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find_dual.py
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find_dual.py
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from __future__ import annotations
from typing import Optional, Set, Tuple, Dict, List
import re
class ExprNode:
"""Represents a node in an expression tree."""
def __init__(self, value: str, left: Optional[ExprNode] = None, right: Optional[ExprNode] = None):
self.value = value
self.left = left
self.right = right
self.node_count = 1 + (left.node_count if left else 0) + (right.node_count if right else 0)
def __repr__(self) -> str:
"""Return a string representation of the node."""
if self.left and self.right:
return f"({self.left} {self.value} {self.right})"
return self.value
def get_leafs(self) -> Set[str]:
"""Collect and return all leaf node values in the tree."""
def traverse(node, leaves):
if not node:
return
if not node.left and not node.right:
leaves.add(node.value)
else:
traverse(node.left, leaves)
traverse(node.right, leaves)
leaf_set = set()
traverse(self, leaf_set)
return leaf_set
def reverse(self):
"""Create a new ExprNode with reversed structure and adjusted operators."""
if not self.left and not self.right:
return ExprNode(self.value)
else:
new_left = self.right.reverse() if self.right else None
new_right = self.left.reverse() if self.left else None
return ExprNode(self.value, new_left, new_right)
def is_same_under_rewriting(left: ExprNode, right: ExprNode):
"""
Check if two expression trees are equivalent under variable renaming.
Returns mappings for left and right trees if they're the same, else None.
"""
if left.node_count != right.node_count:
return None
def traverse(node, mapping):
if not node.left and not node.right:
if node.value not in mapping:
if node.value in mapping.values():
return None
mapping[node.value] = len(mapping)
return mapping[node.value]
if not node.left or not node.right:
return None
left_result = traverse(node.left, mapping)
right_result = traverse(node.right, mapping)
if left_result is None or right_result is None:
return None
return (node.value, left_result, right_result)
mapping1 = {}
left_structure = traverse(left, mapping1)
mapping2 = {}
right_structure = traverse(right, mapping2)
if left_structure == right_structure:
return {v: k for k, v in mapping1.items()}, {v: k for k, v in mapping2.items()}
return None
class Parser:
"""A simple parser for mathematical expressions."""
def __init__(self, expression: str):
self.expression = expression.replace(' ', '')
self.index = 0
self.length = len(self.expression)
def parse(self):
"""Parse the entire expression."""
return self.parse_expression()
def parse_expression(self):
"""Parse an expression, handling composition operators."""
nodes = [self.parse_term()]
while self.current_char() in ['∘', '.']:
op = self.current_char()
self.advance()
right = self.parse_term()
nodes.append(op)
nodes.append(right)
# Build the tree (left-associative)
node = nodes[0]
for i in range(1, len(nodes), 2):
node = ExprNode(nodes[i], left=node, right=nodes[i+1])
return node
def parse_term(self):
"""Parse a term (variable or parenthesized expression)."""
char = self.current_char()
if char == '(':
self.advance()
node = self.parse_expression()
if self.current_char() != ')':
raise ValueError("Mismatched parentheses")
self.advance()
return node
else:
return self.parse_variable()
def parse_variable(self):
"""Parse a variable."""
match = re.match(r'[a-zA-Z_]\w*', self.expression[self.index:])
if not match:
raise ValueError(f"Invalid character at index {self.index}")
var = match.group(0)
self.index += len(var)
return ExprNode(var)
def current_char(self):
"""Return the current character or None if at the end."""
return self.expression[self.index] if self.index < self.length else None
def advance(self):
"""Move to the next character."""
self.index += 1
def expr_to_prefix(node: ExprNode):
"""Convert an expression tree to prefix notation."""
if node.value == '∘':
left = expr_to_prefix(node.left)
right = expr_to_prefix(node.right)
return f"f({left}, {right})"
else:
return node.value
def make_tree(equation: str):
"""Create an expression tree from an equation string."""
lhs_expr, rhs_expr = equation.split('=')
parser_lhs = Parser(lhs_expr)
tree_lhs = parser_lhs.parse()
parser_rhs = Parser(rhs_expr)
tree_rhs = parser_rhs.parse()
return ExprNode("=", left=tree_lhs, right=tree_rhs)
def flip_top_most(node: ExprNode):
"""Flip the left and right children of the root node."""
return ExprNode(node.value, left=node.right, right=node.left)
def main():
trees = []
for line in open("../equational_theories/AllEquations.lean"):
if "equation" in line and ":=" in line:
equation_number = line.split("equation")[1].split()[0]
trees.append((int(equation_number), make_tree(line.split(":=")[1].strip())))
seen = {}
for eq_num1, tree1 in trees:
reversed_tree1 = tree1.reverse()
for eq_num2, tree2 in trees:
if eq_num1 >= eq_num2:
continue
if is_same_under_rewriting(reversed_tree1, tree2) or is_same_under_rewriting(reversed_tree1, flip_top_most(tree2)):
print(f"| Equation{eq_num1}[{tree1}] | Equation{eq_num2}[{tree2}] |")
seen[eq_num1] = True
seen[eq_num2] = True
print("Unseen:")
for eq_num, tree in trees:
if eq_num not in seen:
print(f"* Equation{eq_num}[{tree}]")
if __name__ == "__main__":
main()