Archive for the ‘maths’ Category

Test Driven Program Synthesis

July 9, 2014

The idea of generating a program has been around for quite some time.

Now there are IDE’s which can create the scaffolding code so that programmers need to fill in just the application logic.

What I am thinking is little math and little of code generation. I am trying to link 2 different concepts

  1. Newton–Raphson method (’s_method): briefly this helps us approximating a function (f) by  going over a given set of x and f(x). the more the set of x -> f(x) the more accurate our f will be.
  2. TDD ( here we have a set of tests and we write code so that the tests pass, test is an input/output mapping like x -> f(x)

Clubbing them together:

can we use both of these together to generate the function (f) ?

one issue would be that newton-raphson method works on real numbers, and we can say our functions work on byte arrays or strings.

for this can we map a string to a real number so that test cases are converted from string -> f(string) to x -> f(x)


some links to read further:



May 17, 2007

This number read as .9 recurring is an interesting one. .9 recurring

A wikipedia article

It leaves me in awe…

If 0.999… = 1

Then what would 0.888… would be is it 0.9, it should not be coz 0.8999… = 0.9

and can 0.8(888…) can this be 0.89? if it is then what is the difference?


So is it 0.888… < 0.8999… < 0.9


So if we have a class of numbers lets say recurring terminating

0.888… < 0.888…5 < 0.888…5999… < 0.888…6 < 0.9 < 0.999…


This is just a vague idea, but probably we will never contemplate the outcomes of our understanding. This faintly reminds me of Gödel’s incompleteness theorems