From 47fe6a8bdda94021d6a9820597190ed6163347b3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?S=C3=A9bastien=20Michelland?=
 <sebastien.michelland@protonmail.com>
Date: Mon, 18 Jul 2022 17:38:35 +0100
Subject: [PATCH] very basic attempt at generalizing monad arguments

---
 HBind/ElabHdo.lean | 33 ++++++++++++++++++++---------
 Main.lean          | 53 ++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 76 insertions(+), 10 deletions(-)

diff --git a/HBind/ElabHdo.lean b/HBind/ElabHdo.lean
index c9ccd55..436347a 100644
--- a/HBind/ElabHdo.lean
+++ b/HBind/ElabHdo.lean
@@ -126,17 +126,30 @@ private partial def extractBind (expectedType? : Option Expr) : TermElabM Extrac
   | some r => return r
   | none   => throwError "invalid 'do' notation, expected type is not a monad application{indentExpr expectedType}\nYou can use the `do` notation in pure code by writing `Id.run do` instead of `do`, where `Id` is the identity monad."
 
--- TODO: Update generalizeBindUniverse to support monads applied to arguments
 private def generalizeBindUniverse (bindInfo: ExtractMonadResult): TermElabM ExtractMonadResult := do
-  match bindInfo.m with
-  | .const name levels => do
-    trace[Elab.do] s!"Found monad constant {name} with levels {levels}"
-    let gm ← mkConstWithLevelParams name
-    trace[Elab.do] s!"Generalizing into {gm}"
-    return { bindInfo with m := gm }
-  | _ =>
-    trace[Elab.do] s!"Failed to generalize levels for monad: {bindInfo.m}"
-    return bindInfo
+  let rec genAppliedConst: Expr → TermElabM Expr
+    | .const name levels => do
+      trace[Elab.do] s!"Found monad constant {name} with levels {levels}"
+      let gm ← mkConstWithLevelParams name
+      trace[Elab.do] s!"Generalizing {name} into {gm}"
+      return gm
+    | .app func arg => do
+      -- TODO: Simply erasing the universe levels of the argument is fragile
+      let arg: TermElabM Expr :=
+        match arg with
+        | .const name _ => do
+          let e ← mkConstWithFreshMVarLevels name
+          trace[Elab.do] s!"Generalizing {arg} into {e}"
+          return e
+        | e => do
+          return e
+      mkAppM' (← genAppliedConst func) #[← arg]
+    | e => do
+      trace[Elab.do] s!"Failed to generalize levels for monad: {bindInfo.m}"
+      return e
+  let m ← genAppliedConst bindInfo.m
+  trace[Elab.do] s!"Final monad: {m}"
+  return { bindInfo with m := m }
 
 namespace HDo
 
diff --git a/Main.lean b/Main.lean
index 8645d33..9a77b62 100644
--- a/Main.lean
+++ b/Main.lean
@@ -64,3 +64,56 @@ def test_IO: IO Unit := hdo
   IO.println "hBind"
   return ()
 #print test_IO
+
+--== Tests with a custom monad ==============================================--
+
+-- We have to decouple the universes of the parameter `E: Type u → Type v` from
+-- those of `R: Type w` since the latter is going to vary, but not the former
+inductive ITree (E: Type u → Type v) (R: Type w): Type _ :=
+  | Ret (r: R)
+  | Vis {T: Type _} (e: E T) (k: T → ITree E R)
+
+namespace ITree
+def ITree.pure (r: R): ITree E R :=
+  Ret r
+def ITree.bind (t: ITree E T) (k: T → ITree E R) :=
+  match t with
+  | Ret r => k r
+  | Vis e kt => Vis e (fun x => bind (kt x) k)
+
+instance: Monad (ITree E) where
+  pure := ITree.pure
+  bind := ITree.bind
+
+instance: HBind (ITree E) (ITree E) where
+  hBind {R₁: Type _} {R₂: Type _} (t: ITree E R₁) (k: R₁ → ITree E R₂):
+    ITree E R₂ := ITree.bind t k
+
+inductive PVoid: Type u → Type v :=
+
+inductive E00 {α: Type _} {β: Type}: Type → Type :=
+  | getNat: (n: Nat) → E00 Nat
+
+inductive E01: Type → Type 1 :=
+  | call: {α β: Type} → (f: α → β) → (x: α) → E01 β
+
+inductive E11: Type 1 → Type 1 :=
+  | mkConst: {R: Type} → (x: R) → E11 (ITree PVoid.{0,0} R)
+  | trigger: {E: Type → Type} → {T: Type} → (e: E T) → E11 (ITree E T)
+
+inductive Euv: Type u → Type _ :=
+  | run: {E: Type u → Type v} → {R: Type u} → (t: ITree E R) → Euv R
+
+example: ITree PVoid Nat :=
+  HBind.hBind (m := ITree PVoid) getD0 fun _ =>
+  HBind.hBind (m := ITree PVoid) getD1 fun _ =>
+  pure 0
+
+example: ITree PVoid Nat := hdo
+  let _ ← getD0
+  let _ ← getDx.{4}
+  let _ ← getD1
+  pure 0
+
+example: ITree PVoid (ITree PVoid Nat) := hdo
+  pure (.Ret 0)