feat: math expression language implementation

.python-version

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+3.12

Makefile

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+all: check test
+
+.PHONY: check
+check:
+	uvx ty check
+
+.PHONY: test
+test:
+	uv run pytest

README.md

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+# A function plotter in python
+
+A recreational programming project.
+The idea is to implement a simple math expression language and simple features to plot functions.

pyproject.toml

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+[project]
+name = "plotter"
+version = "0.1.0"
+description = "Add your description here"
+readme = "README.md"
+authors = [
+    { name = "Domenico Testa", email = "domenico.testa@gmail.com" }
+]
+requires-python = ">=3.12"
+dependencies = []
+
+[project.scripts]
+plotter = "plotter:main"
+
+[build-system]
+requires = ["uv_build>=0.9.27,<0.10.0"]
+build-backend = "uv_build"
+
+[dependency-groups]
+dev = [
+    "pytest>=9.0.2",
+]

src/plotter/__init__.py

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+def main() -> None:
+    print("Hello from plotter!")

src/plotter/parser.py

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+# Parsing is the process of turning a sequence
+# of tokens into a tree representation:
+#
+#                             Add
+#                  Parser     / \
+#  "1 + 2 * 3"    ------->   1  Mul
+#                               / \
+#                              2   3
+from __future__ import annotations
+
+from abc import ABC, abstractmethod
+from collections import deque
+from collections.abc import Iterator
+from dataclasses import dataclass
+from enum import Enum
+from functools import partial
+import math
+import operator
+
+# The first step is to generate a list of tokens.
+# Tokens are the supported symbol classes, they have a type tag
+
+
+class TokenType(Enum):
+    ERROR = -1
+    OPERATOR = 0
+    VARIABLE = 1
+    SEPARATOR = 2
+    FLOAT = 3
+    FUNCTION = 4
+
+
+# The token can optionally capture a string value.
+# This will be used later by the parser to build the synctatic tree.
+
+
+@dataclass
+class Token:
+    type: TokenType
+    value: str | None = None
+
+
+operators: set[str] = {"+", "-", "*", "/", "^"}
+functions: set[str] = {"abs", "cos", "sin", "tan", "atan", "exp", "ln", "log"}
+separators: set[str] = {"(", ")"}
+variables: set[str] = {"x"}
+
+
+# The lexer is a generator function that yields token as it scans the input string
+def lex(input: str) -> Iterator[Token]:
+    i = 0
+
+    while i < len(input):
+        char = input[i]
+
+        # whitespace
+        if char.isspace():
+            i += 1
+            continue
+
+        # separators
+        if char in separators:
+            yield Token(type=TokenType.SEPARATOR, value=char)
+            i += 1
+            continue
+
+        # operators
+        if char in operators:
+            yield Token(type=TokenType.OPERATOR, value=char)
+            i += 1
+            continue
+
+        # variables
+        if char in variables:
+            yield Token(type=TokenType.VARIABLE, value=char)
+            i += 1
+            continue
+
+        # functions
+        if char.isalpha():
+            j = i + 1
+            while j < len(input) and input[j].isalpha():
+                j += 1
+
+            name = input[i:j]
+            if name not in functions:
+                yield Token(
+                    type=TokenType.ERROR, value=f"unknown function name '{name}'"
+                )
+                return
+
+            yield Token(type=TokenType.FUNCTION, value=name)
+
+            i = j
+            continue
+
+        # float numbers
+        if (
+            char.isdigit()
+            or (char == ".")
+            or (
+                (char == "+" and input[i + 1].isdigit())
+                or (char == "-" and input[i + 1].isdigit())
+            )
+        ):
+            j = i + 1
+
+            has_dot = char == "."
+            while j < len(input) and (input[j].isdigit() or input[j] == "."):
+                has_dot = has_dot or input[j] == "."
+                j += 1
+
+            if has_dot:
+                if input[j - 1] == ".":
+                    yield Token(
+                        type=TokenType.ERROR, value="number after dot was expected"
+                    )
+                    return
+
+            yield Token(type=TokenType.FLOAT, value=input[i:j])
+            i = j
+            continue
+
+        yield Token(type=TokenType.ERROR, value="not an accepted character")
+        return
+
+
+class Expression(ABC):
+    @abstractmethod
+    def eval(self, x: float) -> float:
+        pass
+
+
+@dataclass
+class Atom(Expression):
+    token: Token
+
+    def eval(self, x: float) -> float:
+        if self.token.type == TokenType.VARIABLE:
+            return x
+        if self.token.type == TokenType.FLOAT:
+            return float(self.token.value or 0)
+
+        return 0.0
+
+
+@dataclass
+class FunctionExpression(Expression):
+    function: str
+    argument: Expression
+
+    _funcs = {
+        "abs": abs,
+        "sin": math.sin,
+        "cos": math.cos,
+        "tan": math.tan,
+        "atan": math.atan,
+        "exp": math.exp,
+        "ln": partial(math.log, base=math.e),
+        "log": math.log10,
+    }
+
+    def eval(self, x: float) -> float:
+        func = self._funcs.get(self.function)
+        if not func:
+            raise ValueError(f"Unknown function {self.function}")
+        return func(x)
+
+
+@dataclass
+class InfixExpression(Expression):
+    operator: str
+    lvalue: Expression
+    rvalue: Expression
+
+    _ops = {
+        "+": operator.add,
+        "-": operator.sub,
+        "*": operator.mul,
+        "/": operator.truediv,
+        "^": operator.pow,
+    }
+
+    _binding_power = {
+        "+": (1, 2),
+        "-": (1, 2),
+        "*": (3, 4),
+        "/": (3, 4),
+        "^": (4, 5),
+    }
+
+    # Prefix binding power for unary minus (lower than ^, so -2^3 = -(2^3))
+    _prefix_binding_power = {"-": 3}
+
+    def eval(self, x: float) -> float:
+        op_func = self._ops.get(self.operator)
+        if not op_func:
+            raise ValueError(f"Unknown operator {self.operator}")
+        return op_func(self.lvalue.eval(x), self.rvalue.eval(x))
+
+
+class Parser:
+    def __init__(self, tokens: Iterator[Token]):
+        self.tokens = deque(tokens)
+
+    def peek(self) -> Token | None:
+        return self.tokens[0] if self.tokens else None
+
+    def consume(self) -> Token:
+        return self.tokens.popleft()
+
+    def _parse_expression_bp(self, min_bp: int) -> Expression:
+        token = self.consume()
+
+        if token.type == TokenType.SEPARATOR and token.value == "(":
+            lhs = self._parse_expression_bp(0)
+            self.consume()  # consume closing ')'
+        elif token.type == TokenType.FUNCTION and token.value is not None:
+            self.consume()  # consume opening '('
+            argument = self._parse_expression_bp(0)
+            self.consume()  # consume closing ')'
+            lhs = FunctionExpression(function=token.value, argument=argument)
+        elif token.type == TokenType.OPERATOR and token.value == "-":
+            # Unary minus: desugar to 0 - operand
+            prefix_bp = InfixExpression._prefix_binding_power["-"]
+            operand = self._parse_expression_bp(prefix_bp)
+            lhs = InfixExpression(
+                operator="-",
+                lvalue=Atom(Token(type=TokenType.FLOAT, value="0")),
+                rvalue=operand,
+            )
+        else:
+            lhs = Atom(token)
+
+        while True:
+            op = self.peek()
+            if op is None or op.value is None:
+                break
+
+            if op.type != TokenType.OPERATOR:
+                break
+
+            l_bp, r_bp = InfixExpression._binding_power[op.value]
+            if l_bp < min_bp:
+                break
+
+            self.consume()
+
+            rhs = self._parse_expression_bp(r_bp)
+            lhs = InfixExpression(operator=op.value, lvalue=lhs, rvalue=rhs)
+
+        return lhs
+
+    def parse_expression(self) -> Expression:
+        return self._parse_expression_bp(min_bp=0)
+
+
+def parse(expression: str) -> Expression:
+    return Parser(lex(expression)).parse_expression()
+
+
+def eval_in_range(
+    expression: str, start: float, stop: float, increment: float
+) -> list[float]:
+    if stop < start:
+        raise ValueError("range must be provided in crescent order")
+
+    parsed_expression = parse(expression)
+
+    n = 1
+    x = start
+    values = []
+    while x < stop:
+        x += increment
+        n += 1
+        values.append(parsed_expression.eval(x))
+    return values

tests/test_parser.py

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+import pytest
+
+from plotter.parser import (
+    lex,
+    parse,
+    Atom,
+    Token,
+    TokenType,
+    InfixExpression,
+    FunctionExpression,
+)
+
+
+@pytest.mark.parametrize(
+    "expression, expected",
+    [
+        ("+", [Token(type=TokenType.OPERATOR, value="+")]),
+        ("x", [Token(type=TokenType.VARIABLE, value="x")]),
+        (".", [Token(type=TokenType.ERROR, value="number after dot was expected")]),
+        ("1.", [Token(type=TokenType.ERROR, value="number after dot was expected")]),
+        (".1", [Token(type=TokenType.FLOAT, value=".1")]),
+        ("3.14", [Token(type=TokenType.FLOAT, value="3.14")]),
+        (
+            "2 + 3",
+            [
+                Token(type=TokenType.FLOAT, value="2"),
+                Token(type=TokenType.OPERATOR, value="+"),
+                Token(type=TokenType.FLOAT, value="3"),
+            ],
+        ),
+        (
+            "x - 4.5",
+            [
+                Token(type=TokenType.VARIABLE, value="x"),
+                Token(type=TokenType.OPERATOR, value="-"),
+                Token(type=TokenType.FLOAT, value="4.5"),
+            ],
+        ),
+        (
+            "x - 4.5 * 2.34 + 5.2",
+            [
+                Token(type=TokenType.VARIABLE, value="x"),
+                Token(type=TokenType.OPERATOR, value="-"),
+                Token(type=TokenType.FLOAT, value="4.5"),
+                Token(type=TokenType.OPERATOR, value="*"),
+                Token(type=TokenType.FLOAT, value="2.34"),
+                Token(type=TokenType.OPERATOR, value="+"),
+                Token(type=TokenType.FLOAT, value="5.2"),
+            ],
+        ),
+        (
+            "(x - 4.5) * (2.34 + 5.2)",
+            [
+                Token(type=TokenType.SEPARATOR, value="("),
+                Token(type=TokenType.VARIABLE, value="x"),
+                Token(type=TokenType.OPERATOR, value="-"),
+                Token(type=TokenType.FLOAT, value="4.5"),
+                Token(type=TokenType.SEPARATOR, value=")"),
+                Token(type=TokenType.OPERATOR, value="*"),
+                Token(type=TokenType.SEPARATOR, value="("),
+                Token(type=TokenType.FLOAT, value="2.34"),
+                Token(type=TokenType.OPERATOR, value="+"),
+                Token(type=TokenType.FLOAT, value="5.2"),
+                Token(type=TokenType.SEPARATOR, value=")"),
+            ],
+        ),
+        (
+            "sin(x) * 2.0",
+            [
+                Token(type=TokenType.FUNCTION, value="sin"),
+                Token(type=TokenType.SEPARATOR, value="("),
+                Token(type=TokenType.VARIABLE, value="x"),
+                Token(type=TokenType.SEPARATOR, value=")"),
+                Token(type=TokenType.OPERATOR, value="*"),
+                Token(type=TokenType.FLOAT, value="2.0"),
+            ],
+        ),
+        (
+            "3.14 * coz(x)",
+            [
+                Token(type=TokenType.FLOAT, value="3.14"),
+                Token(type=TokenType.OPERATOR, value="*"),
+                Token(type=TokenType.ERROR, value="unknown function name 'coz'"),
+            ],
+        ),
+        (
+            "3.14 * cos(2.4 * x) ^ 0.5",
+            [
+                Token(type=TokenType.FLOAT, value="3.14"),
+                Token(type=TokenType.OPERATOR, value="*"),
+                Token(type=TokenType.FUNCTION, value="cos"),
+                Token(type=TokenType.SEPARATOR, value="("),
+                Token(type=TokenType.FLOAT, value="2.4"),
+                Token(type=TokenType.OPERATOR, value="*"),
+                Token(type=TokenType.VARIABLE, value="x"),
+                Token(type=TokenType.SEPARATOR, value=")"),
+                Token(type=TokenType.OPERATOR, value="^"),
+                Token(type=TokenType.FLOAT, value="0.5"),
+            ],
+        ),
+    ],
+)
+def test_lexer(expression, expected):
+    assert list(lex(expression)) == expected
+
+
+@pytest.mark.parametrize(
+    "expression, expected",
+    argvalues=[
+        ("3.14", Atom(Token(type=TokenType.FLOAT, value="3.14"))),
+        (
+            "2 + 2",
+            InfixExpression(
+                operator="+",
+                lvalue=Atom(token=Token(type=TokenType.FLOAT, value="2")),
+                rvalue=Atom(token=Token(type=TokenType.FLOAT, value="2")),
+            ),
+        ),
+        (
+            "2 + 3 * 4 + 5",
+            InfixExpression(
+                operator="+",
+                lvalue=InfixExpression(
+                    operator="+",
+                    lvalue=Atom(Token(type=TokenType.FLOAT, value="2")),
+                    rvalue=InfixExpression(
+                        operator="*",
+                        lvalue=Atom(Token(type=TokenType.FLOAT, value="3")),
+                        rvalue=Atom(Token(type=TokenType.FLOAT, value="4")),
+                    ),
+                ),
+                rvalue=Atom(Token(type=TokenType.FLOAT, value="5")),
+            ),
+        ),
+        (
+            "(2 + 3) * (4 + 5)",
+            InfixExpression(
+                operator="*",
+                lvalue=InfixExpression(
+                    operator="+",
+                    lvalue=Atom(Token(type=TokenType.FLOAT, value="2")),
+                    rvalue=Atom(Token(type=TokenType.FLOAT, value="3")),
+                ),
+                rvalue=InfixExpression(
+                    operator="+",
+                    lvalue=Atom(Token(type=TokenType.FLOAT, value="4")),
+                    rvalue=Atom(Token(type=TokenType.FLOAT, value="5")),
+                ),
+            ),
+        ),
+        (
+            "sin(x) + cos(x)",
+            InfixExpression(
+                operator="+",
+                lvalue=FunctionExpression(
+                    function="sin",
+                    argument=Atom(token=Token(type=TokenType.VARIABLE, value="x")),
+                ),
+                rvalue=FunctionExpression(
+                    function="cos",
+                    argument=Atom(token=Token(type=TokenType.VARIABLE, value="x")),
+                ),
+            ),
+        ),
+    ],
+)
+def test_parser(expression, expected):
+    assert parse(expression) == expected
+
+
+# Helper to create the desugared unary minus AST (0 - operand)
+def _neg(operand):
+    return InfixExpression(
+        operator="-",
+        lvalue=Atom(Token(type=TokenType.FLOAT, value="0")),
+        rvalue=operand,
+    )
+
+
+@pytest.mark.parametrize(
+    "expression, expected",
+    argvalues=[
+        # Simple unary minus: -x => 0 - x
+        (
+            "-x",
+            _neg(Atom(Token(type=TokenType.VARIABLE, value="x"))),
+        ),
+        # Double negation: --x => 0 - (0 - x)
+        (
+            "--x",
+            _neg(_neg(Atom(Token(type=TokenType.VARIABLE, value="x")))),
+        ),
+        # Subtract a negative: 1 - -2 => 1 - (0 - 2)
+        (
+            "1 - -2",
+            InfixExpression(
+                operator="-",
+                lvalue=Atom(Token(type=TokenType.FLOAT, value="1")),
+                rvalue=_neg(Atom(Token(type=TokenType.FLOAT, value="2"))),
+            ),
+        ),
+        # Negate function result: -sin(x) => 0 - sin(x)
+        (
+            "-sin(x)",
+            _neg(
+                FunctionExpression(
+                    function="sin",
+                    argument=Atom(Token(type=TokenType.VARIABLE, value="x")),
+                )
+            ),
+        ),
+        # Precedence: -2^3 should be -(2^3), not (-2)^3
+        # With binding power 3, unary minus binds looser than ^ (4,5)
+        (
+            "-2^3",
+            _neg(
+                InfixExpression(
+                    operator="^",
+                    lvalue=Atom(Token(type=TokenType.FLOAT, value="2")),
+                    rvalue=Atom(Token(type=TokenType.FLOAT, value="3")),
+                )
+            ),
+        ),
+        # Explicit parens: (-2)^3 groups the negation first
+        (
+            "(-2)^3",
+            InfixExpression(
+                operator="^",
+                lvalue=_neg(Atom(Token(type=TokenType.FLOAT, value="2"))),
+                rvalue=Atom(Token(type=TokenType.FLOAT, value="3")),
+            ),
+        ),
+    ],
+)
+def test_unary_minus(expression, expected):
+    assert parse(expression) == expected
+
+
+@pytest.mark.parametrize(
+    "expression, x, expected",
+    [
+        ("-x", 5, -5),
+        ("--x", 5, 5),
+        ("1 - -2", 0, 3),
+        ("-2^3", 0, -8),  # -(2^3) = -8
+        ("(-2)^3", 0, -8),  # (-2)^3 = -8
+        ("-2^2", 0, -4),  # -(2^2) = -4
+        ("(-2)^2", 0, 4),  # (-2)^2 = 4
+    ],
+)
+def test_unary_minus_eval(expression, x, expected):
+    assert parse(expression).eval(x) == expected

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