80

Author: TwoFX

HumanEvalLean/HumanEval80.lean

@@ -1,7 +1,77 @@
 module
+import Std.Tactic.Do
+import Std
+import all Init.Data.Range.Polymorphic.UpwardEnumerable -- UpwardEnumerable.least not exposed
 
-def is_happy : Unit :=
-  ()
+open Std Std.Do
+
+def isHappy (s : String) : Bool := Id.run do
+  if s.length < 3 then
+    return false
+
+  let a := s.toList.toArray
+  for h : i in *...a.size - 2 do
+    if a[i] = a[i + 1] ∨ a[i + 1] = a[i + 2] ∨ a[i] = a[i + 2] then
+      return false
+
+  return true
+
+theorem Nat.eq_add_of_toList_rio_eq_append_cons {a : Nat} {pref cur suff}
+    (h : (*...a).toList = pref ++ cur :: suff) :
+    cur = pref.length := by
+  have := Rio.eq_succMany?_of_toList_eq_append_cons h
+  simpa [PRange.UpwardEnumerable.least, PRange.least?] using this
+
+set_option mvcgen.warning false in
+theorem isHappy_iff {s : String} :
+    isHappy s = true ↔ 3 ≤ s.length ∧ (∀ (a b c : Char), [a, b, c] <:+: s.toList → a ≠ b ∧ b ≠ c ∧ a ≠ c) := by
+  generalize hwp : isHappy s = wp
+  apply Id.of_wp_run_eq hwp
+  mvcgen
+  invariants
+  · .withEarlyReturn
+      (fun cur _ => ⌜∀ a b c : Char, [a, b, c] <:+: s.toList.take (cur.pos + 2) → a ≠ b ∧ b ≠ c ∧ a ≠ c⌝)
+      (fun r _ => ⌜r = false ∧ ∃ a b c : Char, [a, b, c] <:+: s.toList ∧ (a = b ∨ b = c ∨ a = c)⌝)
+  next => grind
+  next hsl a pref cur suff h b heq ih =>
+    subst a
+    obtain rfl := Nat.eq_add_of_toList_rio_eq_append_cons h
+    have := congrArg List.length h
+    simp only [List.size_toArray, String.length_toList, Rio.length_toList, Nat.size_rio,
+      List.length_append, List.length_cons, reduceCtorEq, List.Cursor.pos_mk, ne_eq, false_and,
+      Option.some.injEq, Bool.false_eq, true_and, and_self_left, exists_eq_left, false_or] at this ⊢
+    refine ⟨_, _, _, ?_, heq⟩
+    simp only [List.getElem_toArray]
+    rw [List.infix_iff_getElem?]
+    refine ⟨pref.length, ?_⟩
+    simp only [List.length_cons, List.length_nil, Nat.zero_add, Nat.reduceAdd, String.length_toList]
+    exact ⟨by grind, by rintro (_|_|_|i) hi <;> grind⟩
+  next hsl a pref cur suff h b heq ih =>
+    subst a
+    obtain rfl := Nat.eq_add_of_toList_rio_eq_append_cons h
+    have := congrArg List.length h
+    simp only [List.size_toArray, String.length_toList, Std.Rio.length_toList, Nat.size_rio,
+      List.length_append, List.length_cons, List.Cursor.pos_mk, ne_eq, reduceCtorEq, false_and,
+      and_false, exists_const, or_false, List.length_nil, Nat.zero_add, true_and] at this ih ⊢
+    intro a b c
+    rw [List.take_add_one, getElem?_pos _ _ (by simp; omega), Option.toList_some,
+      List.infix_concat_iff, or_imp]
+    refine ⟨?_, ih.2 a b c⟩
+    simp only [List.take_add_one, List.append_assoc]
+    repeat rw [getElem?_pos _ _ (by simp; omega), Option.toList_some]
+    rw [← List.nil_append [a, b, c], List.suffix_append_inj_of_length_eq (by simp)]
+    grind
+  next h a =>
+    simp
+    intro a b c hs
+    have := hs.length_le
+    grind
+  next h a r h₁ h₂ =>
+    subst a
+    simp [h₁] at ⊢ h₂
+    refine ⟨by omega, ?_⟩
+    rwa [Nat.sub_add_cancel (by omega), ← String.length_toList, List.take_length] at h₂
+  next => grind
 
 /-!
 ## Prompt
@@ -29,7 +99,7 @@ def is_happy(s):
       return False
 
     for i in range(len(s) - 2):
-      
+
       if s[i] == s[i+1] or s[i+1] == s[i+2] or s[i] == s[i+2]:
         return False
     return True
@@ -50,4 +120,4 @@ def check(candidate):
     assert candidate("iopaxpoi") == True , "iopaxpoi"
     assert candidate("iopaxioi") == False , "iopaxioi"
 ```
--/
+-/