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 solve this problem, we need to evaluate mathematical expressions that include basic arithmetic operations, parentheses, and trigonometric functions (sine and cosine). The expressions follow a specific grammar structure, which we need to parse and evaluate correctly. ### Approach 1. **Tokenization**: Convert the input string into a list of tokens. Tokens include numbers, operators (`+`, `-`, `*`, `/`), parentheses (`(` and `)`), and trigonometric functions (`sin` and `cos`). This step also skips any whitespace in the input. 2. **Recursive Descent Parsing**: Use a recursive descent parser to process the tokens according to the given grammar. This parser handles operator precedence and associativity by breaking down the expression into terms and factors. 3. **Evaluation**: Evaluate the parsed structure on-the-fly by applying the operations as they are parsed. This includes arithmetic operations and applying trigonometric functions to their respective arguments. ### Solution Code 

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import math

def evaluate(expr):
    tokens = tokenize(expr)
    pos = 0  # Current position in the tokens list

    def peek():
        return tokens[pos] if pos < len(tokens) else None

    def consume():
        nonlocal pos
        pos += 1

    def parse_expression():
        val = parse_term()
        while peek() in ('+', '-'):
            op = peek()
            consume()
            term_val = parse_term()
            if op == '+':
                val += term_val
            else:
                val -= term_val
        return val

    def parse_term():
        val = parse_factor()
        while peek() in ('*', '/'):
            op = peek()
            consume()
            factor_val = parse_factor()
            if op == '*':
                val *= factor_val
            else:
                val /= factor_val
        return val

    def parse_factor():
        token = peek()
        if token is None:
            raise ValueError("Unexpected end of input")
        if token == '(':
            consume()
            expr_val = parse_expression()
            if peek() != ')':
                raise ValueError("Missing closing parenthesis")
            consume()
            return expr_val
        elif token in ('sin', 'cos'):
            consume()
            func = math.sin if token == 'sin' else math.cos
            factor_val = parse_factor()
            return func(factor_val)
        elif token.isdigit():
            consume()
            return int(token)
        else:
            raise ValueError(f"Unexpected token {token} in factor")

    result = parse_expression()
    if pos != len(tokens):
        raise ValueError("Unexpected tokens remaining")
    return result

def tokenize(s):
    tokens = []
    i = 0
    n = len(s)
    while i < n:
        if s[i].isspace():
            i += 1
            continue
        elif s[i].isdigit():
            j = i
            while j < n and s[j].isdigit():
                j += 1
            tokens.append(s[i:j])
            i = j
        elif s[i].isalpha():
            j = i
            while j < n and s[j].isalpha():
                j += 1
            word = s[i:j]
            if word not in ('sin', 'cos'):
                raise ValueError(f"Unknown function {word}")
            tokens.append(word)
            i = j
        elif s[i] in '+-*/()':
            tokens.append(s[i])
            i += 1
        else:
            raise ValueError(f"Invalid character '{s[i]}'")
    return tokens
### Explanation 1. **Tokenization**: The `tokenize` function processes the input string into a list of tokens, ignoring whitespace and validating characters. Numbers and trigonometric functions are identified and converted into appropriate tokens. 2. **Parsing and Evaluation**: The parser functions (`parse_expression`, `parse_term`, `parse_factor`) recursively process the tokens. They handle operator precedence by evaluating terms and factors first, and associativity by iteratively applying operations from left to right. 3. **Trigonometric Functions**: The parser recognizes `sin` and `cos` tokens, applies the corresponding trigonometric function to the parsed factor (which could be a number or a nested expression), and returns the result in radians. This approach ensures that the input expression is parsed and evaluated according to the specified grammar, handling arithmetic operations and trigonometric functions accurately.

Extract Code

I extracted the following code from that output: 

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import math

def evaluate(expr):
    tokens = tokenize(expr)
    pos = 0  # Current position in the tokens list

    def peek():
        return tokens[pos] if pos < len(tokens) else None

    def consume():
        nonlocal pos
        pos += 1

    def parse_expression():
        val = parse_term()
        while peek() in ('+', '-'):
            op = peek()
            consume()
            term_val = parse_term()
            if op == '+':
                val += term_val
            else:
                val -= term_val
        return val

    def parse_term():
        val = parse_factor()
        while peek() in ('*', '/'):
            op = peek()
            consume()
            factor_val = parse_factor()
            if op == '*':
                val *= factor_val
            else:
                val /= factor_val
        return val

    def parse_factor():
        token = peek()
        if token is None:
            raise ValueError("Unexpected end of input")
        if token == '(':
            consume()
            expr_val = parse_expression()
            if peek() != ')':
                raise ValueError("Missing closing parenthesis")
            consume()
            return expr_val
        elif token in ('sin', 'cos'):
            consume()
            func = math.sin if token == 'sin' else math.cos
            factor_val = parse_factor()
            return func(factor_val)
        elif token.isdigit():
            consume()
            return int(token)
        else:
            raise ValueError(f"Unexpected token {token} in factor")

    result = parse_expression()
    if pos != len(tokens):
        raise ValueError("Unexpected tokens remaining")
    return result

def tokenize(s):
    tokens = []
    i = 0
    n = len(s)
    while i < n:
        if s[i].isspace():
            i += 1
            continue
        elif s[i].isdigit():
            j = i
            while j < n and s[j].isdigit():
                j += 1
            tokens.append(s[i:j])
            i = j
        elif s[i].isalpha():
            j = i
            while j < n and s[j].isalpha():
                j += 1
            word = s[i:j]
            if word not in ('sin', 'cos'):
                raise ValueError(f"Unknown function {word}")
            tokens.append(word)
            i = j
        elif s[i] in '+-*/()':
            tokens.append(s[i])
            i += 1
        else:
            raise ValueError(f"Invalid character '{s[i]}'")
    return tokens

Run Code Interpreter

Running the following program: 

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import math

def evaluate(expr):
    tokens = tokenize(expr)
    pos = 0  # Current position in the tokens list

    def peek():
        return tokens[pos] if pos < len(tokens) else None

    def consume():
        nonlocal pos
        pos += 1

    def parse_expression():
        val = parse_term()
        while peek() in ('+', '-'):
            op = peek()
            consume()
            term_val = parse_term()
            if op == '+':
                val += term_val
            else:
                val -= term_val
        return val

    def parse_term():
        val = parse_factor()
        while peek() in ('*', '/'):
            op = peek()
            consume()
            factor_val = parse_factor()
            if op == '*':
                val *= factor_val
            else:
                val /= factor_val
        return val

    def parse_factor():
        token = peek()
        if token is None:
            raise ValueError("Unexpected end of input")
        if token == '(':
            consume()
            expr_val = parse_expression()
            if peek() != ')':
                raise ValueError("Missing closing parenthesis")
            consume()
            return expr_val
        elif token in ('sin', 'cos'):
            consume()
            func = math.sin if token == 'sin' else math.cos
            factor_val = parse_factor()
            return func(factor_val)
        elif token.isdigit():
            consume()
            return int(token)
        else:
            raise ValueError(f"Unexpected token {token} in factor")

    result = parse_expression()
    if pos != len(tokens):
        raise ValueError("Unexpected tokens remaining")
    return result

def tokenize(s):
    tokens = []
    i = 0
    n = len(s)
    while i < n:
        if s[i].isspace():
            i += 1
            continue
        elif s[i].isdigit():
            j = i
            while j < n and s[j].isdigit():
                j += 1
            tokens.append(s[i:j])
            i = j
        elif s[i].isalpha():
            j = i
            while j < n and s[j].isalpha():
                j += 1
            word = s[i:j]
            if word not in ('sin', 'cos'):
                raise ValueError(f"Unknown function {word}")
            tokens.append(word)
            i = j
        elif s[i] in '+-*/()':
            tokens.append(s[i])
            i += 1
        else:
            raise ValueError(f"Invalid character '{s[i]}'")
    return tokens





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