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[D] Program synthesis and Godel numbering

I had a little thought.

If we were to construct a godel numbering of a language then we can be sure that any random program we generate is valid.

There is such a language called Jot. It consists of a binary string which maps to the combinatory logic.

https://www.nyu.edu/projects/barker/Iota/

A compiler taking us from unlambda to jot exists:

https://tromp.github.io/cl/lazy-k.html

So one could take all the programs written in unlambda and use them as training material, rather than using a custom domain-specific language. Also, it is possible to map from various other languages to unlamda. So we have a pipe all the way down to a representation that has no possible syntax errors.

Where every string represents a valid program we do not have to worry about invalid syntax. We can simply evaluate the program for a limited time and examine the output.

As well as applying this technique to the existing program synthesis techniques you could also construct a GAN.

Then use the manifold of pre-existing programs constructed by it to inform the search for useful programs.

I’m sure this is all pie in the sky, but I have to let these ideas out onto the internet or I start to self destruct!

submitted by /u/MemeBox
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