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

Here's a Python function that evaluates expressions based on the given BNF-style grammar: 

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import math

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

def tokenize(expression):
    tokens = []
    i = 0
    while i < len(expression):
        if expression[i].isdigit():
            num = ""
            while i < len(expression) and expression[i].isdigit():
                num += expression[i]
                i += 1
            tokens.append(num)
        elif expression[i] in "+-*/()":
            tokens.append(expression[i])
            i += 1
        elif expression[i:i+3] == "sin":
            tokens.append("sin")
            i += 3
        elif expression[i:i+3] == "cos":
            tokens.append("cos")
            i += 3
        elif expression[i].isspace():
            i += 1
        else:
            raise ValueError(f"Invalid character: {expression[i]}")
    return tokens

def parse_expression(tokens):
    value = parse_term(tokens)
    while tokens and tokens[0] in "+-":
        op = tokens.pop(0)
        term = parse_term(tokens)
        if op == "+":
            value += term
        else:
            value -= term
    return value

def parse_term(tokens):
    value = parse_factor(tokens)
    while tokens and tokens[0] in "*/":
        op = tokens.pop(0)
        factor = parse_factor(tokens)
        if op == "*":
            value *= factor
        else:
            value /= factor
    return value

def parse_factor(tokens):
    if not tokens:
        raise ValueError("Unexpected end of expression")
    
    token = tokens.pop(0)
    if token.isdigit():
        return float(token)
    elif token == "(":
        value = parse_expression(tokens)
        if not tokens or tokens.pop(0) != ")":
            raise ValueError("Mismatched parentheses")
        return value
    elif token in ["sin", "cos"]:
        factor = parse_factor(tokens)
        return math.sin(factor) if token == "sin" else math.cos(factor)
    else:
        raise ValueError(f"Unexpected token: {token}")

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")
This implementation follows the grammar rules you provided: 1. The `evaluate` function is the entry point. It tokenizes the input string and then calls `parse_expression`. 2. The `tokenize` function converts the input string into a list of tokens, handling numbers, operators, parentheses, and the trigonometric functions. 3. `parse_expression` handles addition and subtraction operations. 4. `parse_term` handles multiplication and division operations. 5. `parse_factor` handles numbers, parenthesized expressions, and trigonometric functions. 6. The order of operations is maintained by the recursive structure of the parsing functions. The example usage at the end demonstrates how to use the `evaluate` function with the expression "sin(3 + 2 * 4) - cos(15)". This implementation assumes that the input is well-formed according to the grammar. It will raise a `ValueError` for some types of invalid input, but it may not catch all possible errors.

Extract Code

I extracted the following code from that output: 

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import math

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

def tokenize(expression):
    tokens = []
    i = 0
    while i < len(expression):
        if expression[i].isdigit():
            num = ""
            while i < len(expression) and expression[i].isdigit():
                num += expression[i]
                i += 1
            tokens.append(num)
        elif expression[i] in "+-*/()":
            tokens.append(expression[i])
            i += 1
        elif expression[i:i+3] == "sin":
            tokens.append("sin")
            i += 3
        elif expression[i:i+3] == "cos":
            tokens.append("cos")
            i += 3
        elif expression[i].isspace():
            i += 1
        else:
            raise ValueError(f"Invalid character: {expression[i]}")
    return tokens

def parse_expression(tokens):
    value = parse_term(tokens)
    while tokens and tokens[0] in "+-":
        op = tokens.pop(0)
        term = parse_term(tokens)
        if op == "+":
            value += term
        else:
            value -= term
    return value

def parse_term(tokens):
    value = parse_factor(tokens)
    while tokens and tokens[0] in "*/":
        op = tokens.pop(0)
        factor = parse_factor(tokens)
        if op == "*":
            value *= factor
        else:
            value /= factor
    return value

def parse_factor(tokens):
    if not tokens:
        raise ValueError("Unexpected end of expression")
    
    token = tokens.pop(0)
    if token.isdigit():
        return float(token)
    elif token == "(":
        value = parse_expression(tokens)
        if not tokens or tokens.pop(0) != ")":
            raise ValueError("Mismatched parentheses")
        return value
    elif token in ["sin", "cos"]:
        factor = parse_factor(tokens)
        return math.sin(factor) if token == "sin" else math.cos(factor)
    else:
        raise ValueError(f"Unexpected token: {token}")

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")

Run Code Interpreter

Running the following program: 

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import math

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

def tokenize(expression):
    tokens = []
    i = 0
    while i < len(expression):
        if expression[i].isdigit():
            num = ""
            while i < len(expression) and expression[i].isdigit():
                num += expression[i]
                i += 1
            tokens.append(num)
        elif expression[i] in "+-*/()":
            tokens.append(expression[i])
            i += 1
        elif expression[i:i+3] == "sin":
            tokens.append("sin")
            i += 3
        elif expression[i:i+3] == "cos":
            tokens.append("cos")
            i += 3
        elif expression[i].isspace():
            i += 1
        else:
            raise ValueError(f"Invalid character: {expression[i]}")
    return tokens

def parse_expression(tokens):
    value = parse_term(tokens)
    while tokens and tokens[0] in "+-":
        op = tokens.pop(0)
        term = parse_term(tokens)
        if op == "+":
            value += term
        else:
            value -= term
    return value

def parse_term(tokens):
    value = parse_factor(tokens)
    while tokens and tokens[0] in "*/":
        op = tokens.pop(0)
        factor = parse_factor(tokens)
        if op == "*":
            value *= factor
        else:
            value /= factor
    return value

def parse_factor(tokens):
    if not tokens:
        raise ValueError("Unexpected end of expression")
    
    token = tokens.pop(0)
    if token.isdigit():
        return float(token)
    elif token == "(":
        value = parse_expression(tokens)
        if not tokens or tokens.pop(0) != ")":
            raise ValueError("Mismatched parentheses")
        return value
    elif token in ["sin", "cos"]:
        factor = parse_factor(tokens)
        return math.sin(factor) if token == "sin" else math.cos(factor)
    else:
        raise ValueError(f"Unexpected token: {token}")

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")





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) = -0.240302 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

Here's a Python function that evaluates expressions based on the given BNF-style grammar: 

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import math

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

def tokenize(s):
    tokens = []
    i = 0
    while i < len(s):
        if s[i].isdigit():
            num = ''
            while i < len(s) and s[i].isdigit():
                num += s[i]
                i += 1
            tokens.append(('NUMBER', float(num)))
        elif s[i] in '+-*/()':
            tokens.append(('OPERATOR', s[i]))
            i += 1
        elif s[i:i+3] == 'sin':
            tokens.append(('FUNCTION', 'sin'))
            i += 3
        elif s[i:i+3] == 'cos':
            tokens.append(('FUNCTION', 'cos'))
            i += 3
        elif s[i].isspace():
            i += 1
        else:
            raise ValueError(f"Invalid character: {s[i]}")
    return tokens

def parse_expression(tokens):
    value = parse_term(tokens)
    while tokens and tokens[0][1] in '+-':
        op = tokens.pop(0)[1]
        term = parse_term(tokens)
        if op == '+':
            value += term
        else:
            value -= term
    return value

def parse_term(tokens):
    value = parse_factor(tokens)
    while tokens and tokens[0][1] in '*/':
        op = tokens.pop(0)[1]
        factor = parse_factor(tokens)
        if op == '*':
            value *= factor
        else:
            value /= factor
    return value

def parse_factor(tokens):
    if not tokens:
        raise ValueError("Unexpected end of expression")
    
    token = tokens.pop(0)
    if token[0] == 'NUMBER':
        return token[1]
    elif token[1] == '(':
        value = parse_expression(tokens)
        if not tokens or tokens.pop(0)[1] != ')':
            raise ValueError("Mismatched parentheses")
        return value
    elif token[0] == 'FUNCTION':
        factor = parse_factor(tokens)
        if token[1] == 'sin':
            return math.sin(factor)
        elif token[1] == 'cos':
            return math.cos(factor)
    else:
        raise ValueError(f"Unexpected token: {token}")

# Example usage
expression = "sin(3 + 2 * 4) - cos(15)"
result = evaluate(expression)
print(f"{expression} = {result:.6f}")
This implementation follows the grammar rules you provided: 1. The `tokenize` function breaks the input string into tokens. 2. The `parse_expression`, `parse_term`, and `parse_factor` functions implement the recursive descent parser for the grammar. 3. The `evaluate` function is the entry point that tokenizes the input and starts the parsing process. The parser handles: - Basic arithmetic operations (+, -, *, /) - Parentheses for grouping - `sin` and `cos` functions - Proper operator precedence (*, / before +, -) When you run this code with the example you provided, it outputs: 
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sin(3 + 2 * 4) - cos(15) = -0.240302
This result is correct to six decimal places, which matches the expected output in your example. Note that this implementation assumes all numbers are in decimal notation and doesn't handle exponents or other advanced notations. It also uses Python's built-in `math.sin` and `math.cos` functions, which work with radians, not degrees.

Extract Code

I extracted the following code from that output: 

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import math

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

def tokenize(s):
    tokens = []
    i = 0
    while i < len(s):
        if s[i].isdigit():
            num = ''
            while i < len(s) and s[i].isdigit():
                num += s[i]
                i += 1
            tokens.append(('NUMBER', float(num)))
        elif s[i] in '+-*/()':
            tokens.append(('OPERATOR', s[i]))
            i += 1
        elif s[i:i+3] == 'sin':
            tokens.append(('FUNCTION', 'sin'))
            i += 3
        elif s[i:i+3] == 'cos':
            tokens.append(('FUNCTION', 'cos'))
            i += 3
        elif s[i].isspace():
            i += 1
        else:
            raise ValueError(f"Invalid character: {s[i]}")
    return tokens

def parse_expression(tokens):
    value = parse_term(tokens)
    while tokens and tokens[0][1] in '+-':
        op = tokens.pop(0)[1]
        term = parse_term(tokens)
        if op == '+':
            value += term
        else:
            value -= term
    return value

def parse_term(tokens):
    value = parse_factor(tokens)
    while tokens and tokens[0][1] in '*/':
        op = tokens.pop(0)[1]
        factor = parse_factor(tokens)
        if op == '*':
            value *= factor
        else:
            value /= factor
    return value

def parse_factor(tokens):
    if not tokens:
        raise ValueError("Unexpected end of expression")
    
    token = tokens.pop(0)
    if token[0] == 'NUMBER':
        return token[1]
    elif token[1] == '(':
        value = parse_expression(tokens)
        if not tokens or tokens.pop(0)[1] != ')':
            raise ValueError("Mismatched parentheses")
        return value
    elif token[0] == 'FUNCTION':
        factor = parse_factor(tokens)
        if token[1] == 'sin':
            return math.sin(factor)
        elif token[1] == 'cos':
            return math.cos(factor)
    else:
        raise ValueError(f"Unexpected token: {token}")

Run Code Interpreter

Running the following program: 

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import math

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

def tokenize(s):
    tokens = []
    i = 0
    while i < len(s):
        if s[i].isdigit():
            num = ''
            while i < len(s) and s[i].isdigit():
                num += s[i]
                i += 1
            tokens.append(('NUMBER', float(num)))
        elif s[i] in '+-*/()':
            tokens.append(('OPERATOR', s[i]))
            i += 1
        elif s[i:i+3] == 'sin':
            tokens.append(('FUNCTION', 'sin'))
            i += 3
        elif s[i:i+3] == 'cos':
            tokens.append(('FUNCTION', 'cos'))
            i += 3
        elif s[i].isspace():
            i += 1
        else:
            raise ValueError(f"Invalid character: {s[i]}")
    return tokens

def parse_expression(tokens):
    value = parse_term(tokens)
    while tokens and tokens[0][1] in '+-':
        op = tokens.pop(0)[1]
        term = parse_term(tokens)
        if op == '+':
            value += term
        else:
            value -= term
    return value

def parse_term(tokens):
    value = parse_factor(tokens)
    while tokens and tokens[0][1] in '*/':
        op = tokens.pop(0)[1]
        factor = parse_factor(tokens)
        if op == '*':
            value *= factor
        else:
            value /= factor
    return value

def parse_factor(tokens):
    if not tokens:
        raise ValueError("Unexpected end of expression")
    
    token = tokens.pop(0)
    if token[0] == 'NUMBER':
        return token[1]
    elif token[1] == '(':
        value = parse_expression(tokens)
        if not tokens or tokens.pop(0)[1] != ')':
            raise ValueError("Mismatched parentheses")
        return value
    elif token[0] == 'FUNCTION':
        factor = parse_factor(tokens)
        if token[1] == 'sin':
            return math.sin(factor)
        elif token[1] == 'cos':
            return math.cos(factor)
    else:
        raise ValueError(f"Unexpected token: {token}")





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

To implement an evaluator for this grammar, we'll use a recursive descent parser along with a tokenizer. Here's a Python implementation that should handle the given grammar: 

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import math
import re

class Token:
    def __init__(self, type, value):
        self.type = type
        self.value = value

def tokenize(expression):
    token_specification = [
        ('NUMBER',   r'\d+(\.\d*)?'),
        ('PLUS',     r'\+'),
        ('MINUS',    r'-'),
        ('MULTIPLY', r'\*'),
        ('DIVIDE',   r'/'),
        ('LPAREN',   r'\('),
        ('RPAREN',   r'\)'),
        ('SIN',      r'sin'),
        ('COS',      r'cos'),
        ('SKIP',     r'[ \t]+'),
    ]
    tok_regex = '|'.join('(?P<%s>%s)' % pair for pair in token_specification)
    for mo in re.finditer(tok_regex, expression):
        kind = mo.lastgroup
        value = mo.group()
        if kind == 'NUMBER':
            value = float(value)
        elif kind == 'SKIP':
            continue
        yield Token(kind, value)

class Parser:
    def __init__(self, tokens):
        self.tokens = tokens
        self.current_token = next(self.tokens, None)

    def eat(self, token_type):
        if self.current_token and self.current_token.type == token_type:
            self.current_token = next(self.tokens, None)
        else:
            raise ValueError(f'Expected {token_type}')

    def factor(self):
        if self.current_token.type == 'NUMBER':
            value = self.current_token.value
            self.eat('NUMBER')
            return value
        elif self.current_token.type == 'LPAREN':
            self.eat('LPAREN')
            result = self.expression()
            self.eat('RPAREN')
            return result
        elif self.current_token.type in ['SIN', 'COS']:
            op = self.current_token.type
            self.eat(op)
            value = self.factor()
            return math.sin(value) if op == 'SIN' else math.cos(value)
        else:
            raise ValueError('Invalid factor')

    def term(self):
        result = self.factor()
        while self.current_token and self.current_token.type in ['MULTIPLY', 'DIVIDE']:
            if self.current_token.type == 'MULTIPLY':
                self.eat('MULTIPLY')
                result *= self.factor()
            elif self.current_token.type == 'DIVIDE':
                self.eat('DIVIDE')
                result /= self.factor()
        return result

    def expression(self):
        result = self.term()
        while self.current_token and self.current_token.type in ['PLUS', 'MINUS']:
            if self.current_token.type == 'PLUS':
                self.eat('PLUS')
                result += self.term()
            elif self.current_token.type == 'MINUS':
                self.eat('MINUS')
                result -= self.term()
        return result

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

# Test the function
print(evaluate("sin(3 + 2 * 4) - cos(15)"))
This implementation includes: 1. A `Token` class to represent tokens. 2. A `tokenize` function that converts the input string into a stream of tokens. 3. A `Parser` class that implements the recursive descent parser. 4. The `evaluate` function that ties everything together. The parser follows the grammar rules: - `expression` handles addition and subtraction. - `term` handles multiplication and division. - `factor` handles numbers, parentheses, and prefix operations (sin and cos). When you run this code with the example `"sin(3 + 2 * 4) - cos(15)"`, it should output a value close to -0.240302 (there might be a small difference due to floating-point arithmetic). This implementation should be able to handle all expressions that conform to the given grammar. It includes error checking for unexpected tokens, but you might want to add more robust error handling for production use.

Extract Code

I extracted the following code from that output: 

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import math
import re

class Token:
    def __init__(self, type, value):
        self.type = type
        self.value = value

def tokenize(expression):
    token_specification = [
        ('NUMBER',   r'\d+(\.\d*)?'),
        ('PLUS',     r'\+'),
        ('MINUS',    r'-'),
        ('MULTIPLY', r'\*'),
        ('DIVIDE',   r'/'),
        ('LPAREN',   r'\('),
        ('RPAREN',   r'\)'),
        ('SIN',      r'sin'),
        ('COS',      r'cos'),
        ('SKIP',     r'[ \t]+'),
    ]
    tok_regex = '|'.join('(?P<%s>%s)' % pair for pair in token_specification)
    for mo in re.finditer(tok_regex, expression):
        kind = mo.lastgroup
        value = mo.group()
        if kind == 'NUMBER':
            value = float(value)
        elif kind == 'SKIP':
            continue
        yield Token(kind, value)

class Parser:
    def __init__(self, tokens):
        self.tokens = tokens
        self.current_token = next(self.tokens, None)

    def eat(self, token_type):
        if self.current_token and self.current_token.type == token_type:
            self.current_token = next(self.tokens, None)
        else:
            raise ValueError(f'Expected {token_type}')

    def factor(self):
        if self.current_token.type == 'NUMBER':
            value = self.current_token.value
            self.eat('NUMBER')
            return value
        elif self.current_token.type == 'LPAREN':
            self.eat('LPAREN')
            result = self.expression()
            self.eat('RPAREN')
            return result
        elif self.current_token.type in ['SIN', 'COS']:
            op = self.current_token.type
            self.eat(op)
            value = self.factor()
            return math.sin(value) if op == 'SIN' else math.cos(value)
        else:
            raise ValueError('Invalid factor')

    def term(self):
        result = self.factor()
        while self.current_token and self.current_token.type in ['MULTIPLY', 'DIVIDE']:
            if self.current_token.type == 'MULTIPLY':
                self.eat('MULTIPLY')
                result *= self.factor()
            elif self.current_token.type == 'DIVIDE':
                self.eat('DIVIDE')
                result /= self.factor()
        return result

    def expression(self):
        result = self.term()
        while self.current_token and self.current_token.type in ['PLUS', 'MINUS']:
            if self.current_token.type == 'PLUS':
                self.eat('PLUS')
                result += self.term()
            elif self.current_token.type == 'MINUS':
                self.eat('MINUS')
                result -= self.term()
        return result

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

# Test the function
print(evaluate("sin(3 + 2 * 4) - cos(15)"))

Run Code Interpreter

Running the following program: 

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import math
import re

class Token:
    def __init__(self, type, value):
        self.type = type
        self.value = value

def tokenize(expression):
    token_specification = [
        ('NUMBER',   r'\d+(\.\d*)?'),
        ('PLUS',     r'\+'),
        ('MINUS',    r'-'),
        ('MULTIPLY', r'\*'),
        ('DIVIDE',   r'/'),
        ('LPAREN',   r'\('),
        ('RPAREN',   r'\)'),
        ('SIN',      r'sin'),
        ('COS',      r'cos'),
        ('SKIP',     r'[ \t]+'),
    ]
    tok_regex = '|'.join('(?P<%s>%s)' % pair for pair in token_specification)
    for mo in re.finditer(tok_regex, expression):
        kind = mo.lastgroup
        value = mo.group()
        if kind == 'NUMBER':
            value = float(value)
        elif kind == 'SKIP':
            continue
        yield Token(kind, value)

class Parser:
    def __init__(self, tokens):
        self.tokens = tokens
        self.current_token = next(self.tokens, None)

    def eat(self, token_type):
        if self.current_token and self.current_token.type == token_type:
            self.current_token = next(self.tokens, None)
        else:
            raise ValueError(f'Expected {token_type}')

    def factor(self):
        if self.current_token.type == 'NUMBER':
            value = self.current_token.value
            self.eat('NUMBER')
            return value
        elif self.current_token.type == 'LPAREN':
            self.eat('LPAREN')
            result = self.expression()
            self.eat('RPAREN')
            return result
        elif self.current_token.type in ['SIN', 'COS']:
            op = self.current_token.type
            self.eat(op)
            value = self.factor()
            return math.sin(value) if op == 'SIN' else math.cos(value)
        else:
            raise ValueError('Invalid factor')

    def term(self):
        result = self.factor()
        while self.current_token and self.current_token.type in ['MULTIPLY', 'DIVIDE']:
            if self.current_token.type == 'MULTIPLY':
                self.eat('MULTIPLY')
                result *= self.factor()
            elif self.current_token.type == 'DIVIDE':
                self.eat('DIVIDE')
                result /= self.factor()
        return result

    def expression(self):
        result = self.term()
        while self.current_token and self.current_token.type in ['PLUS', 'MINUS']:
            if self.current_token.type == 'PLUS':
                self.eat('PLUS')
                result += self.term()
            elif self.current_token.type == 'MINUS':
                self.eat('MINUS')
                result -= self.term()
        return result

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

# Test the function
print(evaluate("sin(3 + 2 * 4) - cos(15)"))





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

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

Here's a Python function that evaluates expressions based on the given BNF-style grammar: 

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import math

def evaluate(expr):
    def parse_expression():
        nonlocal index
        result = parse_term()
        while index < len(expr) and expr[index] in ['+', '-']:
            op = expr[index]
            index += 1
            if op == '+':
                result += parse_term()
            else:
                result -= parse_term()
        return result

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

    def parse_factor():
        nonlocal index
        if expr[index].isdigit():
            return parse_number()
        elif expr[index] == '(':
            index += 1
            result = parse_expression()
            index += 1  # Skip closing parenthesis
            return result
        else:
            return parse_prefix_op()

    def parse_prefix_op():
        nonlocal index
        if expr[index:index+3] == 'sin':
            index += 3
            return math.sin(parse_factor())
        elif expr[index:index+3] == 'cos':
            index += 3
            return math.cos(parse_factor())
        else:
            raise ValueError("Invalid prefix operator")

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

    index = 0
    expr = expr.replace(" ", "")  # Remove all spaces
    return parse_expression()

# Test the function
print(evaluate("sin(3 + 2 * 4) - cos(15)"))  # Should print approximately -0.240302
This implementation uses recursive descent parsing to evaluate the expression. Here's a breakdown of the function: 1. We define nested functions for each non-terminal in the grammar: `parse_expression`, `parse_term`, `parse_factor`, `parse_prefix_op`, and `parse_number`. 2. Each function implements the corresponding production rules, calling other functions as needed. 3. We use a global `index` variable to keep track of our position in the input string. 4. The `parse_expression` and `parse_term` functions handle left-associative operators (+, -, *, /) by repeatedly applying the operator to the result of the previous operation and the next term/factor. 5. The `parse_factor` function handles numbers, parenthesized expressions, and prefix operators. 6. The `parse_prefix_op` function recognizes 'sin' and 'cos' and applies the corresponding math function. 7. The `parse_number` function parses multi-digit numbers. 8. We remove all spaces from the input string to simplify parsing. This implementation assumes that the input is well-formed according to the grammar. It doesn't include extensive error checking, so invalid inputs may cause unexpected behavior or errors. You can test the function with different expressions, for example: 
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print(evaluate("2 + 3 * 4"))  # Should print 14
print(evaluate("(2 + 3) * 4"))  # Should print 20
print(evaluate("sin(30) + cos(60)"))  # Should print approximately 0.9996
Note that this function uses radians for trigonometric functions, as is standard in Python's math library. If you need to work with degrees, you'll need to convert them to radians first.

Extract Code

I extracted the following code from that output: 

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import math

def evaluate(expr):
    def parse_expression():
        nonlocal index
        result = parse_term()
        while index < len(expr) and expr[index] in ['+', '-']:
            op = expr[index]
            index += 1
            if op == '+':
                result += parse_term()
            else:
                result -= parse_term()
        return result

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

    def parse_factor():
        nonlocal index
        if expr[index].isdigit():
            return parse_number()
        elif expr[index] == '(':
            index += 1
            result = parse_expression()
            index += 1  # Skip closing parenthesis
            return result
        else:
            return parse_prefix_op()

    def parse_prefix_op():
        nonlocal index
        if expr[index:index+3] == 'sin':
            index += 3
            return math.sin(parse_factor())
        elif expr[index:index+3] == 'cos':
            index += 3
            return math.cos(parse_factor())
        else:
            raise ValueError("Invalid prefix operator")

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

    index = 0
    expr = expr.replace(" ", "")  # Remove all spaces
    return parse_expression()

Run Code Interpreter

Running the following program: 

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import math

def evaluate(expr):
    def parse_expression():
        nonlocal index
        result = parse_term()
        while index < len(expr) and expr[index] in ['+', '-']:
            op = expr[index]
            index += 1
            if op == '+':
                result += parse_term()
            else:
                result -= parse_term()
        return result

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

    def parse_factor():
        nonlocal index
        if expr[index].isdigit():
            return parse_number()
        elif expr[index] == '(':
            index += 1
            result = parse_expression()
            index += 1  # Skip closing parenthesis
            return result
        else:
            return parse_prefix_op()

    def parse_prefix_op():
        nonlocal index
        if expr[index:index+3] == 'sin':
            index += 3
            return math.sin(parse_factor())
        elif expr[index:index+3] == 'cos':
            index += 3
            return math.cos(parse_factor())
        else:
            raise ValueError("Invalid prefix operator")

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

    index = 0
    expr = expr.replace(" ", "")  # Remove all spaces
    return parse_expression()





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

To evaluate expressions based on the given BNF-style grammar, we can implement a recursive descent parser along with an evaluation mechanism. Here's a Python function that accomplishes this: 

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import math

def evaluate(expr):
    def parse_expression():
        result = parse_term()
        while True:
            if peek() == '+':
                consume()
                result += parse_term()
            elif peek() == '-':
                consume()
                result -= parse_term()
            else:
                return result

    def parse_term():
        result = parse_factor()
        while True:
            if peek() == '*':
                consume()
                result *= parse_factor()
            elif peek() == '/':
                consume()
                divisor = parse_factor()
                if divisor == 0:
                    raise ValueError("Division by zero")
                result /= divisor
            else:
                return result

    def parse_factor():
        if peek() == '(':
            consume()
            result = parse_expression()
            if peek() != ')':
                raise ValueError("Mismatched parentheses")
            consume()
            return result
        elif peek() in ['s', 'c']:  # sin or cos
            op = consume(3)
            if op == 'sin':
                return math.sin(parse_factor())
            elif op == 'cos':
                return math.cos(parse_factor())
        else:
            return parse_number()

    def parse_number():
        num = ''
        while peek() and peek().isdigit():
            num += consume()
        if not num:
            raise ValueError("Expected number")
        return float(num)

    def peek():
        return expr[0] if expr else ''

    def consume(n=1):
        nonlocal expr
        token = expr[:n]
        expr = expr[n:]
        return token

    # Remove whitespace
    expr = ''.join(expr.split())
    
    result = parse_expression()
    if expr:  # If there's anything left in the expression, it's invalid
        raise ValueError("Invalid expression")
    return result

# Test the function
print(evaluate("sin(3 + 2 * 4) - cos(15)"))  # Should output approximately -0.240302
This implementation does the following: 1. We define nested functions for each non-terminal in the grammar: `parse_expression`, `parse_term`, `parse_factor`, and `parse_number`. 2. Each function implements the corresponding production rules, calling other functions as needed. 3. We use `peek()` to look at the next character without consuming it, and `consume()` to remove characters from the input string. 4. The `parse_factor` function handles both parentheses and prefix operators (sin and cos). 5. We use Python's `math` module for sin and cos functions. 6. Error handling is included for division by zero, mismatched parentheses, and invalid expressions. 7. Whitespace is removed from the input string before parsing. This implementation assumes that numbers are integers or floating-point numbers without a decimal point. If you need to support decimal points in numbers, you would need to modify the `parse_number` function accordingly. The function will raise a `ValueError` if the expression is invalid according to the grammar. You can test it with different expressions, for example: 
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print(evaluate("2 + 3 * 4"))  # Should output 14
print(evaluate("sin(0) + cos(0)"))  # Should output 1
print(evaluate("(1 + 2) * (3 + 4)"))  # Should output 21
This implementation provides a basic framework for evaluating mathematical expressions based on the given grammar. Note that it doesn't handle negative numbers as written; you'd need to extend it to support unary minus if that's required.

Extract Code

I extracted the following code from that output: 

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import math

def evaluate(expr):
    def parse_expression():
        result = parse_term()
        while True:
            if peek() == '+':
                consume()
                result += parse_term()
            elif peek() == '-':
                consume()
                result -= parse_term()
            else:
                return result

    def parse_term():
        result = parse_factor()
        while True:
            if peek() == '*':
                consume()
                result *= parse_factor()
            elif peek() == '/':
                consume()
                divisor = parse_factor()
                if divisor == 0:
                    raise ValueError("Division by zero")
                result /= divisor
            else:
                return result

    def parse_factor():
        if peek() == '(':
            consume()
            result = parse_expression()
            if peek() != ')':
                raise ValueError("Mismatched parentheses")
            consume()
            return result
        elif peek() in ['s', 'c']:  # sin or cos
            op = consume(3)
            if op == 'sin':
                return math.sin(parse_factor())
            elif op == 'cos':
                return math.cos(parse_factor())
        else:
            return parse_number()

    def parse_number():
        num = ''
        while peek() and peek().isdigit():
            num += consume()
        if not num:
            raise ValueError("Expected number")
        return float(num)

    def peek():
        return expr[0] if expr else ''

    def consume(n=1):
        nonlocal expr
        token = expr[:n]
        expr = expr[n:]
        return token

    # Remove whitespace
    expr = ''.join(expr.split())
    
    result = parse_expression()
    if expr:  # If there's anything left in the expression, it's invalid
        raise ValueError("Invalid expression")
    return result

Run Code Interpreter

Running the following program: 

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import math

def evaluate(expr):
    def parse_expression():
        result = parse_term()
        while True:
            if peek() == '+':
                consume()
                result += parse_term()
            elif peek() == '-':
                consume()
                result -= parse_term()
            else:
                return result

    def parse_term():
        result = parse_factor()
        while True:
            if peek() == '*':
                consume()
                result *= parse_factor()
            elif peek() == '/':
                consume()
                divisor = parse_factor()
                if divisor == 0:
                    raise ValueError("Division by zero")
                result /= divisor
            else:
                return result

    def parse_factor():
        if peek() == '(':
            consume()
            result = parse_expression()
            if peek() != ')':
                raise ValueError("Mismatched parentheses")
            consume()
            return result
        elif peek() in ['s', 'c']:  # sin or cos
            op = consume(3)
            if op == 'sin':
                return math.sin(parse_factor())
            elif op == 'cos':
                return math.cos(parse_factor())
        else:
            return parse_number()

    def parse_number():
        num = ''
        while peek() and peek().isdigit():
            num += consume()
        if not num:
            raise ValueError("Expected number")
        return float(num)

    def peek():
        return expr[0] if expr else ''

    def consume(n=1):
        nonlocal expr
        token = expr[:n]
        expr = expr[n:]
        return token

    # Remove whitespace
    expr = ''.join(expr.split())
    
    result = parse_expression()
    if expr:  # If there's anything left in the expression, it's invalid
        raise ValueError("Invalid expression")
    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