setup CI and tidy to use typos for spellchecking and fix few typos

compiler/rustc_next_trait_solver/src/solve/effect_goals.rs

@@ -73,7 +73,7 @@ where
     /// Register additional assumptions for aliases corresponding to `[const]` item bounds.
     ///
     /// Unlike item bounds, they are not simply implied by the well-formedness of the alias.
-    /// Instead, they only hold if the const conditons on the alias also hold. This is why
+    /// Instead, they only hold if the const conditions on the alias also hold. This is why
     /// we also register the const conditions of the alias after matching the goal against
     /// the assumption.
     fn consider_additional_alias_assumptions(

compiler/rustc_next_trait_solver/src/solve/eval_ctxt/canonical.rs

@@ -88,7 +88,7 @@ where
     /// This takes the `shallow_certainty` which represents whether we're confident
     /// that the final result of the current goal only depends on the nested goals.
     ///
-    /// In case this is `Certainy::Maybe`, there may still be additional nested goals
+    /// In case this is `Certainty::Maybe`, there may still be additional nested goals
     /// or inference constraints required for this candidate to be hold. The candidate
     /// always requires all already added constraints and nested goals.
     #[instrument(level = "trace", skip(self), ret)]

compiler/rustc_next_trait_solver/src/solve/normalizes_to/inherent.rs

@@ -42,7 +42,7 @@ where
         // Right now this includes both the impl and the assoc item where bounds,
         // and I don't think the assoc item where-bounds are allowed to be coinductive.
         //
-        // Projecting to the IAT also "steps out the impl contructor", so we would have
+        // Projecting to the IAT also "steps out the impl constructor", so we would have
         // to be very careful when changing the impl where-clauses to be productive.
         self.add_goals(
             GoalSource::Misc,

compiler/rustc_next_trait_solver/src/solve/trait_goals.rs

@@ -1301,7 +1301,7 @@ where
     D: SolverDelegate<Interner = I>,
     I: Interner,
 {
-    /// FIXME(#57893): For backwards compatability with the old trait solver implementation,
+    /// FIXME(#57893): For backwards compatibility with the old trait solver implementation,
     /// we need to handle overlap between builtin and user-written impls for trait objects.
     ///
     /// This overlap is unsound in general and something which we intend to fix separately.