Rework "long type names" printing logic

Make it so more type-system types can be printed in a shortened version (like `Predicate`s).

Centralize printing the information about the "full type name path".

Make the "long type path" for the file where long types are written part of `Diag`, so that it becomes easier to keep track of it, and ensure it will always will be printed out last in the diagnostic by making its addition to the output implicit.

Tweak the shortening of types in "expected/found" labels.

Remove dead file `note.rs`.

compiler/rustc_errors/src/diagnostic.rs

@@ -4,6 +4,7 @@ use std::hash::{Hash, Hasher};
 use std::marker::PhantomData;
 use std::ops::{Deref, DerefMut};
 use std::panic;
+use std::path::PathBuf;
 use std::thread::panicking;
 
 use rustc_data_structures::fx::FxIndexMap;
@@ -301,6 +302,7 @@ pub struct DiagInner {
 
     pub is_lint: Option<IsLint>,
 
+    pub long_ty_path: Option<PathBuf>,
     /// With `-Ztrack_diagnostics` enabled,
     /// we print where in rustc this error was emitted.
     pub(crate) emitted_at: DiagLocation,
@@ -324,6 +326,7 @@ impl DiagInner {
             args: Default::default(),
             sort_span: DUMMY_SP,
             is_lint: None,
+            long_ty_path: None,
             emitted_at: DiagLocation::caller(),
         }
     }
@@ -1293,9 +1296,37 @@ impl<'a, G: EmissionGuarantee> Diag<'a, G> {
     /// `cancel`, etc. Afterwards, `drop` is the only code that will be run on
     /// `self`.
     fn take_diag(&mut self) -> DiagInner {
+        if let Some(path) = &self.long_ty_path {
+            self.note(format!(
+                "the full name for the type has been written to '{}'",
+                path.display()
+            ));
+            self.note("consider using `--verbose` to print the full type name to the console");
+        }
         Box::into_inner(self.diag.take().unwrap())
     }
 
+    /// This method allows us to access the path of the file where "long types" are written to.
+    ///
+    /// When calling `Diag::emit`, as part of that we will check if a `long_ty_path` has been set,
+    /// and if it has been then we add a note mentioning the file where the "long types" were
+    /// written to.
+    ///
+    /// When calling `tcx.short_string()` after a `Diag` is constructed, the preferred way of doing
+    /// so is `tcx.short_string(ty, diag.long_ty_path())`. The diagnostic itself is the one that
+    /// keeps the existence of a "long type" anywhere in the diagnostic, so the note telling the
+    /// user where we wrote the file to is only printed once at most, *and* it makes it much harder
+    /// to forget to set it.
+    ///
+    /// If the diagnostic hasn't been created before a "short ty string" is created, then you should
+    /// ensure that this method is called to set it `*diag.long_ty_path() = path`.
+    ///
+    /// As a rule of thumb, if you see or add at least one `tcx.short_string()` call anywhere, in a
+    /// scope, `diag.long_ty_path()` should be called once somewhere close by.
+    pub fn long_ty_path(&mut self) -> &mut Option<PathBuf> {
+        &mut self.long_ty_path
+    }
+
     /// Most `emit_producing_guarantee` functions use this as a starting point.
     fn emit_producing_nothing(mut self) {
         let diag = self.take_diag();