Cleanup Diverge.lean

1 files changed, 13 insertions, 0 deletions

diff --git a/backends/lean/Base/Primitives.lean b/backends/lean/Base/Primitives.lean
index d6cc0bad..1185a07d 100644
--- a/backends/lean/Base/Primitives.lean
+++ b/backends/lean/Base/Primitives.lean
@@ -94,6 +94,10 @@ instance : Bind Result where
 instance : Pure Result where
   pure := fun x => ret x
 
+@[simp] theorem bind_ret (x : α) (f : α → Result β) : bind (.ret x) f = f x := by simp [bind]
+@[simp] theorem bind_fail (x : Error) (f : α → Result β) : bind (.fail x) f = .fail x := by simp [bind]
+@[simp] theorem bind_div (f : α → Result β) : bind .div f = .div := by simp [bind]
+
 /- CUSTOM-DSL SUPPORT -/
 
 -- Let-binding the Result of a monadic operation is oftentimes not sufficient,
@@ -124,6 +128,15 @@ macro "let" e:term " <-- " f:term : doElem =>
   let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
   .ret r
 
+@[simp] theorem bind_tc_ret (x : α) (f : α → Result β) :
+  (do let y ← .ret x; f y) = f x := by simp [Bind.bind, bind]
+
+@[simp] theorem bind_tc_fail (x : Error) (f : α → Result β) :
+  (do let y ← fail x; f y) = fail x := by simp [Bind.bind, bind]
+
+@[simp] theorem bind_tc_div (f : α → Result β) :
+  (do let y ← div; f y) = div := by simp [Bind.bind, bind]
+
 ----------------------
 -- MACHINE INTEGERS --
 ----------------------