MCP Tools Reference

Complete reference for all QWED-MCP verification tools with detailed examples and parameters.

verify_math

Verify mathematical calculations using the SymPy symbolic mathematics engine.

Description

The verify_math tool performs symbolic computation to verify that a claimed mathematical result is correct. It doesn't just check numerical values - it performs the actual mathematical operation and compares the symbolic result.

Parameters

Parameter	Type	Required	Default	Description
`expression`	string	Yes	-	Mathematical expression (e.g., `x^2`, `sin(x)`, `3x + 5`)
`claimed_result`	string	Yes	-	The result to verify
`operation`	enum	No	`evaluate`	One of: `derivative`, `integral`, `simplify`, `solve`, `evaluate`

Operations

Operation	Description	Example
`derivative`	Compute derivative with respect to x	`d/dx(x^2) = 2x`
`integral`	Compute indefinite integral	`∫x dx = x^2/2`
`simplify`	Simplify expression	`(x^2-1)/(x-1) = x+1`
`solve`	Solve equation for x	`x^2 - 4 = 0 → x = ±2`
`evaluate`	Evaluate/simplify (default)	`2+2 = 4`

Examples

Basic Derivative

{
  "expression": "x^3",
  "claimed_result": "3*x^2",
  "operation": "derivative"
}

Response:

✅ VERIFIED
Result: Calculation verified
Expected: 3*x**2
Actual: 3*x**2
Operation: derivative

Integral Verification

{
  "expression": "2*x",
  "claimed_result": "x^2",
  "operation": "integral"
}

Response:

✅ VERIFIED
Result: Calculation verified
Expected: x**2
Actual: x**2
Operation: integral

Wrong Calculation (Caught!)

{
  "expression": "x^2",
  "claimed_result": "x",
  "operation": "derivative"
}

Response:

❌ FAILED
Result: Calculation incorrect
Expected: 2*x
Actual: x
Operation: derivative

Complex Expressions

{
  "expression": "sin(x)^2 + cos(x)^2",
  "claimed_result": "1",
  "operation": "simplify"
}

Response:

✅ VERIFIED
Result: Calculation verified
Expected: 1
Actual: 1
Operation: simplify

Supported Syntax

Notation	Meaning
`x^2` or `x**2`	x squared
`sqrt(x)`	Square root
`sin(x)`, `cos(x)`, `tan(x)`	Trigonometric functions
`log(x)`	Natural logarithm
`exp(x)`	Exponential (e^x)
`pi`	π (3.14159...)
`e`	Euler's number (2.71828...)

verify_logic

Verify logical arguments using the Z3 SMT solver.

Description

The verify_logic tool uses satisfiability modulo theories (SMT) to determine if a conclusion logically follows from given premises. It performs proof by contradiction: if the premises AND NOT(conclusion) is unsatisfiable, then the argument is valid.

Parameters

Parameter	Type	Required	Description
`premises`	array[string]	Yes	List of premise statements
`conclusion`	string	Yes	The conclusion to verify

Supported Logic Formats

Pattern	Example	Meaning
`A implies B`	"rain implies wet"	If A then B
`if A then B`	"if rain then wet"	If A then B
`A and B`	"hot and sunny"	Both A and B
`A or B`	"rain or snow"	A or B or both
`not A`	"not cold"	Negation
`all X are Y`	"all humans are mortal"	For all X, X is Y
`X is Y`	"Socrates is human"	X has property Y

Examples

Classic Syllogism

{
  "premises": [
    "all humans are mortal",
    "Socrates is human"
  ],
  "conclusion": "Socrates is mortal"
}

Response:

✅ VERIFIED
Message: The conclusion logically follows from the premises
Method: proof by contradiction (Z3 SMT solver)

Modus Ponens

{
  "premises": [
    "A implies B",
    "A"
  ],
  "conclusion": "B"
}

Response:

✅ VERIFIED
Message: The conclusion logically follows from the premises

Invalid Argument (Caught!)

{
  "premises": [
    "A implies B",
    "B"
  ],
  "conclusion": "A"
}

Response:

❌ FAILED
Message: The conclusion does not logically follow from the premises
Counterexample: A counterexample exists where premises are true but conclusion is false

Complex Reasoning

{
  "premises": [
    "if raining then ground is wet",
    "if ground is wet then slippery",
    "raining"
  ],
  "conclusion": "slippery"
}

Response:

✅ VERIFIED
Message: The conclusion logically follows from the premises

verify_code

Check code for security vulnerabilities using AST (Abstract Syntax Tree) analysis.

Description

The verify_code tool performs static analysis on code to detect dangerous patterns and potential security vulnerabilities. It uses AST parsing for accurate detection rather than simple string matching.

Parameters

Parameter	Type	Required	Description
`code`	string	Yes	Code to analyze
`language`	enum	Yes	One of: `python`, `javascript`, `sql`

Detected Patterns

Python

Pattern	Severity	Why Dangerous
`eval()`	🔴 Critical	Executes arbitrary code
`exec()`	🔴 Critical	Executes arbitrary code
`compile()`	🔴 Critical	Can compile malicious code
`__import__()`	🟠 High	Dynamic imports
`os.system()`	🔴 Critical	Shell command execution
`subprocess.*`	🟠 High	Process spawning
`pickle.loads()`	🔴 Critical	Arbitrary code execution
`open()`	🟡 Medium	File system access

JavaScript

Pattern	Severity	Why Dangerous
`eval()`	🔴 Critical	Executes arbitrary code
`Function()`	🔴 Critical	Creates executable code
`innerHTML =`	🟠 High	XSS vulnerability
`document.write()`	🟠 High	XSS vulnerability
`setTimeout(string)`	🔴 Critical	Code injection

SQL

Pattern	Severity	Why Dangerous
String concatenation	🟠 High	SQL injection risk
`--` comments	🟡 Medium	May indicate injection
`UNION SELECT`	🔴 Critical	Data exfiltration

Examples

Dangerous Python Code

{
  "code": "result = eval(user_input)",
  "language": "python"
}

Response:

❌ FAILED
Message: Found 1 security issue(s)
Issues: ["Dangerous function call: eval()"]

Multiple Issues

{
  "code": "import os\nos.system(input())\nexec(data)",
  "language": "python"
}

Response:

❌ FAILED
Message: Found 3 security issue(s)
Issues: [
  "Dangerous function call: exec()",
  "Dangerous pattern: os.system",
  "Potentially dangerous pattern: subprocess"
]

Safe Code

{
  "code": "def add(a, b):\n    return a + b",
  "language": "python"
}

Response:

✅ VERIFIED
Message: No security issues detected
Issues: []

XSS in JavaScript

{
  "code": "element.innerHTML = userContent",
  "language": "javascript"
}

Response:

❌ FAILED
Message: Found 1 security issue(s)
Issues: ["Potential XSS: Direct innerHTML assignment"]

verify_sql

Detect SQL injection vulnerabilities and validate queries.

Description

The verify_sql tool analyzes SQL queries for injection patterns, dangerous operations, and schema compliance. It can optionally validate against a whitelist of allowed tables.

Parameters

Parameter	Type	Required	Description
`query`	string	Yes	SQL query to verify
`allowed_tables`	array[string]	No	Optional whitelist of allowed table names

Detected Patterns

Injection Patterns

Pattern	Description
`' OR '1'='1`	Classic always-true injection
`' OR 1=1`	Numeric tautology
`'; --`	Comment injection
`UNION SELECT`	Data exfiltration
`/.../`	Block comments (may hide payload)

Dangerous Operations

Pattern	Description
`DROP TABLE`	Table deletion
`DROP DATABASE`	Database deletion
`TRUNCATE TABLE`	Data deletion
`DELETE FROM ... (no WHERE)`	Mass deletion
`UPDATE ... (no WHERE)`	Mass update
`xp_cmdshell`	SQL Server command execution

Examples

SQL Injection Detected

{
  "query": "SELECT * FROM users WHERE id = '1' OR '1'='1'"
}

Response:

❌ FAILED
Message: Found 2 issue(s) in SQL query
Issues: [
  "Potential SQL injection: '\\s*OR\\s+'1'\\s*=\\s*'1",
  "Suspicious tautology detected: 1\\s*=\\s*1"
]

Missing WHERE Clause

{
  "query": "DELETE FROM users"
}

Response:

❌ FAILED
Message: Found 1 issue(s) in SQL query
Issues: ["Warning: DELETE without WHERE clause"]

Table Whitelist Violation

{
  "query": "SELECT * FROM admin_secrets",
  "allowed_tables": ["users", "products", "orders"]
}

Response:

❌ FAILED
Message: Found 1 issue(s) in SQL query
Issues: ["Unauthorized table access: admin_secrets"]

Safe Query

{
  "query": "SELECT name, email FROM users WHERE id = ?",
  "allowed_tables": ["users"]
}

Response:

✅ VERIFIED
Message: SQL query passed verification
Issues: []

verify_banking_compliance

Verify banking logic (loans, tax, forex) using QWED Finance Guard.

Description

The verify_banking_compliance tool checks financial calculations for regulatory compliance errors. It specifically detects common "logic traps" where LLMs apply premiums or rates incorrectly (e.g., charging seniors MORE instead of giving discounts).

Parameters

Parameter	Type	Required	Description
`scenario`	string	Yes	The banking scenario description (e.g., "Senior Citizen Loan approval")
`llm_output`	string	Yes	The LLM's reasoning or calculation to verify

Examples

Senior Citizen Premium Trap (Caught!)

{
  "scenario": "Senior Citizen Loan approval",
  "llm_output": "Approving loan for 65yo with base rate 7% + premium 0.5% = 7.5% total"
}

Response:

🛑 BLOCKED by QWED Finance: Senior Citizen Premium (0.50%) applied incorrectly. Logic Trap Detected.

Valid Calculation

{
  "scenario": "Standard personal loan",
  "llm_output": "Base rate 8% for 5-year term. Monthly payment: $202.76"
}

Response:

✅ VERIFIED
Result: Calculation verified. Base rate 8% for 5-year term. Monthly payment: $202.76 is compliant.

verify_commerce_transaction

Verify e-commerce transactions for "Penny Slicing" attacks and tax errors using QWED UCP.

Description

The verify_commerce_transaction tool parses JSON cart data and verifies that totals, taxes, and discounts are mathematically correct. It catches common AI errors like floating-point rounding issues and "Phantom Discount" attacks.

Parameters

Parameter	Type	Required	Description
`cart_json`	string	Yes	Complete cart/checkout state as JSON string

Cart JSON Schema

{
  "items": [
    {"name": "Product", "price": 99.99, "quantity": 2}
  ],
  "subtotal": 199.98,
  "tax_rate": 0.08,
  "tax": 16.00,
  "discount": 10.00,
  "total": 205.98
}

Examples

Penny Slicing Attack (Caught!)

{
  "cart_json": "{\"items\": [{\"name\": \"Widget\", \"price\": 99.99, \"quantity\": 1}], \"subtotal\": 99.99, \"tax\": 7.99, \"total\": 107.97}"
}

Response:

🛑 QWED UCP: BLOCKED. Tax mismatch: expected 8.00, got 7.99. Penny slicing detected.

Valid Transaction

{
  "cart_json": "{\"items\": [{\"name\": \"Book\", \"price\": 29.99, \"quantity\": 2}], \"subtotal\": 59.98, \"tax\": 4.80, \"total\": 64.78}"
}

Response:

✅ QWED UCP: Transaction Approved. Tax and Totals are exact.

Error Handling

All tools return consistent error responses:

{
  "verified": false,
  "message": "Error description",
  "error": "Technical error details"
}

Common Errors

Error	Cause	Solution
`Could not parse expression`	Invalid math syntax	Check expression format
`SymPy not installed`	Missing dependency	Run `pip install sympy`
`Z3 solver not installed`	Missing dependency	Run `pip install z3-solver`
`Unsupported language`	Invalid language param	Use `python`, `javascript`, or `sql`

verify_math​

Description​

Parameters​

Operations​

Examples​

Basic Derivative​

Integral Verification​

Wrong Calculation (Caught!)​

Complex Expressions​

Supported Syntax​

verify_logic​

Description​

Parameters​

Supported Logic Formats​

Examples​

Classic Syllogism​

Modus Ponens​

Invalid Argument (Caught!)​

Complex Reasoning​

verify_code​

Description​

Parameters​

Detected Patterns​

Python​

JavaScript​

SQL​

Examples​

Dangerous Python Code​

Multiple Issues​

Safe Code​

XSS in JavaScript​

verify_sql​

Description​

Parameters​

Detected Patterns​

Injection Patterns​

Dangerous Operations​

Examples​

SQL Injection Detected​

Missing WHERE Clause​

Table Whitelist Violation​

Safe Query​

verify_banking_compliance​

Description​

Parameters​

Examples​

Senior Citizen Premium Trap (Caught!)​

Valid Calculation​

verify_commerce_transaction​

Description​

Parameters​

Cart JSON Schema​

Examples​

Penny Slicing Attack (Caught!)​

Valid Transaction​

Error Handling​

Common Errors​

verify_math

Description

Parameters

Operations

Examples

Basic Derivative

Integral Verification

Wrong Calculation (Caught!)

Complex Expressions

Supported Syntax

verify_logic

Description

Parameters

Supported Logic Formats

Examples

Classic Syllogism

Modus Ponens

Invalid Argument (Caught!)

Complex Reasoning

verify_code

Description

Parameters

Detected Patterns

Python

JavaScript

SQL

Examples

Dangerous Python Code

Multiple Issues

Safe Code

XSS in JavaScript

verify_sql

Description

Parameters

Detected Patterns

Injection Patterns

Dangerous Operations

Examples

SQL Injection Detected

Missing WHERE Clause

Table Whitelist Violation

Safe Query

verify_banking_compliance

Description

Parameters

Examples

Senior Citizen Premium Trap (Caught!)

Valid Calculation

verify_commerce_transaction

Description

Parameters

Cart JSON Schema

Examples

Penny Slicing Attack (Caught!)

Valid Transaction

Error Handling

Common Errors