symbolic_abstract
Convert concrete expressions into abstract variables for mathematical reasoning, simplification, or proof generation by mapping tokens to symbols and creating structured prompts.
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
| Name | Required | Description | Default |
|---|---|---|---|
| expression | Yes | ||
| mapping_hint | No | ||
| goal | No |
Implementation Reference
- The core handler function for the 'symbolic_abstract' tool, decorated with @mcp.tool(). It validates input using SymbolicAbstractInput schema and generates a structured JSON-like prompt template for abstracting expressions into symbols.@mcp.tool() def symbolic_abstract( expression: str, mapping_hint: Optional[str] = None, goal: Optional[str] = None, ) -> str: """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. """ try: model = SymbolicAbstractInput( expression=expression, mapping_hint=mapping_hint, goal=goal ) except ValidationError as e: return f"Input Validation Error: {e}" normalized_hint = model.mapping_hint or "<none>" normalized_goal = model.goal or "<general>" template = """ /symbolic.abstract{{ intent="Abstract concrete tokens into symbolic variables to enable general reasoning", input={{ expression="{expression}", mapping_hint="{mapping_hint}", goal="{goal}" }}, process=[ /tokenize{{action="Identify meaningful tokens/entities in the expression"}}, /assign_symbols{{action="Map tokens to abstract symbols with reversible table"}}, /restatement{{action="Restate the problem using only symbols"}}, /constraints{{action="Preserve constraints or relationships between symbols"}} ], output={{ abstract_form="Symbolic restatement of the expression/problem", symbol_table="Mapping of symbols -> original tokens", invariants="Constraints/relations maintained in abstraction", next_steps="How to use the abstraction for the stated goal" }} }} """ return template.format( expression=model.expression, mapping_hint=normalized_hint, goal=normalized_goal, )
- Pydantic input model (schema) used for validating parameters of the symbolic_abstract tool: required 'expression' and optional 'mapping_hint', 'goal'.class SymbolicAbstractInput(BaseModel): expression: str = Field( ..., min_length=1, description="The raw text or equation to abstract." ) mapping_hint: Optional[str] = Field( None, description="Optional guidance for token-to-symbol mapping." ) goal: Optional[str] = Field(None, description="Optional downstream task.")
- src/context_engineering_mcp/server.py:22-22 (registration)Invocation of register_thinking_models on the FastMCP server instance, which defines and registers the symbolic_abstract tool (along with other cognitive tools).register_thinking_models(mcp)