diff --git a/compiler/rustc_const_eval/src/transform/check_consts/qualifs.rs b/compiler/rustc_const_eval/src/transform/check_consts/qualifs.rs
index 015a4aa94cd42..963654e466b58 100644
--- a/compiler/rustc_const_eval/src/transform/check_consts/qualifs.rs
+++ b/compiler/rustc_const_eval/src/transform/check_consts/qualifs.rs
@@ -7,6 +7,7 @@ use rustc_hir::LangItem;
 use rustc_infer::infer::TyCtxtInferExt;
 use rustc_middle::mir;
 use rustc_middle::mir::*;
+use rustc_middle::ty::TypeVisitableExt;
 use rustc_middle::ty::{self, subst::SubstsRef, AdtDef, Ty};
 use rustc_trait_selection::traits::{
     self, ImplSource, Obligation, ObligationCause, ObligationCtxt, SelectionContext,
@@ -91,7 +92,8 @@ impl Qualif for HasMutInterior {
     }
 
     fn in_any_value_of_ty<'tcx>(cx: &ConstCx<'_, 'tcx>, ty: Ty<'tcx>) -> bool {
-        !ty.is_freeze(cx.tcx, cx.param_env)
+        // Pessimistically assume opaque types are `!Freeze`
+        ty.has_opaque_types() || !ty.is_freeze(cx.tcx, cx.param_env)
     }
 
     fn in_adt_inherently<'tcx>(
diff --git a/compiler/rustc_mir_transform/src/lib.rs b/compiler/rustc_mir_transform/src/lib.rs
index fa8257cf9849c..e703b2f518e6a 100644
--- a/compiler/rustc_mir_transform/src/lib.rs
+++ b/compiler/rustc_mir_transform/src/lib.rs
@@ -19,6 +19,7 @@ extern crate tracing;
 #[macro_use]
 extern crate rustc_middle;
 
+use hir::ConstContext;
 use required_consts::RequiredConstsVisitor;
 use rustc_const_eval::util;
 use rustc_data_structures::fx::FxIndexSet;
@@ -231,8 +232,12 @@ fn mir_const_qualif(tcx: TyCtxt<'_>, def: LocalDefId) -> ConstQualifs {
     let const_kind = tcx.hir().body_const_context(def);
 
     // No need to const-check a non-const `fn`.
-    if const_kind.is_none() {
-        return Default::default();
+    match const_kind {
+        Some(ConstContext::Const | ConstContext::Static(_)) | Some(ConstContext::ConstFn) => {}
+        None => span_bug!(
+            tcx.def_span(def),
+            "`mir_const_qualif` should only be called on const fns and const items"
+        ),
     }
 
     // N.B., this `borrow()` is guaranteed to be valid (i.e., the value
@@ -297,7 +302,21 @@ fn mir_promoted(
     // Ensure that we compute the `mir_const_qualif` for constants at
     // this point, before we steal the mir-const result.
     // Also this means promotion can rely on all const checks having been done.
-    let const_qualifs = tcx.mir_const_qualif(def);
+
+    let const_qualifs = match tcx.def_kind(def) {
+        DefKind::Fn | DefKind::AssocFn | DefKind::Closure
+            if tcx.constness(def) == hir::Constness::Const
+                || tcx.is_const_default_method(def.to_def_id()) =>
+        {
+            tcx.mir_const_qualif(def)
+        }
+        DefKind::AssocConst
+        | DefKind::Const
+        | DefKind::Static(_)
+        | DefKind::InlineConst
+        | DefKind::AnonConst => tcx.mir_const_qualif(def),
+        _ => ConstQualifs::default(),
+    };
     let mut body = tcx.mir_const(def).steal();
     if let Some(error_reported) = const_qualifs.tainted_by_errors {
         body.tainted_by_errors = Some(error_reported);
diff --git a/tests/ui/consts/const-fn-cycle-tait.rs b/tests/ui/consts/const-fn-cycle-tait.rs
new file mode 100644
index 0000000000000..f8a63ea00c961
--- /dev/null
+++ b/tests/ui/consts/const-fn-cycle-tait.rs
@@ -0,0 +1,17 @@
+#![feature(type_alias_impl_trait)]
+
+//! Test that we pessimistically assume the `Drop` impl of
+//! a hidden type is not const.
+
+pub struct Parser<H>(H);
+
+type Tait = impl Sized;
+
+const fn constrain() -> Tait {}
+
+pub const fn take(_: Tait) {}
+//~^ ERROR: destructor of `Tait` cannot be evaluated at compile-time
+
+fn main() {
+    println!("Hello, world!");
+}
diff --git a/tests/ui/consts/const-fn-cycle-tait.stderr b/tests/ui/consts/const-fn-cycle-tait.stderr
new file mode 100644
index 0000000000000..3e025178a25bc
--- /dev/null
+++ b/tests/ui/consts/const-fn-cycle-tait.stderr
@@ -0,0 +1,11 @@
+error[E0493]: destructor of `Tait` cannot be evaluated at compile-time
+  --> $DIR/const-fn-cycle-tait.rs:12:19
+   |
+LL | pub const fn take(_: Tait) {}
+   |                   ^         - value is dropped here
+   |                   |
+   |                   the destructor for this type cannot be evaluated in constant functions
+
+error: aborting due to previous error
+
+For more information about this error, try `rustc --explain E0493`.
diff --git a/tests/ui/consts/const-fn-cycle.rs b/tests/ui/consts/const-fn-cycle.rs
new file mode 100644
index 0000000000000..033f9f0a1a735
--- /dev/null
+++ b/tests/ui/consts/const-fn-cycle.rs
@@ -0,0 +1,29 @@
+//! Discovered in https://github.com/rust-lang/rust/issues/112602.
+//! This caused a cycle error, which made no sense.
+//! Removing the `const` part of the `many` function would make the
+//! test pass again.
+//! The issue was that we were running const qualif checks on
+//! `const fn`s, but never using them. During const qualif checks we tend
+//! to end up revealing opaque types (the RPIT in `many`'s return type),
+//! which can quickly lead to cycles.
+
+// check-pass
+
+pub struct Parser<H>(H);
+
+impl<H, T> Parser<H>
+where
+    H: for<'a> Fn(&'a str) -> T,
+{
+    pub const fn new(handler: H) -> Parser<H> {
+        Parser(handler)
+    }
+
+    pub const fn many<'s>(&'s self) -> Parser<impl for<'a> Fn(&'a str) -> Vec<T> + 's> {
+        Parser::new(|_| unimplemented!())
+    }
+}
+
+fn main() {
+    println!("Hello, world!");
+}
diff --git a/tests/ui/consts/const-promoted-opaque.atomic.stderr b/tests/ui/consts/const-promoted-opaque.atomic.stderr
new file mode 100644
index 0000000000000..38c3cadab056a
--- /dev/null
+++ b/tests/ui/consts/const-promoted-opaque.atomic.stderr
@@ -0,0 +1,41 @@
+error[E0493]: destructor of `Foo` cannot be evaluated at compile-time
+  --> $DIR/const-promoted-opaque.rs:25:26
+   |
+LL |     let _: &'static _ = &FOO;
+   |                          ^^^ the destructor for this type cannot be evaluated in constants
+...
+LL | };
+   | - value is dropped here
+
+error[E0716]: temporary value dropped while borrowed
+  --> $DIR/const-promoted-opaque.rs:25:26
+   |
+LL |     let _: &'static _ = &FOO;
+   |            ----------    ^^^ creates a temporary value which is freed while still in use
+   |            |
+   |            type annotation requires that borrow lasts for `'static`
+...
+LL | };
+   | - temporary value is freed at the end of this statement
+
+error[E0492]: constants cannot refer to interior mutable data
+  --> $DIR/const-promoted-opaque.rs:30:19
+   |
+LL | const BAZ: &Foo = &FOO;
+   |                   ^^^^ this borrow of an interior mutable value may end up in the final value
+
+error[E0716]: temporary value dropped while borrowed
+  --> $DIR/const-promoted-opaque.rs:34:26
+   |
+LL |     let _: &'static _ = &FOO;
+   |            ----------    ^^^ creates a temporary value which is freed while still in use
+   |            |
+   |            type annotation requires that borrow lasts for `'static`
+LL |
+LL | }
+   | - temporary value is freed at the end of this statement
+
+error: aborting due to 4 previous errors
+
+Some errors have detailed explanations: E0492, E0493, E0716.
+For more information about an error, try `rustc --explain E0492`.
diff --git a/tests/ui/consts/const-promoted-opaque.rs b/tests/ui/consts/const-promoted-opaque.rs
new file mode 100644
index 0000000000000..265cfa44b2f55
--- /dev/null
+++ b/tests/ui/consts/const-promoted-opaque.rs
@@ -0,0 +1,36 @@
+// revisions: string unit atomic
+#![feature(type_alias_impl_trait)]
+
+//! Check that we do not cause cycle errors when trying to
+//! obtain information about interior mutability of an opaque type.
+//! This used to happen, because when the body-analysis failed, we
+//! checked the type instead, but the constant was also defining the
+//! hidden type of the opaque type. Thus we ended up relying on the
+//! result of our analysis to compute the result of our analysis.
+
+//[unit] check-pass
+
+type Foo = impl Sized;
+
+#[cfg(string)]
+const FOO: Foo = String::new();
+
+#[cfg(atomic)]
+const FOO: Foo = std::sync::atomic::AtomicU8::new(42);
+
+#[cfg(unit)]
+const FOO: Foo = ();
+
+const BAR: () = {
+    let _: &'static _ = &FOO;
+    //[string,atomic]~^ ERROR: destructor of `Foo` cannot be evaluated at compile-time
+    //[string,atomic]~| ERROR: temporary value dropped while borrowed
+};
+
+const BAZ: &Foo = &FOO;
+//[string,atomic]~^ ERROR: constants cannot refer to interior mutable data
+
+fn main() {
+    let _: &'static _ = &FOO;
+    //[string,atomic]~^ ERROR: temporary value dropped while borrowed
+}
diff --git a/tests/ui/consts/const-promoted-opaque.string.stderr b/tests/ui/consts/const-promoted-opaque.string.stderr
new file mode 100644
index 0000000000000..38c3cadab056a
--- /dev/null
+++ b/tests/ui/consts/const-promoted-opaque.string.stderr
@@ -0,0 +1,41 @@
+error[E0493]: destructor of `Foo` cannot be evaluated at compile-time
+  --> $DIR/const-promoted-opaque.rs:25:26
+   |
+LL |     let _: &'static _ = &FOO;
+   |                          ^^^ the destructor for this type cannot be evaluated in constants
+...
+LL | };
+   | - value is dropped here
+
+error[E0716]: temporary value dropped while borrowed
+  --> $DIR/const-promoted-opaque.rs:25:26
+   |
+LL |     let _: &'static _ = &FOO;
+   |            ----------    ^^^ creates a temporary value which is freed while still in use
+   |            |
+   |            type annotation requires that borrow lasts for `'static`
+...
+LL | };
+   | - temporary value is freed at the end of this statement
+
+error[E0492]: constants cannot refer to interior mutable data
+  --> $DIR/const-promoted-opaque.rs:30:19
+   |
+LL | const BAZ: &Foo = &FOO;
+   |                   ^^^^ this borrow of an interior mutable value may end up in the final value
+
+error[E0716]: temporary value dropped while borrowed
+  --> $DIR/const-promoted-opaque.rs:34:26
+   |
+LL |     let _: &'static _ = &FOO;
+   |            ----------    ^^^ creates a temporary value which is freed while still in use
+   |            |
+   |            type annotation requires that borrow lasts for `'static`
+LL |
+LL | }
+   | - temporary value is freed at the end of this statement
+
+error: aborting due to 4 previous errors
+
+Some errors have detailed explanations: E0492, E0493, E0716.
+For more information about an error, try `rustc --explain E0492`.