FoxySheep 1.2.3

Mathematica parser and translator

This is the Robert Jacobson’s Python implementation of the FoxySheep parser and lexer for Mathematica. It has been stripped down and reorganized a bit.

Examples

When installed, the command-line translator is called foxy-sheep which can convert Mathematica InputForm to Mathematica FullForm without having Mathematica installed: To run the code interactively:

$ foxy-sheep
Enter a Mathematica expression. Enter either an empty line, Ctrl-C, or Ctrl-D to exit.
In[1]:= 1+2
Plus[1,2]
In[1]:=D[4 x^2]
D[Times[4,Power[x,2]]]
In[1]:=
$

The first few examples from Fast Introduction for Math Students

foxy-sheep -o python
Enter a Mathematica expression. Enter either an empty line, Ctrl-C, or Ctrl-D to exit.
In[1]:= 2 + 2
(2 + 2)

Out[1]=4
In[2]:= 1 + 2 + 3
(1 + 2 + 3)

Out[2]=6
In[3]:= % + 4
(Out() + 4)

Out[3]=10
In[4]:= 5 + 2 * 3 - 7.5
(5 + 2 * 3 -
decimal.Decimal(7.5))

In[5]:= ((5 - 3) ^ (1 + 2))/ 4
((5 - 3) ** (1 + 2) / 4)

Out[5]=2.0
In[6]:= GCD[12,15]
math.gcd(12, 15)

Out[6]=3
In[7]:= {1, 2, 3}
[1, 2, 3]

Out[7]=[1, 2, 3]

To call from Python:

from FoxySheep import if2ff, if2python
print(if2ff("x^2-3x+4")
# Prints: Plus[Power[x,2],Times[-1,3,x],4]
print(if2ff("x^2-3x+4")
# Prints (x ** 2 + -1 * 3)

For more demos run foxy-sheep --file pytest/parse_expressions/SO1.m or with other Mathamatica files in pytest/parse_expressions.

For help on foxy-sheep, run foxy-sheep --help.

Conversion to Python

A very crude translator to Python has been started. While there are still a lot of details to be filled out, some of the basics are there.

Here are some examples:

167.5 -> decimal.Decimal(167.5)
15^^8 -> int(15, 8)
132`  -> (132)
1 / 10 3 -> (1 / 10 * 3)
x^2 + y^2 -> (x ** 2 + y ** 2)
GCD[12, 15] -> math.gcd(12, 15)
Range[10] -> range(10)
{a, b, c, d}[[3]] -> [a, b, c, d][2]  # Handles 0-1 conversion
{a, b, c, d, e, f}[[2 ;; 4]] -> [a, b, c, d, e, f][1:3] # ditto

Conversion to Python is done via transforming “InputForm” input to an “OutputForm” parse tree, and then using that to convert to a Python AST. Finally a Python module, astor, is used to dump this to text.

Why do we go through this more complicated for translating one string to another?

By keeping the structure as an AST we can contemplate more powerful transformations and make use of routines that exist for working with Python AST’s.

For example, translating {1,2,3} + 2 into Python, while not handled now, can be done by looking at the types of the operands of plus, and noticing one is a scalar while the other is a list.

Regenerating the lexer/parser

To change the grammar you’ll need the ANTLR Parser Generator (antlr4), version 4.7.x installed.

To (re)generate the lexer/parser you need to

$ make

The resulting files are placed in FoxySheep/generated.

Files generated by ANTLR4 are assumed to be in a subdirectory called generated containing an empty __init__.py file. See the Makefile for details.

FoxySheepLexer Must Subclass Lexer

In order for the generated antlr4 lexer to work we need to patch the generated Python lexer FoxySheep.lexer.py; The patch file FoxySheep.lexer.py.patch does this. The Makefile target for FoxySheepParser.py contains the patch command.

If patching is not done you’ll get an AttributeError exception in the lexer you try to run it such as through foxy-sheep.

AttributeError: 'FoxySheepLexer' object has no attribute 'checkAdditiveOp'

See Also

FoxySheep