93 lines
1.8 KiB
Markdown
93 lines
1.8 KiB
Markdown
|
---
|
||
|
|
title: fibonacci in maude and ats
|
||
|
|
date: 2022-10-24
|
||
|
|
tags: [computer, maude, ATS]
|
||
|
|
...
|
||
|
|
|
||
|
|
i might submit these [here], if i can be bothered to get a new github account.
|
||
|
|
|
||
|
|
[here]: https://braxtonhall.ca/fib/
|
||
|
|
|
||
|
|
:::aside
|
||
|
|
update: i did it
|
||
|
|
:::
|
||
|
|
|
||
|
|
|
||
|
|
# maude
|
||
|
|
|
||
|
|
```maude
|
||
|
|
smod FIB is
|
||
|
|
pr LIST{Nat} .
|
||
|
|
|
||
|
|
vars M N : Nat .
|
||
|
|
var Ns : List{Nat} .
|
||
|
|
|
||
|
|
rl [start]: nil => 0 1 .
|
||
|
|
rl [next]: Ns M N => Ns M N (M + N) .
|
||
|
|
rl [drop]: Ns N => N .
|
||
|
|
|
||
|
|
strats fib fibgo : Nat @ List{Nat} .
|
||
|
|
sd fib(N) := start ; fibgo(N) .
|
||
|
|
sd fibgo(0) := top(drop) .
|
||
|
|
sd fibgo(s(N)) := top(next) ; fibgo(N) .
|
||
|
|
endsm
|
||
|
|
```
|
||
|
|
|
||
|
|
```
|
||
|
|
Maude> srew nil using fib(10) .
|
||
|
|
srewrite in FIB : nil using fib(10) .
|
||
|
|
|
||
|
|
Solution 1
|
||
|
|
rewrites: 8330 in 12ms cpu (12ms real) (694166 rewrites/second)
|
||
|
|
result NzNat: 89
|
||
|
|
|
||
|
|
No more solutions.
|
||
|
|
rewrites: 8469 in 12ms cpu (13ms real) (705750 rewrites/second)
|
||
|
|
```
|
||
|
|
|
||
|
|
|
||
|
|
# ats
|
||
|
|
|
||
|
|
```ats
|
||
|
|
#include "share/atspre_define.hats"
|
||
|
|
#include "share/atspre_staload.hats"
|
||
|
|
|
||
|
|
// is_fib(i, n): n is the i-th fibonacci number
|
||
|
|
dataprop is_fib(int, int) =
|
||
|
|
| F0(0, 0) | F1(1, 1)
|
||
|
|
| {i, m, n : nat} Fplus(i + 2, m + n) of (is_fib(i, m), is_fib(i + 1, n))
|
||
|
|
|
||
|
|
typedef fib(i : int) = [n : nat] (is_fib(i, n) | int(n))
|
||
|
|
|
||
|
|
fun fib {t : nat} .<>. (t : int(t)) :<> fib(t) =
|
||
|
|
let
|
||
|
|
// m, n : accs
|
||
|
|
// i : index of m
|
||
|
|
// t : target index
|
||
|
|
fun go {m, n, i, t : nat | i <= t} .<t - i>.
|
||
|
|
(M : is_fib(i, m), N : is_fib(i + 1, n) |
|
||
|
|
m : int(m), n : int(n), i : int(i), t : int(t)) :<>
|
||
|
|
fib(t) =
|
||
|
|
if i = t then
|
||
|
|
(M | m)
|
||
|
|
else
|
||
|
|
go(N, Fplus(M, N) | n, m + n, i + 1, t)
|
||
|
|
in
|
||
|
|
go(F0, F1 | 0, 1, 0, t)
|
||
|
|
end
|
||
|
|
|
||
|
|
fun fib_(i : Nat) : Nat = let val (_ | res) = fib(i) in res end
|
||
|
|
|
||
|
|
implement main0() = println!("fib(15) = ", fib_(15))
|
||
|
|
```
|
||
|
|
|
||
|
|
```sh
|
||
|
|
$ make fib
|
||
|
|
$ ./fib
|
||
|
|
fib(15) = 610
|
||
|
|
```
|
||
|
|
|
||
|
|
same makefile as [last time].
|
||
|
|
|
||
|
|
[last time]: ./2022-09-16-ats.html#install
|