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symbolic_abstract

Replace concrete terms in an expression with abstract symbols to enable logical reasoning, simplification, or proof generation. Provide the raw expression, optional mapping hints, and goal to get a reversible symbol table.

Instructions

Convert a concrete expression into abstract variables for reasoning.

    Args:
        expression: The raw text or equation to abstract.
        mapping_hint: Optional guidance for token-to-symbol mapping.
        goal: Optional downstream task (e.g., simplify, prove, generalize).

    Returns:
        Structured prompt that maps tokens to symbols, restates the problem
        abstractly, and provides a reversible mapping table.
    

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
expressionYes
mapping_hintNo
goalNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior3/5

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

With no annotations provided, the description bears full responsibility for behavioral disclosure. It describes the output as a 'Structured prompt...' and mentions a reversible mapping table, but does not specify side effects (e.g., whether it modifies state), authentication needs, or error conditions. The description adds moderate transparency but lacks depth.

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 concise (under 100 words) and front-loaded with the purpose statement. It uses a structured docstring format for parameters and returns, which is efficient. However, the parameter descriptions are indented, making it slightly less scannable than a flat list, but still clear.

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

Completeness4/5

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

Given the tool's moderate complexity (3 parameters, 1 required, no enums, output schema present), the description adequately covers input, optional parameters, and output structure. It does not cover edge cases or error handling, but for a transformation tool, the provided information is largely complete.

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 input schema has 0% description coverage, so the description must compensate. It provides meaningful explanations for each parameter: 'The raw text or equation to abstract' for expression, 'Optional guidance for token-to-symbol mapping' for mapping_hint, and 'Optional downstream task (e.g., simplify, prove, generalize)' for goal. This adds clarity beyond the schema's titles.

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

Purpose5/5

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

The description clearly states the tool's function: 'Convert a concrete expression into abstract variables for reasoning.' This uses a specific verb (convert) and resource (concrete expression) and outcome (abstract variables), distinguishing it from sibling tools that focus on retrieval (e.g., get_cell_protocol) or other reasoning tasks (e.g., backtracking).

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. There is no mention of context, prerequisites, or when not to use it. Sibling tools like analyze_task_complexity or backtracking are not referenced, so an agent has no basis for selection.

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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