HumanEval51 (#186)

* Formalization, Solution and Proof for HumanEval51

* style changes

* /s/no_vowels/NoVowels

Author: mfornet

HumanEvalLean/HumanEval51.lean

@@ -1,5 +1,50 @@
-def remove_vowels : Unit :=
-  ()
+import Std.Data.Iterators.Combinators.FilterMap
+
+def IsSubseq (s₁ : String) (s₂ : String) : Prop :=
+  List.Sublist s₁.toList s₂.toList
+
+def vowels : List Char := ['a', 'e', 'i', 'o', 'u', 'A', 'E', 'I', 'O', 'U']
+
+def NoVowels (s : String) : Prop :=
+  List.all s.toList (· ∉ vowels)
+
+def MaximalFor [LE α] (P : ι → Prop) (f : ι → α) (x : ι) : Prop :=
+  -- Same as MaximalFor in Mathlib
+  P x ∧ ∀ y : ι, P y → f x ≤ f y → f y ≤ f x
+
+def RemoveVowelsIff (solution : String → String) : Prop :=
+    (s x : String) → (solution s = x) → MaximalFor (fun i => NoVowels i ∧ IsSubseq i s) (String.length) x
+
+def removeVowels (s : String) : String :=
+    String.mk (s.toList.filter (· ∉ vowels))
+
+example : removeVowels "abcdef" = "bcdf" := by native_decide
+example : removeVowels "abcdef\nghijklm" = "bcdf\nghjklm" := by native_decide
+example : removeVowels "aaaaa" = "" := by native_decide
+example : removeVowels "aaBAA" = "B" := by native_decide
+example : removeVowels "zbcd" = "zbcd" := by native_decide
+
+theorem IsSubseq.length_le {s t : String} (hst : IsSubseq s t) :
+    s.length ≤ t.length :=
+  List.Sublist.length_le hst
+
+theorem IsSubseq.removeVowels {s t : String} (hst : IsSubseq s t) :
+    IsSubseq (removeVowels s) (removeVowels t) :=
+  hst.filter _
+
+theorem removeVowels_eq_self {s : String} :
+    removeVowels s = s ↔ NoVowels s := by
+  simp [String.ext_iff, NoVowels, removeVowels]
+
+theorem removeVowels_correct : RemoveVowelsIff removeVowels := by
+  simp [RemoveVowelsIff]
+  intro s
+  constructor
+  · simp [NoVowels, removeVowels, IsSubseq]
+  · simp only [and_imp]
+    intro y hnv hss hle
+    rw [← removeVowels_eq_self.2 hnv]
+    exact IsSubseq.length_le (IsSubseq.removeVowels hss)
 
 /-!
 ## Prompt
@@ -49,4 +94,4 @@ def check(candidate):
     assert candidate('ybcd') == 'ybcd'
 
 ```
--/
+-/