67

Author: TwoFX

HumanEvalLean/HumanEval67.lean

@@ -1,7 +1,75 @@
 module
+import Std.Data.String.ToNat
 
-def fruit_distribution : Unit :=
-  ()
+def fruitDistribution (s : String) (n : Nat) : Nat :=
+  n - ((s.split ' ').filterMap String.Slice.toNat?).fold (init := 0) (· + ·)
+
+example : fruitDistribution "5 apples and 6 oranges" 19 = 8 := by native_decide
+example : fruitDistribution "5 apples and 6 oranges" 21= 10 := by native_decide
+example : fruitDistribution "0 apples and 1 oranges" 3 = 2 := by native_decide
+example : fruitDistribution "1 apples and 0 oranges" 3 = 2 := by native_decide
+example : fruitDistribution "2 apples and 3 oranges" 100 = 95 := by native_decide
+example : fruitDistribution "2 apples and 3 oranges" 5 = 0 := by native_decide
+example : fruitDistribution "1 apples and 100 oranges" 120 = 19 := by native_decide
+
+inductive Word
+  | number : Nat → Word
+  | nonNumber : (s : String) →
+      (hs : s.isNat = false := by simp [← Bool.not_eq_true, String.isNat_iff]) →
+      (hs' : ' ' ∉ s.toList := by simp) → Word
+
+def Word.toNat? : Word → Option Nat
+  | .number n => some n
+  | .nonNumber .. => none
+
+def Word.toString : Word → String
+  | .number n => ToString.toString n
+  | .nonNumber s _ _ => s
+
+@[simp]
+theorem Word.toNat?_comp_toString : String.toNat? ∘ Word.toString = Word.toNat? := by
+  ext1 w
+  match w with
+  | .number n => simp [Word.toNat?, Word.toString]
+  | .nonNumber s hs hs' => simp [Word.toNat?, Word.toString, hs]
+
+@[simp]
+theorem Word.space_notin_toList_toString {w : Word} : ' ' ∉ w.toString.toList := by
+  match w with
+  | .number n =>
+    simp only [toString, Nat.toString_eq_repr, Nat.toList_repr, ↓Char.isValue]
+    intro h
+    simpa using Nat.isDigit_of_mem_toDigits (by decide) (by decide) h
+  | .nonNumber _ _ hs' => exact hs'
+
+@[simp]
+theorem String.isNat_empty : "".isNat = false := by
+  simp [← Bool.not_eq_true, isNat_iff]
+
+@[simp]
+theorem String.toNat?_empty : "".toNat? = none := by
+  simp
+
+theorem fruitDistribution_intercalate_toString (l : List Word) (n : Nat) :
+    fruitDistribution (" ".intercalate (l.map Word.toString)) n = n - (l.filterMap Word.toNat?).sum := by
+  rw [fruitDistribution]
+  simp +instances only [String.reduceToSingleton]
+  rw [← Std.Iter.foldl_toList, Std.Iter.toList_filterMap]
+  rw [← String.Slice.toNat?_comp_copy, ← List.filterMap_map,
+    String.toList_split_intercalate (by simp), ← List.sum_eq_foldl]
+  simp only [List.map_eq_nil_iff]
+  split <;> simp_all
+
+theorem fruitDistribution_sentence {n₁ n₂ n : Nat} :
+    fruitDistribution (toString n₁ ++ " apples and " ++ toString n₂ ++ " oranges") n = n - n₁ - n₂ := by
+  have := fruitDistribution_intercalate_toString [.number n₁, .nonNumber "apples", .nonNumber "and", .number n₂, .nonNumber "oranges"] n
+  simp only [List.map_cons, Word.toString, Nat.toString_eq_repr, List.map_nil,
+    String.intercalate_cons_cons, String.reduceAppend, String.intercalate_singleton, Word.toNat?,
+    Option.some.injEq, List.filterMap_cons_some, List.filterMap_cons_none, List.filterMap_nil,
+    List.sum_cons, List.sum_nil, Nat.add_zero, ← Nat.sub_sub] at this
+  rw [← this]
+  congr 1
+  simp [← String.toList_inj]
 
 /-!
 ## Prompt
@@ -10,10 +78,10 @@ def fruit_distribution : Unit :=
 
 def fruit_distribution(s,n):
     """
-    In this task, you will be given a string that represents a number of apples and oranges 
-    that are distributed in a basket of fruit this basket contains 
-    apples, oranges, and mango fruits. Given the string that represents the total number of 
-    the oranges and apples and an integer that represent the total number of the fruits 
+    In this task, you will be given a string that represents a number of apples and oranges
+    that are distributed in a basket of fruit this basket contains
+    apples, oranges, and mango fruits. Given the string that represents the total number of
+    the oranges and apples and an integer that represent the total number of the fruits
     in the basket return the number of the mango fruits in the basket.
     for examble:
     fruit_distribution("5 apples and 6 oranges", 19) ->19 - 5 - 6 = 8
@@ -47,4 +115,4 @@ def check(candidate):
     assert candidate("2 apples and 3 oranges",5) == 0
     assert candidate("1 apples and 100 oranges",120) == 19
 ```
--/
+-/