def first_power_of_x_r(tree, entire):
""""Performs x = x ^ 1
Give the x as cursor
"""
one = Tree("suc", [Token("NUMBER", "0")])
power = Tree("pow", [])
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
power.children = [tree, one]
tree = power
grandparent.children[treeindex] = tree
return grandparent, entire
else:
power.children = [tree, one]
entire = power
return tree, entire
def plus_zero_r(tree, entire):
""""
Performs x = x + 0
"""
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
if child is tree:
treeindex = e
add = Tree("add", [])
zerotoken = Token("NUMBER", "0")
add.children = [tree, zerotoken]
grandparent.children[treeindex] = add
return tree, entire
else:
add = Tree("add", [])
zerotoken = Token("NUMBER", "0")
add.children = [tree, zerotoken]
entire = add
return tree, entire
def times_identity_r(tree, entire):
""""Performs x = x * 1
Give the x as cursor
"""
mul = Tree("mul", [])
one = Tree("suc", [Token("NUMBER", "0")])
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
# Check this
mul.children = [tree, one]
tree = mul
grandparent.children[treeindex] = tree
return grandparent, entire
else:
mul.children = [entire, one]
entire = mul
return tree, entire
def distributivity_power_times_r(tree, entire):
""""
Performs x ^ z * x ^ z = (x * y) ^ z
"""
# TODO Check this with the axioms
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
x = tree.children[0].children[0]
z = tree.children[0].children[1]
y = tree.children[1].children[0]
z2 = tree.children[1].children[1]
assert z == z2
op1 = Tree("pow", [])
op2 = Tree("mul", [])
op2.children = [x, y]
op1.children = [op2, z]
tree = op1
grandparent.children[treeindex] = tree
return tree, entire
else:
x = entire.children[0].children[0]
z = entire.children[0].children[1]
y = entire.children[1].children[0]
z2 = entire.children[1].children[1]
assert z == z2
op1 = Tree("pow", [])
op2 = Tree("mul", [])
op2.children = [x, y]
op1.children = [op2, z]
entire = op1
return tree, entire
def distributivity_power_plus_r(tree, entire):
""""
Performs x ^ y * x ^ z = x ^ (y + z)
"""
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
x = tree.children[0].children[0]
x2 = tree.children[1].children[0]
assert x == x2
y = tree.children[0].children[1]
z = tree.children[1].children[1]
op1 = Tree("pow", [])
op2 = Tree("add", [])
op2.children = [y, z]
op1.children = [x, op2]
tree = op1
grandparent.children[treeindex] = tree
return tree, entire
else:
x = entire.children[0].children[0]
x2 = entire.children[1].children[0]
assert x == x2
y = entire.children[0].children[1]
z = entire.children[1].children[1]
op1 = Tree("pow", [])
op2 = Tree("add", [])
op2.children = [y, z]
op1.children = [x, op2]
entire = op1
return tree, entire
def recursive_times_l(tree, entire):
"""" Performs x * s(y) = x * y + x
Supply the cursor at *
"""
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
# Make the new add node
add = Tree("add", [])
# This cop seems unnecessary too
# Leaving it for reference
# cop = tree
grandparent.children[treeindex] = add
# Copy the x term that will be in both multiply and add op
x = copy.deepcopy(tree.children[0])
# Move the child over the S() to the y
tree.children[1] = tree.children[1].children[0]
# Give the add node its children
add.children = [tree, x]
return grandparent, entire
else:
# Need a new op, the add
add = Tree("add", [])
# Cop is unnecessary
# cop = entire
x = copy.deepcopy(entire.children[0])
entire.children[1] = entire.children[1].children[0]
add.children = [entire, x]
entire = add
return tree, entire
def distributivity_power_power_l(tree, entire):
""""
Performs (x ^ y) ^ z= x ^ (y * z)
"""
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
x = tree.children[0].children[0]
y = tree.children[0].children[1]
z = tree.children[1]
op1 = Tree("mul", [])
op2 = Tree("pow", [])
op1.children = [y, z]
op2.children = [x, op1]
tree = op2
grandparent.children[treeindex] = tree
return tree, entire
else:
x = entire.children[0].children[0]
y = entire.children[0].children[1]
z = entire.children[1]
op1 = Tree("mul", [])
op2 = Tree("pow", [])
op1.children = [y, z]
op2.children = [x, op1]
entire = op2
return tree, entire
def insert_cursor_node(tree, entire):
if hasattr(tree, "parent") and tree.parent is not None:
gp = tree.parent
# copy = tree
cursor_tag = Tree("cursor", [])
cursor_tag.children = [tree]
for e, child in enumerate(gp.children):
# print(child, tree, e)
if child is tree:
gp.children[e] = cursor_tag
return entire
else:
cursor_tag = Tree("cursor", [])
cursor_tag.children = [tree]
return cursor_tag
def recursive_power_l(tree, entire):
"""" Performs x ^ s(y) = x ^ y * x
Supply the cursor at *
"""
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
# Make the new mul node
mul = Tree("mul", [])
grandparent.children[treeindex] = mul
# Copy the x term that will be in both power and mul op
x = copy.deepcopy(tree.children[0])
# Move the child over the S() to the y
tree.children[1] = tree.children[1].children[0]
# Give the mul node its children
mul.children = [tree, x]
return grandparent, entire
else:
# Need a new op, the mul
mul = Tree("mul", [])
x = copy.deepcopy(entire.children[0])
entire.children[1] = entire.children[1].children[0]
mul.children = [entire, x]
entire = mul
return tree, entire
def recursive_times_r(tree, entire):
""""
Performs
x * y + x -> x * s(y)
"""
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
new_suc = Tree("suc", [])
# cop = tree
new_root = tree.children[0]
new_suc.children = [new_root.children[1]]
new_root.children[1] = new_suc
grandparent.children[treeindex] = new_root
return tree, entire
else:
new_suc = Tree("suc", [])
# cop = entire
new_root = entire.children[0]
y = new_root.children[1]
new_suc.children = [y]
new_root.children[1] = new_suc
entire = new_root
return tree, entire
def distributivity_power_times_l(tree, entire):
""""
Performs (x * y) ^ z = x ^ z * x ^ z
"""
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
z = tree.children[1]
x = tree.children[0].children[0]
y = tree.children[0].children[1]
z2 = copy.deepcopy(z)
op1 = Tree("pow", [])
op2 = Tree("pow", [])
op3 = Tree("mul", [])
op1.children = [x, z]
op2.children = [y, z2]
op3.children = [op1, op2]
tree = op3
grandparent.children[treeindex] = tree
return tree, entire
else:
z = entire.children[1]
x = entire.children[0].children[0]
y = entire.children[0].children[1]
z2 = copy.deepcopy(z)
op1 = Tree("pow", [])
op2 = Tree("pow", [])
op3 = Tree("mul", [])
op1.children = [x, z]
op2.children = [y, z2]
op3.children = [op1, op2]
entire = op3
return tree, entire
def distributivity_power_plus_l(tree, entire):
""""
Performs x ^ (y + z) = x ^ y * x ^ z
"""
if hasattr(tree, "parent") and tree.parent is not None:
grandparent = tree.parent
for e, child in enumerate(grandparent.children):
# print(child, tree, e)
if child is tree:
treeindex = e
x = tree.children[0]
y = tree.children[1].children[0]
z = tree.children[1].children[1]
x2 = copy.deepcopy(x)
op1 = Tree("pow", [])
op2 = Tree("pow", [])
op3 = Tree("mul", [])
op1.children = [x, y]
op2.children = [x2, z]
op3.children = [op1, op2]
tree = op3
grandparent.children[treeindex] = tree
return tree, entire
else:
x = entire.children[0]
y = entire.children[1].children[0]
z = entire.children[1].children[1]
x2 = copy.deepcopy(x)
op1 = Tree("pow", [])
op2 = Tree("pow", [])
op3 = Tree("mul", [])
op1.children = [x, y]
op2.children = [x2, z]
op3.children = [op1, op2]
entire = op3
return tree, entire
def _add_new_token(tree: Tree, new_token: Token) -> Tree:
tree.children = [new_token]
return tree