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Diffstat (limited to 'readme.md')
| -rw-r--r-- | readme.md | 18 |
1 files changed, 9 insertions, 9 deletions
@@ -77,14 +77,14 @@ as ðĨðĶ. The successor function can be written as ðĶĒð§: - ðĶð§ðĶðĶĒð§ðĨðĶ $\rightsquigarrow\lambda\lambda(10)$ â (Church numeral 1) -- ðĶð§ðĶð§ðïļðĶĒð§ðĶĒð§ðĨðĶ $\rightsquigarrow\lambda(1(10))$ â (Church - numeral 2) +- ðĶð§ðĶð§ðïļðĶĒð§ðĶĒð§ðĨðĶ $\rightsquigarrow\lambda\lambda(1(10))$ â + (Church numeral 2) Similarly, one can very obviously translate the Church addition function to ðŠ―ð§. Now, to calculate $1+2$ based on their increments from zero: - ðĶðĶðïļð§ðïļð§ðĶð§ðïļð§ðïļðŠ―ð§ðĶĒð§ðĶĒð§ðĨðĶðĶĒð§ðĨðĶ - $\rightsquigarrow\lambda(1(1(10)))$ â (Church numeral 3) + $\rightsquigarrow\lambda\lambda(1(1(10)))$ â (Church numeral 3) Also: ð§ is $a\cdot b$, ðĶ is $n^n$ and ðĶðĶ $a^b$. @@ -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 $\Sigma=\{ðĶĒðĨ\}$ (SK) is Turing -complete, since the semantics allow an initial construction of ðĶ using -`((ðĶĒ ðĨ) ðĨ)`. 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 `ðĶXðĶĒðĨ`. Similarly, `(s (k X))` is +equivalent to `ðĶðĶð§ðĶĒðĨX`. This can be extended for arbitrary long terms +using increasingly more complicated construction of composition +combinators. ------------------------------------------------------------------------ |