Code for The $\mathbf{Y}$-Combinator for LLMs:Solving Long-Context Rot with $\lambda$-Calculus: a framework for long-context reasoning that replaces free-form recursive code generation with a typed functional runtime grounded in $\lambda$-calculus.

Direct LLM inference and standard RLM inference are constrained by context windows and can rely on hard-to-predict decomposition strategies. $\lambda$-RLM addresses this by:

• Planning decomposition ahead of execution with a deterministic recursive strategy
• Expressing inference through functional structure, with model calls at local steps and symbolic operators for composition
• Breaking long inputs into manageable chunks that fit within the model context window
• Applying the model only to bounded leaf subproblems and combining intermediate results through structured operators such as SPLIT, MAP, FILTER, REDUCE, CONCAT and CROSS.

From the project root (the directory containing pyproject.toml):

conda create -n lambda-rlm python=3.11 -y
conda activate lambda-rlm

pip install -e .

The project supports multiple API-compatible model providers. For example, you can request a NVIDIA NIM API key or a TOGETHER AI API key to access the available model backends. Set your API key as an environment variable:

export NVIDIA_API_KEY="nvapi-..."

export TOGETHER_API_KEY="tgp_..."

• sniah — Sequential-NIAH examples loaded from the public GitHub JSONL source
• oolong — single-document QA examples loaded from THUDM/LongBench-v2
• browsecomp — multi-document QA examples loaded from THUDM/LongBench-v2
• codeqa — code repository understanding examples loaded from a local JSONL file or from THUDM/LongBench-v2

import os
from rlm import LambdaRLM

document = """
This report discusses the development of a new battery technology.
It covers technical design choices, manufacturing trade-offs, safety concerns,
cost reduction strategies, and future commercialization plans.

One section focuses on performance improvements in energy density.
Another section discusses supply-chain risks and regulatory constraints.
The final section outlines expected market impact and open research questions.
"""

prompt = f"""Context:
{document}

Question: Summarize the main ideas discussed in this document.

Answer:"""

rlm = LambdaRLM(
    backend_kwargs={
        "model_name": "meta/llama-3.3-70b-instruct",
        "api_key": os.environ["NVIDIA_API_KEY"],
        "base_url": "https://integrate.api.nvidia.com/v1",
    }
)

result = rlm.completion(prompt)
print(result.response)

This repository uses upstream Normal RLM components for comparison: https://github.com/alexzhang13/rlm

The upstream code is licensed under the MIT License. See THIRD_PARTY_NOTICES.md for attribution and licensing details.

Key files:

• rlm/core/rlm.py — main REPL-based RLM loop
• rlm/environments/local_repl.py — sandboxed Python REPL execution, context storage, and helper functions
• rlm/utils/parsing.py — parsing of repl code blocks and FINAL markers; formatting of execution output back into the model history
• rlm/clients/openai.py — OpenAI-compatible client used with NVIDIA NIM

• rlm/lambda_rlm.py — LambdaRLM implementation, including task detection, planning, and deterministic execution through $\Phi$

The benchmark entry point is used to run the supported datasets under the same setup and compare behavior, latency and output quality across Normal RLM (rlm) and Lambda-RLM (lambda_rlm).

python benchmarks/benchmark.py --datasets sniah --model meta/llama-3.3-70b-instruct --methods rlm lambda_rlm --n-samples-per-bucket 2 --max-iter 8 --max-depth 2 --context-window 100000 --output-dir ./results/llama-3.3-70b-instruct

Outputs are written to the specified output directory, typically including:

• results.json
• stats.json
• averages.json

python benchmarks/benchmark.py --datasets sniah --model meta/llama-3.3-70b-instruct --methods rlm --n-samples-per-bucket 2 --max-iter 8 --max-depth 2 --context-window 100000 --output-dir ./results/llama-3.3-70b-instruct_rlm

python benchmarks/benchmark.py --datasets sniah --model meta/llama-3.3-70b-instruct --methods lambda_rlm --n-samples-per-bucket 2 --max-iter 8 --max-depth 2 --context-window 100000 --output-dir ./results/llama-3.3-70b-instruct_lambda_rlm