a bunch of stuff sorry

posts/fib.md

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+---
+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