Initial Query

Given this BNF-style grammar write a Python function `evaluate(str)` that evaluates the expression <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term> <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor> <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor> <prefix-op> ::= 'sin' | 'cos' <number> ::= <digit> | <number> <digit> <digit> ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' For example you can evaluate this sin(3 + 2 * 4) - cos(15) = -0.240302

LLM Generation

Query

Given this BNF-style grammar write a Python function `evaluate(str)` that evaluates the expression <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term> <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor> <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor> <prefix-op> ::= 'sin' | 'cos' <number> ::= <digit> | <number> <digit> <digit> ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' For example you can evaluate this sin(3 + 2 * 4) - cos(15) = -0.240302

Output

# Recursive Descent Parser for Arithmetic Expressions I'll implement a recursive descent parser that follows the grammar you provided. This approach creates functions that directly correspond to each rule in the grammar. 

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import math

def evaluate(s):
    # Remove whitespace from the input string
    s = s.replace(' ', '')
    
    # Use a list to track position so it can be modified in nested functions
    pos = [0]
    
    # Parse an expression: <term> | <expression> '+' <term> | <expression> '-' <term>
    def parse_expression():
        left = parse_term()
        
        while pos[0] < len(s) and s[pos[0]] in ['+', '-']:
            op = s[pos[0]]
            pos[0] += 1
            right = parse_term()
            
            if op == '+':
                left += right
            else:  # op == '-'
                left -= right
                
        return left
    
    # Parse a term: <factor> | <term> '*' <factor> | <term> '/' <factor>
    def parse_term():
        left = parse_factor()
        
        while pos[0] < len(s) and s[pos[0]] in ['*', '/']:
            op = s[pos[0]]
            pos[0] += 1
            right = parse_factor()
            
            if op == '*':
                left *= right
            else:  # op == '/'
                left /= right
                
        return left
    
    # Parse a factor: <number> | '(' <expression> ')' | <prefix-op> <factor>
    def parse_factor():
        if pos[0] < len(s) and s[pos[0]].isdigit():
            return parse_number()
        elif pos[0] < len(s) and s[pos[0]] == '(':
            pos[0] += 1  # Skip '('
            result = parse_expression()
            if pos[0] >= len(s) or s[pos[0]] != ')':
                raise ValueError("Expected closing parenthesis")
            pos[0] += 1  # Skip ')'
            return result
        elif pos[0] + 3 <= len(s) and s[pos[0]:pos[0]+3] == 'sin':
            pos[0] += 3  # Skip 'sin'
            return math.sin(parse_factor())
        elif pos[0] + 3 <= len(s) and s[pos[0]:pos[0]+3] == 'cos':
            pos[0] += 3  # Skip 'cos'
            return math.cos(parse_factor())
        else:
            raise ValueError(f"Unexpected character at position {pos[0]}")
    
    # Parse a number: <digit> | <number> <digit>
    def parse_number():
        start = pos[0]
        while pos[0] < len(s) and s[pos[0]].isdigit():
            pos[0] += 1
        return int(s[start:pos[0]])
    
    # Start parsing from the beginning
    result = parse_expression()
    
    # Ensure the entire string was parsed
    if pos[0] < len(s):
        raise ValueError(f"Unexpected character at position {pos[0]}: {s[pos[0]]}")
    
    return result
## Example Execution: Let's trace how this parser handles your example: `sin(3 + 2 * 4) - cos(15)` 1. We parse this as an expression 2. First term: `sin(3 + 2 * 4)` - This is a factor with the prefix-op 'sin' - Inside the parentheses, we evaluate `3 + 2 * 4` - First parse `3` as a term - Then parse `2 * 4` as a term = 8 - So `3 + 8 = 11` - Apply sin to 11 radians 3. We see a '-' operator and continue parsing 4. Second term: `cos(15)` - This is a factor with the prefix-op 'cos' - Apply cos to 15 radians 5. Final result: `sin(11) - cos(15)` ≈ -0.240302 This implementation correctly handles the operator precedence defined in your grammar: - sin/cos has highest precedence - Multiplication/division has middle precedence - Addition/subtraction has lowest precedence

Extract Code

I extracted the following code from that output: 

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import math

def evaluate(s):
    # Remove whitespace from the input string
    s = s.replace(' ', '')
    
    # Use a list to track position so it can be modified in nested functions
    pos = [0]
    
    # Parse an expression: <term> | <expression> '+' <term> | <expression> '-' <term>
    def parse_expression():
        left = parse_term()
        
        while pos[0] < len(s) and s[pos[0]] in ['+', '-']:
            op = s[pos[0]]
            pos[0] += 1
            right = parse_term()
            
            if op == '+':
                left += right
            else:  # op == '-'
                left -= right
                
        return left
    
    # Parse a term: <factor> | <term> '*' <factor> | <term> '/' <factor>
    def parse_term():
        left = parse_factor()
        
        while pos[0] < len(s) and s[pos[0]] in ['*', '/']:
            op = s[pos[0]]
            pos[0] += 1
            right = parse_factor()
            
            if op == '*':
                left *= right
            else:  # op == '/'
                left /= right
                
        return left
    
    # Parse a factor: <number> | '(' <expression> ')' | <prefix-op> <factor>
    def parse_factor():
        if pos[0] < len(s) and s[pos[0]].isdigit():
            return parse_number()
        elif pos[0] < len(s) and s[pos[0]] == '(':
            pos[0] += 1  # Skip '('
            result = parse_expression()
            if pos[0] >= len(s) or s[pos[0]] != ')':
                raise ValueError("Expected closing parenthesis")
            pos[0] += 1  # Skip ')'
            return result
        elif pos[0] + 3 <= len(s) and s[pos[0]:pos[0]+3] == 'sin':
            pos[0] += 3  # Skip 'sin'
            return math.sin(parse_factor())
        elif pos[0] + 3 <= len(s) and s[pos[0]:pos[0]+3] == 'cos':
            pos[0] += 3  # Skip 'cos'
            return math.cos(parse_factor())
        else:
            raise ValueError(f"Unexpected character at position {pos[0]}")
    
    # Parse a number: <digit> | <number> <digit>
    def parse_number():
        start = pos[0]
        while pos[0] < len(s) and s[pos[0]].isdigit():
            pos[0] += 1
        return int(s[start:pos[0]])
    
    # Start parsing from the beginning
    result = parse_expression()
    
    # Ensure the entire string was parsed
    if pos[0] < len(s):
        raise ValueError(f"Unexpected character at position {pos[0]}: {s[pos[0]]}")
    
    return result

Run Code Interpreter

Running the following program: 

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import math

def evaluate(s):
    # Remove whitespace from the input string
    s = s.replace(' ', '')
    
    # Use a list to track position so it can be modified in nested functions
    pos = [0]
    
    # Parse an expression: <term> | <expression> '+' <term> | <expression> '-' <term>
    def parse_expression():
        left = parse_term()
        
        while pos[0] < len(s) and s[pos[0]] in ['+', '-']:
            op = s[pos[0]]
            pos[0] += 1
            right = parse_term()
            
            if op == '+':
                left += right
            else:  # op == '-'
                left -= right
                
        return left
    
    # Parse a term: <factor> | <term> '*' <factor> | <term> '/' <factor>
    def parse_term():
        left = parse_factor()
        
        while pos[0] < len(s) and s[pos[0]] in ['*', '/']:
            op = s[pos[0]]
            pos[0] += 1
            right = parse_factor()
            
            if op == '*':
                left *= right
            else:  # op == '/'
                left /= right
                
        return left
    
    # Parse a factor: <number> | '(' <expression> ')' | <prefix-op> <factor>
    def parse_factor():
        if pos[0] < len(s) and s[pos[0]].isdigit():
            return parse_number()
        elif pos[0] < len(s) and s[pos[0]] == '(':
            pos[0] += 1  # Skip '('
            result = parse_expression()
            if pos[0] >= len(s) or s[pos[0]] != ')':
                raise ValueError("Expected closing parenthesis")
            pos[0] += 1  # Skip ')'
            return result
        elif pos[0] + 3 <= len(s) and s[pos[0]:pos[0]+3] == 'sin':
            pos[0] += 3  # Skip 'sin'
            return math.sin(parse_factor())
        elif pos[0] + 3 <= len(s) and s[pos[0]:pos[0]+3] == 'cos':
            pos[0] += 3  # Skip 'cos'
            return math.cos(parse_factor())
        else:
            raise ValueError(f"Unexpected character at position {pos[0]}")
    
    # Parse a number: <digit> | <number> <digit>
    def parse_number():
        start = pos[0]
        while pos[0] < len(s) and s[pos[0]].isdigit():
            pos[0] += 1
        return int(s[start:pos[0]])
    
    # Start parsing from the beginning
    result = parse_expression()
    
    # Ensure the entire string was parsed
    if pos[0] < len(s):
        raise ValueError(f"Unexpected character at position {pos[0]}: {s[pos[0]]}")
    
    return result





answer = round(evaluate('sin(35+2*4)-cos(15)'), 5)
expected = -0.07209
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Initial Query

Given this BNF-style grammar write a Python function `evaluate(str)` that evaluates the expression <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term> <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor> <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor> <prefix-op> ::= 'sin' | 'cos' <number> ::= <digit> | <number> <digit> <digit> ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' For example you can evaluate this sin(3 + 2 * 4) - cos(15) = -0.240302

LLM Generation

Query

Given this BNF-style grammar write a Python function `evaluate(str)` that evaluates the expression <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term> <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor> <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor> <prefix-op> ::= 'sin' | 'cos' <number> ::= <digit> | <number> <digit> <digit> ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' For example you can evaluate this sin(3 + 2 * 4) - cos(15) = -0.240302

Output

# Expression Evaluator using Recursive Descent Parsing Below is a Python implementation of an expression evaluator that follows the given BNF grammar. This solution uses recursive descent parsing, which matches the structure of the grammar nicely. 

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import math

def evaluate(expression_str):
    """
    Evaluates a mathematical expression based on the specified grammar.
    
    Args:
        expression_str: A string containing the expression to evaluate
        
    Returns:
        The numeric result of evaluating the expression
    """
    # Remove whitespace
    expression_str = expression_str.replace(" ", "")
    
    # Initialize the parsing position
    pos = [0]  # Using a list so it can be modified within nested function calls
    
    # Parse and evaluate the expression
    result = parse_expression(expression_str, pos)
    
    # Check if we consumed the entire input
    if pos[0] < len(expression_str):
        raise ValueError(f"Unexpected character '{expression_str[pos[0]]}' at position {pos[0]}")
    
    return result

def parse_expression(expr, pos):
    """Parse expressions following the rule: <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term>"""
    left = parse_term(expr, pos)
    
    while pos[0] < len(expr):
        if expr[pos[0]] == '+':
            pos[0] += 1
            right = parse_term(expr, pos)
            left += right
        elif expr[pos[0]] == '-':
            pos[0] += 1
            right = parse_term(expr, pos)
            left -= right
        else:
            break
            
    return left

def parse_term(expr, pos):
    """Parse terms following the rule: <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor>"""
    left = parse_factor(expr, pos)
    
    while pos[0] < len(expr):
        if expr[pos[0]] == '*':
            pos[0] += 1
            right = parse_factor(expr, pos)
            left *= right
        elif expr[pos[0]] == '/':
            pos[0] += 1
            right = parse_factor(expr, pos)
            left /= right
        else:
            break
            
    return left

def parse_factor(expr, pos):
    """Parse factors following the rule: <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor>"""
    if pos[0] >= len(expr):
        raise ValueError("Unexpected end of expression")
    
    # Check for prefix operators (sin, cos)
    if pos[0] + 3 <= len(expr) and expr[pos[0]:pos[0]+3] == 'sin':
        pos[0] += 3
        factor_value = parse_factor(expr, pos)
        return math.sin(factor_value)
    
    if pos[0] + 3 <= len(expr) and expr[pos[0]:pos[0]+3] == 'cos':
        pos[0] += 3
        factor_value = parse_factor(expr, pos)
        return math.cos(factor_value)
    
    # Check for parenthesized expression
    if expr[pos[0]] == '(':
        pos[0] += 1
        result = parse_expression(expr, pos)
        
        if pos[0] >= len(expr) or expr[pos[0]] != ')':
            raise ValueError("Missing closing parenthesis")
        
        pos[0] += 1
        return result
    
    # Must be a number
    return parse_number(expr, pos)

def parse_number(expr, pos):
    """Parse a number following the rules: <number> ::= <digit> | <number> <digit>"""
    start = pos[0]
    
    while pos[0] < len(expr) and expr[pos[0]].isdigit():
        pos[0] += 1
    
    if start == pos[0]:
        raise ValueError(f"Expected a number at position {pos[0]}")
    
    return int(expr[start:pos[0]])
## Example Usage: 
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# Test with the given example
result = evaluate("sin(3 + 2 * 4) - cos(15)")
print(result)  # Should output approximately -0.240302
## Explanation: 1. The algorithm uses recursive descent parsing to evaluate the expression according to operator precedence. 2. Each part of the grammar is implemented as a separate function: - `parse_expression` handles addition and subtraction - `parse_term` handles multiplication and division - `parse_factor` handles numbers, parenthesized expressions, and trig functions - `parse_number` parses integer literals 3. The program follows standard mathematical conventions, where: - Multiplication and division have higher precedence than addition and subtraction - Functions like sin and cos take their argument as a factor - Parentheses can be used to override default precedence This parser handles the given example correctly, producing a result close to -0.240302.

Extract Code

I extracted the following code from that output: 

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import math

def evaluate(expression_str):
    """
    Evaluates a mathematical expression based on the specified grammar.
    
    Args:
        expression_str: A string containing the expression to evaluate
        
    Returns:
        The numeric result of evaluating the expression
    """
    # Remove whitespace
    expression_str = expression_str.replace(" ", "")
    
    # Initialize the parsing position
    pos = [0]  # Using a list so it can be modified within nested function calls
    
    # Parse and evaluate the expression
    result = parse_expression(expression_str, pos)
    
    # Check if we consumed the entire input
    if pos[0] < len(expression_str):
        raise ValueError(f"Unexpected character '{expression_str[pos[0]]}' at position {pos[0]}")
    
    return result

def parse_expression(expr, pos):
    """Parse expressions following the rule: <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term>"""
    left = parse_term(expr, pos)
    
    while pos[0] < len(expr):
        if expr[pos[0]] == '+':
            pos[0] += 1
            right = parse_term(expr, pos)
            left += right
        elif expr[pos[0]] == '-':
            pos[0] += 1
            right = parse_term(expr, pos)
            left -= right
        else:
            break
            
    return left

def parse_term(expr, pos):
    """Parse terms following the rule: <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor>"""
    left = parse_factor(expr, pos)
    
    while pos[0] < len(expr):
        if expr[pos[0]] == '*':
            pos[0] += 1
            right = parse_factor(expr, pos)
            left *= right
        elif expr[pos[0]] == '/':
            pos[0] += 1
            right = parse_factor(expr, pos)
            left /= right
        else:
            break
            
    return left

def parse_factor(expr, pos):
    """Parse factors following the rule: <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor>"""
    if pos[0] >= len(expr):
        raise ValueError("Unexpected end of expression")
    
    # Check for prefix operators (sin, cos)
    if pos[0] + 3 <= len(expr) and expr[pos[0]:pos[0]+3] == 'sin':
        pos[0] += 3
        factor_value = parse_factor(expr, pos)
        return math.sin(factor_value)
    
    if pos[0] + 3 <= len(expr) and expr[pos[0]:pos[0]+3] == 'cos':
        pos[0] += 3
        factor_value = parse_factor(expr, pos)
        return math.cos(factor_value)
    
    # Check for parenthesized expression
    if expr[pos[0]] == '(':
        pos[0] += 1
        result = parse_expression(expr, pos)
        
        if pos[0] >= len(expr) or expr[pos[0]] != ')':
            raise ValueError("Missing closing parenthesis")
        
        pos[0] += 1
        return result
    
    # Must be a number
    return parse_number(expr, pos)

def parse_number(expr, pos):
    """Parse a number following the rules: <number> ::= <digit> | <number> <digit>"""
    start = pos[0]
    
    while pos[0] < len(expr) and expr[pos[0]].isdigit():
        pos[0] += 1
    
    if start == pos[0]:
        raise ValueError(f"Expected a number at position {pos[0]}")
    
    return int(expr[start:pos[0]])

Run Code Interpreter

Running the following program: 

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import math

def evaluate(expression_str):
    """
    Evaluates a mathematical expression based on the specified grammar.
    
    Args:
        expression_str: A string containing the expression to evaluate
        
    Returns:
        The numeric result of evaluating the expression
    """
    # Remove whitespace
    expression_str = expression_str.replace(" ", "")
    
    # Initialize the parsing position
    pos = [0]  # Using a list so it can be modified within nested function calls
    
    # Parse and evaluate the expression
    result = parse_expression(expression_str, pos)
    
    # Check if we consumed the entire input
    if pos[0] < len(expression_str):
        raise ValueError(f"Unexpected character '{expression_str[pos[0]]}' at position {pos[0]}")
    
    return result

def parse_expression(expr, pos):
    """Parse expressions following the rule: <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term>"""
    left = parse_term(expr, pos)
    
    while pos[0] < len(expr):
        if expr[pos[0]] == '+':
            pos[0] += 1
            right = parse_term(expr, pos)
            left += right
        elif expr[pos[0]] == '-':
            pos[0] += 1
            right = parse_term(expr, pos)
            left -= right
        else:
            break
            
    return left

def parse_term(expr, pos):
    """Parse terms following the rule: <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor>"""
    left = parse_factor(expr, pos)
    
    while pos[0] < len(expr):
        if expr[pos[0]] == '*':
            pos[0] += 1
            right = parse_factor(expr, pos)
            left *= right
        elif expr[pos[0]] == '/':
            pos[0] += 1
            right = parse_factor(expr, pos)
            left /= right
        else:
            break
            
    return left

def parse_factor(expr, pos):
    """Parse factors following the rule: <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor>"""
    if pos[0] >= len(expr):
        raise ValueError("Unexpected end of expression")
    
    # Check for prefix operators (sin, cos)
    if pos[0] + 3 <= len(expr) and expr[pos[0]:pos[0]+3] == 'sin':
        pos[0] += 3
        factor_value = parse_factor(expr, pos)
        return math.sin(factor_value)
    
    if pos[0] + 3 <= len(expr) and expr[pos[0]:pos[0]+3] == 'cos':
        pos[0] += 3
        factor_value = parse_factor(expr, pos)
        return math.cos(factor_value)
    
    # Check for parenthesized expression
    if expr[pos[0]] == '(':
        pos[0] += 1
        result = parse_expression(expr, pos)
        
        if pos[0] >= len(expr) or expr[pos[0]] != ')':
            raise ValueError("Missing closing parenthesis")
        
        pos[0] += 1
        return result
    
    # Must be a number
    return parse_number(expr, pos)

def parse_number(expr, pos):
    """Parse a number following the rules: <number> ::= <digit> | <number> <digit>"""
    start = pos[0]
    
    while pos[0] < len(expr) and expr[pos[0]].isdigit():
        pos[0] += 1
    
    if start == pos[0]:
        raise ValueError(f"Expected a number at position {pos[0]}")
    
    return int(expr[start:pos[0]])





answer = round(evaluate('sin(35+2*4)-cos(15)'), 5)
expected = -0.07209
assert answer == expected, f'Wrong answer; got {answer} instead of {expected}'
print('All tests passed')
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True