53 (#264)

This PR solves problem 53.

Author: datokrat

.claude/skills/restructure-solutions/SKILL.md

@@ -102,8 +102,10 @@ example : solution'' ... := ...
 
 ## Notes
 
-- Use `native_decide` for tests involving iterators or complex computations that don't reduce well
-- Use `decide` for tests involving simple recursive functions or monadic code
+- Use the `cbv` tactic for tests when possible. It might fail to reduce some special constructs.
+- If `cbv` fails, use `decide` (for simple recursive functions or monadic code) or `native_decide`
+  (for tests involving iterators or complex computations that don't reduce well).
+- If you use `cbv`, use `set_option cbv.warning false`.
 - Preserve all comments, attributes, and proof code exactly as they are
 - Helper lemmas that are used across multiple solutions should stay in the first Verification section where they appear
 - Problem number X can be found in `HumanEvalLean/HumanEvalX.lean`

HumanEvalLean/HumanEval53.lean

@@ -1,7 +1,43 @@
 module
 
-def add : Unit :=
-  ()
+set_option cbv.warning false
+
+/-!
+## Implementation
+
+Lean supports addition out of the box, so we just reference to it and to the lemmas verifying its
+behavior.
+-/
+
+/-- info: Nat.add : Nat → Nat → Nat -/
+#guard_msgs in
+#check Nat.add
+
+/-! ## Tests -/
+
+example : Nat.add 0 1 = 1 := by cbv
+example : Nat.add 1 0 = 1 := by cbv
+example : Nat.add 2 3 = 5 := by cbv
+example : Nat.add 5 7 = 12 := by cbv
+example : Nat.add 7 5 = 12 := by cbv
+
+/-! ## Verification -/
+
+/-- info: Nat.add_zero (n : Nat) : n + 0 = n -/
+#guard_msgs in
+#check Nat.add_zero
+
+/-- info: Nat.zero_add (n : Nat) : 0 + n = n -/
+#guard_msgs in
+#check Nat.zero_add
+
+/-- info: Nat.add_assoc (n m k : Nat) : n + m + k = n + (m + k) -/
+#guard_msgs in
+#check Nat.add_assoc
+
+/-- info: Nat.add_comm (n m : Nat) : n + m = m + n -/
+#guard_msgs in
+#check Nat.add_comm
 
 /-!
 ## Prompt
@@ -46,4 +82,4 @@ def check(candidate):
         assert candidate(x, y) == x + y
 
 ```
--/
+-/