A simple dialog system for Sage in natural language

Goal

Develop a command-line tool able to take commands in natural language and have them executed by Sage (an open-source Computer Algebra System ¹)

How to use it

Building

You'll need:

• ghc
• curl (so that cabal install curl succeeds)
• a way to call Sage on a terminal (usually sage command. It assumes it's in your PATH)
• A POSIX system
• and, of course, GF

Checkout the mathematics grammar library from:

 svn co svn://molto-project.eu/mgl

Go into the sage directory and make it:

cd mgl/sage
make

The first time you make it will fail, asking you to make modifications in the Sage installation. Please refer to the installation page.

Now try to build gfsage again²:

make

The system as been tested in Mac (OS X 10.7) and Linux (Ubuntu).

Usage

Run the tool as:

./gfsage english

giving the input language as argument. It will take some seconds to start the server. After that it will reply with some server information and will show the prompt:

    sage>

You can then enter your query:

    sage> compute the product of the octal number 12 and the binary number 100.
    (3) 40
    answer: it is 40 .

To show that a CAS is actually behind the scene, let's try something symbolic:

    sage> compute the greatest common divisor of x and the product of x and y.
    (4) x
    answer: it is x .

and compare it with:

    sage> compute the greatest common divisor of x and the sum of x and y.
    (5) 1
    answer: it is 1 .

Sage does the right thing in both cases, x and y being unbound numeric variables.

    sage> compute the second iterated derivative of the cosine at pi.
    (6) 1
    answer: it is 1 .

Exiting

Exit the session by issuing CRTL+D: This way the server exits cleanly.

Just another example in a different language:

    ./gfsage spanish
    Login into localhost at port 9000
    Session ID is c1ef10dfd49e4fdb3214fa6d3a3b9c92
    waiting... EmptyBlock 2
    finished handshake. Session is c1ef10dfd49e4fdb3214fa6d3a3b9c92
    sage> calcula la parte imaginaria  de la derivada de la exponencial en pi.
    (4) 0
    answer: es 0 .

More recent examples involving integer literals and integration:

    sage> compute the sum of 1, 2, 3, 4 and 5.
    (3) 15
    answer: it is 15 .
   
    sage> compute the summation of x when x ranges from 1 to 100.
    (4) 5050
    answer: it is 5050 .

    sage> compute the integral of the cosine from 0 to the quotient of pi and 2.
    waiting... (5) 1
    answer: it is 1 .

    sage> compute the integral of the function mapping x to the square root of x from 1 to 2.
    (6) 4/3*sqrt(2) - 2/3
    answer: it is 4 over 3 times the square root of 2 minus the quotient of 2 and 3 .

Other invocation options

Use english:

gfsage      

Use LANGUAGE:

gfsage LANGUAGE

General invocation:

gfsage [OPTIONS]

where OPTIONS are:

Limitations

• On Darwin (OS X 10.6 and 10.7) a bug in the Sage part makes the system unresponsive after some computations (between 7 and 10)
• On some machines, it takes time for the Sage server to respond.

This condition is signaled by the message:

gfsage: Connecting CurlCouldntConnect 

I used a Linux virtual machine to reproduce this condition and find that, sometimes, it takes about 10 retries for the server to catch, but then it stays running ok for hours. My guess is that is related to some timeout limit in the server. Killing the orphaned python processes from the previous retries might help too (killall python).