From 3afddd5749dbd9c432543db5d93df882d88893f0 Mon Sep 17 00:00:00 2001
From: Julia Markus Himmel <2065352+TwoFX@users.noreply.github.com>
Date: Mon, 23 Mar 2026 14:54:42 +0000
Subject: [PATCH] 18

---
 HumanEvalLean/HumanEval18.lean | 46 +++++++++++++++++++++++++++++++---
 1 file changed, 43 insertions(+), 3 deletions(-)

diff --git a/HumanEvalLean/HumanEval18.lean b/HumanEvalLean/HumanEval18.lean
index fdcd12e..8ba5d35 100644
--- a/HumanEvalLean/HumanEval18.lean
+++ b/HumanEvalLean/HumanEval18.lean
@@ -1,7 +1,47 @@
 module
 
-def how_many_times : Unit :=
-  ()
+-- This compiles to a tight loop calling `memcpy` a bunch of times
+def howManyTimes (string substring : String) : Nat :=
+  string.positions.filter (fun p => (string.sliceFrom p.1).startsWith substring) |>.length
+
+example : howManyTimes "" "a" = 0 := by native_decide
+example : howManyTimes "aaa" "a" = 3 := by native_decide
+example : howManyTimes "aaaa" "aa" = 3 := by native_decide
+example : howManyTimes "xyxyxyx" "x" = 4 := by native_decide
+example : howManyTimes "cacacacac" "cac" = 4 := by native_decide
+example : howManyTimes "john doe" "john" = 1 := by native_decide
+
+def howManyTimesSpec [DecidableEq α] (string substring : List α) : Nat :=
+  ((0...=string.length).toList.filter (fun i => (string.drop i).take substring.length = substring)).length
+
+theorem howManyTimes_eq {string substring : String} (h : substring ≠ "") :
+    howManyTimes string substring = howManyTimesSpec string.toList substring.toList := by
+  simp only [howManyTimes, ne_eq,
+    ← Std.Iter.length_toList_eq_length, Std.Iter.toList_filter, String.toList_positions,
+    howManyTimesSpec, String.length_toList, Nat.zero_le, Nat.toList_rcc_eq_append,
+    List.filter_append, List.filter_cons, decide_eq_true_eq, List.filter_nil, List.length_append]
+  rw [if_neg (by simpa [← String.length_toList])]
+  simp only [List.length_nil, Nat.add_zero]
+  suffices ∀ (p : string.Pos) (t₁ t₂ : String), p.Splits t₁ t₂ →
+      (List.filter (fun p => (string.sliceFrom p.val).startsWith substring)
+        (String.Model.positionsFrom p)).length =
+      (List.filter (fun i => decide (List.take substring.length (List.drop i string.toList) = substring.toList))
+        (t₁.length...string.length).toList).length by
+    simpa using this string.startPos "" string
+  intro p t₁ t₂ ht
+  induction p using String.Pos.next_induction generalizing t₁ t₂ with
+  | next p hp ih =>
+    obtain ⟨t₂, rfl⟩ := ht.exists_eq_singleton_append hp
+    rw [String.Model.positionsFrom_eq_cons hp, List.filter_cons, Nat.toList_rco_eq_cons]
+    · rw [List.filter_cons, apply_ite List.length, apply_ite List.length]
+      simp only [String.Slice.startsWith_string_iff, ne_eq, List.length_cons, ih _ _ ht.next,
+        String.append_singleton, String.length_push, decide_eq_true_eq]
+      congr
+      simp [ht.eq_append, ht.copy_sliceFrom_eq, List.prefix_iff_eq_take, eq_comm]
+    · have := congrArg String.length ht.eq_append
+      simp at this
+      omega
+  | endPos => simp_all
 
 /-!
 ## Prompt
@@ -49,4 +89,4 @@ def check(candidate):
     assert candidate('cacacacac', 'cac') == 4
     assert candidate('john doe', 'john') == 1
 ```
--/
\ No newline at end of file
+-/