LMQL (Language Model Query Language) from ETH Zurich provides categorical constraint-based generation for LLMs.
Installation
pip install lmql
Core Concepts
LMQL maps to categorical structures:
- Query: Morphism
Context → ConstrainedOutput - Constraints: Subobject classifier restricting output space
- Variables: Typed placeholders forming product types
- Distributions: Probability monad over token sequences
Basic Queries
Simple Constrained Generation
import lmql
@lmql.query
def greet(name):
'''lmql
"Hello, [GREETING]" where len(GREETING) < 50
return GREETING
'''
result = greet("Alice")
Multiple Variables (Product Type)
@lmql.query
def analyze_sentiment():
'''lmql
"Analyze: 'I love this product!'\n"
"Sentiment: [SENTIMENT]\n" where SENTIMENT in ["positive", "negative", "neutral"]
"Confidence: [CONFIDENCE]\n" where CONFIDENCE in ["low", "medium", "high"]
return {"sentiment": SENTIMENT, "confidence": CONFIDENCE}
'''
Constraint Types
Length Constraints
@lmql.query
def constrained_summary(text):
'''lmql
"Summarize in exactly 3 sentences:\n{text}\n"
"Summary: [SUMMARY]" where len(SUMMARY.split('.')) == 3
return SUMMARY
'''
Choice Constraints (Coproduct)
@lmql.query
def classify_intent():
'''lmql
"User: I want to book a flight\n"
"Intent: [INTENT]" where INTENT in [
"booking", "cancellation", "inquiry", "complaint"
]
return INTENT
'''
Regex Constraints
import re
@lmql.query
def extract_email():
'''lmql
"Contact: john.doe@example.com\n"
"Extracted email: [EMAIL]" where re.match(r'^[\w\.-]+@[\w\.-]+\.\w+$', EMAIL)
return EMAIL
'''
Numeric Constraints
@lmql.query
def rate_quality():
'''lmql
"Rate the quality (1-10): [RATING]" where int(RATING) >= 1 and int(RATING) <= 10
return int(RATING)
'''
Logical Operators
Conjunction (AND)
@lmql.query
def structured_response():
'''lmql
"Response: [TEXT]" where (
len(TEXT) >= 50 and
len(TEXT) <= 200 and
TEXT[0].isupper() and
TEXT.endswith('.')
)
return TEXT
'''
Disjunction (OR)
@lmql.query
def flexible_format():
'''lmql
"Answer: [ANSWER]" where (
ANSWER in ["yes", "no"] or
ANSWER.startswith("Maybe")
)
return ANSWER
'''
Negation
@lmql.query
def safe_generation():
'''lmql
"Story: [STORY]" where not any(
word in STORY.lower()
for word in ["violence", "harm", "danger"]
)
return STORY
'''
Distribution Control
Temperature and Sampling
@lmql.query(model="gpt-4", temperature=0.7, max_tokens=100)
def creative_generation():
'''lmql
"Write a creative opening: [OPENING]"
return OPENING
'''
Beam Search
@lmql.query(decoder="beam", n=3)
def multiple_options():
'''lmql
"Suggest: [SUGGESTION]" where len(SUGGESTION) < 50
return SUGGESTION
'''
Structured Output Patterns
JSON Generation
@lmql.query
def generate_json():
'''lmql
"{"
" \"name\": \"[NAME]\"," where len(NAME) < 30
" \"age\": [AGE]," where int(AGE) > 0 and int(AGE) < 150
" \"city\": \"[CITY]\"" where len(CITY) < 50
"}"
return {"name": NAME, "age": int(AGE), "city": CITY}
'''
List Generation
@lmql.query
def generate_list(n: int):
'''lmql
"List {n} items:\n"
for i in range(n):
"- [ITEM]\n" where len(ITEM) < 30
return [ITEM for _ in range(n)]
'''
Categorical Patterns
Functor: Mapping Over Constrained Outputs
def map_constraint(query_fn, transform):
"""Functor mapping over constrained generation."""
@lmql.query
def mapped_query(*args, **kwargs):
result = query_fn(*args, **kwargs)
return transform(result)
return mapped_query
# Usage
upper_greet = map_constraint(greet, str.upper)
Monad: Sequencing Constrained Generations
@lmql.query
def chained_generation(topic):
'''lmql
"Topic: {topic}\n"
"First, generate an outline:\n[OUTLINE]" where len(OUTLINE) < 200
"\nNow expand the first point:\n[EXPANSION]" where len(EXPANSION) < 500
return {"outline": OUTLINE, "expansion": EXPANSION}
'''
Natural Transformation: Constraint Lifting
def lift_to_list(single_query, n):
"""Natural transformation: single → list of n."""
@lmql.query
def list_query(*args, **kwargs):
results = []
for _ in range(n):
result = single_query(*args, **kwargs)
results.append(result)
return results
return list_query
Integration with Python
Type Hints
from typing import Literal
from pydantic import BaseModel
class SentimentResult(BaseModel):
sentiment: Literal["positive", "negative", "neutral"]
score: float
@lmql.query
def typed_sentiment(text: str) -> SentimentResult:
'''lmql
"Analyze: {text}\n"
"Sentiment: [SENT]" where SENT in ["positive", "negative", "neutral"]
"Score: [SCORE]" where float(SCORE) >= 0 and float(SCORE) <= 1
return SentimentResult(sentiment=SENT, score=float(SCORE))
'''
Async Queries
import asyncio
@lmql.query
async def async_classify(texts: list[str]):
'''lmql
results = []
for text in texts:
"Classify '{text}': [LABEL]" where LABEL in ["spam", "ham"]
results.append(LABEL)
return results
'''
# Usage
results = asyncio.run(async_classify(["hello", "buy now!!!"]))
Debugging Constraints
@lmql.query(debug=True)
def debug_query():
'''lmql
"Generate: [OUTPUT]" where (
len(OUTPUT) > 10 and
OUTPUT.startswith("The")
)
return OUTPUT
'''
Model Configuration
import lmql
# OpenAI
lmql.model("openai/gpt-4", api_key="...")
# Anthropic
lmql.model("anthropic/claude-3-opus", api_key="...")
# Local models
lmql.model("local:llama-7b", endpoint="http://localhost:8000")
Categorical Guarantees
LMQL provides these categorical guarantees:
- Constraint Satisfaction: Output always satisfies declared constraints
- Type Safety: Variables respect declared types
- Compositionality: Queries compose preserving constraints
- Determinism: Same constraints yield same output space
- Subobject Classification: Constraints define precise output subsets