Constraint Solver MCP Server

A specialized MCP server for validating variable assignments against mathematical and logical constraints, enabling systematic constraint satisfaction checking.

Architecture

This server follows the MCP Code Mode architecture, separating concerns into three layers:

1. Core (src/core/): Pure business logic and types (no MCP dependencies).
2. Code Mode (src/codemode/): Programmable TypeScript API exported for use by other applications/agents.
3. MCP Adapter (src/mcp/): Protocol adapter that exposes the Code Mode API as an MCP server.

Code Mode API (Programmable Usage)

You can use the Constraint Solver directly in your TypeScript applications:

import { ConstraintSolver } from "@wemake.cx/constraint-solver";

const solver = new ConstraintSolver();

const result = await solver.check({
  variables: {
    x: 10,
    y: 5
  },
  constraints: ["x > 0", "y <= x", "x + y < 20"]
});

if (result.satisfied) {
  console.log("All constraints satisfied!");
} else {
  console.log("Unsatisfied constraints:", result.unsatisfied);
}

MCP Usage

Core Concepts

Variables

The server works with named variables that have numeric values:

• Variable Name: String identifier for the variable
• Variable Value: Numeric value assigned to the variable
• Variable Set: Collection of all variables in the constraint system

Example variables:

{
  "x": 10,
  "y": 5,
  "temperature": 25.5,
  "count": 100
}

Constraints

Constraints are boolean expressions that must evaluate to true:

• Mathematical Constraints: Arithmetic relationships between variables
• Logical Constraints: Boolean logic expressions
• Comparison Constraints: Equality and inequality checks
• Range Constraints: Bounds checking for variables

Example constraints:

[
  "x > 0", // Simple comparison
  "y <= x", // Variable relationship
  "x + y < 20", // Arithmetic expression
  "temperature >= 0 && temperature <= 100", // Range constraint
  "count % 2 === 0" // Modulo constraint
];

Constraint Satisfaction

The system evaluates all constraints against the variable assignments:

• Satisfied: All constraints evaluate to true
• Unsatisfied: One or more constraints evaluate to false
• Violation Report: List of specific constraints that failed
• Validation Result: Boolean satisfaction status with details

Safety and Security

Constraint evaluation uses safe JavaScript evaluation:

• Sandboxed Execution: Constraints run in isolated function scope
• Error Handling: Invalid expressions return false rather than throwing
• Limited Scope: Only provided variables are accessible
• No Side Effects: Evaluation is purely functional

API Tools

• constraintSolver
  • Validates variable assignments against constraint expressions
  • Input: Constraint satisfaction problem
    • variables (object): Variable name-value pairs (numeric values only)
    • constraints (array): Array of boolean expression strings
  • Output: Constraint satisfaction result
    • satisfied (boolean): Whether all constraints are satisfied
    • unsatisfied (array): List of constraint expressions that failed

Setup

bunx

{
  "mcpServers": {
    "Constraint Solver": {
      "command": "bunx",
      "args": ["@wemake.cx/constraint-solver@latest"]
    }
  }
}

bunx with custom settings

The server supports various configuration options:

{
  "mcpServers": {
    "Constraint Solver": {
      "command": "bunx",
      "args": ["@wemake.cx/constraint-solver@latest"],
      "env": {
        "CONSTRAINT_MAX_VARIABLES": "100",
        "CONSTRAINT_MAX_EXPRESSIONS": "50",
        "CONSTRAINT_TIMEOUT_MS": "5000",
        "CONSTRAINT_DEBUG_MODE": "false"
      }
    }
  }
}

• CONSTRAINT_MAX_VARIABLES: Maximum number of variables per request (default: 100)
• CONSTRAINT_MAX_EXPRESSIONS: Maximum number of constraint expressions (default: 50)
• CONSTRAINT_TIMEOUT_MS: Timeout for constraint evaluation in milliseconds (default: 5000)
• CONSTRAINT_DEBUG_MODE: Enable detailed debugging output (default: false)

System Prompt

The prompt for utilizing constraint solving should focus on systematic validation:

Follow these steps for constraint solving:

1. Problem Definition:
   - Identify all relevant variables and their current values
   - Define clear constraints that must be satisfied
   - Express constraints as boolean expressions using JavaScript syntax
   - Consider edge cases and boundary conditions

2. Constraint Formulation:
   - Use mathematical operators: +, -, \*, /, %, \*\*
   - Use comparison operators: >, <, >=, <=, ===, !==
   - Use logical operators: &&, ||, !
   - Reference variables by their exact names
   - Ensure expressions evaluate to boolean values

3. Validation Process:
   - Submit variables and constraints to the constraint solver
   - Review satisfaction status and any violations
   - Analyze unsatisfied constraints to understand failures
   - Iterate on variable values or constraint definitions as needed

4. Solution Refinement:
   - Adjust variable values to satisfy constraints
   - Modify constraints if they are too restrictive
   - Add additional constraints for completeness
   - Verify final solution meets all requirements

5. Documentation:
   - Document the constraint system for future reference
   - Explain the rationale behind each constraint
   - Record any assumptions or limitations
   - Plan for constraint system maintenance and updates