Dataset Viewer
id
stringlengths 15
31
| source_file
stringclasses 2
values | construct_type
stringclasses 3
values | construct_name
stringlengths 10
26
| original_code
stringlengths 31
145
| corrupted_code
stringlengths 32
146
| error_info
dict | repair_target
stringlengths 16
127
| domain
stringclasses 2
values | language
stringclasses 1
value | imports
stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
addition_identity_2571
|
manual_examples
|
theorem
|
addition_identity
|
theorem addition_identity (n : ℕ) : n + 0 = n := by simp
|
theorem addition_identity (n : ℕ) : n ++ 0 = n := by simp
|
{
"corrupted_token": " ++ ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " + "
}
|
theorem addition_identity (n : ℕ) : n + 0 = n := by simp
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
complex_re_add_8723
|
manual_examples
|
theorem
|
complex_re_add
|
theorem complex_re_add (z w : ℂ) : (z + w).re = z.re + w.re := by simp
|
theorem complex_re_add (z w : ℝ) : (z + w).re = z.re + w.re := by simp
|
{
"corrupted_token": "ℝ",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "ℂ"
}
|
theorem complex_re_add (z w : ℂ) : (z + w).re = z.re + w.re := by simp
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
double_def_1590
|
manual_examples
|
def
|
double_def
|
def double (n : ℕ) : ℕ := n + n
|
def double (n : Natt) : ℕ := n + n
|
{
"corrupted_token": "Natt",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "ℕ"
}
|
def double (n : ℕ) : ℕ := n + n
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
matrix_scalar_distributive_3902
|
manual_examples
|
theorem
|
matrix_scalar_distributive
|
theorem matrix_scalar_distributive (c : ℂ) (A B : Matrix (Fin 2) (Fin 2) ℂ) : c • (A + B) = c • A + c • B := by simp [smul_add]
|
theorem matrix_scalar_distributive (c : ℂ) (A B : Matrix (Finn 2) (Fin 2) ℂ) : c • (A + B) = c • A + c • B := by simp [smul_add]
|
{
"corrupted_token": "Finn",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "Fin"
}
|
theorem matrix_scalar_distributive (c : ℂ) (A B : Matrix (Fin 2) (Fin 2) ℂ) : c • (A + B) = c • A + c • B := by simp [smul_add]
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
subtraction_self_8199
|
manual_examples
|
theorem
|
subtraction_self
|
theorem subtraction_self (n : ℕ) : n - n = 0 := by simp
|
theorem subtraction_self (n : ℕ) : n - n = 0 := byy simp
|
{
"corrupted_token": "byy",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "by"
}
|
theorem subtraction_self (n : ℕ) : n - n = 0 := by simp
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
complex_zero_mul_8661
|
manual_examples
|
theorem
|
complex_zero_mul
|
theorem complex_zero_mul (z : ℂ) : 0 * z = 0 := by simp
|
theorem complex_zero_mul (z : ℂ) : 0 * z = 0 := by simpp
|
{
"corrupted_token": "simpp",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "simp"
}
|
theorem complex_zero_mul (z : ℂ) : 0 * z = 0 := by simp
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
matrix_mul_one_2955
|
manual_examples
|
theorem
|
matrix_mul_one
|
theorem matrix_mul_one (A : Matrix (Fin 2) (Fin 2) ℂ) : A * 1 = A := by simp
|
theorem matrix_mul_one (A : Matrix (Fin 2) (Fin 2) ℂ) : A ** 1 = A := by simp
|
{
"corrupted_token": " ** ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " * "
}
|
theorem matrix_mul_one (A : Matrix (Fin 2) (Fin 2) ℂ) : A * 1 = A := by simp
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
complex_im_add_7170
|
manual_examples
|
theorem
|
complex_im_add
|
theorem complex_im_add (z w : ℂ) : (z + w).im = z.im + w.im := by simp
|
theorem complex_im_add (z w : ℂ) : (z + w).im = z.im + w.im := byy simp
|
{
"corrupted_token": "byy",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "by"
}
|
theorem complex_im_add (z w : ℂ) : (z + w).im = z.im + w.im := by simp
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
complex_add_conjugate_7145
|
manual_examples
|
theorem
|
complex_add_conjugate
|
theorem complex_add_conjugate (z w : ℂ) : star (z + w) = star z + star w := by rw [star_add]
|
theorem complex_add_conjugate (z w : ℂ) : star (z + w) == star z + star w := by rw [star_add]
|
{
"corrupted_token": " == ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " = "
}
|
theorem complex_add_conjugate (z w : ℂ) : star (z + w) = star z + star w := by rw [star_add]
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
matrix_one_mul_2874
|
manual_examples
|
theorem
|
matrix_one_mul
|
theorem matrix_one_mul (A : Matrix (Fin 2) (Fin 2) ℂ) : 1 * A = A := by simp
|
theorem matrix_one_mul (A : Matrix (Fin 2) (Fin 2) ℂ) : 1 * A = A := byy simp
|
{
"corrupted_token": "byy",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "by"
}
|
theorem matrix_one_mul (A : Matrix (Fin 2) (Fin 2) ℂ) : 1 * A = A := by simp
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
complex_one_mul_8672
|
manual_examples
|
theorem
|
complex_one_mul
|
theorem complex_one_mul (z : ℂ) : 1 * z = z := by simp
|
theorem complex_one_mul (z : ℂ) : 1 * z = z := byy simp
|
{
"corrupted_token": "byy",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "by"
}
|
theorem complex_one_mul (z : ℂ) : 1 * z = z := by simp
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
addition_commutative_6128
|
manual_examples
|
theorem
|
addition_commutative
|
theorem addition_commutative (a b : ℕ) : a + b = b + a := by rw [Nat.add_comm]
|
theorem addition_commutative (a b : Natt) : a + b = b + a := by rw [Nat.add_comm]
|
{
"corrupted_token": "Natt",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "ℕ"
}
|
theorem addition_commutative (a b : ℕ) : a + b = b + a := by rw [Nat.add_comm]
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
multiplication_commutative_6319
|
manual_examples
|
theorem
|
multiplication_commutative
|
theorem multiplication_commutative (a b : ℕ) : a * b = b * a := by rw [Nat.mul_comm]
|
theorem multiplication_commutative (a b : ℕ) : a * b == b * a := by rw [Nat.mul_comm]
|
{
"corrupted_token": " == ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " = "
}
|
theorem multiplication_commutative (a b : ℕ) : a * b = b * a := by rw [Nat.mul_comm]
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
distributive_law_4132
|
manual_examples
|
theorem
|
distributive_law
|
theorem distributive_law (a b c : ℕ) : a * (b + c) = a * b + a * c := by rw [Nat.mul_add]
|
theorem distributive_law (a b c : ℕ) : a * (b ++ c) = a * b + a * c := by rw [Nat.mul_add]
|
{
"corrupted_token": " ++ ",
"corruption_successful": true,
"error_type": "operator_error",
"original_token": " + "
}
|
theorem distributive_law (a b c : ℕ) : a * (b + c) = a * b + a * c := by rw [Nat.mul_add]
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
matrix_neg_neg_9564
|
manual_examples
|
theorem
|
matrix_neg_neg
|
theorem matrix_neg_neg (A : Matrix (Fin 2) (Fin 2) ℂ) : -(-A) = A := by simp
|
theorem matrix_neg_neg (A : Matrix (Finn 2) (Fin 2) ℂ) : -(-A) = A := by simp
|
{
"corrupted_token": "Finn",
"corruption_successful": true,
"error_type": "type_error",
"original_token": "Fin"
}
|
theorem matrix_neg_neg (A : Matrix (Fin 2) (Fin 2) ℂ) : -(-A) = A := by simp
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
square_def_7948
|
manual_examples
|
def
|
square_def
|
def square (n : ℕ) : ℕ := n * n
|
deff square (n : ℕ) : ℕ := n * n
|
{
"corrupted_token": "deff",
"corruption_successful": true,
"error_type": "syntax_error",
"original_token": "def"
}
|
def square (n : ℕ) : ℕ := n * n
|
quantum_information_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
matrix_trace_linear_9001
|
enhanced_povm_theory
|
lemma
|
matrix_trace_linear
|
lemma matrix_trace_linear (A B : Matrix (Fin 2) (Fin 2) ℂ) : Matrix.trace (A + B) = Matrix.trace A + Matrix.trace B := by simp [Matrix.trace_add]
|
lemma matrix_trace_linear (A B : Matrix (Fin 2) (Fin 2) ℂ) : Matrix.trace (A + B) = Matrix.trace A + Matrix.trace B := by simp [Matrix.trace_addd]
|
{
"corrupted_token": "Matrix.trace_addd",
"corruption_successful": true,
"error_type": "name_error",
"original_token": "Matrix.trace_add"
}
|
Matrix.trace_add
|
matrix_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
matrix_trace_zero_9002
|
enhanced_povm_theory
|
lemma
|
matrix_trace_zero
|
lemma matrix_trace_zero : Matrix.trace (0 : Matrix (Fin 2) (Fin 2) ℂ) = 0 := by simp [Matrix.trace_zero]
|
lemma matrix_trace_zero : Matrix.trace (0 : Matrix (Fin 2) (Fin 2) ℂ) = 0 := by simp [Matrix.trace_zeero]
|
{
"corrupted_token": "Matrix.trace_zeero",
"corruption_successful": true,
"error_type": "name_error",
"original_token": "Matrix.trace_zero"
}
|
Matrix.trace_zero
|
matrix_theory
|
lean4
|
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Algebra.Module.Basic
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Basic
|
README.md exists but content is empty.
- Downloads last month
- 46