create_custom_problem

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

With no annotations, the description carries full burden. It states the result is immutable and private, but does not detail side effects like ownership, storage implications, or access restrictions. More context would improve transparency.

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

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

The description is extremely concise with no filler, front-loading the core purpose. Every sentence adds value, making it efficient for an AI agent.

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

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

Given no output schema and 4 weakly documented parameters, the description covers creation and use but lacks detail on return format, privacy implications, and the exact nature of 'solver-participation Playground run.' It is adequate but not fully self-contained.

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

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

Schema description coverage is 0%, and the description adds minimal value: it explains auto-derivation of lhs_name/rhs_name but fails to clarify the meaning of lhs_text and rhs_text. The description assumes domain knowledge, leaving parameters largely undefined.

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

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

The description clearly states the tool creates an immutable private Lean statement pair, specifying the resource and action. It distinguishes from siblings like delete_custom_problem and get_custom_problem by focusing on creation and immutability.

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

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

The description provides usage context (playground.write) and explains that omitted name parameters are auto-derived. It guides the agent to use the returned id for subsequent playground runs, but does not explicitly mention when not to use or alternative tools.

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