Use the lambda to chemlambda parser to see when the translation doesn’t work

I use the parser page mainly and other pages will be mentioned in the text.

So chemlambda does not solve the problem of finding a purely local conversion of lambda terms to graphs, which can be further reduced by a purely local random algorithm, always. This is one of the reasons I insist both into going outside lambda calculus and into looking at possible applications in real chemistry, where some molecules (programs) do reduce predictively and the span of the cascade of reactions (reductions) is much larger than one can achieve via massive brutal try-everything on a supercomputer strategy.

Let’s see: choose

(\a.a a)(\x.((\b.b b)(\y.y x)))

it should reduce to the omega combinator, but read the comment too. I saw this lambda term, with a similar behaviour, in [arXiv:1701.04691], section 4.

Another example took me by surprise. Now you can choose “omega from S,I combinators”, i.e. the term

(\S.\I.S I I (S I I)) (\x.\y.\z.(x z) (y z)) \x.x

It works well, but l previously used a related term, actually a mol file, which corresponds to the term where I replace I by S K K in S I I (S I I), i.e. the term

S (S K K) (S K K) (S (S K K) (S K K))

To see the reduction of this term (mol file) go to this page and choose “omega from S,K combinators”. You can also see how indeed S K K reduces to I.

But initially in the parser page menu I had  the term

(\S.\K.S (S K K) (S K K) (S (S K K) (S K K))) (\x.\y.\z.(x z) (y z)) (\x.(\y.x))

It should reduce well but it does not. The reason is close to the reason the first lambda term does not reduce well.

Now some bright side of it. Look at this page to see that the ouroboros quine is mortal. I believed it is obviously imortal until recently. Now I started to believe that imortal quines in chemlambda are rare. Yes, there are candidates like (the graph obtained from) omega, or why not (try with the parser) 4 omega

(\f.(\x.(f(f (f (f x)))))) ((\x.x x) (\x.x x))

and there are quines like the “spark_243501” (shown in the menu of this page) with a small range of behaviours. On the contrary, all quines in IC are imortal.

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