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

Below is one acceptable solution. It implements a recursive‐descent parser according to the given grammar. For example, evaluating   sin(3 + 2 * 4) - cos(15) returns approximately –0.240302. In the code we maintain a pointer into the string and define functions for each non‐terminal: expression, term, and factor. Note that the prefix functions “sin” and “cos” are recognized by checking the next characters. Here is the complete code: ------------------------------------------------ import math def evaluate(s): # "pos" is our current pointer into the string. pos = 0 # helper to skip whitespace def skip(): nonlocal pos while pos < len(s) and s[pos].isspace(): pos += 1 # <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term> def parse_expression(): nonlocal pos val = parse_term() skip() while pos < len(s) and s[pos] in '+-': op = s[pos] pos += 1 skip() right = parse_term() if op == '+': val += right else: val -= right skip() return val # <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor> def parse_term(): nonlocal pos val = parse_factor() skip() while pos < len(s) and s[pos] in '*/': op = s[pos] pos += 1 skip() right = parse_factor() if op == '*': val *= right else: val /= right skip() return val # <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor> def parse_factor(): nonlocal pos skip() # check for prefix operators 'sin' or 'cos' if s[pos:pos+3] == 'sin': pos += 3 skip() # The factor after 'sin' may itself be an expression wrapped in parentheses, so we parse a factor. return math.sin(parse_factor()) elif s[pos:pos+3] == 'cos': pos += 3 skip() return math.cos(parse_factor()) elif s[pos] == '(': pos += 1 # consume '(' val = parse_expression() skip() if pos >= len(s) or s[pos] != ')': raise Exception("Missing closing parenthesis") pos += 1 # consume ')' return val else: # <number> ::= <digit> | <number> <digit> start = pos while pos < len(s) and s[pos].isdigit(): pos += 1 if start == pos: raise Exception("Number expected") return float(s[start:pos]) result = parse_expression() skip() if pos != len(s): raise Exception("Unexpected characters at end of input") return result # Test the function with the provided sample: if __name__ == '__main__': expr = "sin(3 + 2 * 4) - cos(15)" result = evaluate(expr) print(f"{expr} = {result:.6f}") ------------------------------------------------ Explanation: 1. The function evaluate(s) sets up a pointer pos into the string s. 2. The helper functions skip any whitespace. 3. parse_expression calls parse_term and then looks for '+' or '-' and loops. 4. parse_term calls parse_factor and then uses '*' or '/'. 5. parse_factor handles numbers (a sequence of digits), also handles parenthesized expressions, and finally checks for the prefix operators “sin” and “cos” (consuming exactly three characters). 6. math.sin and math.cos are used to compute the trigonometric values. 7. At the end, if there are any characters left unparsed, an exception is raised. When you run this code, it prints:   sin(3 + 2 * 4) - cos(15) = -0.240302 which is the expected result.

Extract Code

I extracted the following code from that output: 

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import math

def evaluate(s):
    # "pos" is our current pointer into the string.
    pos = 0

    # helper to skip whitespace
    def skip():
        nonlocal pos
        while pos < len(s) and s[pos].isspace():
            pos += 1

    # <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term>
    def parse_expression():
        nonlocal pos
        val = parse_term()
        skip()
        while pos < len(s) and s[pos] in '+-':
            op = s[pos]
            pos += 1
            skip()
            right = parse_term()
            if op == '+':
                val += right
            else:
                val -= right
            skip()
        return val

    # <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor>
    def parse_term():
        nonlocal pos
        val = parse_factor()
        skip()
        while pos < len(s) and s[pos] in '*/':
            op = s[pos]
            pos += 1
            skip()
            right = parse_factor()
            if op == '*':
                val *= right
            else:
                val /= right
            skip()
        return val

    # <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor>
    def parse_factor():
        nonlocal pos
        skip()
        # check for prefix operators 'sin' or 'cos'
        if s[pos:pos+3] == 'sin':
            pos += 3
            skip()
            # The factor after 'sin' may itself be an expression wrapped in parentheses, so we parse a factor.
            return math.sin(parse_factor())
        elif s[pos:pos+3] == 'cos':
            pos += 3
            skip()
            return math.cos(parse_factor())
        elif s[pos] == '(':
            pos += 1  # consume '('
            val = parse_expression()
            skip()
            if pos >= len(s) or s[pos] != ')':
                raise Exception("Missing closing parenthesis")
            pos += 1  # consume ')'
            return val
        else:
            # <number> ::= <digit> | <number> <digit>
            start = pos
            while pos < len(s) and s[pos].isdigit():
                pos += 1
            if start == pos:
                raise Exception("Number expected")
            return float(s[start:pos])

    result = parse_expression()
    skip()
    if pos != len(s):
        raise Exception("Unexpected characters at end of input")
    return result

Run Code Interpreter

Running the following program: 

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import math

def evaluate(s):
    # "pos" is our current pointer into the string.
    pos = 0

    # helper to skip whitespace
    def skip():
        nonlocal pos
        while pos < len(s) and s[pos].isspace():
            pos += 1

    # <expression> ::= <term> | <expression> '+' <term> | <expression> '-' <term>
    def parse_expression():
        nonlocal pos
        val = parse_term()
        skip()
        while pos < len(s) and s[pos] in '+-':
            op = s[pos]
            pos += 1
            skip()
            right = parse_term()
            if op == '+':
                val += right
            else:
                val -= right
            skip()
        return val

    # <term> ::= <factor> | <term> '*' <factor> | <term> '/' <factor>
    def parse_term():
        nonlocal pos
        val = parse_factor()
        skip()
        while pos < len(s) and s[pos] in '*/':
            op = s[pos]
            pos += 1
            skip()
            right = parse_factor()
            if op == '*':
                val *= right
            else:
                val /= right
            skip()
        return val

    # <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor>
    def parse_factor():
        nonlocal pos
        skip()
        # check for prefix operators 'sin' or 'cos'
        if s[pos:pos+3] == 'sin':
            pos += 3
            skip()
            # The factor after 'sin' may itself be an expression wrapped in parentheses, so we parse a factor.
            return math.sin(parse_factor())
        elif s[pos:pos+3] == 'cos':
            pos += 3
            skip()
            return math.cos(parse_factor())
        elif s[pos] == '(':
            pos += 1  # consume '('
            val = parse_expression()
            skip()
            if pos >= len(s) or s[pos] != ')':
                raise Exception("Missing closing parenthesis")
            pos += 1  # consume ')'
            return val
        else:
            # <number> ::= <digit> | <number> <digit>
            start = pos
            while pos < len(s) and s[pos].isdigit():
                pos += 1
            if start == pos:
                raise Exception("Number expected")
            return float(s[start:pos])

    result = parse_expression()
    skip()
    if pos != len(s):
        raise Exception("Unexpected characters at end of input")
    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

Below is one acceptable solution. This code uses a recursive descent parser following your grammar: ------------------------------------------------------------ import math def evaluate(s): # Remove whitespace for simpler parsing. s = s.replace(" ", "") pos = 0 def parse_expression(): nonlocal pos # <expression> ::= <term> { ('+' | '-') <term> } value = parse_term() while pos < len(s) and s[pos] in '+-': op = s[pos] pos += 1 next_val = parse_term() if op == '+': value += next_val else: value -= next_val return value def parse_term(): nonlocal pos # <term> ::= <factor> { ('*' | '/') <factor> } value = parse_factor() while pos < len(s) and s[pos] in '*/': op = s[pos] pos += 1 next_val = parse_factor() if op == '*': value *= next_val else: value /= next_val return value def parse_factor(): nonlocal pos # <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor> if pos < len(s): # Check for prefix operators "sin" and "cos" if s.startswith("sin", pos): pos += 3 # consume "sin" # expect an opening parenthesis optionally # According to the grammar sin applies to a factor, so we could either have sin<number> or sin(<expression>) value = parse_factor() return math.sin(value) if s.startswith("cos", pos): pos += 3 # consume "cos" value = parse_factor() return math.cos(value) # Check for parenthesis if s[pos] == "(": pos += 1 # consume '(' value = parse_expression() if pos < len(s) and s[pos] == ")": pos += 1 # consume ')' else: raise ValueError("Missing closing parenthesis") return value # Otherwise it must be a number. return parse_number() raise ValueError("Unexpected end of expression") def parse_number(): nonlocal pos # <number> ::= <digit> | <number> <digit> start = pos while pos < len(s) and s[pos].isdigit(): pos += 1 if start == pos: raise ValueError("Expected a number at position {}".format(pos)) return float(s[start:pos]) result = parse_expression() if pos < len(s): raise ValueError("Unexpected character at position {}".format(pos)) return result # Example usage: if __name__ == '__main__': expr = "sin(3 + 2 * 4) - cos(15)" result = evaluate(expr) print("Result =", round(result, 6)) ------------------------------------------------------------ Explanation: 1. The parser first strips out all spaces. We then use the functions • parse_expression() to handle addition and subtraction, • parse_term() to handle multiplication and division, • parse_factor() to handle numbers, parenthesized expressions, or the prefix operators "sin" and "cos". 2. The parse_number() function collects one or more digits and converts them into a float. 3. The prefix operators are detected using s.startswith("sin", pos) and similarly for "cos". 4. White space removal and error checks ensure that the whole string is consumed. If you run the example expression "sin(3 + 2 * 4) - cos(15)" the output rounds to approximately -0.240302, as desired.

Extract Code

I extracted the following code from that output: 

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import math

def evaluate(s):
    # Remove whitespace for simpler parsing.
    s = s.replace(" ", "")
    pos = 0

    def parse_expression():
        nonlocal pos
        # <expression> ::= <term> { ('+' | '-') <term> }
        value = parse_term()
        while pos < len(s) and s[pos] in '+-':
            op = s[pos]
            pos += 1
            next_val = parse_term()
            if op == '+':
                value += next_val
            else:
                value -= next_val
        return value

    def parse_term():
        nonlocal pos
        # <term> ::= <factor> { ('*' | '/') <factor> }
        value = parse_factor()
        while pos < len(s) and s[pos] in '*/':
            op = s[pos]
            pos += 1
            next_val = parse_factor()
            if op == '*':
                value *= next_val
            else:
                value /= next_val
        return value

    def parse_factor():
        nonlocal pos
        # <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor>
        if pos < len(s):
            # Check for prefix operators "sin" and "cos"
            if s.startswith("sin", pos):
                pos += 3  # consume "sin"
                value = parse_factor()
                return math.sin(value)
            if s.startswith("cos", pos):
                pos += 3  # consume "cos"
                value = parse_factor()
                return math.cos(value)
            # Check for parenthesis
            if s[pos] == "(":
                pos += 1  # consume '('
                value = parse_expression()
                if pos < len(s) and s[pos] == ")":
                    pos += 1  # consume ')'
                else:
                    raise ValueError("Missing closing parenthesis")
                return value
            # Otherwise it must be a number.
            return parse_number()
        raise ValueError("Unexpected end of expression")

    def parse_number():
        nonlocal pos
        # <number> ::= <digit> | <number> <digit>
        start = pos
        while pos < len(s) and s[pos].isdigit():
            pos += 1
        if start == pos:
            raise ValueError("Expected a number at position {}".format(pos))
        return float(s[start:pos])
    
    result = parse_expression()
    if pos < len(s):
        raise ValueError("Unexpected character at position {}".format(pos))
    return result

Run Code Interpreter

Running the following program: 

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import math

def evaluate(s):
    # Remove whitespace for simpler parsing.
    s = s.replace(" ", "")
    pos = 0

    def parse_expression():
        nonlocal pos
        # <expression> ::= <term> { ('+' | '-') <term> }
        value = parse_term()
        while pos < len(s) and s[pos] in '+-':
            op = s[pos]
            pos += 1
            next_val = parse_term()
            if op == '+':
                value += next_val
            else:
                value -= next_val
        return value

    def parse_term():
        nonlocal pos
        # <term> ::= <factor> { ('*' | '/') <factor> }
        value = parse_factor()
        while pos < len(s) and s[pos] in '*/':
            op = s[pos]
            pos += 1
            next_val = parse_factor()
            if op == '*':
                value *= next_val
            else:
                value /= next_val
        return value

    def parse_factor():
        nonlocal pos
        # <factor> ::= <number> | '(' <expression> ')' | <prefix-op> <factor>
        if pos < len(s):
            # Check for prefix operators "sin" and "cos"
            if s.startswith("sin", pos):
                pos += 3  # consume "sin"
                value = parse_factor()
                return math.sin(value)
            if s.startswith("cos", pos):
                pos += 3  # consume "cos"
                value = parse_factor()
                return math.cos(value)
            # Check for parenthesis
            if s[pos] == "(":
                pos += 1  # consume '('
                value = parse_expression()
                if pos < len(s) and s[pos] == ")":
                    pos += 1  # consume ')'
                else:
                    raise ValueError("Missing closing parenthesis")
                return value
            # Otherwise it must be a number.
            return parse_number()
        raise ValueError("Unexpected end of expression")

    def parse_number():
        nonlocal pos
        # <number> ::= <digit> | <number> <digit>
        start = pos
        while pos < len(s) and s[pos].isdigit():
            pos += 1
        if start == pos:
            raise ValueError("Expected a number at position {}".format(pos))
        return float(s[start:pos])
    
    result = parse_expression()
    if pos < len(s):
        raise ValueError("Unexpected character at position {}".format(pos))
    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