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