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The agent uses LLM reasoning to propose proof steps, which are then validated by Lean's type checker and kernel, ensuring mathematical correctness. This creates a feedback loop where failed proof attempts inform the LLM's next generation strategy, enabling iterative refinement of formal proofs without manual intervention.","intents":["I want to prove a mathematical theorem formally without writing every proof step manually","I need to verify that my mathematical claims are logically sound and catch edge cases","I want to generate boilerplate proof scaffolding and let the AI fill in the details","I need to refactor existing proofs when definitions change"],"best_for":["formal verification researchers and mathematicians","teams building trustworthy software with mathematical guarantees","developers integrating formal methods into critical systems"],"limitations":["Proof synthesis success depends on LLM reasoning quality; complex theorems may require human guidance","Lean 4 ecosystem is smaller than mainstream languages; fewer libraries and community resources","Proof generation latency can be high for deeply nested or interdependent theorems","Requires understanding of Lean 4 syntax and formal logic; not accessible to non-mathematicians"],"requires":["Lean 4 (latest version with mathlib4)","API access to LLM provider (Mistral or compatible)","Basic understanding of formal logic and proof tactics"],"input_types":["theorem statements in Lean 4 syntax","partial proofs with holes (sorry)","informal mathematical descriptions"],"output_types":["complete Lean 4 proof terms","tactic-based proofs","proof verification results with error messages"],"categories":["code-generation-editing","formal-verification"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"hn-47404796__cap_1","uri":"capability://code.generation.editing.formal.specification.extraction.from.natural.language","name":"formal specification extraction from natural language","description":"Leanstral can parse informal mathematical or algorithmic descriptions in natural language and convert them into formal Lean 4 specifications with type signatures and invariant constraints. The agent uses semantic understanding to identify key concepts, relationships, and constraints, then maps them to appropriate Lean 4 types, definitions, and lemma statements. This bridges the gap between human intent and formal logic without requiring developers to manually translate specifications.","intents":["I have an algorithm described in English and need to formalize it as a Lean definition","I want to extract the core properties and invariants from a system design document","I need to convert informal requirements into formal specifications that can be verified"],"best_for":["teams transitioning from informal specifications to formal verification","researchers documenting mathematical algorithms formally","safety-critical system developers who need formal requirements"],"limitations":["Ambiguous or underspecified natural language may produce incorrect formal translations","Requires domain expertise to validate that extracted specifications match intent","Cannot infer implicit assumptions or context not explicitly stated in the description","Works best with mathematical or algorithmic descriptions; less effective for system-level requirements"],"requires":["Lean 4 installed","Clear, structured natural language descriptions (pseudo-code preferred)","Domain knowledge to validate extracted specifications"],"input_types":["natural language algorithm descriptions","pseudo-code","mathematical notation in text form","informal requirement documents"],"output_types":["Lean 4 type definitions","function signatures with preconditions and postconditions","invariant statements","lemma templates"],"categories":["code-generation-editing","text-generation-language"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"hn-47404796__cap_2","uri":"capability://planning.reasoning.interactive.proof.debugging.with.counterexample.generation","name":"interactive proof debugging with counterexample generation","description":"When a proof attempt fails, Leanstral analyzes the Lean kernel error messages and uses the LLM to generate potential counterexamples or identify logical gaps in the proof strategy. The agent can suggest alternative proof approaches, identify missing lemmas, or propose strengthened hypotheses. This interactive loop allows developers to understand why a proof failed and iteratively refine their approach without manually reading dense Lean error messages.","intents":["My proof failed and I don't understand why; help me debug it","I want to see a counterexample that violates my theorem statement","Suggest alternative proof strategies when my current approach is stuck","Help me identify which lemmas or definitions I'm missing"],"best_for":["Lean 4 developers learning formal verification","researchers debugging complex mathematical proofs","teams building formally verified systems who need faster iteration"],"limitations":["Counterexample generation may be incomplete for undecidable properties","LLM suggestions may not always be mathematically sound; require human verification","Debugging latency increases with proof complexity and error message length","Cannot suggest proofs for theorems that are actually false"],"requires":["Lean 4 with failed proof state","LLM API access","Understanding of Lean error message format"],"input_types":["Lean 4 proof code with errors","kernel error messages","theorem statements"],"output_types":["suggested proof tactics and strategies","potential counterexamples","identified missing lemmas","refined theorem statements"],"categories":["planning-reasoning","code-generation-editing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"hn-47404796__cap_3","uri":"capability://memory.knowledge.codebase.aware.proof.generation.with.context.indexing","name":"codebase-aware proof generation with context indexing","description":"Leanstral maintains an index of available lemmas, definitions, and theorems in the Lean codebase and uses this context to inform proof synthesis. When generating proofs, the agent retrieves relevant lemmas from the index and incorporates them into the proof strategy, avoiding redundant proofs and leveraging existing mathematical infrastructure. This context-aware approach reduces proof generation time and increases success rates by grounding the LLM in the actual available tools.","intents":["Generate proofs that reuse existing lemmas from mathlib4 or my project","I want the agent to know about my custom definitions and theorems","Avoid duplicate proofs by discovering similar existing theorems","Suggest lemmas that might be useful for my proof"],"best_for":["large Lean projects with extensive theorem libraries","teams building on top of mathlib4","researchers maintaining formal mathematics repositories"],"limitations":["Index maintenance overhead increases with codebase size; indexing large projects may be slow","Retrieval quality depends on semantic similarity; may miss relevant lemmas with different naming","Index must be kept in sync with codebase changes; stale index leads to missed opportunities","Context window limitations may prevent including all relevant lemmas for complex proofs"],"requires":["Lean 4 project with existing theorems and lemmas","Indexing infrastructure (vector embeddings or semantic search)","Sufficient memory to maintain codebase index"],"input_types":["Lean 4 project directory","theorem statements to prove","proof goals"],"output_types":["proofs using indexed lemmas","list of relevant lemmas from codebase","proof with citations to used theorems"],"categories":["memory-knowledge","code-generation-editing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"hn-47404796__cap_4","uri":"capability://code.generation.editing.formal.verification.of.code.properties.with.lean.integration","name":"formal verification of code properties with lean integration","description":"Leanstral can extract properties from source code (e.g., function contracts, loop invariants, type constraints) and automatically generate Lean specifications and proofs that verify these properties hold. The agent bridges imperative or functional code with formal logic by translating code semantics into Lean definitions, then proving that the code satisfies its specification. This enables trustworthy code by providing mathematical guarantees about correctness.","intents":["I want to prove that my sorting algorithm is correct","Verify that my cryptographic implementation satisfies security properties","Generate formal proofs that my code handles all edge cases","Create machine-checkable evidence that my code meets its specification"],"best_for":["developers of safety-critical systems (aerospace, medical, financial)","cryptography and security engineers","teams building formally verified libraries"],"limitations":["Code extraction to Lean is lossy; some runtime properties (performance, memory usage) cannot be formally verified","Requires code to be written in a style amenable to formal verification; imperative code with side effects is harder to verify","Proof generation time scales with code complexity; large functions may timeout","Requires understanding of both the code and formal logic to validate extracted specifications"],"requires":["Source code in supported language (Lean 4, or translatable from Python/Rust/Go)","Clear specification of properties to verify","Lean 4 environment with mathlib4"],"input_types":["source code files","function signatures with contracts","property specifications in natural language or formal logic"],"output_types":["Lean 4 code specifications","formal proofs of correctness","verification reports with coverage"],"categories":["code-generation-editing","safety-moderation"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"hn-47404796__cap_5","uri":"capability://planning.reasoning.multi.step.proof.planning.with.tactic.decomposition","name":"multi-step proof planning with tactic decomposition","description":"Leanstral breaks down complex proof goals into smaller subgoals and generates a proof plan before attempting tactic execution. The agent uses LLM reasoning to decompose the goal structure, identify intermediate lemmas needed, and order proof steps logically. This planning phase reduces backtracking and improves proof synthesis success rates by ensuring the LLM understands the overall proof strategy before committing to specific tactics.","intents":["Generate a proof outline before filling in the details","Break down a complex theorem into manageable subgoals","Understand the logical structure of a proof before implementation","Identify which lemmas are needed before attempting the proof"],"best_for":["developers proving complex theorems with many dependencies","teams teaching formal verification","researchers working on large mathematical proofs"],"limitations":["Planning overhead adds latency; simple proofs may be slower with planning","Proof plans may be suboptimal; LLM reasoning about proof structure is not always sound","Plan changes if intermediate lemmas fail; requires replanning","Cannot plan proofs for theorems that are actually false"],"requires":["Lean 4 with theorem statement","LLM with sufficient reasoning capability","Proof goal in a form amenable to decomposition"],"input_types":["theorem statements","proof goals","available lemmas and definitions"],"output_types":["proof plans with subgoal structure","tactic sequences","dependency graphs between lemmas"],"categories":["planning-reasoning","code-generation-editing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"hn-47404796__cap_6","uri":"capability://search.retrieval.automated.lemma.discovery.and.suggestion","name":"automated lemma discovery and suggestion","description":"Leanstral analyzes proof goals and suggests relevant lemmas from the codebase or mathlib4 that might help prove the goal. The agent uses semantic similarity between the goal and available lemmas to rank suggestions, then presents them to the developer with explanations of how they might apply. This accelerates proof development by reducing the time spent searching for relevant theorems.","intents":["I'm stuck on a proof; suggest lemmas that might help","Find all theorems about a specific mathematical concept","Discover lemmas I didn't know existed that are relevant to my proof","Understand how existing theorems relate to my goal"],"best_for":["Lean developers learning the mathlib4 library","researchers exploring mathematical domains","teams building on top of large theorem libraries"],"limitations":["Semantic similarity may miss relevant lemmas with different terminology","Ranking quality depends on embedding quality; popular lemmas may be over-suggested","Suggestion latency increases with library size","Suggested lemmas may not directly apply; require adaptation or composition"],"requires":["Indexed Lean codebase or mathlib4","Semantic search infrastructure (embeddings)","Proof goal in Lean syntax"],"input_types":["proof goals","theorem statements","mathematical concepts in natural language"],"output_types":["ranked list of relevant lemmas","explanations of lemma applicability","proof sketches using suggested lemmas"],"categories":["search-retrieval","memory-knowledge"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"hn-47404796__cap_7","uri":"capability://code.generation.editing.proof.refactoring.and.optimization.with.tactic.rewriting","name":"proof refactoring and optimization with tactic rewriting","description":"Leanstral can analyze existing proofs and suggest refactorings that improve clarity, reduce length, or improve performance. The agent identifies redundant tactics, suggests more efficient proof strategies, and can automatically rewrite proofs using different approaches. This enables developers to maintain clean, efficient proofs as specifications evolve and new lemmas become available.","intents":["My proof is too long; help me simplify it","Refactor my proof to use newer lemmas from mathlib4","Find more elegant proof strategies for my theorem","Optimize proof performance by reducing tactic execution time"],"best_for":["developers maintaining large proof libraries","teams upgrading mathlib4 versions","researchers publishing formally verified results"],"limitations":["Refactored proofs may be less readable despite being shorter","Optimization suggestions may not preserve proof semantics; require verification","Refactoring latency increases with proof size","Cannot refactor proofs that are already optimal"],"requires":["Existing Lean 4 proof","Access to available lemmas and tactics","Lean 4 environment for validation"],"input_types":["Lean 4 proof code","proof goals and states"],"output_types":["refactored proof code","optimization suggestions with metrics","alternative proof strategies"],"categories":["code-generation-editing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"hn-47404796__cap_8","uri":"capability://data.processing.analysis.formal.specification.generation.from.test.cases","name":"formal specification generation from test cases","description":"Leanstral can analyze unit tests or property-based tests and infer formal specifications that capture the tested behavior. The agent extracts invariants and properties from test cases, then generates Lean specifications that formalize these properties. This bridges the gap between informal testing and formal verification by automatically extracting formal requirements from existing test suites.","intents":["Convert my unit tests into formal specifications","Extract properties from property-based tests and formalize them","Generate Lean specifications that capture my test coverage","Identify gaps between my tests and formal specifications"],"best_for":["teams transitioning from testing to formal verification","developers with comprehensive test suites","projects seeking to formalize existing behavior"],"limitations":["Extracted specifications may be incomplete; tests don't cover all cases","Inferred properties may be overly specific to test cases; poor generalization","Cannot extract properties not explicitly tested","Requires test cases to be well-structured and representative"],"requires":["Unit tests or property-based tests in supported format","Lean 4 environment","Code under test in a form amenable to formalization"],"input_types":["unit test files","property-based test specifications","test assertions and expected behaviors"],"output_types":["Lean 4 specifications","formal properties and invariants","test coverage analysis"],"categories":["data-processing-analysis","code-generation-editing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"hn-47404796__cap_9","uri":"capability://code.generation.editing.interactive.proof.assistant.with.real.time.feedback","name":"interactive proof assistant with real-time feedback","description":"Leanstral provides real-time feedback as developers write proofs, suggesting tactics, identifying errors, and offering corrections before proof compilation. The agent monitors the proof state and provides context-aware suggestions based on the current goal, available lemmas, and proof history. This interactive experience accelerates proof development by reducing compile-test-fix cycles.","intents":["Get real-time suggestions as I write my proof","Identify errors in my proof before compilation","Understand what the current goal requires","Explore alternative proof strategies interactively"],"best_for":["Lean developers learning formal verification","teams developing proofs collaboratively","researchers exploring proof spaces interactively"],"limitations":["Real-time feedback latency depends on LLM response time; may be slow for complex goals","Suggestions may be incorrect or misleading; require developer judgment","Requires continuous LLM API access; not suitable for offline development","Context window limitations may prevent full proof history from being considered"],"requires":["Lean 4 IDE integration (VS Code or similar)","Real-time LLM API access","Proof state tracking infrastructure"],"input_types":["partial proof code","proof goals in progress","developer queries"],"output_types":["tactic suggestions","error messages with explanations","proof state visualizations"],"categories":["code-generation-editing","planning-reasoning"],"confidence":0.5,"matches":0,"success_rate":0}],"trust":{"score":49,"verified":false,"data_access_risk":"high","permissions":["Lean 4 (latest version with mathlib4)","API access to LLM provider (Mistral or compatible)","Basic understanding of formal logic and proof tactics","Lean 4 installed","Clear, structured natural language descriptions (pseudo-code preferred)","Domain knowledge to validate extracted specifications","Lean 4 with failed proof state","LLM API access","Understanding of Lean error message format","Lean 4 project with existing theorems and lemmas"],"failure_modes":["Proof synthesis success depends on LLM reasoning quality; complex theorems may require human guidance","Lean 4 ecosystem is smaller than mainstream languages; fewer libraries and community resources","Proof generation latency can be high for deeply nested or interdependent theorems","Requires understanding of Lean 4 syntax and formal logic; not accessible to non-mathematicians","Ambiguous or underspecified natural language may produce incorrect formal translations","Requires domain expertise to validate that extracted specifications match intent","Cannot infer implicit assumptions or context not explicitly stated in the description","Works best with mathematical or algorithmic descriptions; less effective for system-level requirements","Counterexample generation may be incomplete for undecidable properties","LLM suggestions may not always be mathematically sound; require human verification","builder identity is not verified yet","no observed match outcomes yet"],"rank_breakdown":{"adoption":0.92,"quality":0.3,"ecosystem":0.21000000000000002,"match_graph":0.25,"freshness":0.75,"weights":{"adoption":0.25,"quality":0.25,"ecosystem":0.1,"match_graph":0.28,"freshness":0.12}},"observed_outcomes":{"matches":0,"success_rate":0,"avg_confidence":0,"top_intents":[],"last_matched_at":null},"maintenance":{"status":"active","updated_at":"2026-05-24T12:16:23.326Z","last_scraped_at":"2026-05-04T08:10:16.627Z","last_commit":null},"community":{"stars":null,"forks":null,"weekly_downloads":null,"model_downloads":null,"model_likes":null}},"distribution":{"claim_url":"https://unfragile.ai/submit?claim=leanstral-open-source-agent-for-trustworthy-coding","compare_url":"https://unfragile.ai/compare?artifact=leanstral-open-source-agent-for-trustworthy-coding"}},"signature":"dlxzYIy+DUwdd9ntMHQGDUGm+nJ0xSZRGWMJ/2YsuFYB2DzpRk/wgcLI8bjldFGI6NHcXvs56j0bhpO7aacPCQ==","signedAt":"2026-06-23T10:28:06.537Z","signedBy":"unfragile.ai","version":1},"_links":{"self":"https://unfragile.ai/api/v1/passport/leanstral-open-source-agent-for-trustworthy-coding","artifact":"https://unfragile.ai/leanstral-open-source-agent-for-trustworthy-coding","verify":"https://unfragile.ai/api/v1/verify?slug=leanstral-open-source-agent-for-trustworthy-coding","publicKey":"https://unfragile.ai/api/v1/trust-passport-public-key","spec":"https://unfragile.ai/trust","schema":"https://unfragile.ai/schema.json","docs":"https://unfragile.ai/docs"}}