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author | funemy | 2022-10-25 07:14:52 +0000 |
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committer | funemy | 2022-10-25 07:14:52 +0000 |
commit | 998ef837b43203319397f191036a97a5adc42220 (patch) | |
tree | 920558bd60d282c663fd2da1cd4144cac1849a1d /entries/pkoronkevich | |
parent | fdac6c60e115297a58f5b81da0c4b7f18ac758f2 (diff) | |
parent | ce7544a6db594f7d3dfad0d7dc65d01515e57ad6 (diff) |
Merge branch 'main' of github.com:braxtonhall/fib
Diffstat (limited to 'entries/pkoronkevich')
-rw-r--r-- | entries/pkoronkevich/tex/README.md | 1 | ||||
-rw-r--r-- | entries/pkoronkevich/tex/fib.tex | 29 | ||||
-rw-r--r-- | entries/pkoronkevich/tex/render.pdf | bin | 0 -> 21807 bytes | |||
-rw-r--r-- | entries/pkoronkevich/tex/render.png | bin | 0 -> 387387 bytes |
4 files changed, 30 insertions, 0 deletions
diff --git a/entries/pkoronkevich/tex/README.md b/entries/pkoronkevich/tex/README.md new file mode 100644 index 0000000..225773b --- /dev/null +++ b/entries/pkoronkevich/tex/README.md @@ -0,0 +1 @@ +<img src="./render.png" alt="fib.tex preview">
\ No newline at end of file diff --git a/entries/pkoronkevich/tex/fib.tex b/entries/pkoronkevich/tex/fib.tex new file mode 100644 index 0000000..cef9138 --- /dev/null +++ b/entries/pkoronkevich/tex/fib.tex @@ -0,0 +1,29 @@ +\documentclass[11pt]{article} +\usepackage[fleqn]{amsmath} + +\newcommand{\one}{\lambda f . \lambda x . f \ x} +\newcommand{\two}{\lambda f . \lambda x . f \ (f \ x)} +\newcommand{\tru}{\lambda x . \lambda y . x} +\newcommand{\flse}{\lambda x . \lambda y . y} +\newcommand{\isz}{\lambda n . n \ (\lambda c . \flse) \ \tru} +\newcommand{\ife}{\lambda p . \lambda a . \lambda b . p \ a \ b} +\newcommand{\suc}{\lambda n . \lambda f . \lambda x . f \ (n \ f \ x)} +\newcommand{\plus}{\lambda m . \lambda n . m \ (\suc) \ n} +\newcommand{\pred}{\lambda n . \lambda f . \lambda x . n \ (\lambda g . \lambda h . h \ (g \ f)) \ (\lambda u . x) \ (\lambda u . u)} +\newcommand{\sub}{\lambda m . \lambda n . n \ (\pred) \ m} +\newcommand{\lleq}{\lambda m . \lambda n . \\ \qquad \isz \ ((\sub) \\ \qquad \ m \ n)} +\newcommand{\fix}{\lambda g . (\lambda x . g \ (x \ x)) \ (\lambda x . g \ (x \ x))} +\newcommand{\appo}[2]{#1 \ #2} +\newcommand{\appt}[3]{#1 \ #2 \ #3} + +\begin{document} +\begin{gather*} + \fix \\ % recursive function application + \quad \lambda r . \lambda n . (\ife) \\ % of fib, which takes itself and n, if expression + \quad \ \appt{(\lleq)}{n}{\one} \\ % if n less than or equal to one + \quad \ (\one) \\ % if so, return 1 + \quad \ (\plus) \\ % if not, add + \qquad \appo{r}{(\appo{(\pred)}{n})} \\ % the first recursive call, n - 1, to + \qquad \appo{r}{(\appt{(\sub)}{n}{\two})} % the second recursive call, n - 2 +\end{gather*} +\end{document} diff --git a/entries/pkoronkevich/tex/render.pdf b/entries/pkoronkevich/tex/render.pdf Binary files differnew file mode 100644 index 0000000..8ee60c7 --- /dev/null +++ b/entries/pkoronkevich/tex/render.pdf diff --git a/entries/pkoronkevich/tex/render.png b/entries/pkoronkevich/tex/render.png Binary files differnew file mode 100644 index 0000000..a1896a2 --- /dev/null +++ b/entries/pkoronkevich/tex/render.png |