Fix Ltac2 `Array.init` exponential overhead

Previously, `Array.init` was computing the first element of the array
twice, resulting in exponential overhead in the number of recursive
nestings of `Array.init`.  Notably, since `Array.map` is implemented in
terms of `Array.init`, this exponential blowup shows up in any term
traversal based on `Array.map` over the arguments of application nodes.

Fixes #14011

3 files changed, 28 insertions, 1 deletions

diff --git a/doc/changelog/04-tactics/14012-ltac2-array-init.rst b/doc/changelog/04-tactics/14012-ltac2-array-init.rst
new file mode 100644
index 0000000000..c79fc7e29a
--- /dev/null
+++ b/doc/changelog/04-tactics/14012-ltac2-array-init.rst
@@ -0,0 +1,4 @@
+- **Fixed:**
+  Ltac2 ``Array.init`` no longer incurs exponential overhead when used
+  recursively (`#14012 <https://github.com/coq/coq/pull/14012>`_, fixes `#14011
+  <https://github.com/coq/coq/issues/14011>`_, by Jason Gross).
diff --git a/test-suite/bugs/closed/bug_14011.v b/test-suite/bugs/closed/bug_14011.v
new file mode 100644
index 0000000000..c1d3ce7a89
--- /dev/null
+++ b/test-suite/bugs/closed/bug_14011.v
@@ -0,0 +1,23 @@
+(** Test that Ltac2 Array.init doesn't compute the first argument twice, and has the correct asymptotics when nested *)
+Require Import Ltac2.Ltac2.
+Ltac2 Type rec singleton := [ Single (int) | Arr (singleton array) ].
+Ltac2 rec init_rec (n : int) :=
+  match Int.equal n 0 with
+  | true => Single 0
+  | false => Arr (Array.init 1 (fun _ => init_rec (Int.sub n 1)))
+  end.
+Ltac2 rec timing (n : int) :=
+  (match Int.equal n 0 with
+   | true => ()
+   | false => timing (Int.sub n 1)
+   end;
+  Message.print (Message.concat (Message.of_int n) (Message.of_string ": "));
+  let _ := Control.time None (fun _ => init_rec n) in
+  ()).
+(** Should take less than 0.1 seconds if the asymptotics are correct.
+Previous behavior was to take an expected 1 million times the age of
+the universe.  Capping the time at 100 seconds seems like a reasonable
+middle ground between these times, as I expect that compilation of Coq
+itself will not finish in reasonable time if the computer is running
+1000x slower than modern machines. *)
+Timeout 100 Ltac2 Eval timing 100.
diff --git a/user-contrib/Ltac2/Array.v b/user-contrib/Ltac2/Array.v
index 5adba829c5..b5e7f37c9f 100644
--- a/user-contrib/Ltac2/Array.v
+++ b/user-contrib/Ltac2/Array.v
@@ -70,7 +70,7 @@ Ltac2 init (l : int) (f : int->'a) :=
   | true => empty ()
   | false =>
       let arr:=make l (f 0) in
-      init_aux arr 0 (length arr) f;
+      init_aux arr 1 (Int.sub l 1) f;
       arr
   end.