Evaluate your pipelines or individual components.
Module answer_exact_match
AnswerExactMatchEvaluator
An answer exact match evaluator class.
The evaluator that checks if the predicted answers matches any of the ground truth answers exactly. The result is a number from 0.0 to 1.0, it represents the proportion of predicted answers that matched one of the ground truth answers. There can be multiple ground truth answers and multiple predicted answers as input.
Usage example:
from haystack.components.evaluators import AnswerExactMatchEvaluator
evaluator = AnswerExactMatchEvaluator()
result = evaluator.run(
ground_truth_answers=["Berlin", "Paris"],
predicted_answers=["Berlin", "Lyon"],
)
print(result["individual_scores"])
# [1, 0]
print(result["score"])
# 0.5
AnswerExactMatchEvaluator.run
@component.output_types(individual_scores=List[int], score=float)
def run(ground_truth_answers: List[str],
predicted_answers: List[str]) -> Dict[str, Any]
Run the AnswerExactMatchEvaluator on the given inputs.
The ground_truth_answers and retrieved_answers must have the same length.
Arguments:
ground_truth_answers: A list of expected answers.predicted_answers: A list of predicted answers.
Returns:
A dictionary with the following outputs:
individual_scores- A list of 0s and 1s, where 1 means that the predicted answer matched one of the ground truth.score- A number from 0.0 to 1.0 that represents the proportion of questions where any predicted answer matched one of the ground truth answers.
Module context_relevance
ContextRelevanceEvaluator
Evaluator that checks if a provided context is relevant to the question.
An LLM separates the answer into multiple statements and checks whether the statement can be inferred from the context or not. The final score for the full answer is a number from 0.0 to 1.0. It represents the proportion of statements that can be inferred from the provided contexts.
Usage example:
from haystack.components.evaluators import ContextRelevanceEvaluator
questions = ["Who created the Python language?"]
contexts = [
[
"Python, created by Guido van Rossum in the late 1980s, is a high-level general-purpose programming language. Its design philosophy emphasizes code readability, and its language constructs aim to help programmers write clear, logical code for both small and large-scale software projects."
],
]
evaluator = ContextRelevanceEvaluator()
result = evaluator.run(questions=questions, contexts=contexts)
print(result["score"])
# 1.0
print(result["individual_scores"])
# [1.0]
print(result["results"])
# [{'statements': ['Python, created by Guido van Rossum in the late 1980s.'], 'statement_scores': [1], 'score': 1.0}]
ContextRelevanceEvaluator.__init__
def __init__(examples: Optional[List[Dict[str, Any]]] = None,
api: str = "openai",
api_key: Secret = Secret.from_env_var("OPENAI_API_KEY"))
Creates an instance of ContextRelevanceEvaluator.
Arguments:
examples: Optional few-shot examples conforming to the expected input and output format of ContextRelevanceEvaluator. Default examples will be used if none are provided. Each example must be a dictionary with keys "inputs" and "outputs". "inputs" must be a dictionary with keys "questions" and "contexts". "outputs" must be a dictionary with "statements" and "statement_scores". Expected format: [{ "inputs": { "questions": "What is the capital of Italy?", "contexts": ["Rome is the capital of Italy."], }, "outputs": { "statements": ["Rome is the capital of Italy."], "statement_scores": [1], }, }]api: The API to use for calling an LLM through a Generator. Supported APIs: "openai".api_key: The API key.
ContextRelevanceEvaluator.run
@component.output_types(individual_scores=List[int],
score=float,
results=List[Dict[str, Any]])
def run(questions: List[str], contexts: List[List[str]]) -> Dict[str, Any]
Run the LLM evaluator.
Arguments:
questions: A list of questions.contexts: A list of lists of contexts. Each list of contexts corresponds to one question.
Returns:
A dictionary with the following outputs:
score: Mean context relevance score over all the provided input questions.individual_scores: A list of context relevance scores for each input question.results: A list of dictionaries withstatementsandstatement_scoresfor each input context.
ContextRelevanceEvaluator.from_dict
@classmethod
def from_dict(cls, data: Dict[str, Any]) -> "ContextRelevanceEvaluator"
Deserialize this component from a dictionary.
Arguments:
data: The dictionary representation of this component.
Returns:
The deserialized component instance.
ContextRelevanceEvaluator.validate_init_parameters
def validate_init_parameters(inputs: List[Tuple[str, Type[List]]],
outputs: List[str], examples: List[Dict[str,
Any]])
Validate the init parameters.
Arguments:
inputs: The inputs to validate.outputs: The outputs to validate.examples: The examples to validate.
Raises:
ValueError: If the inputs are not a list of tuples with a string and a type of list. If the outputs are not a list of strings. If the examples are not a list of dictionaries. If any example does not have keys "inputs" and "outputs" with values that are dictionaries with string keys.
ContextRelevanceEvaluator.prepare_template
def prepare_template() -> str
Prepare the prompt template.
Combine instructions, inputs, outputs, and examples into one prompt template with the following format: Instructions:
Generate the response in JSON format with the following keys: Consider the instructions and the examples below to determine those values.
Examples:
Inputs: Outputs:
Returns:
The prompt template.
ContextRelevanceEvaluator.to_dict
def to_dict() -> Dict[str, Any]
Serialize this component to a dictionary.
Returns:
The serialized component as a dictionary.
ContextRelevanceEvaluator.validate_input_parameters
@staticmethod
def validate_input_parameters(expected: Dict[str, Any],
received: Dict[str, Any]) -> None
Validate the input parameters.
Arguments:
expected: The expected input parameters.received: The received input parameters.
Raises:
ValueError: If not all expected inputs are present in the received inputs If the received inputs are not lists or have different lengths
ContextRelevanceEvaluator.validate_outputs
@staticmethod
def validate_outputs(expected: List[str], received: str) -> None
Validate the output.
Arguments:
expected: Names of expected outputsreceived: Names of received outputs
Raises:
ValueError: If not all expected outputs are present in the received outputs
Module document_map
DocumentMAPEvaluator
A Mean Average Precision (MAP) evaluator for documents.
Evaluator that calculates the mean average precision of the retrieved documents, a metric that measures how high retrieved documents are ranked. Each question can have multiple ground truth documents and multiple retrieved documents.
DocumentMAPEvaluator doesn't normalize its inputs, the DocumentCleaner component
should be used to clean and normalize the documents before passing them to this evaluator.
Usage example:
from haystack import Document
from haystack.components.evaluators import DocumentMAPEvaluator
evaluator = DocumentMAPEvaluator()
result = evaluator.run(
ground_truth_documents=[
[Document(content="France")],
[Document(content="9th century"), Document(content="9th")],
],
retrieved_documents=[
[Document(content="France")],
[Document(content="9th century"), Document(content="10th century"), Document(content="9th")],
],
)
print(result["individual_scores"])
# [1.0, 0.8333333333333333]
print(result["score"])
# 0.9166666666666666
DocumentMAPEvaluator.run
@component.output_types(score=float, individual_scores=List[float])
def run(ground_truth_documents: List[List[Document]],
retrieved_documents: List[List[Document]]) -> Dict[str, Any]
Run the DocumentMAPEvaluator on the given inputs.
All lists must have the same length.
Arguments:
ground_truth_documents: A list of expected documents for each question.retrieved_documents: A list of retrieved documents for each question.
Returns:
A dictionary with the following outputs:
score- The average of calculated scores.individual_scores- A list of numbers from 0.0 to 1.0 that represents how high retrieved documents are ranked.
Module document_mrr
DocumentMRREvaluator
Evaluator that calculates the mean reciprocal rank of the retrieved documents.
MRR measures how high the first retrieved document is ranked. Each question can have multiple ground truth documents and multiple retrieved documents.
DocumentMRREvaluator doesn't normalize its inputs, the DocumentCleaner component
should be used to clean and normalize the documents before passing them to this evaluator.
Usage example:
from haystack import Document
from haystack.components.evaluators import DocumentMRREvaluator
evaluator = DocumentMRREvaluator()
result = evaluator.run(
ground_truth_documents=[
[Document(content="France")],
[Document(content="9th century"), Document(content="9th")],
],
retrieved_documents=[
[Document(content="France")],
[Document(content="9th century"), Document(content="10th century"), Document(content="9th")],
],
)
print(result["individual_scores"])
# [1.0, 1.0]
print(result["score"])
# 1.0
DocumentMRREvaluator.run
@component.output_types(score=float, individual_scores=List[float])
def run(ground_truth_documents: List[List[Document]],
retrieved_documents: List[List[Document]]) -> Dict[str, Any]
Run the DocumentMRREvaluator on the given inputs.
ground_truth_documents and retrieved_documents must have the same length.
Arguments:
ground_truth_documents: A list of expected documents for each question.retrieved_documents: A list of retrieved documents for each question.
Returns:
A dictionary with the following outputs:
score- The average of calculated scores.individual_scores- A list of numbers from 0.0 to 1.0 that represents how high the first retrieved document is ranked.
Module document_recall
RecallMode
Enum for the mode to use for calculating the recall score.
RecallMode.from_str
@staticmethod
def from_str(string: str) -> "RecallMode"
Convert a string to a RecallMode enum.
DocumentRecallEvaluator
Evaluator that calculates the Recall score for a list of documents.
Returns both a list of scores for each question and the average. There can be multiple ground truth documents and multiple predicted documents as input.
Usage example:
from haystack import Document
from haystack.components.evaluators import DocumentRecallEvaluator
evaluator = DocumentRecallEvaluator()
result = evaluator.run(
ground_truth_documents=[
[Document(content="France")],
[Document(content="9th century"), Document(content="9th")],
],
retrieved_documents=[
[Document(content="France")],
[Document(content="9th century"), Document(content="10th century"), Document(content="9th")],
],
)
print(result["individual_scores"])
# [1.0, 1.0]
print(result["score"])
# 1.0
DocumentRecallEvaluator.__init__
def __init__(mode: Union[str, RecallMode] = RecallMode.SINGLE_HIT)
Create a DocumentRecallEvaluator component.
Arguments:
mode: Mode to use for calculating the recall score.
DocumentRecallEvaluator.run
@component.output_types(score=float, individual_scores=List[float])
def run(ground_truth_documents: List[List[Document]],
retrieved_documents: List[List[Document]]) -> Dict[str, Any]
Run the DocumentRecallEvaluator on the given inputs.
ground_truth_documents and retrieved_documents must have the same length.
Arguments:
ground_truth_documents: A list of expected documents for each question.retrieved_documents: A list of retrieved documents for each question. A dictionary with the following outputs:score- The average of calculated scores.invididual_scores- A list of numbers from 0.0 to 1.0 that represents the proportion of matching documents retrieved. If the mode issingle_hit, the individual scores are 0 or 1.
DocumentRecallEvaluator.to_dict
def to_dict() -> Dict[str, Any]
Serializes the component to a dictionary.
Returns:
Dictionary with serialized data.
Module document_recall
RecallMode
Enum for the mode to use for calculating the recall score.
RecallMode.from_str
@staticmethod
def from_str(string: str) -> "RecallMode"
Convert a string to a RecallMode enum.
DocumentRecallEvaluator
Evaluator that calculates the Recall score for a list of documents.
Returns both a list of scores for each question and the average. There can be multiple ground truth documents and multiple predicted documents as input.
Usage example:
from haystack import Document
from haystack.components.evaluators import DocumentRecallEvaluator
evaluator = DocumentRecallEvaluator()
result = evaluator.run(
ground_truth_documents=[
[Document(content="France")],
[Document(content="9th century"), Document(content="9th")],
],
retrieved_documents=[
[Document(content="France")],
[Document(content="9th century"), Document(content="10th century"), Document(content="9th")],
],
)
print(result["individual_scores"])
# [1.0, 1.0]
print(result["score"])
# 1.0
DocumentRecallEvaluator.__init__
def __init__(mode: Union[str, RecallMode] = RecallMode.SINGLE_HIT)
Create a DocumentRecallEvaluator component.
Arguments:
mode: Mode to use for calculating the recall score.
DocumentRecallEvaluator.run
@component.output_types(score=float, individual_scores=List[float])
def run(ground_truth_documents: List[List[Document]],
retrieved_documents: List[List[Document]]) -> Dict[str, Any]
Run the DocumentRecallEvaluator on the given inputs.
ground_truth_documents and retrieved_documents must have the same length.
Arguments:
ground_truth_documents: A list of expected documents for each question.retrieved_documents: A list of retrieved documents for each question. A dictionary with the following outputs:score- The average of calculated scores.invididual_scores- A list of numbers from 0.0 to 1.0 that represents the proportion of matching documents retrieved. If the mode issingle_hit, the individual scores are 0 or 1.
DocumentRecallEvaluator.to_dict
def to_dict() -> Dict[str, Any]
Serializes the component to a dictionary.
Returns:
Dictionary with serialized data.
Module faithfulness
FaithfulnessEvaluator
Evaluator that checks if a generated answer can be inferred from the provided contexts.
An LLM separates the answer into multiple statements and checks whether the statement can be inferred from the context or not. The final score for the full answer is a number from 0.0 to 1.0. It represents the proportion of statements that can be inferred from the provided contexts.
Usage example:
from haystack.components.evaluators import FaithfulnessEvaluator
questions = ["Who created the Python language?"]
contexts = [
[
"Python, created by Guido van Rossum in the late 1980s, is a high-level general-purpose programming language. Its design philosophy emphasizes code readability, and its language constructs aim to help programmers write clear, logical code for both small and large-scale software projects."
],
]
predicted_answers = ["Python is a high-level general-purpose programming language that was created by George Lucas."]
evaluator = FaithfulnessEvaluator()
result = evaluator.run(questions=questions, contexts=contexts, predicted_answers=predicted_answers)
print(result["individual_scores"])
# [0.5]
print(result["score"])
# 0.5
print(result["results"])
# [{'statements': ['Python is a high-level general-purpose programming language.',
'Python was created by George Lucas.'], 'statement_scores': [1, 0], 'score': 0.5}]
FaithfulnessEvaluator.__init__
def __init__(examples: Optional[List[Dict[str, Any]]] = None,
api: str = "openai",
api_key: Secret = Secret.from_env_var("OPENAI_API_KEY"))
Creates an instance of FaithfulnessEvaluator.
Arguments:
examples: Optional few-shot examples conforming to the expected input and output format of FaithfulnessEvaluator. Default examples will be used if none are provided. Each example must be a dictionary with keys "inputs" and "outputs". "inputs" must be a dictionary with keys "questions", "contexts", and "predicted_answers". "outputs" must be a dictionary with "statements" and "statement_scores". Expected format: [{ "inputs": { "questions": "What is the capital of Italy?", "contexts": ["Rome is the capital of Italy."], "predicted_answers": "Rome is the capital of Italy with more than 4 million inhabitants.", }, "outputs": { "statements": ["Rome is the capital of Italy.", "Rome has more than 4 million inhabitants."], "statement_scores": [1, 0], }, }]api: The API to use for calling an LLM through a Generator. Supported APIs: "openai".api_key: The API key.
FaithfulnessEvaluator.run
@component.output_types(individual_scores=List[int],
score=float,
results=List[Dict[str, Any]])
def run(questions: List[str], contexts: List[List[str]],
predicted_answers: List[str]) -> Dict[str, Any]
Run the LLM evaluator.
Arguments:
questions: A list of questions.contexts: A nested list of contexts that correspond to the questions.predicted_answers: A list of predicted answers.
Returns:
A dictionary with the following outputs:
score: Mean faithfulness score over all the provided input answers.individual_scores: A list of faithfulness scores for each input answer.results: A list of dictionaries withstatementsandstatement_scoresfor each input answer.
FaithfulnessEvaluator.from_dict
@classmethod
def from_dict(cls, data: Dict[str, Any]) -> "FaithfulnessEvaluator"
Deserialize this component from a dictionary.
Arguments:
data: The dictionary representation of this component.
Returns:
The deserialized component instance.
FaithfulnessEvaluator.validate_init_parameters
def validate_init_parameters(inputs: List[Tuple[str, Type[List]]],
outputs: List[str], examples: List[Dict[str,
Any]])
Validate the init parameters.
Arguments:
inputs: The inputs to validate.outputs: The outputs to validate.examples: The examples to validate.
Raises:
ValueError: If the inputs are not a list of tuples with a string and a type of list. If the outputs are not a list of strings. If the examples are not a list of dictionaries. If any example does not have keys "inputs" and "outputs" with values that are dictionaries with string keys.
FaithfulnessEvaluator.prepare_template
def prepare_template() -> str
Prepare the prompt template.
Combine instructions, inputs, outputs, and examples into one prompt template with the following format: Instructions:
Generate the response in JSON format with the following keys: Consider the instructions and the examples below to determine those values.
Examples:
Inputs: Outputs:
Returns:
The prompt template.
FaithfulnessEvaluator.to_dict
def to_dict() -> Dict[str, Any]
Serialize this component to a dictionary.
Returns:
The serialized component as a dictionary.
FaithfulnessEvaluator.validate_input_parameters
@staticmethod
def validate_input_parameters(expected: Dict[str, Any],
received: Dict[str, Any]) -> None
Validate the input parameters.
Arguments:
expected: The expected input parameters.received: The received input parameters.
Raises:
ValueError: If not all expected inputs are present in the received inputs If the received inputs are not lists or have different lengths
FaithfulnessEvaluator.validate_outputs
@staticmethod
def validate_outputs(expected: List[str], received: str) -> None
Validate the output.
Arguments:
expected: Names of expected outputsreceived: Names of received outputs
Raises:
ValueError: If not all expected outputs are present in the received outputs
Module llm_evaluator
LLMEvaluator
Uses an LLM to evaluate inputs based on a prompt containing instructions and examples.
The default API requires an OpenAI API key to be provided as an environment variable "OPENAI_API_KEY".
The inputs are lists that are user-defined depending on the desired metric.
The output is a dictionary with a key results containing a list of evaluation results.
Each result is a dictionary with user-defined keys and values of either 0 for FALSE or 1 for TRUE respectively.
Usage example:
from typing import List
from haystack.components.evaluators import LLMEvaluator
evaluator = LLMEvaluator(
instructions="Is this answer problematic for children?",
inputs=[("predicted_answers", List[str])],
outputs=["score"],
examples=[
{"inputs": {"predicted_answers": "Damn, this is straight outta hell!!!"}, "outputs": {"score": 1}},
{"inputs": {"predicted_answers": "Football is the most popular sport."}, "outputs": {"score": 0}},
],
)
predicted_answers = [
"Football is the most popular sport with around 4 billion followers worldwide",
"Python language was created by Guido van Rossum.",
]
results = evaluator.run(predicted_answers=predicted_answers)
print(results)
# {'results': [{'score': 0}, {'score': 0}]}
LLMEvaluator.__init__
def __init__(instructions: str,
inputs: List[Tuple[str, Type[List]]],
outputs: List[str],
examples: List[Dict[str, Any]],
*,
api: str = "openai",
api_key: Secret = Secret.from_env_var("OPENAI_API_KEY"))
Creates an instance of LLMEvaluator.
Arguments:
instructions: The prompt instructions to use for evaluation. Should be a question about the inputs that can be answered with yes or no.inputs: The inputs that the component expects as incoming connections and that it evaluates. Each input is a tuple of an input name and input type. Input types must be lists.outputs: Output names of the evaluation results. They correspond to keys in the output dictionary.examples: Few-shot examples conforming to the expected input and output format as defined in theinputsandoutputsparameters. Each example is a dictionary with keys "inputs" and "outputs" They contain the input and output as dictionaries respectively.api: The API to use for calling an LLM through a Generator. Supported APIs: "openai".api_key: The API key.
LLMEvaluator.validate_init_parameters
def validate_init_parameters(inputs: List[Tuple[str, Type[List]]],
outputs: List[str], examples: List[Dict[str,
Any]])
Validate the init parameters.
Arguments:
inputs: The inputs to validate.outputs: The outputs to validate.examples: The examples to validate.
Raises:
ValueError: If the inputs are not a list of tuples with a string and a type of list. If the outputs are not a list of strings. If the examples are not a list of dictionaries. If any example does not have keys "inputs" and "outputs" with values that are dictionaries with string keys.
LLMEvaluator.run
@component.output_types(results=List[Dict[str, Any]])
def run(**inputs) -> Dict[str, Any]
Run the LLM evaluator.
Arguments:
inputs: The input values to evaluate. The keys are the input names and the values are lists of input values.
Returns:
A dictionary with a single results entry that contains a list of results.
Each result is a dictionary containing the keys as defined in the outputs parameter of the LLMEvaluator
and the evaluation results as the values.
LLMEvaluator.prepare_template
def prepare_template() -> str
Prepare the prompt template.
Combine instructions, inputs, outputs, and examples into one prompt template with the following format: Instructions:
Generate the response in JSON format with the following keys: Consider the instructions and the examples below to determine those values.
Examples:
Inputs: Outputs:
Returns:
The prompt template.
LLMEvaluator.to_dict
def to_dict() -> Dict[str, Any]
Serialize this component to a dictionary.
Returns:
The serialized component as a dictionary.
LLMEvaluator.from_dict
@classmethod
def from_dict(cls, data: Dict[str, Any]) -> "LLMEvaluator"
Deserialize this component from a dictionary.
Arguments:
data: The dictionary representation of this component.
Returns:
The deserialized component instance.
LLMEvaluator.validate_input_parameters
@staticmethod
def validate_input_parameters(expected: Dict[str, Any],
received: Dict[str, Any]) -> None
Validate the input parameters.
Arguments:
expected: The expected input parameters.received: The received input parameters.
Raises:
ValueError: If not all expected inputs are present in the received inputs If the received inputs are not lists or have different lengths
LLMEvaluator.validate_outputs
@staticmethod
def validate_outputs(expected: List[str], received: str) -> None
Validate the output.
Arguments:
expected: Names of expected outputsreceived: Names of received outputs
Raises:
ValueError: If not all expected outputs are present in the received outputs
Module sas_evaluator
SASEvaluator
SASEvaluator computes the Semantic Answer Similarity (SAS) between a list of predictions and a list of ground truths.
It's usually used in Retrieval Augmented Generation (RAG) pipelines to evaluate the quality of the generated answers.
The SAS is computed using a pre-trained model from the Hugging Face model hub. The model can be either a
Bi-Encoder or a Cross-Encoder. The choice of the model is based on the model parameter.
Usage example:
from haystack.components.evaluators.sas_evaluator import SASEvaluator
evaluator = SASEvaluator(model="cross-encoder/ms-marco-MiniLM-L-6-v2")
evaluator.warm_up()
ground_truths = [
"A construction budget of US $2.3 billion",
"The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
"The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
]
predictions = [
"A construction budget of US $2.3 billion",
"The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
"The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
]
result = evaluator.run(
ground_truths_answers=ground_truths, predicted_answers=predictions
)
print(result["score"])
# 0.9999673763910929
print(result["individual_scores"])
# [0.9999765157699585, 0.999968409538269, 0.9999572038650513]
SASEvaluator.__init__
def __init__(
model: str = "sentence-transformers/paraphrase-multilingual-mpnet-base-v2",
batch_size: int = 32,
device: Optional[ComponentDevice] = None,
token: Secret = Secret.from_env_var("HF_API_TOKEN", strict=False))
Creates a new instance of SASEvaluator.
Arguments:
model: SentenceTransformers semantic textual similarity model, should be path or string pointing to a downloadable model.batch_size: Number of prediction-label pairs to encode at once.device: The device on which the model is loaded. IfNone, the default device is automatically selected.token: The Hugging Face token for HTTP bearer authorization. You can find your HF token in your account settings
SASEvaluator.to_dict
def to_dict() -> Dict[str, Any]
Serialize this component to a dictionary.
Returns:
The serialized component as a dictionary.
SASEvaluator.from_dict
@classmethod
def from_dict(cls, data: Dict[str, Any]) -> "SASEvaluator"
Deserialize this component from a dictionary.
Arguments:
data: The dictionary representation of this component.
Returns:
The deserialized component instance.
SASEvaluator.warm_up
def warm_up()
Initializes the component.
SASEvaluator.run
@component.output_types(score=float, individual_scores=List[float])
def run(ground_truth_answers: List[str],
predicted_answers: List[str]) -> Dict[str, Any]
SASEvaluator component run method.
Run the SASEvaluator to compute the Semantic Answer Similarity (SAS) between a list of predicted answers and a list of ground truth answers. Both must be list of strings of same length.
Arguments:
ground_truth_answers: A list of expected answers for each question.predicted_answers: A list of generated answers for each question.
Returns:
A dictionary with the following outputs:
score: Mean SAS score over all the predictions/ground-truth pairs.individual_scores: A list of similarity scores for each prediction/ground-truth pair.