# SPL: Orchestrating Workflows with Declarative Deterministic-Probabilistic Composition

arXiv: https://arxiv.org/abs/2607.07727 · HTML: https://mlsanity.com/paper/2607.07727/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 18 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [LLM+P: Empowering Large Language Models with Optimal Planning Proficiency](https://mlsanity.com/paper/2304.11477/) (2023)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [HyperTree Proof Search for Neural Theorem Proving](https://mlsanity.com/paper/2205.11491/) (2022)
- [Blueprint First, Model Second: A Framework for Deterministic LLM Workflow](https://mlsanity.com/paper/2508.02721/) (2025)
- [MCP-Solver: Integrating Language Models with Constraint Programming Systems](https://mlsanity.com/paper/2501.00539/) (2024)
- [Open Agent Specification (Agent Spec): A Unified Representation for AI Agents](https://mlsanity.com/paper/2510.04173/) (2025)
- [Compiled AI: Deterministic Code Generation for LLM-Based Workflow Automation](https://mlsanity.com/paper/2604.05150/) (2026)
- [Agentics 2.0: Logical Transduction Algebra for Agentic Data Workflows](https://mlsanity.com/paper/2603.04241/) (2026)
- [DUPLEX: Agentic Dual-System Planning via LLM-Driven Information Extraction](https://mlsanity.com/paper/2603.23909/) (2026)

## Abstract (arXiv)

We present SPL (Structured Prompt Language), a declarative language that composes deterministic and probabilistic computation modes in a single specification. While existing frameworks separate these -- orchestration systems (AutoGen, CrewAI, LangGraph) for LLM calls, symbolic tools (SymPy, SageMath, Lean) for computation -- SPL unifies them. It provides GENERATE/EVALUATE for probabilistic computation and SOLVE/ASSERT for deterministic computation, sharing syntax, variable bindings, and runtime routing. A .spl specification runs unchanged across local nodes (Ollama), cloud APIs (OpenRouter, Anthropic), and distributed grids (Momagrid), with model and verifier selection deferred to invocation time. We validate SPL through an extensive 78-recipe cookbook and a controlled 1,200-run experiment (10 models x 20 problems x 2 arms x 3 repetitions; the 20 problems span 6 difficulty tiers). The solver arm achieves 82-93% machine-verified correctness (sonnet-4-6: 85%, gemma4:e2b: 93%) while the LLM-only arm measures output production without mathematical verification, making the comparison one of verified correctness against unverified fluency. A backend difficulty gradient emerges (SymPy 78%, Sage 54%), and the dominant failure mode is solver_error (kernel-rejected expressions), not format non-compliance.