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SKI Combinator Calculus
- deleted 2y ago[deleted]
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- deleted 2y ago[deleted]
- marvinborner 2y agoI 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/ https://infinite-apply.marvinborner.de/ [1]: https://neal.fun/infinite-craft/ https://neal.fun/infinite-craft/
- tromp 2y agoI 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.
- marvinborner 2y agoYes, 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
- tromp 2y agoThe 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.