52 lines
847 B
Markdown
52 lines
847 B
Markdown
# Collatz Conjecture
|
|
|
|
Collatz Conjecture (Snowflake / `3n+1`) done in the GHC Type System.
|
|
|
|
## Running
|
|
|
|
in `ghci` load the file:
|
|
|
|
```
|
|
:load collatz.hs
|
|
```
|
|
|
|
and run with the following:
|
|
|
|
```
|
|
:t solution (nil :: X)
|
|
```
|
|
|
|
where `X` is the church encoding using `S n` and `Z`, ie
|
|
|
|
`(S (S (S Z)))` is the number `3`
|
|
|
|
## Example
|
|
|
|
```
|
|
*Main> :t solution (nil :: (S (S (S Z))))
|
|
solution (nil :: (S (S (S Z))))
|
|
:: Cons
|
|
(S (S (S Z)))
|
|
(Cons
|
|
(S (S (S (S (S (S (S (S (S (S Z))))))))))
|
|
(Cons
|
|
(S (S (S (S (S Z)))))
|
|
(Cons
|
|
(S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S Z))))))))))))))))
|
|
(Cons
|
|
(S (S (S (S (S (S (S (S Z))))))))
|
|
(Cons
|
|
(S (S (S (S Z))))
|
|
(Cons
|
|
(S (S Z))
|
|
(Cons
|
|
(S Z)
|
|
Nil)))))))
|
|
```
|
|
|
|
which translates to the following list:
|
|
|
|
```
|
|
[ 3 10 5 16 8 4 2 1 ]
|
|
```
|