SKI Combinator Calculus

en.wikipedia.org

30 pointsbarrister4 comments

I built a fun game [0] that shows the power of SKI calculus. Similar to infinite craft [1], you start with a base of elements (S and K combinators) and build your way up to any lambda term!

[0]: https://infinite-apply.marvinborner.de/

[1]: https://neal.fun/infinite-craft/

I managed to build X as S (K (S (K (S S (K (S (K (S S (K K))) K)))) K)) S.

Instead of all the dragging and aligning, wouldn't it be simpler if you could just click on one combinator to use as function, and then on another to use as argument? You could do away with the whole canvas.

Yes, good idea. Maybe I'll add it as an additional method of application. The motivation here was not to find an efficient way to construct terms, but as a fun interpretation of infinite craft. A much simpler solution would obviously be to type the term directly :D

The most recent change is

> The simplest possible term forming a basis is X = λx λy λz. x z (y (λ_.z)), which satisfies X (X X) (X (X X) X X X X X) = K, and X (X (X X (X X (X X))(X (X (X X (X X)))))) X X = S.

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