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

To evaluate the given expression based on the BNF-style grammar, we can implement a recursive descent parser. This type of parser will break down the problem by creating functions that correspond to each rule in the grammar. For mathematical operations, we'll also import Python's `math` module for trigonometric functions. Here's an implementation: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
import math

def evaluate_expression(input_str):
    return ExpressionParser(input_str).parse()

class ExpressionParser:
    def __init__(self, input_str):
        self.input_str = input_str.replace(" ", "")  # Remove spaces for simplicity
        self.index = 0

    def parse(self):
        return self.expression()

    def current_char(self):
        if self.index < len(self.input_str):
            return self.input_str[self.index]
        return None

    def consume(self):
        self.index += 1

    def number(self):
        start_index = self.index
        while self.current_char() and self.current_char().isdigit():
            self.consume()
        return int(self.input_str[start_index:self.index])

    def factor(self):
        if self.current_char() == '(':
            self.consume()  # Consume '('
            result = self.expression()
            self.consume()  # Consume ')'
            return result
        elif self.current_char().isdigit():
            return self.number()
        else:  # Check for prefix-op
            start_index = self.index
            while self.current_char() and not self.current_char().isdigit() and self.current_char() not in ['+', '-', '*', '/', '(', ')']:
                self.consume()
            op = self.input_str[start_index:self.index]
            if op == 'sin':
                return math.sin(self.factor())
            elif op == 'cos':
                return math.cos(self.factor())
            else:
                raise ValueError(f"Unexpected operator: {op}")

    def term(self):
        result = self.factor()
        while self.current_char() in ['*', '/']:
            if self.current_char() == '*':
                self.consume()
                result *= self.factor()
            elif self.current_char() == '/':
                self.consume()
                result /= self.factor()
        return result

    def expression(self):
        result = self.term()
        while self.current_char() in ['+', '-']:
            if self.current_char() == '+':
                self.consume()
                result += self.term()
            elif self.current_char() == '-':
                self.consume()
                result -= self.term()
        return result

# Example usage:
expr = "sin(3 + 2 * 4) - cos(15)"
result = evaluate_expression(expr)
print(f"{expr} = {result}")
This code defines a class `ExpressionParser` that takes the input string and processes it according to the rules defined in the grammar. By recursively calling the methods corresponding to each grammar rule, it can evaluate complex expressions including nested operations and trigonometric functions. The `parse` method kicks off the parsing process and returns the final result. Keep in mind, this is a basic implementation. For more complex grammars or for better error handling, you might need to enhance this code accordingly, including better handling of invalid inputs or support for more functions and operators.

Extract Code

I extracted the following code from that output: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
import math

def evaluate_expression(input_str):
    return ExpressionParser(input_str).parse()

class ExpressionParser:
    def __init__(self, input_str):
        self.input_str = input_str.replace(" ", "")  # Remove spaces for simplicity
        self.index = 0

    def parse(self):
        return self.expression()

    def current_char(self):
        if self.index < len(self.input_str):
            return self.input_str[self.index]
        return None

    def consume(self):
        self.index += 1

    def number(self):
        start_index = self.index
        while self.current_char() and self.current_char().isdigit():
            self.consume()
        return int(self.input_str[start_index:self.index])

    def factor(self):
        if self.current_char() == '(':
            self.consume()  # Consume '('
            result = self.expression()
            self.consume()  # Consume ')'
            return result
        elif self.current_char().isdigit():
            return self.number()
        else:  # Check for prefix-op
            start_index = self.index
            while self.current_char() and not self.current_char().isdigit() and self.current_char() not in ['+', '-', '*', '/', '(', ')']:
                self.consume()
            op = self.input_str[start_index:self.index]
            if op == 'sin':
                return math.sin(self.factor())
            elif op == 'cos':
                return math.cos(self.factor())
            else:
                raise ValueError(f"Unexpected operator: {op}")

    def term(self):
        result = self.factor()
        while self.current_char() in ['*', '/']:
            if self.current_char() == '*':
                self.consume()
                result *= self.factor()
            elif self.current_char() == '/':
                self.consume()
                result /= self.factor()
        return result

    def expression(self):
        result = self.term()
        while self.current_char() in ['+', '-']:
            if self.current_char() == '+':
                self.consume()
                result += self.term()
            elif self.current_char() == '-':
                self.consume()
                result -= self.term()
        return result

# Example usage:
expr = "sin(3 + 2 * 4) - cos(15)"
result = evaluate_expression(expr)
print(f"{expr} = {result}")

Run Code Interpreter

Running the following program: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
import math

def evaluate_expression(input_str):
    return ExpressionParser(input_str).parse()

class ExpressionParser:
    def __init__(self, input_str):
        self.input_str = input_str.replace(" ", "")  # Remove spaces for simplicity
        self.index = 0

    def parse(self):
        return self.expression()

    def current_char(self):
        if self.index < len(self.input_str):
            return self.input_str[self.index]
        return None

    def consume(self):
        self.index += 1

    def number(self):
        start_index = self.index
        while self.current_char() and self.current_char().isdigit():
            self.consume()
        return int(self.input_str[start_index:self.index])

    def factor(self):
        if self.current_char() == '(':
            self.consume()  # Consume '('
            result = self.expression()
            self.consume()  # Consume ')'
            return result
        elif self.current_char().isdigit():
            return self.number()
        else:  # Check for prefix-op
            start_index = self.index
            while self.current_char() and not self.current_char().isdigit() and self.current_char() not in ['+', '-', '*', '/', '(', ')']:
                self.consume()
            op = self.input_str[start_index:self.index]
            if op == 'sin':
                return math.sin(self.factor())
            elif op == 'cos':
                return math.cos(self.factor())
            else:
                raise ValueError(f"Unexpected operator: {op}")

    def term(self):
        result = self.factor()
        while self.current_char() in ['*', '/']:
            if self.current_char() == '*':
                self.consume()
                result *= self.factor()
            elif self.current_char() == '/':
                self.consume()
                result /= self.factor()
        return result

    def expression(self):
        result = self.term()
        while self.current_char() in ['+', '-']:
            if self.current_char() == '+':
                self.consume()
                result += self.term()
            elif self.current_char() == '-':
                self.consume()
                result -= self.term()
        return result

# Example usage:
expr = "sin(3 + 2 * 4) - cos(15)"
result = evaluate_expression(expr)
print(f"{expr} = {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: sin(3 + 2 * 4) - cos(15) = -0.24030229369188216 Traceback (most recent call last): File "/usr/src/app/main.py", line 80, in <module> answer = round(evaluate('sin(35+2*4)-cos(15)'), 5) ^^^^^^^^ NameError: name 'evaluate' is not defined

Substring Evaluation

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

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

To evaluate the given expression as per the provided BNF-style grammar, we can follow these steps: 1. Parse the input string according to the grammar rules. 2. Evaluate the parsed structure. This can be done using a recursive approach, where each non-terminal in the grammar corresponds to a function in the code. We'll also need to handle the conversion of numeric strings to actual numbers and support the evaluation of the 'sin' and 'cos' operations. Here's how you could implement this: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
import math

def evaluate_expression(expression):
    # This is the entry point for evaluating an expression
    result, remaining = parse_expression(expression)
    if remaining:  # If there's any input left unparsed, it's an error
        raise ValueError(f"Unexpected characters left after parsing: {remaining}")
    return result

def parse_expression(input_str):
    # Parse <expression>
    result, remaining = parse_term(input_str)
    while remaining and remaining[0] in ['+', '-']:
        op = remaining[0]
        next_term, remaining = parse_term(remaining[1:])
        if op == '+':
            result += next_term
        else:
            result -= next_term
    return result, remaining

def parse_term(input_str):
    # Parse <term>
    result, remaining = parse_factor(input_str)
    while remaining and remaining[0] in ['*', '/']:
        op = remaining[0]
        next_factor, remaining = parse_factor(remaining[1:])
        if op == '*':
            result *= next_factor
        else:
            result /= next_factor
    return result, remaining

def parse_factor(input_str):
    # Parse <factor>
    if input_str.startswith(('sin', 'cos')):
        op, remaining = input_str[:3], input_str[3:]
        factor_result, remaining = parse_factor(remaining)
        if op == 'sin':
            return math.sin(factor_result), remaining
        else:
            return math.cos(factor_result), remaining
    elif input_str[0] == '(':
        expr_result, remaining = parse_expression(input_str[1:])
        if remaining[0] != ')':
            raise ValueError("Expected ')' after expression.")
        return expr_result, remaining[1:]
    else:
        return parse_number(input_str)

def parse_number(input_str):
    # Parse <number>
    num_str = ''
    index = 0
    while index < len(input_str) and input_str[index].isdigit():
        num_str += input_str[index]
        index += 1
    if not num_str:
        raise ValueError("Expected a number, found none.")
    return float(num_str), input_str[index:]

def evaluate(input_str):
    try:
        result = evaluate_expression(input_str)
        return result
    except ValueError as e:
        print(f"Error evaluating expression: {e}")
        return None

# Example usage
if __name__ == "__main__":
    print(evaluate("sin(3 + 2 * 4) - cos(15)"))  # Your example
This code breaks down the evaluation process according to your grammar. Each function handles a specific part of the grammar, calling others recursively as needed. Note that this implementation assumes that the input is well-formed; it may not gracefully handle all forms of malformed input.

Extract Code

I extracted the following code from that output: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
import math

def evaluate_expression(expression):
    # This is the entry point for evaluating an expression
    result, remaining = parse_expression(expression)
    if remaining:  # If there's any input left unparsed, it's an error
        raise ValueError(f"Unexpected characters left after parsing: {remaining}")
    return result

def parse_expression(input_str):
    # Parse <expression>
    result, remaining = parse_term(input_str)
    while remaining and remaining[0] in ['+', '-']:
        op = remaining[0]
        next_term, remaining = parse_term(remaining[1:])
        if op == '+':
            result += next_term
        else:
            result -= next_term
    return result, remaining

def parse_term(input_str):
    # Parse <term>
    result, remaining = parse_factor(input_str)
    while remaining and remaining[0] in ['*', '/']:
        op = remaining[0]
        next_factor, remaining = parse_factor(remaining[1:])
        if op == '*':
            result *= next_factor
        else:
            result /= next_factor
    return result, remaining

def parse_factor(input_str):
    # Parse <factor>
    if input_str.startswith(('sin', 'cos')):
        op, remaining = input_str[:3], input_str[3:]
        factor_result, remaining = parse_factor(remaining)
        if op == 'sin':
            return math.sin(factor_result), remaining
        else:
            return math.cos(factor_result), remaining
    elif input_str[0] == '(':
        expr_result, remaining = parse_expression(input_str[1:])
        if remaining[0] != ')':
            raise ValueError("Expected ')' after expression.")
        return expr_result, remaining[1:]
    else:
        return parse_number(input_str)

def parse_number(input_str):
    # Parse <number>
    num_str = ''
    index = 0
    while index < len(input_str) and input_str[index].isdigit():
        num_str += input_str[index]
        index += 1
    if not num_str:
        raise ValueError("Expected a number, found none.")
    return float(num_str), input_str[index:]

def evaluate(input_str):
    try:
        result = evaluate_expression(input_str)
        return result
    except ValueError as e:
        print(f"Error evaluating expression: {e}")
        return None

# Example usage
if __name__ == "__main__":
    print(evaluate("sin(3 + 2 * 4) - cos(15)"))  # Your example

Run Code Interpreter

Running the following program: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
import math

def evaluate_expression(expression):
    # This is the entry point for evaluating an expression
    result, remaining = parse_expression(expression)
    if remaining:  # If there's any input left unparsed, it's an error
        raise ValueError(f"Unexpected characters left after parsing: {remaining}")
    return result

def parse_expression(input_str):
    # Parse <expression>
    result, remaining = parse_term(input_str)
    while remaining and remaining[0] in ['+', '-']:
        op = remaining[0]
        next_term, remaining = parse_term(remaining[1:])
        if op == '+':
            result += next_term
        else:
            result -= next_term
    return result, remaining

def parse_term(input_str):
    # Parse <term>
    result, remaining = parse_factor(input_str)
    while remaining and remaining[0] in ['*', '/']:
        op = remaining[0]
        next_factor, remaining = parse_factor(remaining[1:])
        if op == '*':
            result *= next_factor
        else:
            result /= next_factor
    return result, remaining

def parse_factor(input_str):
    # Parse <factor>
    if input_str.startswith(('sin', 'cos')):
        op, remaining = input_str[:3], input_str[3:]
        factor_result, remaining = parse_factor(remaining)
        if op == 'sin':
            return math.sin(factor_result), remaining
        else:
            return math.cos(factor_result), remaining
    elif input_str[0] == '(':
        expr_result, remaining = parse_expression(input_str[1:])
        if remaining[0] != ')':
            raise ValueError("Expected ')' after expression.")
        return expr_result, remaining[1:]
    else:
        return parse_number(input_str)

def parse_number(input_str):
    # Parse <number>
    num_str = ''
    index = 0
    while index < len(input_str) and input_str[index].isdigit():
        num_str += input_str[index]
        index += 1
    if not num_str:
        raise ValueError("Expected a number, found none.")
    return float(num_str), input_str[index:]

def evaluate(input_str):
    try:
        result = evaluate_expression(input_str)
        return result
    except ValueError as e:
        print(f"Error evaluating expression: {e}")
        return None

# Example usage
if __name__ == "__main__":
    print(evaluate("sin(3 + 2 * 4) - cos(15)"))  # Your example





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: Error evaluating expression: Expected ')' after expression. None 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

To evaluate expressions defined by the provided BNF-style grammar, we'll write a Python function that processes the input string step by step. This function will need to handle the precedence of operations as defined by the grammar: parentheses and prefix operations (like `sin` and `cos`) have the highest precedence, followed by multiplication and division, and finally addition and subtraction. We'll use a recursive descent parser approach, where we have a function or a block of code for each rule in the grammar. This approach is straightforward for implementing parsers for simple grammars like the one provided. Here's how to implement the `evaluate` function: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
import math

def tokenize(expression):
    tokens = []
    i = 0
    while i < len(expression):
        if expression[i].isspace():
            i += 1
            continue
        elif expression[i].isdigit():
            num = expression[i]
            i += 1
            while i < len(expression) and expression[i].isdigit():
                num += expression[i]
                i += 1
            tokens.append(('NUMBER', int(num)))
        elif expression[i] in "+-*/()":
            tokens.append((expression[i], expression[i]))
            i += 1
        elif expression[i:i+3] in ["sin", "cos"]:
            tokens.append((expression[i:i+3], expression[i:i+3]))
            i += 3
        else:
            raise ValueError("Unknown character: {}".format(expression[i]))
    tokens.append(('EOF', None))
    return tokens

def parse_factor(tokens):
    token, value = tokens.pop(0)
    if token == 'NUMBER':
        return value
    elif token in ['sin', 'cos']:
        factor_value = parse_factor(tokens)
        if token == 'sin':
            return math.sin(factor_value)
        else:
            return math.cos(factor_value)
    elif token == '(':
        expr_value = parse_expression(tokens)
        if tokens.pop(0)[0] != ')':
            raise ValueError("Missing closing parenthesis")
        return expr_value
    else:
        raise ValueError("Unexpected token: {}".format(token))

def parse_term(tokens):
    left = parse_factor(tokens)
    while tokens[0][0] in ['*', '/']:
        op, _ = tokens.pop(0)
        right = parse_factor(tokens)
        if op == '*':
            left *= right
        else:
            left /= right
    return left

def parse_expression(tokens):
    left = parse_term(tokens)
    while tokens[0][0] in ['+', '-']:
        op, _ = tokens.pop(0)
        right = parse_term(tokens)
        if op == '+':
            left += right
        else:
            left -= right
    return left

def evaluate(expression):
    tokens = tokenize(expression)
    return parse_expression(tokens)

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result}")
Explanation of the approach: 1. **Tokenization**: The `tokenize` function goes through the input string and breaks it down into a list of recognizable tokens (e.g., numbers, operators, parentheses, `sin`, `cos`). 2. **Parsing**: The parsing functions (`parse_expression`, `parse_term`, `parse_factor`) work recursively to evaluate the expression according to the grammar rules. Each function corresponds to a rule in the grammar and calls others as necessary to process its components. 3. **Evaluation**: As the parser goes through the expression, it evaluates the operations in the correct order, taking into account the precedence rules defined by the grammar. This approach allows for the modular handling of each grammar rule and can be extended or modified relatively easily for changes in the grammar or additional features.

Extract Code

I extracted the following code from that output: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
import math

def tokenize(expression):
    tokens = []
    i = 0
    while i < len(expression):
        if expression[i].isspace():
            i += 1
            continue
        elif expression[i].isdigit():
            num = expression[i]
            i += 1
            while i < len(expression) and expression[i].isdigit():
                num += expression[i]
                i += 1
            tokens.append(('NUMBER', int(num)))
        elif expression[i] in "+-*/()":
            tokens.append((expression[i], expression[i]))
            i += 1
        elif expression[i:i+3] in ["sin", "cos"]:
            tokens.append((expression[i:i+3], expression[i:i+3]))
            i += 3
        else:
            raise ValueError("Unknown character: {}".format(expression[i]))
    tokens.append(('EOF', None))
    return tokens

def parse_factor(tokens):
    token, value = tokens.pop(0)
    if token == 'NUMBER':
        return value
    elif token in ['sin', 'cos']:
        factor_value = parse_factor(tokens)
        if token == 'sin':
            return math.sin(factor_value)
        else:
            return math.cos(factor_value)
    elif token == '(':
        expr_value = parse_expression(tokens)
        if tokens.pop(0)[0] != ')':
            raise ValueError("Missing closing parenthesis")
        return expr_value
    else:
        raise ValueError("Unexpected token: {}".format(token))

def parse_term(tokens):
    left = parse_factor(tokens)
    while tokens[0][0] in ['*', '/']:
        op, _ = tokens.pop(0)
        right = parse_factor(tokens)
        if op == '*':
            left *= right
        else:
            left /= right
    return left

def parse_expression(tokens):
    left = parse_term(tokens)
    while tokens[0][0] in ['+', '-']:
        op, _ = tokens.pop(0)
        right = parse_term(tokens)
        if op == '+':
            left += right
        else:
            left -= right
    return left

def evaluate(expression):
    tokens = tokenize(expression)
    return parse_expression(tokens)

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result}")

Run Code Interpreter

Running the following program: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
import math

def tokenize(expression):
    tokens = []
    i = 0
    while i < len(expression):
        if expression[i].isspace():
            i += 1
            continue
        elif expression[i].isdigit():
            num = expression[i]
            i += 1
            while i < len(expression) and expression[i].isdigit():
                num += expression[i]
                i += 1
            tokens.append(('NUMBER', int(num)))
        elif expression[i] in "+-*/()":
            tokens.append((expression[i], expression[i]))
            i += 1
        elif expression[i:i+3] in ["sin", "cos"]:
            tokens.append((expression[i:i+3], expression[i:i+3]))
            i += 3
        else:
            raise ValueError("Unknown character: {}".format(expression[i]))
    tokens.append(('EOF', None))
    return tokens

def parse_factor(tokens):
    token, value = tokens.pop(0)
    if token == 'NUMBER':
        return value
    elif token in ['sin', 'cos']:
        factor_value = parse_factor(tokens)
        if token == 'sin':
            return math.sin(factor_value)
        else:
            return math.cos(factor_value)
    elif token == '(':
        expr_value = parse_expression(tokens)
        if tokens.pop(0)[0] != ')':
            raise ValueError("Missing closing parenthesis")
        return expr_value
    else:
        raise ValueError("Unexpected token: {}".format(token))

def parse_term(tokens):
    left = parse_factor(tokens)
    while tokens[0][0] in ['*', '/']:
        op, _ = tokens.pop(0)
        right = parse_factor(tokens)
        if op == '*':
            left *= right
        else:
            left /= right
    return left

def parse_expression(tokens):
    left = parse_term(tokens)
    while tokens[0][0] in ['+', '-']:
        op, _ = tokens.pop(0)
        right = parse_term(tokens)
        if op == '+':
            left += right
        else:
            left -= right
    return left

def evaluate(expression):
    tokens = tokenize(expression)
    return parse_expression(tokens)

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {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: sin(3 + 2 * 4) - cos(15) = -0.24030229369188216 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

To evaluate the expression defined by the given BNF-style grammar, we'll write a Python function named `evaluate`. The function will parse and evaluate expressions recursively according to the defined grammar rules. The evaluation will involve basic arithmetic operations, as well as handling of trigonometric functions (sin and cos) for the prefix operations. We'll start by implementing a basic parser that can handle the grammar's elements step by step, from parsing numbers, factors, terms, to full expressions. 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
import math

def parse_number(s, index):
    number = 0
    while index < len(s) and s[index].isdigit():
        number = number * 10 + int(s[index])
        index += 1
    return number, index

def parse_factor(s, index):
    if s[index] == '(':
        value, index = parse_expression(s, index + 1)
        if s[index] == ')':
            index += 1
        return value, index
    elif s[index:index+3] == 'sin' or s[index:index+3] == 'cos':
        op = s[index:index+3]
        value, index = parse_factor(s, index + 3)
        if op == 'sin':
            return math.sin(value), index
        else:
            return math.cos(value), index
    else:
        return parse_number(s, index)

def parse_term(s, index):
    value, index = parse_factor(s, index)
    while index < len(s) and s[index] in '*/':
        op = s[index]
        index += 1
        right, index = parse_factor(s, index)
        if op == '*':
            value *= right
        else:
            value /= right
    return value, index

def parse_expression(s, index):
    value, index = parse_term(s, index)
    while index < len(s) and s[index] in '+-':
        op = s[index]
        index += 1
        right, index = parse_term(s, index)
        if op == '+':
            value += right
        else:
            value -= right
    return value, index

def evaluate(s):
    s = s.replace(" ", "")  # Remove spaces to simplify parsing
    result, _ = parse_expression(s, 0)
    return result

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result}")
This implementation breaks down the parsing and evaluation process according to the provided grammar. It starts with the smallest parts of the grammar (numbers and factors) and builds up to handle more complex expressions involving arithmetic and trigonometric operations. Note: This code assumes the input string `s` is valid according to the given grammar and does not include thorough error handling for invalid inputs or malformed expressions. Additional checks and error handling mechanisms can be added based on specific requirements.

Extract Code

I extracted the following code from that output: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
import math

def parse_number(s, index):
    number = 0
    while index < len(s) and s[index].isdigit():
        number = number * 10 + int(s[index])
        index += 1
    return number, index

def parse_factor(s, index):
    if s[index] == '(':
        value, index = parse_expression(s, index + 1)
        if s[index] == ')':
            index += 1
        return value, index
    elif s[index:index+3] == 'sin' or s[index:index+3] == 'cos':
        op = s[index:index+3]
        value, index = parse_factor(s, index + 3)
        if op == 'sin':
            return math.sin(value), index
        else:
            return math.cos(value), index
    else:
        return parse_number(s, index)

def parse_term(s, index):
    value, index = parse_factor(s, index)
    while index < len(s) and s[index] in '*/':
        op = s[index]
        index += 1
        right, index = parse_factor(s, index)
        if op == '*':
            value *= right
        else:
            value /= right
    return value, index

def parse_expression(s, index):
    value, index = parse_term(s, index)
    while index < len(s) and s[index] in '+-':
        op = s[index]
        index += 1
        right, index = parse_term(s, index)
        if op == '+':
            value += right
        else:
            value -= right
    return value, index

def evaluate(s):
    s = s.replace(" ", "")  # Remove spaces to simplify parsing
    result, _ = parse_expression(s, 0)
    return result

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result}")

Run Code Interpreter

Running the following program: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
import math

def parse_number(s, index):
    number = 0
    while index < len(s) and s[index].isdigit():
        number = number * 10 + int(s[index])
        index += 1
    return number, index

def parse_factor(s, index):
    if s[index] == '(':
        value, index = parse_expression(s, index + 1)
        if s[index] == ')':
            index += 1
        return value, index
    elif s[index:index+3] == 'sin' or s[index:index+3] == 'cos':
        op = s[index:index+3]
        value, index = parse_factor(s, index + 3)
        if op == 'sin':
            return math.sin(value), index
        else:
            return math.cos(value), index
    else:
        return parse_number(s, index)

def parse_term(s, index):
    value, index = parse_factor(s, index)
    while index < len(s) and s[index] in '*/':
        op = s[index]
        index += 1
        right, index = parse_factor(s, index)
        if op == '*':
            value *= right
        else:
            value /= right
    return value, index

def parse_expression(s, index):
    value, index = parse_term(s, index)
    while index < len(s) and s[index] in '+-':
        op = s[index]
        index += 1
        right, index = parse_term(s, index)
        if op == '+':
            value += right
        else:
            value -= right
    return value, index

def evaluate(s):
    s = s.replace(" ", "")  # Remove spaces to simplify parsing
    result, _ = parse_expression(s, 0)
    return result

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {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: sin(3 + 2 * 4) - cos(15) = -0.24030229369188216 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

To tackle this problem, we'll build a simple recursive descent parser based on the provided grammar. The `evaluate` function will parse the input string according to the rules defined in the BNF grammar and compute the result. Note that we will use Python's built-in `math` library for computing sine and cosine values. Let's break down the implementation according to the grammar: 1. **Expression**: Handles addition and subtraction operations. 2. **Term**: Handles multiplication and division operations. 3. **Factor**: Deals with numbers, expressions enclosed in parentheses, and operations prefixed by `sin` or `cos`. 4. **Prefix-op**: Applies the sine or cosine operation to a factor. 5. **Number**: Parses numeric values. Here's the Python code implementing the above logic: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
import math

class Parser:
    def __init__(self, expression):
        self.tokens = self.tokenize(expression)
        self.current_token = None
        self.next_token()
    
    def tokenize(self, expression):
        # Tokenize the input string: numbers, parentheses, operators, and prefix-ops
        tokens = []
        i = 0
        while i < len(expression):
            if expression[i].isspace():
                i += 1
            elif expression[i].isdigit():
                num = expression[i]
                i += 1
                while i < len(expression) and expression[i].isdigit():
                    num += expression[i]
                    i += 1
                tokens.append(('NUMBER', float(num)))
            elif expression[i] in '+-*/()':
                tokens.append(expression[i])
                i += 1
            elif expression[i:i+3] == 'sin' or expression[i:i+3] == 'cos':
                tokens.append(expression[i:i+3])
                i += 3
            else:
                raise ValueError("Unknown character: {}".format(expression[i]))
        tokens.append(('EOF', None))
        return tokens
    
    def next_token(self):
        self.current_token = self.tokens.pop(0)
    
    def parse_expression(self):
        result = self.parse_term()
        while self.current_token in ('+', '-'):
            if self.current_token == '+':
                self.next_token()
                result += self.parse_term()
            elif self.current_token == '-':
                self.next_token()
                result -= self.parse_term()
        return result
    
    def parse_term(self):
        result = self.parse_factor()
        while self.current_token in ('*', '/'):
            if self.current_token == '*':
                self.next_token()
                result *= self.parse_factor()
            elif self.current_token == '/':
                self.next_token()
                divisor = self.parse_factor()
                if divisor == 0:
                    raise ValueError("Division by zero")
                result /= divisor
        return result
    
    def parse_factor(self):
        if self.current_token == '(':
            self.next_token()  # skip '('
            result = self.parse_expression()
            if self.current_token != ')':
                raise ValueError("Expected ')'")
            self.next_token()  # skip ')'
            return result
        elif self.current_token in ['sin', 'cos']:
            op = self.current_token
            self.next_token()
            if op == 'sin':
                return math.sin(self.parse_factor())
            else:
                return math.cos(self.parse_factor())
        elif isinstance(self.current_token, tuple) and self.current_token[0] == 'NUMBER':
            value = self.current_token[1]
            self.next_token()
            return value
        else:
            raise ValueError("Unexpected token: {}".format(self.current_token))
    
    def evaluate(self):
        return self.parse_expression()

def evaluate(expression):
    parser = Parser(expression)
    return parser.evaluate()

# Example usage
print(evaluate("sin(3 + 2 * 4) - cos(15)"))  # This should output something close to -0.240302
This code provides a basic implementation of the required functionality. Note that it directly evaluates the expressions as it parses them. Error handling is minimal, and more robust error checking (such as for invalid tokens or syntax errors) can be implemented as needed.

Extract Code

I extracted the following code from that output: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
import math

class Parser:
    def __init__(self, expression):
        self.tokens = self.tokenize(expression)
        self.current_token = None
        self.next_token()
    
    def tokenize(self, expression):
        # Tokenize the input string: numbers, parentheses, operators, and prefix-ops
        tokens = []
        i = 0
        while i < len(expression):
            if expression[i].isspace():
                i += 1
            elif expression[i].isdigit():
                num = expression[i]
                i += 1
                while i < len(expression) and expression[i].isdigit():
                    num += expression[i]
                    i += 1
                tokens.append(('NUMBER', float(num)))
            elif expression[i] in '+-*/()':
                tokens.append(expression[i])
                i += 1
            elif expression[i:i+3] == 'sin' or expression[i:i+3] == 'cos':
                tokens.append(expression[i:i+3])
                i += 3
            else:
                raise ValueError("Unknown character: {}".format(expression[i]))
        tokens.append(('EOF', None))
        return tokens
    
    def next_token(self):
        self.current_token = self.tokens.pop(0)
    
    def parse_expression(self):
        result = self.parse_term()
        while self.current_token in ('+', '-'):
            if self.current_token == '+':
                self.next_token()
                result += self.parse_term()
            elif self.current_token == '-':
                self.next_token()
                result -= self.parse_term()
        return result
    
    def parse_term(self):
        result = self.parse_factor()
        while self.current_token in ('*', '/'):
            if self.current_token == '*':
                self.next_token()
                result *= self.parse_factor()
            elif self.current_token == '/':
                self.next_token()
                divisor = self.parse_factor()
                if divisor == 0:
                    raise ValueError("Division by zero")
                result /= divisor
        return result
    
    def parse_factor(self):
        if self.current_token == '(':
            self.next_token()  # skip '('
            result = self.parse_expression()
            if self.current_token != ')':
                raise ValueError("Expected ')'")
            self.next_token()  # skip ')'
            return result
        elif self.current_token in ['sin', 'cos']:
            op = self.current_token
            self.next_token()
            if op == 'sin':
                return math.sin(self.parse_factor())
            else:
                return math.cos(self.parse_factor())
        elif isinstance(self.current_token, tuple) and self.current_token[0] == 'NUMBER':
            value = self.current_token[1]
            self.next_token()
            return value
        else:
            raise ValueError("Unexpected token: {}".format(self.current_token))
    
    def evaluate(self):
        return self.parse_expression()

def evaluate(expression):
    parser = Parser(expression)
    return parser.evaluate()

# Example usage
print(evaluate("sin(3 + 2 * 4) - cos(15)"))  # This should output something close to -0.240302

Run Code Interpreter

Running the following program: 

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
import math

class Parser:
    def __init__(self, expression):
        self.tokens = self.tokenize(expression)
        self.current_token = None
        self.next_token()
    
    def tokenize(self, expression):
        # Tokenize the input string: numbers, parentheses, operators, and prefix-ops
        tokens = []
        i = 0
        while i < len(expression):
            if expression[i].isspace():
                i += 1
            elif expression[i].isdigit():
                num = expression[i]
                i += 1
                while i < len(expression) and expression[i].isdigit():
                    num += expression[i]
                    i += 1
                tokens.append(('NUMBER', float(num)))
            elif expression[i] in '+-*/()':
                tokens.append(expression[i])
                i += 1
            elif expression[i:i+3] == 'sin' or expression[i:i+3] == 'cos':
                tokens.append(expression[i:i+3])
                i += 3
            else:
                raise ValueError("Unknown character: {}".format(expression[i]))
        tokens.append(('EOF', None))
        return tokens
    
    def next_token(self):
        self.current_token = self.tokens.pop(0)
    
    def parse_expression(self):
        result = self.parse_term()
        while self.current_token in ('+', '-'):
            if self.current_token == '+':
                self.next_token()
                result += self.parse_term()
            elif self.current_token == '-':
                self.next_token()
                result -= self.parse_term()
        return result
    
    def parse_term(self):
        result = self.parse_factor()
        while self.current_token in ('*', '/'):
            if self.current_token == '*':
                self.next_token()
                result *= self.parse_factor()
            elif self.current_token == '/':
                self.next_token()
                divisor = self.parse_factor()
                if divisor == 0:
                    raise ValueError("Division by zero")
                result /= divisor
        return result
    
    def parse_factor(self):
        if self.current_token == '(':
            self.next_token()  # skip '('
            result = self.parse_expression()
            if self.current_token != ')':
                raise ValueError("Expected ')'")
            self.next_token()  # skip ')'
            return result
        elif self.current_token in ['sin', 'cos']:
            op = self.current_token
            self.next_token()
            if op == 'sin':
                return math.sin(self.parse_factor())
            else:
                return math.cos(self.parse_factor())
        elif isinstance(self.current_token, tuple) and self.current_token[0] == 'NUMBER':
            value = self.current_token[1]
            self.next_token()
            return value
        else:
            raise ValueError("Unexpected token: {}".format(self.current_token))
    
    def evaluate(self):
        return self.parse_expression()

def evaluate(expression):
    parser = Parser(expression)
    return parser.evaluate()

# Example usage
print(evaluate("sin(3 + 2 * 4) - cos(15)"))  # This should output something close to -0.240302





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: -0.24030229369188216 All tests passed

Substring Evaluation

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