`addop` |
`[+-]` |
a `+` or a `-` |

`mulop` |
`[*/]` |
a `*` or a `/` |

`spaces` |
`\s+` |
One or more spaces |

This is sufficient to define our parser with SP.

Grammar of the expression recognizer:

```
def Calc():
number = R(r'[0-9]+')
addop = R('[+-]')
mulop = R('[*/]')
with Separator(r'\s+'):
expr = Rule()
fact = Rule()
fact |= addop & fact
fact |= '(' & expr & ')'
fact |= number
term = fact & ( mulop & fact )[:]
expr |= term & ( addop & term )[:]
return expr
```

`Calc`

is the name of the Python function that returns a parser. This function returns `expr`

which is the *axiom*^{3} of the grammar.

`expr`

and `fact`

are recursive rules. They are first declared as empty rules (`expr = Rule()`

) and alternatives are later added (`expr |= ...`

).

Slices are used to implement repetitions. `foo[:]`

parses `foo`

zero or more times, which is equivalent to `foo*`

in a classical grammar notation.

The grammar can also be defined with the mini grammar language provided by SP:

```
def Calc():
return compile("""
number = r'[0-9]+' ;
addop = r'[+-]' ;
mulop = r'[*/]' ;
separator: r'\s+' ;
!expr = term (addop term)* ;
term = fact (mulop fact)* ;
fact = addop fact ;
fact = '(' expr ')' ;
fact = number ;
""")
```

Here the *axiom*^{4} is identified by `!`

.

With this small grammar we can only recognize a correct expression. We will see in the next sections how to read the actual expression and to compute its value.

The input of the grammar is a string. To do something useful we need to read this string in order to transform it into an expected result.

This string can be read by catching the return value of terminal symbols. By default any terminal symbol returns a string containing the current token. So the token `'('`

always returns the string `'('`

. For some tokens it may be useful to compute a Python object from the token. For example `number`

should return an integer instead of a string, `addop`

and `mulop`

, followed by a number, should return a function corresponding to the operator. That's why we will add a function to the token and rule definitions. So we associate `int`

to `number`

and `op1`

and `op2`

to unary and binary operators.

`int`

is a Python function converting objects to integers and `op1`

and `op2`

are user defined functions.

`op1`

and `op2`

functions:

```
op1 = lambda f,x: {'+':pos, '-':neg}[f](x)
op2 = lambda f,y: lambda x: {'+': add, '-': sub, '*': mul, '/': div}[f](x,y)
# red applyies functions to a number
def red(x, fs):
for f in fs: x = f(x)
return x
```

- To associate a function to a token or a rule it must be applied using
`/`

or`*`

operators: `/`

applies a function to an object returned by a (sub)parser.`*`

applies a function to an tuple of objects returned by a sequence of (sub) parsers.

Token and rule definitions with functions:

```
number = R(r'[0-9]+') / int
fact |= (addop & fact) * op1
term = (fact & ( (mulop & fact) * op2 )[:]) * red
# R(r'[0-9]+') applyed on "42" will return "42".
# R(r'[0-9]+') / int will return int("42")
# addop & fact applyied on "+ 42" will return ('+', 42)
# (addop & fact) * op1 will return op1(*('+', 42)), i.e. op1('+', 42)
# so (addop & fact) * op1 returns +42
# (addop & fact) * op2 will return op2(*('+', 42)), i.e. op2('+', 42)
# so (addop & fact) * op2 returns lambda x: add(x, 42)
# fact & ( (mulop & fact) * op2 )[:] returns a number and a list of functions
# for instance (42, [(lambda x:mul(x, 43)), (lambda x:mul(x, 44))])
# so (fact & ( (mulop & fact) * op2 )[:]) * red applyied on "42*43*44"
# will return red(42, [(lambda x:mul(x, 43)), (lambda x:mul(x, 44))])
# i.e. 42*43*44
```

And with the SP language:

```
number = r'[0-9]+' : `int` ;
addop = r'[+-]' ;
mulop = r'[*/]' ;
fact = addop fact :: `op1` ;
term = fact (mulop fact :: `op2`)* :: `red` ;
# r'[0-9]+' applyed on "42" will return "42".
# r'[0-9]+' : `int` will return int("42")
# "addop fact" applyied on "+ 42" will return ('+', 42)
# "addop fact :: `op1`" will return op1(*('+', 42)), i.e. op1('+', 42)
# so "addop fact :: `op1`" returns +42
# "addop fact :: `op2`" will return op2(*('+', 42)), i.e. op2('+', 42)
# so "addop fact :: `op2`" returns lambda x: add(x, 42)
# "fact (mulop fact :: `op2`)*" returns a number and a list of functions
# for instance (42, [(lambda x:mul(x, 43)), (lambda x:mul(x, 44))])
# so "fact (mulop fact :: `op2`)* :: `red`" applyied on "42*43*44"
# will return red(42, [(lambda x:mul(x, 43)), (lambda x:mul(x, 44))])
# i.e. 42*43*44
```

In the SP language, `:`

(as `/`

) applies a Python function (more generally a callable object) to a value returned by a sequence and `::`

(as `*`

) applies a Python function to several values returned by a sequence.

Here is finally the complete parser.

Expression recognizer and evaluator:

```
from sp import *
def Calc():
from operator import pos, neg, add, sub, mul, truediv as div
op1 = lambda f,x: {'+':pos, '-':neg}[f](x)
op2 = lambda f,y: lambda x: {'+': add, '-': sub, '*': mul, '/': div}[f](x,y)
def red(x, fs):
for f in fs: x = f(x)
return x
number = R(r'[0-9]+') / int
addop = R('[+-]')
mulop = R('[*/]')
with Separator(r'\s+'):
expr = Rule()
fact = Rule()
fact |= (addop & fact) * op1
fact |= '(' & expr & ')'
fact |= number
term = (fact & ( (mulop & fact) * op2 )[:]) * red
expr |= (term & ( (addop & term) * op2 )[:]) * red
return expr
```

Or with SP language:

```
from sp import *
def Calc():
from operator import pos, neg, add, sub, mul, truediv as div
op1 = lambda f,x: {'+':pos, '-':neg}[f](x)
op2 = lambda f,y: lambda x: {'+': add, '-': sub, '*': mul, '/': div}[f](x,y)
def red(x, fs):
for f in fs: x = f(x)
return x
return compile("""
number = r'[0-9]+' : `int` ;
addop = r'[+-]' ;
mulop = r'[*/]' ;
separator: r'\s+' ;
!expr = term (addop term :: `op2`)* :: `red` ;
term = fact (mulop fact :: `op2`)* :: `red` ;
fact = addop fact :: `op1` ;
fact = '(' expr ')' ;
fact = number ;
""")
```

A parser is a simple Python object. This example show how to write a function that returns a parser. The parser can be applied to strings by simply calling the parser.

Writing SP grammars in Python:

```
from sp import *
def MyParser():
parser = ...
return parser
# You can instanciate your parser here
my_parser = MyParser()
# and use it
parsed_object = my_parser(string_to_be_parsed)
```

To use this parser you now just need to instantiate an object.

Complete Python script with expression parser:

```
from sp import *
def Calc():
...
calc = Calc()
while True:
expr = input('Enter an expression: ')
try: print(expr, '=', calc(expr))
except Exception as e: print("%s:"%e.__class__.__name__, e)
```

This tutorial shows some of the possibilities of SP. If you have read it carefully you may be able to start with SP. The next chapters present SP more precisely. They contain more examples to illustrate all the features of SP.

Happy SP'ing!

SP is a package which main function is to provide basic objects to build a complete parser.

The grammar is a Python object.

Grammar embedding example:

```
def Foo():
bar = R('bar')
return bar
```

Then you can use the new generated parser. The parser is simply a Python object.

Parser usage example:

```
test = "bar"
my_parser = Foo()
x = my_parser(test) # Parses "bar"
print x
```

SP grammars are Python objects. SP grammars may contain two parts:

- Tokens
are built by the

`R`

or`K`

keywords.- Rules
are described after tokens in a

`Separator`

context.

Example of SP grammar structure:

```
def Foo():
# Tokens
number = R(r'\d+') / int
# Rules
with Separator(r'\s+'):
S = number[:]
return S
foo = Foo()
result = foo("42 43 44") # return [42, 43, 44]
```

The lexer is based on the *re*^{5} module. SP profits from the power of Python regular expressions. This document assumes the reader is familiar with regular expressions.

You can use the syntax of regular expressions as expected by the *re*^{6} module.

Tokens can be explicitly defined by the `R`

, `K`

and `Separator`

keywords.

Expression | Usage |
---|---|

`R` |
defines a regular token. The token is defined with a regular expression and returns a string (or a tuple of strings if the regular expression defines groups). |

`K` |
defines a token that returns nothing (useful for keywords for instance). The keyword is defined by an identifier (in this case word boundaries are expected around the keyword) or another string (in this case the pattern is not considered as a regular expression). The token just recognizes a keyword and returns nothing. |

`Separator` |
is a context manager used to define separators for the rules defined in the context. The token is defined with a regular expression and returns nothing. |

A token can be defined by:

- a name
which identifies the token. This name is used by the parser.

- a regular expression
which describes what to match to recognize the token.

- an action
which can translate the matched text into a Python object. It can be a function of one argument or a non callable object. If it is not callable, it will be returned for each token otherwise it will be applied to the text of the token and the result will be returned. This action is optional. By default the token text is returned.

Token definition examples:

```
integer = R(r'\d+') / int
identifier = R(r'[a-zA-Z]\w*\b')
boolean = R(r'(True|False)\b') / (lambda b: b=='True')
spaces = K(r'\s+')
comments = K(r'#.*')
with Separator(spaces|comments):
# rules defined here will use spaces and comments as separators
atom = '(' & expr & ')'
```

There are two kinds of tokens. Tokens defined by the `R`

or `K`

keywords are parsed by the parser and tokens defined by the `Separator`

keyword are considered as separators (white spaces or comments for example) and are wiped out by the lexer.

The word boundary `\b`

can be used to avoid recognizing "True" at the beginning of "Truexyz".

If the regular expression defines groups, the parser returns a tuple containing these groups:

```
couple = R('<(\d+)-(\d+)>')
couple("<42-43>") == ('42', '43')
```

If the regular expression defines only one group, the parser returns the value of this group:

```
first = R('<(\d+)-\d+>')
first("<42-43>") == '42'
```

Unwanted groups can be avoided using `(?:...)`

.

A name can be given to a token to make error messages easier to read:

`couple = R('<(\d+)-(\d+)>', name="couple")`

Regular expressions can be compiled using specific compilation options. Options are defined in the `re`

module:

`token = R('...', flags=re.IGNORECASE|re.DOTALL)`

`re`

defines the following flags:

- I (IGNORECASE)
Perform case-insensitive matching.

- L (LOCALE)
Make

`\w`

,`\W`

,`\b`

,`\B`

, dependent on the current locale.- M (MULTILINE)
`"^"`

matches the beginning of lines (after a newline) as well as the string.`"$"`

matches the end of lines (before a newline) as well as the end of the string.- S (DOTALL)
`"."`

matches any character at all, including the newline.- X (VERBOSE)
Ignore whitespace and comments for nicer looking RE's.

- U (UNICODE)
Make

`\w`

,`\W`

,`\b`

,`\B`

, dependent on the Unicode locale

Tokens can also be defined on the fly. Their definition are then inlined in the grammar rules. This feature may be useful for keywords or punctuation signs.

In this case tokens can be written without the `R`

or `K`

keywords. They are considered as keywords (as defined by `K`

).

Inline token definition examples:

```
IfThenElse = 'if' & Cond &
'then' & Statement &
'else' & Statement
```

A parser is declared as a Python object.

Rule declarations have two parts. The left side declares the symbol associated to the rule. The right side describes the decomposition of the rule. Both parts of the declaration are separated with an equal sign (`=`

).

Rule declaration example:

`SYMBOL = (A & B) * (lambda a, b: f(a, b))`

Sequences in grammar rules describe in which order symbols should appear in the input string. For example the sequence `A & B`

recognizes an `A`

followed by a `B`

.

For example to say that a `sum`

is a `term`

plus another `term`

you can write:

`Sum = Term & '+' & Term`

Alternatives in grammar rules describe several possible decompositions of a symbol. The infix pipe operator (`|`

) is used to separate alternatives. `A | B`

recognizes either an `A`

or a `B`

. If both `A`

and `B`

can be matched only the first longest match is considered. So the order of alternatives may be very important when two alternatives can match texts of the same size.

For example to say that an `atom`

is an *integer* or an *expression in paranthesis* you can write:

`Atom = integer | '(' & Expr & ')'`

Repetitions in grammar rules describe how many times an expression should be matched.

Expression | Usage |
---|---|

`A[:1]` |
recognizes zero or one `A` . |

`A[:]` |
recognizes zero or more `A` . |

`A[1:]` |
recognizes one or more `A` . |

`A[m:n]` |
recognizes at least m and at most n `A` . |

`A[m:n:s]` |
recognizes at least m and at most n `A` using `s` as a separator. |

Repetitions are greedy. Repetitions are implemented as Python loops. Thus whatever the length of the repetitions, the Python stack will not overflow.

The separator is useful to parse lists. For instance a comma separated parameter list is `parameter[::',']`

.

The following table lists the different structures in increasing precedence order. To override the default precedence you can group expressions with parenthesis.

Precedence in SP expressions:

Structure | Example |
---|---|

Alternative | `A | B` |

Sequence | `A & B` |

Repetitions | `A[x:y]` |

Symbol and grouping | `A` and `( ... )` |

Grammar rules can contain actions as Python functions.

Functions are applied to parsed objects using `/`

or `*`

.

Expression | Value |
---|---|

`parser / function` |
returns function(result of parser). |

`parser * function` |
returns function(*result of parser). |

`*`

can be used to analyse the result of a sequence.

An abstract syntax tree (AST) is an abstract representation of the structure of the input. A node of an AST is a Python object (there is no constraint about its class). AST nodes are completely defined by the user.

AST example (parsing a couple):

```
class Couple:
def __init__(self, a, b):
self.a = a
self.b = b
def Foo():
couple = ('(' & item & ',' & item & ')') * Couple
return couple
```

It is sometimes useful to return a constant. `C`

defines a parser that matches an empty input and returns a constant.

Constant example:

```
number = ( '1' & C("one")
| '2' & C("two")
| '3' & C("three")
)
```

To know the current position in the input string, the `At()`

parser returns an object containing the current index (attribute `index`

) and the corresponding line and column numbers (attributes `line`

and `column`

):

```
position = At() / `lambda p: (p.line, p.column)`
rule = ... & pos & ...
```

Backtracking has a cost. The parser may often try to parse again the same string at the same position. To improve the speed of the parser, some time consuming functions are *memoized*. This drastically fasten the parser but requires more memory. If a lot of string are parsed in a single script this mechanism can slow down the computer because of heavy swap disk usage or even lead to a memory error.

To avoid such problems it is recommended to clean the memoization cache by calling the `sp.clean`

function:

```
import sp
...
for s in a_lot_of_strings:
parse(s)
sp.clean()
```

This document describes the usage of SP with Python 2.6 or Python 3.1. Grammars need some adaptations to work with Python 2.5. or older.

Separators use context managers which don't exist in Python 2.4. Context managers have been introduced in Python 2.5 (`from __future__ import with_statement`

) and in Python 2.6 (as a standard feature). When the context managers are not available, it may be possible to call the `__enter__`

and `__exit__`

method explicitly (tested for Python 2.4).

Python 2.6 and later:

```
number = R(r'\d+') / int
with Separator('\s+'):
coord = number & ',' & number
```

Python 2.5 with `with_statement`

:

```
from __future__ import with_statement
number = R(r'\d+') / int
with Separator('\s+'):
coord = number & ',' & number
```

Python 2.5 or 2.4 (or older but not tested) without `with_statement`

:

```
sep = Separator('\s+')
number = R(r'\d+') / int
sep.__enter__()
coord = number & ',' & number
sep.__exit__()
```

Instead of using Python expressions that can sometimes be difficult to read, it's possible to write grammars in a cleaner syntax and compile these grammar with the `sp.compile`

function. This function takes the grammar as a string parameter. The `sp.compile_file`

function reads the grammar in a separate file.

Here the equivalence between Python expressions and the SP mini language:

SP Python expressions | SP mini language | Description |
---|---|---|

`R("
regular expressionâ€ś)`|` R(â€ťre gexprâ€ś, name=â€ťname")` |
`r
â€śregular expressionâ€ť`|` name.râ€śregexprâ€ť` |
Token defined by a regular expression |

`K("plain text")` `K("plain text", name="name")` |
`"plain text"` `name."plain text"` |
Keyword defined by a non interpreted string |

`t = R('.. .', flags=re.I|re.S)` |
`le xer: I S; t = r'...'` |
Regular expression options |

`with Separator(...):` |
`separator: ... ;` |
Separator definition |

`C(object)` |
``object` ` |
Parses nothing and returns `object` |

`... / function` |
`... : `function` ` |
Parses ... and apply the result to `function` (`function(...)` ) |

`... * function` |
`... :: `function` ` |
Parses ... and apply the result (multiple values) to `function` (`function(*...)` ) |

`... & At() & ...` |
`... @ ...` |
Position in the input string |

`(...)[:]` |
`(...)*` |
Zero or more matches |

`(...)[1:]` |
`(...)+` |
One or more matches |

`(...)[:1]` |
`(...)?` |
Zero or one matche |

`(...)[::S]` |
`[.../S]*` |
Zero or more matches separated by `S` |

`(...)[1::S]` |
`[.../S]+` |
One or more matches separated by `S` |

`A & B & C` |
`A B C` |
Sequence |

`A | B | C` |
`A | B | C` |
Alternative |

`(...)` |
`(...)` |
Grouping |

`rule_name = ...` |
`rule_name = ... ;` |
Rule definition |

`axiom_name = ...` |
`!axiom_name = ... ;` |
Axiom definition |

```
In mathematics, Newick tree format (or Newick notation or New Hampshire tree format)
is a way to represent graph-theoretical trees with edge lengths using parentheses and
commas. It was created by James Archie, William H. E. Day, Joseph Felsenstein, Wayne
Maddison, Christopher Meacham, F. James Rohlf, and David Swofford, at two meetings in
1986, the second of which was at Newick's restaurant in Dover, New Hampshire, USA.
-- Wikipedia, the free encyclopedia
```

The grammar given by Wikipedia is:

```
Tree --> Subtree ";" | Branch ";"
Subtree --> Leaf | Internal
Leaf --> Name
Internal --> "(" BranchSet ")" Name
BranchSet --> Branch | Branch "," BranchSet
Branch --> Subtree Length
Name --> empty | string
Length --> empty | ":" number
```

With very few transformation, this grammar can be converted to a Simple Parser grammar. Only `BranchSet`

is rewritten to use a comma separated list parser:

```
Tree = Subtree ';' | Branch ';' ;
Subtree = Leaf | Internal ;
Leaf = Name ;
Internal = '(' [Branch/',']+ ')' Name ;
Branch = Subtree Length ;
Name = r'[^;:,()]*';
Length = '' | ':' r'[0-9.]+' ;
```

Here is the complete parser (newick.py):

In the previous example, the parser computes the value of the expression on the fly, while parsing. It is also possible to build an abstract syntax tree to store an abstract representation of the input. This may be useful when several passes are necessary.

This example shows how to parse an expression (infix, prefix or postfix) and convert it in infix, prefix and postfix notation. The expression is saved in a tree. Each node of the tree correspond to an operator in the expression. Each leaf is a number. Then to write the expression in infix, prefix or postfix notation, we just need to walk through the tree in a particular order.

The AST of this converter has three types of node:

- class Op
is used to store operators (

`+`

,`-`

,`*`

,`/`

,`^`

). It has two sons associated to the sub expressions.- class Atom
is an atomic expression (a number or a symbolic name).

- class Func
is used to store functions.

These classes are instantiated by the init method. The infix, prefix and postfix methods return strings containing the representation of the node in infix, prefix and postfix notation.

```
ident = r'\b(?!sin|cos|tan|min|max)\w+\b' : `Atom` ;
func1 = r'sin' | r'cos' | r'tan' ;
func2 = r'min' | r'max' ;
op = op_add | op_mul | op_pow ;
op_add = r'[+-]' ;
op_mul = r'[*/]' ;
op_pow = r'\^' ;
```

The grammar for infix expressions is similar to the grammar used in the previous example:

```
expr = term (op_add term :: `lambda op, y: lambda x: Op(op, x, y)`)* :: `red` ;
term = fact (op_mul fact :: `lambda op, y: lambda x: Op(op, x, y)`)* :: `red` ;
fact = atom (op_pow fact :: `lambda op, y: lambda x: Op(op, x, y)`)? :: `red` ;
atom = ident ;
atom = '(' expr ')' ;
atom = func1 '(' expr ')' :: `Func` ;
atom = func2 '(' expr ',' expr ')' :: `Func` ;
```

`red`

is a function that applies a list of functions to a value:

```
def red(x, fs):
for f in fs:
x = f(x)
return x
```

The grammar for prefix expressions is very simple. A compound prefix expression is an operator followed by two subexpressions, or a binary function followed by two subexpressions, or a unary function followed by one subexpression:

```
expr_pre = ident ;
expr_pre = op expr_pre expr_pre :: `Op` ;
expr_pre = func1 expr_pre :: `Func` ;
expr_pre = func2 expr_pre expr_pre :: `Func` ;
```

At first sight postfix and infix grammars may be very similar. Only the position of the operators changes. So a compound postfix expression is a first expression followed by a second one and an operator. This rule is left recursive. As SP is a descendant recursive parser, such rules are forbidden to avoid infinite recursion. To remove the left recursion a classical solution is to rewrite the grammar like this:

```
expr_post = ident expr_post_rest :: `lambda x, f: f(x)` ;
expr_post_rest =
( expr_post op :: `lambda y, op: lambda x: Op(op, x, y)`
| expr_post func2 :: `lambda y, f: lambda x: Func(f, x, y)`
| func1 : `lambda f: lambda x: Func(f, x)`
) expr_post_rest :: `lambda f, g: lambda x: g(f(x))` ;
expr_post_rest = `lambda x: x` ;
```

The parser searches for an atomic expression and builds the AST corresponding to the remaining subexpression. `expr_post_rest`

returns a function that builds the complete AST when applied to the first atomic expression. This is a way to simulate inherited attributes.

Using the previous `red`

function and the repetitions, this rule can be rewritten as:

```
expr_post = ident expr_post_rest* :: `red` ;
expr_post_rest =
( expr_post op :: `lambda y, op: lambda x: Op(op, x, y)`
| expr_post func2 :: `lambda y, f: lambda x: Func(f, x, y)`
| func1 : `lambda f: lambda x: Func(f, x)`
) ;
```

or simply:

```
expr_post = ident
( expr_post op :: `lambda y, op: lambda x: Op(op, x, y)`
| expr_post func2 :: `lambda y, f: lambda x: Func(f, x, y)`
| func1 : `lambda f: lambda x: Func(f, x)`
)* :: `red` ;
```

Here is the complete source code (notation.py):

This chapter presents an extension of the calculator described in the tutorial. This calculator has a memory.

The grammar has been rewritten using the SP language.

The calculator has memories. A memory cell is identified by a name. For example, if the user types `pi = 3.14`

, the memory cell named `pi`

will contain the value of `pi`

and `2*pi`

will return `6.28`

.

Note

Another calculator is available as a separate package. Calc is a full featured programmers' calculator. It is scriptable and allows user functions.

Here is the complete source code (calc.py):

Python is a wonderful object oriented programming language available at http://www.python.orgâ†©ď¸Ž

Older

*Python*versions may work (tested with Python 2.4 and 2.5). See the Older Python versions chapter.â†©ď¸ŽThe axiom is the symbol from which the parsing startsâ†©ď¸Ž

The axiom is the symbol from which the parsing startsâ†©ď¸Ž

*re*is a standard Python module. It handles regular expressions. For further information about*re*you can read http://docs.python.org/library/re.htmlâ†©ď¸ŽRead the Python documentation for further information: http://docs.python.org/library/re.html#re-syntaxâ†©ď¸Ž