From dee74ca1f90acb076289286f6f69df65e63604ce Mon Sep 17 00:00:00 2001
From: Jonathan Protzenko
Date: Mon, 23 Jan 2023 18:43:45 -0800
Subject: Write a tactic to discharge integer literal proof obligations

---
 backends/lean/primitives.lean | 27 +++++++++++++++++++++++----
 1 file changed, 23 insertions(+), 4 deletions(-)

(limited to 'backends/lean/primitives.lean')

diff --git a/backends/lean/primitives.lean b/backends/lean/primitives.lean
index b68df5f0..d86c0423 100644
--- a/backends/lean/primitives.lean
+++ b/backends/lean/primitives.lean
@@ -83,12 +83,13 @@ def massert (b:Bool) : result Unit :=
 -- and
 -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
 -- which both contain a fair amount of reasoning already!
-def USize.checked_sub (n: USize) (m: Nat): result USize :=
+def USize.checked_sub (n: USize) (m: USize): result USize :=
   -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
-  if USize.toNat n >= m then
+  if n >= m then
     let n' := USize.toNat n
-    let r := USize.ofNatCore (n' - m) (by
-      have h: n' - m <= n' := by
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
         apply Nat.sub_le_of_le_add
         case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
       apply Nat.lt_of_le_of_lt h
@@ -102,6 +103,24 @@ def USize.checked_sub (n: USize) (m: Nat): result USize :=
 def USize.checked_mul (n: USize) (m: USize): result USize := sorry
 def USize.checked_div (n: USize) (m: USize): result USize := sorry
 
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- Test behavior...
 #eval USize.checked_sub 10 20
 #eval USize.checked_sub 20 10
 -- NOTE: compare with concrete behavior here, which I do not think we want
-- 
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