I have to put this project on hold for a little bit, but since what's there
is cool already I thought I'd mention it here.
"FoxySheep" is the Python portion of Robert Jacobson's Mathematica parser,
with a crude translator to Python.
It also include translation from InputForm to FullForm and can show a parse
tree for either. These are interesting in their own right if you are
wondering how Mathematica will interpret something typed.
However below I'll limit myself to just the InputForm to Python translation.
*Examples: *
foxy-sheep -o python
Enter a Mathematica expression. Enter either an empty line, Ctrl-C, or
Ctrl-D to exit.
in:=* 2 + 2*
(2 + 2)
Out[0]=4
in:= *1 + 2 + 3*
(1 + 2 + 3)
Out[1]=6
in:= *% + 4 *
(Out() + 4)
Out[2]=10
in:= *((5 - 3) ^ (1 + 2))/ 4 *
((5 - 3) ** (1 + 2) / 4)
Out[4]=2.0
in:= *GCD[12,15]*
math.gcd(12, 15)
Out[5]=3
in:= *{1, 2, 3} *
[1, 2, 3]
Out[6]=[1, 2, 3]
And more 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)
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
Some comments about the above. Range[x] gets translated to range(x)
although an argument could be made that it should be list(range(x)). Stuff
like this is easily handled, but I'd probably wait until a use case where
this messes up before addressing.
This project has been use-case driven: if no one (including myself) uses, I
don' t feel compelled to fix. Right now I'm more interested in having the
overall framework better covered.
Even though this handles the "toy" subset of Mathematica, you know the
stuff that one presumes an undergraduate in a compiler class *should * be
able to whip off as a homework excercise, just this subset may be useful.
Just handling numbers in their full glory (with mantissa, exponent, base,
numeric precision, complex parts, fractional parts) is useful.
In fact that is what this StackExchange question convert mathematica math
expression form to python math expression
<https://mathematica.stackexchange.com/questions/85445/convert-mathematica-math-expression-form-to-python-math-expression>
is asking. And in order to handle that I needed added a conversion of E to
math.e. I was tempted to add math.pi as well, but I am holding off on that
until I come across a specific need for that.
There is a lot of low hanging fruit of this sort that can be added. Dozens
of functions and constants could be added.
I will mention that one technique that I use that I find a win for anyone
else who wants to extend this project or do the same thing in another
project: go through the Mathematica tutorials and handle the simple
examples there. For example the subscript examples come from Fast
Introduction for Programmers
<https://www.wolfram.com/language/fast-introduction-for-programmers/en/lists/>.
The tutorial Fast Introduction for Math Students
<https://www.wolfram.com/language/fast-introduction-for-math-students/en/entering-input/>
I've
gone over as well.
I learned about the 1 indexing versus 0 indexing problem by having the
program answer the tests that were posed in the first tutorial.
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 <https://pypi.org/project/astor/>is used to
dump this to text. And that is why some of the examples above have the
outer parenthesis.
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.
The plan for handling this is basically to extend pytype
<https://pypi.org/project/pytype/>to give the types of the two expressions
on either side of "+".
But as I said, right now I have to put this project on hold. It is BSD-2Class
on github <https://github.com/rocky/FoxySheep2>so ohters can feel free to
extend that or fork off of this.
Enjoy!
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