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 based on the given BNF-style grammar, we can use a recursive descent parser. This involves writing functions that correspond to each non-terminal in the grammar and recursively parsing the input string. Here’s a Python implementation of the `evaluate` function: 

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import math
import re

class Parser:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|\+|\-|\*|/|\(|\)|sin|cos', expression)
        self.current_token = None
        self.next_token()

    def next_token(self):
        if self.tokens:
            self.current_token = self.tokens.pop(0)
        else:
            self.current_token = None

    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()
                result /= self.parse_factor()
        return result

    def parse_factor(self):
        if self.current_token == '(':
            self.next_token()
            result = self.parse_expression()
            if self.current_token != ')':
                raise SyntaxError("Expected ')'")
            self.next_token()
            return result
        elif self.current_token in ('sin', 'cos'):
            op = self.current_token
            self.next_token()
            if self.current_token != '(':
                raise SyntaxError("Expected '(' after prefix operator")
            self.next_token()
            arg = self.parse_expression()
            if self.current_token != ')':
                raise SyntaxError("Expected ')'")
            self.next_token()
            if op == 'sin':
                return math.sin(arg)
            elif op == 'cos':
                return math.cos(arg)
        else:
            try:
                result = float(self.current_token)
                self.next_token()
                return result
            except ValueError:
                raise SyntaxError(f"Unexpected token: {self.current_token}")

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

# Example usage:
result = evaluate("sin(3 + 2 * 4) - cos(15)")
print(result)  # Output: -0.240302
### Explanation: 1. **Tokenizer**: The `Parser` class uses a regular expression to tokenize the input string into numbers, operators, and function names. 2. **Recursive Parsing**: - `parse_expression`: Handles addition and subtraction. - `parse_term`: Handles multiplication and division. - `parse_factor`: Handles numbers, parentheses, and prefix operators (`sin`, `cos`). 3. **Evaluation**: - The `evaluate` function initializes the parser and starts parsing from the top-level expression. 4. **Error Handling**: The parser raises `SyntaxError` if it encounters unexpected tokens or missing parentheses. ### Example: For the expression `"sin(3 + 2 * 4) - cos(15)"`, the parser will: - Parse `sin(3 + 2 * 4)` as `math.sin(3 + 2 * 4)`. - Parse `cos(15)` as `math.cos(15)`. - Subtract the two results to get `-0.240302`. This implementation should correctly evaluate expressions according to the given grammar.

Extract Code

I extracted the following code from that output: 

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import math
import re

class Parser:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|\+|\-|\*|/|\(|\)|sin|cos', expression)
        self.current_token = None
        self.next_token()

    def next_token(self):
        if self.tokens:
            self.current_token = self.tokens.pop(0)
        else:
            self.current_token = None

    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()
                result /= self.parse_factor()
        return result

    def parse_factor(self):
        if self.current_token == '(':
            self.next_token()
            result = self.parse_expression()
            if self.current_token != ')':
                raise SyntaxError("Expected ')'")
            self.next_token()
            return result
        elif self.current_token in ('sin', 'cos'):
            op = self.current_token
            self.next_token()
            if self.current_token != '(':
                raise SyntaxError("Expected '(' after prefix operator")
            self.next_token()
            arg = self.parse_expression()
            if self.current_token != ')':
                raise SyntaxError("Expected ')'")
            self.next_token()
            if op == 'sin':
                return math.sin(arg)
            elif op == 'cos':
                return math.cos(arg)
        else:
            try:
                result = float(self.current_token)
                self.next_token()
                return result
            except ValueError:
                raise SyntaxError(f"Unexpected token: {self.current_token}")

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

# Example usage:
result = evaluate("sin(3 + 2 * 4) - cos(15)")
print(result)  # Output: -0.240302

Run Code Interpreter

Running the following program: 

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import math
import re

class Parser:
    def __init__(self, expression):
        self.tokens = re.findall(r'\d+|\+|\-|\*|/|\(|\)|sin|cos', expression)
        self.current_token = None
        self.next_token()

    def next_token(self):
        if self.tokens:
            self.current_token = self.tokens.pop(0)
        else:
            self.current_token = None

    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()
                result /= self.parse_factor()
        return result

    def parse_factor(self):
        if self.current_token == '(':
            self.next_token()
            result = self.parse_expression()
            if self.current_token != ')':
                raise SyntaxError("Expected ')'")
            self.next_token()
            return result
        elif self.current_token in ('sin', 'cos'):
            op = self.current_token
            self.next_token()
            if self.current_token != '(':
                raise SyntaxError("Expected '(' after prefix operator")
            self.next_token()
            arg = self.parse_expression()
            if self.current_token != ')':
                raise SyntaxError("Expected ')'")
            self.next_token()
            if op == 'sin':
                return math.sin(arg)
            elif op == 'cos':
                return math.cos(arg)
        else:
            try:
                result = float(self.current_token)
                self.next_token()
                return result
            except ValueError:
                raise SyntaxError(f"Unexpected token: {self.current_token}")

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

# Example usage:
result = evaluate("sin(3 + 2 * 4) - cos(15)")
print(result)  # Output: -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