Tokenizer

import mathy_core.tokenizer

Motivation¶

We first need an intermediate representation to parse math text into tree structures that encode the Order of Operations of the input. Specifically, we want to build a list of text characters corresponding to relevant tokens for a math expression. That is what the tokenizer does.

The tokenization process treats the input string as an array of characters, iterating over them to produce a list of tokens with type/value properties. While building the collection, the tokenizer also optionally discards extra whitespace characters.

Visual Example¶

For example, consider the input text 8 - (2 + 4) and its token representation.

• The top row contains the token value.
• The bottom row includes the integer type of the token represented by the value.

Code Example¶

Simple tokenization only requires a few lines of code:

from typing import List

from mathy_core import Token, Tokenizer

text = "4x + 2x^3 * 7x"
tokenizer = Tokenizer()
tokens: List[Token] = tokenizer.tokenize(text)

for token in tokens:
    print(f"type: {token.type}, value: {token.value}")

Conceptual Example¶

To better understand the tokenizer, let's build a tokens array manually then compare it to the tokenizer outputs:

from typing import List

from mathy_core import Token, TOKEN_TYPES, Tokenizer

manual_tokens: List[Token] = [
    Token("4", TOKEN_TYPES.Constant),
    Token("x", TOKEN_TYPES.Variable),
    Token("+", TOKEN_TYPES.Plus),
    Token("2", TOKEN_TYPES.Constant),
    Token("", TOKEN_TYPES.EOF),
]
auto_tokens: List[Token] = Tokenizer().tokenize("4x + 2")

for i, token in enumerate(manual_tokens):
    assert auto_tokens[i].value == token.value
    assert auto_tokens[i].type == token.type

API¶

TOKEN_TYPES¶

TOKEN_TYPES(self, args, kwargs)

CloseParen¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Constant¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Divide¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

EOF¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Equal¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Exponent¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Factorial¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Function¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Invalid¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Minus¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Multiply¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

OpenParen¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Pad¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Plus¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Variable¶

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal.

int('0b100', base=0) 4

Tokenizer¶

Tokenizer(self, exclude_padding: bool = True)

eat_token¶

Tokenizer.eat_token(
    self, 
    context: mathy_core.tokenizer.TokenContext, 
    typeFn: Callable[[str], bool], 
) -> str

identify_alphas¶

Tokenizer.identify_alphas(
    self, 
    context: mathy_core.tokenizer.TokenContext, 
) -> int

identify_constants¶

Tokenizer.identify_constants(
    self, 
    context: mathy_core.tokenizer.TokenContext, 
) -> int

identify_operators¶

Tokenizer.identify_operators(
    self, 
    context: mathy_core.tokenizer.TokenContext, 
) -> bool

is_alpha¶

Tokenizer.is_alpha(self, c: str) -> bool

is_number¶

Tokenizer.is_number(self, c: str) -> bool

tokenize¶

Tokenizer.tokenize(self, buffer: str) -> List[mathy_core.tokenizer.Token]