build-expression-tree

name: build-expression-tree description: "For symbolic computation: ASTs, mathematical expressions, code that manipulates code structure, expression transformations."

When to Use

Symbolic math (differentiation, simplification)
Building ASTs for interpreters
Query builders (SQL, API)
Code generation
Expression pattern matching

When NOT to Use

Just need to evaluate once (use direct computation)
No transformation needed
Structure too complex (use existing parser)

The Pattern

Represent expressions as nested data structures (tuples, classes, or trees).

# Tuple representation
expr = ('+', ('*', 'x', 2), 1)  # (x * 2) + 1

# Class representation
class Expr:
    def __init__(self, op, *args):
        self.op, self.args = op, args

    def __add__(self, other):
        return Expr('+', self, other)

    def __mul__(self, other):
        return Expr('*', self, other)

x = Expr('x')
expr = x * 2 + 1  # Builds expression tree

# Recursive evaluation
def evaluate(expr, env):
    if isinstance(expr, str):
        return env[expr]  # Variable lookup
    if isinstance(expr, (int, float)):
        return expr
    op, *args = expr if isinstance(expr, tuple) else (expr.op, *expr.args)
    values = [evaluate(a, env) for a in args]
    return {'+': lambda a,b: a+b, '*': lambda a,b: a*b}[op](*values)

Example (from pytudes Differentiation.ipynb)

class Expression:
    """A symbolic mathematical expression."""
    def __init__(self, op, *args):
        self.op, self.args = op, args

    def __add__(self, other):  return Expression('+', self, other)
    def __radd__(self, other): return Expression('+', other, self)
    def __mul__(self, other):  return Expression('*', self, other)
    def __rmul__(self, other): return Expression('*', other, self)
    def __neg__(self):         return Expression('-', self)

    def __repr__(self):
        if len(self.args) == 1:
            return f"({self.op}{self.args[0]})"
        return f"({self.args[0]} {self.op} {self.args[1]})"

class Function(Expression):
    """A function like sin or cos."""
    def __call__(self, x):
        return Expression(self, x)

# Create symbols and functions
x = Expression('x')
sin, cos = Function('sin'), Function('cos')

# Build expressions naturally
expr = sin(x) + cos(x) * 2
# Expression tree: (+ (sin x) (* (cos x) 2))

# Symbolic differentiation
def D(y, x=x):
    """Differentiate y with respect to x."""
    if y == x: return 1
    if not isinstance(y, Expression): return 0
    op, args = y.op, y.args
    if op == '+': return D(args[0], x) + D(args[1], x)
    if op == '*': return D(args[0], x) * args[1] + args[0] * D(args[1], x)
    if op == sin: return cos(args[0]) * D(args[0], x)
    # ... more rules

Key Principles

Operator overloading: Natural syntax for building trees
radd/rmul for commutativity: Handle 2 + x not just x + 2
Recursive processing: Walk tree to evaluate/transform
Pattern matching on op: Different behavior per operation
Simplification rules: Reduce 0 + x to x, etc.