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MikeyBeez

mcp-geometry-prover

by MikeyBeez

geometry_prove

Proves geometry theorems using symbolic reasoning. Input a problem in AG2 format and get proof status and deduction steps.

Instructions

Prove a geometry theorem using AlphaGeometry2's DDAR engine.

Input format (AG2 problem string):

  • Points with coordinates: "a@x_y = ;"

  • Constraints: "coll a b c" (collinear), "cong a b c d" (congruent), "perp a b c d" (perpendicular), "para a b c d" (parallel), "cyclic a b c d" (concyclic), "eqangle a b c d e f g h" (equal angles)

  • Goal after "?": "cong e p e q" (prove EP = EQ)

Example (IMO 2000 P1): "a@-0.52_0.11 = ; b@-0.19_0.19 = ; ... cong a g1 g1 m, ... ? cong e p e q"

Returns proof status and number of deduction steps.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
problemYesGeometry problem in AG2 format
Behavior3/5

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

No annotations are provided, so the description carries full responsibility for behavioral disclosure. It details the input format and states the return type ('proof status and number of deduction steps'), but it does not mention side effects (likely none), resource requirements, rate limits, or whether modifications occur. While the stated behavior is accurate, it lacks completeness for a tool without annotations.

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

Conciseness4/5

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

The description is well-structured: purpose sentence followed by bullet points for input format and an example. It is informative without being excessively verbose. However, the example section is incomplete (truncated with '...'), which slightly detracts from clarity. Overall, it is appropriately sized for the complexity.

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?

Given the complexity of geometry proving and the absence of an output schema, the description only vaguely describes the return as 'proof status and number of deduction steps.' It does not specify the format or structure of the result, nor does it cover error handling or edge cases. The detailed input format compensates partially, but the output description is insufficient for complete understanding.

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?

Schema coverage is 100% (the schema has a description for the 'problem' parameter), baseline is 3. The description adds significant value by explaining the AG2 problem string format in detail, including point notation, constraint types, and goal format. This enriches the agent's understanding beyond the schema description 'Geometry problem in AG2 format'.

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 states the tool's purpose: 'Prove a geometry theorem using AlphaGeometry2's DDAR engine.' It uses a specific verb ('Prove') and identifies the resource (geometry theorem with AlphaGeometry2). While it doesn't explicitly differentiate from sibling tools (geometry_example, geometry_help), the distinct verb 'prove' implies a different function than example or help, making the purpose clear but not fully differentiating.

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

Usage Guidelines2/5

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

The description provides no guidance on when to use this tool versus alternatives (geometry_example, geometry_help). It does not mention prerequisites, when not to use it, or context for choosing this over siblings. The agent is left to infer that it's for proving theorems, but there is no explicit usage direction or exclusion criteria.

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

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