feat: add Tomas Skrivan's TC resolution improvement

This commit implements the TC resolution improvement suggested by
Tomas at #815.

Closes #815.

src/Lean/Meta/SynthInstance.lean

@@ -422,6 +422,58 @@ def addAnswer (cNode : ConsumerNode) : SynthM Unit := do
       modify fun s => { s with tableEntries := s.tableEntries.insert key newEntry }
       entry.waiters.forM (wakeUp answer)
 
+/--
+  Return `true` if a type of the form `(a_1 : A_1) → ... → (a_n : A_n) → B` has an unused argument `a_i`.
+
+  Remark: This is syntactic check and no reduction is performed.
+-/
+private def hasUnusedArguments : Expr → Bool
+  | Expr.forallE _ d b _ => b.hasLooseBVar 0 || hasUnusedArguments b
+  | _ => false
+
+/--
+  If the type of the metavariable `mvar` has unused argument, return a pair `(α, transformer)`
+  where `α` is a new type without the unused arguments and the `transformer` is a function for coverting a
+  solution with type `α` into a value that can be assigned to `mvar`.
+  Example: suppose `mvar` has type `(a : A) → (b : B a) → (c : C a) → D a c`, the result is the pair
+  ```
+  ((a : A) → (c : C a) → D a c,
+   fun (f : (a : A) → (c : C a) → D a c) (a : A) (b : B a) (c : C a) => f a c
+  )
+  ```
+
+  This method is used to improve the effectiveness of the TC resolution procedure. It was suggested and prototyped by
+  Tomas Skrivan. It improves the support for instances of type `a : A → C` where `a` does not appear in class `C`.
+  When we look for such an instance it is enough to look for an instance `c : C` and then return `fun _ => c`.
+
+  Tomas' approach makes sure that instance of a type like `a : A → C` never gets tabled/cached. More on that later.
+  At the core is the this methos. it takes an expression E and does two things:
+
+  The modification to TC resolution works this way: We are looking for an instance of `E`, if it is tabled
+  just get it as normal, but if not first remove all unused arguments producing `E'`. Now we look up the table again but
+  for `E'`. If it exists, use the transforme to create E. If it does not exists, create a new goal `E'`.
+-/
+private def removeUnusedArguments? (mctx : MetavarContext) (mvar : Expr) : MetaM (Option (Expr × Expr)) :=
+  withMCtx mctx do
+    let mvarType ← instantiateMVars (← inferType mvar)
+    if !hasUnusedArguments mvarType then
+      return none
+    else
+      forallTelescope mvarType fun xs body => do
+        let ys ← xs.foldrM (init := []) fun x ys => do
+          if body.containsFVar x.fvarId! then
+            return x :: ys
+          else if (← ys.anyM fun y => return (← inferType y).containsFVar x.fvarId!) then
+            return x :: ys
+          else
+            return ys
+        let ys := ys.toArray
+        let mvarType' ← mkForallFVars ys body
+        withLocalDeclD `redf mvarType' fun f => do
+          let transformer ← mkLambdaFVars #[f] (← mkLambdaFVars xs (mkAppN f ys))
+          trace[Meta.synthInstance.unusedArgs] "{mvarType}\nhas unused arguments, reduced type{indentExpr mvarType'}\nTransformer{indentExpr transformer}"
+          return some (mvarType', transformer)
+
 /-- Process the next subgoal in the given consumer node. -/
 def consume (cNode : ConsumerNode) : SynthM Unit :=
   match cNode.subgoals with
@@ -431,7 +483,27 @@ def consume (cNode : ConsumerNode) : SynthM Unit :=
      let key ← mkTableKeyFor cNode.mctx mvar
      let entry? ← findEntry? key
      match entry? with
-     | none       => newSubgoal cNode.mctx key mvar waiter
+     | none       =>
+       -- Remove unused arguments and try again, see comment at `removeUnusedArguments?`
+       match (← removeUnusedArguments? cNode.mctx mvar) with
+       | none => newSubgoal cNode.mctx key mvar waiter
+       | some (mvarType', transformer) =>
+         let key' ← mkTableKey cNode.mctx mvarType'
+         match (← findEntry? key') with
+         | none => do
+           let (mctx', mvar') ← withMCtx cNode.mctx do
+             let mvar' ← mkFreshExprMVar mvarType'
+             return (← getMCtx, mvar')
+           newSubgoal mctx' key' mvar' (Waiter.consumerNode { cNode with mctx := mctx', subgoals := mvar'::cNode.subgoals })
+         | some entry' => do
+           let answers' ← entry'.answers.mapM fun a => withMCtx cNode.mctx do
+             let trAnswr := Expr.betaRev transformer #[← instantiateMVars a.result.expr]
+             let trAnswrType ← inferType trAnswr
+             { a with result.expr := trAnswr, resultType := trAnswrType }
+           modify fun s =>
+             { s with
+               resumeStack  := answers'.foldl (fun s answer => s.push (cNode, answer)) s.resumeStack,
+               tableEntries := s.tableEntries.insert key' { entry' with waiters := entry'.waiters.push waiter } }
      | some entry => modify fun s =>
        { s with
          resumeStack  := entry.answers.foldl (fun s answer => s.push (cNode, answer)) s.resumeStack,

tests/lean/run/815.lean

@@ -0,0 +1,47 @@
+def is_smooth {α β} (f : α → β) : Prop := sorry
+
+class IsSmooth {α β} (f : α → β) : Prop where
+  (proof : is_smooth f)
+
+instance identity : IsSmooth fun a : α => a := sorry
+instance const (b : β) : IsSmooth fun a : α => b := sorry
+instance swap (f : α → β → γ) [∀ a, IsSmooth (f a)] : IsSmooth (λ b a => f a b) := sorry
+instance parm (f : α → β → γ) [IsSmooth f] (b : β) : IsSmooth (λ a => f a b) := sorry
+instance comp (f : β → γ) (g : α → β) [IsSmooth f] [IsSmooth g] : IsSmooth (fun a => f (g a)) := sorry
+instance diag (f : β → δ → γ) (g : α → β) (h : α → δ) [IsSmooth f] [∀ b, IsSmooth (f b)] [IsSmooth g] [IsSmooth h] : IsSmooth (λ a => f (g a) (h a)) := sorry
+
+example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] (d : δ) : IsSmooth (λ a => f (g a) d) := by infer_instance
+example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] : IsSmooth (λ a d => f (g a) d) := by infer_instance
+example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] (h : α → α) [IsSmooth h] (d : δ) : IsSmooth (λ a => f (g (h a)) d) := by infer_instance
+example (f : α → β → γ) [∀ a, IsSmooth (f a)] : IsSmooth (λ b a => f a b) := by infer_instance
+example (f : α → β → γ → δ) [∀ a b, IsSmooth (f a b)] : IsSmooth (λ c b a => f a b c) := by infer_instance
+example (f : α → β → γ → δ) [∀ a b, IsSmooth (f a b)] : IsSmooth (λ c a b => f a b c) := by infer_instance
+example (f : α → β → γ → δ → ε) [∀ a b c, IsSmooth (f a b c)] : IsSmooth (λ d a b c => f a b c d) := by infer_instance
+example (f : α → β → γ) [IsSmooth f] (b : β) : IsSmooth (λ a => f a b) := by infer_instance
+example (f : α → β → γ → δ) [IsSmooth f] (b : β) (c : γ) : IsSmooth (λ a => f a b c) := by infer_instance
+example (f : α → β → γ → δ) [IsSmooth f] (b : β) : IsSmooth (λ a c => f a b c) := by infer_instance
+example (f : α → β → γ → δ) [IsSmooth f] (c : γ) : IsSmooth (λ a b => f a b c) := by infer_instance
+example (f : α → β → γ → δ) (b : β) [IsSmooth (λ a => f a b)] : IsSmooth (λ a c => f a b c) := by infer_instance
+example (f : α → β → γ) (g : δ → ε → α) (h : δ → ε → β) [IsSmooth f] [∀ a, IsSmooth (f a)] [IsSmooth g] [IsSmooth h] : IsSmooth (λ x y => f (g x y) (h x y)) := by infer_instance
+example (f : β → δ → γ) (g : α → β) [IsSmooth f] [∀ b, IsSmooth (f b)] [IsSmooth g] (a : α): IsSmooth (λ (h : α → δ) => f (g a) (h a)) := by infer_instance
+example (f : β → δ → γ) (h : α → δ) [IsSmooth f] : IsSmooth (λ (g : α → β) a => f (g a) (h a)) := by infer_instance
+example (f : β → δ → γ) [IsSmooth f] (d : δ) : IsSmooth (λ (g : α → β) a => f (g a) d) := by infer_instance
+example (f : β → γ) (g : β → β) [IsSmooth f] [IsSmooth g] : IsSmooth (fun x => f (g (g x))) := by infer_instance
+example (f : α → β → γ) [∀ a, IsSmooth (f a)] : IsSmooth (λ b a => f a b) := by infer_instance
+example (f : α → β → γ → δ) [∀ a b, IsSmooth (f a b)] : IsSmooth (λ c a b => f a b c) := by infer_instance
+example (f : α → β → γ → δ → ε) [∀ a b c, IsSmooth (f a b c)] : IsSmooth (λ d a b c => f a b c d) := by infer_instance
+example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] (d : δ) : IsSmooth (λ a => f (g a) d) := by infer_instance
+example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] : IsSmooth (λ a d => f (g a) d) := by infer_instance
+example (f : δ → β → γ) [∀ d, IsSmooth (f d)] (g : α → β) [IsSmooth g] : IsSmooth (λ a d => (f d (g a))) := by infer_instance
+
+
+-- Recall Function.comp is not reducible anymore
+instance (f : β → γ) (g : α → β) [IsSmooth f] [IsSmooth g] : IsSmooth (f ∘ g) := by
+  delta Function.comp
+  infer_instance
+
+example (f : β → γ) (g : α → β) [IsSmooth f] [IsSmooth g] : IsSmooth (f ∘ g) := by infer_instance
+
+example (f : β → γ) [IsSmooth f] : IsSmooth λ (g : α → β) => (f ∘ g) := by
+  delta Function.comp
+  infer_instance