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| -rw-r--r-- | readme.md | 18 | ||||
| -rw-r--r-- | samples/biology.birb | 4 |
2 files changed, 9 insertions, 13 deletions
@@ -77,14 +77,14 @@ as 🐥🐦. The successor function can be written as 🦢🐧: - 🐦🐧🐦🦢🐧🐥🐦 $\rightsquigarrow\lambda\lambda(10)$ – (Church numeral 1) -- 🐦🐧🐦🐧🕊️🦢🐧🦢🐧🐥🐦 $\rightsquigarrow\lambda(1(10))$ – (Church - numeral 2) +- 🐦🐧🐦🐧🕊️🦢🐧🦢🐧🐥🐦 $\rightsquigarrow\lambda\lambda(1(10))$ – + (Church numeral 2) Similarly, one can very obviously translate the Church addition function to 🪽🐧. Now, to calculate $1+2$ based on their increments from zero: - 🐦🐦🕊️🐧🕊️🐧🐦🐧🕊️🐧🕊️🪽🐧🦢🐧🦢🐧🐥🐦🦢🐧🐥🐦 - $\rightsquigarrow\lambda(1(1(10)))$ – (Church numeral 3) + $\rightsquigarrow\lambda\lambda(1(1(10)))$ – (Church numeral 3) Also: 🐧 is $a\cdot b$, 🦜 is $n^n$ and 🦚🐦 $a^b$. @@ -124,12 +124,12 @@ sometimes manually converted the term back to birbs. # Turing-completeness -Birb is Turing complete. - -It turns out that even its sub-language $\Sigma=\{🦢🐥\}$ (SK) is Turing -complete, since the semantics allow an initial construction of 🐦 using -`((🦢 🐥) 🐥)`. By doing that, birb is equivalent to the -[Jot](https://esolangs.org/wiki/Jot) variant of Iota calculus. +Birb is Turing complete, since one can construct any term of the +[Jot](https://esolangs.org/wiki/Jot) variant of Iota. A Jot term +`((X s) k)` is equivalent to `🐦X🦢🐥`. Similarly, `(s (k X))` is +equivalent to `🐦🐦🐧🦢🐥X`. This can be extended for arbitrary long terms +using increasingly more complicated construction of composition +combinators. ------------------------------------------------------------------------ diff --git a/samples/biology.birb b/samples/biology.birb deleted file mode 100644 index b71abc8..0000000 --- a/samples/biology.birb +++ /dev/null @@ -1,4 +0,0 @@ -construct list -🐧🦩 - -🦩🦚 |