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nickharris808

formal-proof-mcp

gridlock_check

Certify that a wait-for relation cannot wedge and return the actual cycle when one exists. Supply ranks to also verify strict decrease, which bounds progress.

Instructions

Certify that a wait-for relation cannot wedge. Returns the actual cycle when one exists. Supply ranks to also check strict decrease, which is what bounds progress — acyclicity alone only forbids a cycle.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
edgesYes[[waiter, holder], ...]
ranksNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

A3.8/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations provided, the description carries the behavioral disclosure burden and does reasonably well: it explains the core certification, the cycle-returning behavior, and the semantic role of ranks in proving progress. It still does not state what happens when no cycle exists or whether the operation is side-effect free, but the disclosed behavior is meaningful and non-tautological.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise, front-loaded, and every sentence contributes: purpose, normal return behavior, and optional parameter semantics. There is no filler or repetition.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

The description covers the core purpose and the optional ranks behavior well, but because there is no output schema, it should clarify what the tool returns when no cycle exists and how successful certification is represented. The ranks object format is also left vague, though the parameter is optional.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The schema describes edges as '[[waiter, holder], ...]', and the description adds the wait-for relation context. It also explains that ranks are used to verify strict decrease, giving semantic meaning to an otherwise undocumented object parameter, although the exact shape of the ranks object remains underspecified.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly identifies a specific operation — certifying that a wait-for relation cannot wedge — and explains that it returns the actual cycle when one exists. It is distinct in substance from the sibling tools, though it does not explicitly name any alternative for comparison.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description gives useful contextual guidance: supply ranks to check strict decrease, and notes that acyclicity alone is insufficient for bounded progress. However, it does not explicitly state when to use this tool versus the sibling verification tools or when to prefer another check.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.