Use Table Driven Rules

use-table-driven-rules

When to Use

• Many special cases (simplification rules)
• Configuration-driven behavior
• Lookup tables
• State machines
• Rules that change frequently
• Making rules visible/maintainable

When NOT to Use

• Few simple cases (use if-elif)
• Rules require complex logic
• Order of evaluation matters in complex ways

The Pattern

Store rules in data structures instead of code.

# Instead of:
def simplify(expr):
    if expr == ('+', 0, x): return x
    if expr == ('+', x, 0): return x
    if expr == ('*', 1, x): return x
    ...

# Use table:
simp_rules = {
    ('+', 0, 'x'): 'x',
    ('+', 'x', 0): 'x',
    ('*', 1, 'x'): 'x',
    ('*', 'x', 1): 'x',
    ('*', 0, 'x'): 0,
}

def simplify(expr):
    pattern = generalize(expr)  # Convert to pattern form
    if pattern in simp_rules:
        return instantiate(simp_rules[pattern], expr)
    return expr

Example (from pytudes)

# Simplification table (Differentiation.ipynb)
simp_table = {
    sin(0): 0,
    sin(pi): 0,
    sin(pi/2): 1,
    cos(0): 1,
    cos(pi): -1,
    cos(pi/2): 0,
    tan(0): 0,
    ln(1): 0,
    ln(e): 1,
}

def simp(y):
    """Simplify expression using table and rules."""
    if y in simp_table:
        return simp_table[y]
    # ... additional simplification logic

# Direction vectors (AdventUtils.ipynb)
arrow_direction = {
    '^': (0, -1),  # North
    'v': (0, 1),   # South
    '>': (1, 0),   # East
    '<': (-1, 0),  # West
    '.': (0, 0),   # Stay
}

def move(pos, arrow):
    dx, dy = arrow_direction[arrow]
    return (pos[0] + dx, pos[1] + dy)

# Factor multipliers (pal2.py)
factor = {'left': +1, 'right': -1}

def add_word(self, direction, word):
    self.diff += factor[direction] * len(word)

# Lisp operations (lis.py)
env = {
    '+': op.add,
    '-': op.sub,
    '*': op.mul,
    '/': op.truediv,
}

Key Principles

1. Data over code: Rules as dict entries, not if statements
2. Easy to extend: Adding rule = adding dict entry
3. Visible rules: Can print/inspect the table
4. Consistent lookup: All rules checked same way
5. Fallback logic: Handle missing keys gracefully