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LambdaNode.py
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LambdaNode.py
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import copy
class Node:
"""Summary
var: Variable
num: Number
apply: (M N)
oper: (* M N)
lambda: (lambda.M N)
Method:
frV: fv[(lambda M (M N))]; -> {N}
alpha: alpha[(lambda x (x y)),z]; -> (lambda z (z y))
sub: (lambda x (x y))[y = (u v)]; -> (lambda x (x (u v)))
"""
def __init__(self):
self.type = ''
self.method = ''
self.var = ''
self.free_vars = set({})
self.val = None
self.op = ''
self.left = ''
self.right = ''
self.CONST = 8
def toObj(self, n: int)->str:
result = '{'+ ' '*n + '\n'
tab = ' '*n
if (self.type == 'num'):
result += f"{tab}Type: {self.type}\n{tab}Value: {self.val}\n"
elif(self.type == 'var'):
result += f"{tab}Type: {self.type}\n{tab}Var: {self.var}\n{tab}FreeVar: {self.free_vars}\n"
elif(self.type == 'oper'):
result += f"{tab}Type: {self.type}\n{tab}FreeVar: {self.free_vars}\n{tab}Operator: {self.op}\n{tab}Left: {self.left.toObj(n+self.CONST) if self.left != '' else ''}\n{tab}Right: {self.right.toObj(n+self.CONST) if self.right != '' else ''}\n"
elif(self.type == 'apply'):
result += f"{tab}Type: {self.type}\n{tab}FreeVar: {self.free_vars}\n{tab}Left: {self.left.toObj(n+self.CONST) if self.left != '' else ''}\n{tab}Right: {self.right.toObj(n+self.CONST) if self.right != '' else ''}\n"
elif(self.type == 'lambda'):
result += f"{tab}Type: {self.type}\n{tab}BoundVar: {self.var}\n{tab}FreeVar: {self.free_vars}\n{tab}Left: {self.left.toObj(n+self.CONST) if self.left != '' else ''}\n"
elif (self.type == '' and self.method == 'frV'):
result += f"{tab}Method: {self.method}\n{tab}Left:{self.left.toObj(n+self.CONST) if self.left != '' else ''}\n"
elif (self.type == '' and self.method == 'sub'):
result += f"{tab}Method: {self.method}\n{tab}Substitue Var: {self.var}\n{tab}Sub To:{self.left.toObj(n+self.CONST) if self.left != '' else ''}\n{tab}Sub From: {self.right.toObj(n+self.CONST) if self.right != '' else ''}\n"
elif (self.type == '' and self.method == 'alpha'):
result += f"{tab}Method: {self.method}\n{tab}Replace By: {self.var}\n{tab}Replace In:{self.left.toObj(n+self.CONST) if self.left != '' else ''}\n"
else:
pass
# result += f"{tab}Type: {self.type}\n{tab}BoundVar: {self.var}\n{tab}Var: {self.var}\n{tab}FreeVar: {self.free_vars}\n{tab}Value: {self.val}\n{tab}Operator: {self.op}\n{tab}Left: {self.left.toObj(n+self.CONST) if self.left != '' else ''}\n{tab}Right: {self.right.toObj(n+self.CONST) if self.right != '' else ''}\n"
return result + ' '*(n-2) + '}'
def __str__(self):
return self.toObj(2)
class Solver:
def __init__(self):
pass
@staticmethod
def solvethis(node: Node, exec: int):
if node == None:
return
flag = False
if 1 in exec:
flag = True
if node.method == 'frV':
node = Solver.free_vars(node.left)
print(f"Free variables: {node.free_vars}")
elif node.method == 'alpha':
node = Solver.alpha(node.left, node.var)
print(Solver.tree_to_string(node))
elif node.method == 'sub':
node = Solver.substitue(node.left, [node.var, node.right])
print(Solver.tree_to_string(node))
elif node.type != '':
node = Solver.beta_reduction(node, flag)
print(f"ANSWER>> {Solver.tree_to_string(node)}")
return node
@staticmethod
def tree_to_string(node: Node):
if node.type == 'lambda':
return f"(lambda {node.var} {Solver.tree_to_string(node.left)})"
elif node.type == 'apply':
return f"({Solver.tree_to_string(node.left)} {Solver.tree_to_string(node.right)})"
elif node.type == 'num':
return f"{node.val}"
elif node.type == 'var':
return f"{node.var}"
elif node.type == 'oper':
return f"({node.op} {Solver.tree_to_string(node.left)} {Solver.tree_to_string(node.right)})"
else:
return ""
@staticmethod
def free_vars(node: Node):
if node.left != '':
Solver.free_vars(node.left)
if node.right != '':
Solver.free_vars(node.right)
if node.type == 'var':
node.free_vars = set({node.var})
elif node.type == 'apply' or node.type == 'oper':
node.free_vars = node.left.free_vars.union(node.right.free_vars)
elif node.type == 'lambda':
node.free_vars = node.left.free_vars
if node.var in node.free_vars: node.free_vars.remove(node.var)
return node
@staticmethod
def alpha(node: Node, replace_to: str):
replace_this = node.var
def solve(node: Node, this: str, by: str):
if node.left != '':
solve(node.left, this, by)
if node.right != '':
solve(node.right, this, by)
if node.var == this:
node.var = by
solve(node, replace_this, replace_to)
Solver.free_vars(node)
return node
@staticmethod
def substitue(node: Node, sub: list):
# print(f"SUBSTITUE: {Solver.tree_to_string(node)}")
# print(f"VAR: {sub[0]}")
# print(f"TO: {Solver.tree_to_string(sub[1])}")
save = node
def solve(node: Node, sub: list):
if(node.type == "num"): return node
elif (node.type == 'var') and node.var == sub[0]:
node = sub[1]
elif (node.type == "apply"):
node.left = solve(node.left, sub)
node.right = solve(node.right, sub)
elif (node.type == "oper"):
if(node.left.type != "num"):
node.left = solve(node.left, sub)
if(node.right.type != "num"):
node.right = solve(node.right, sub)
elif (node.type == "lambda"):
if(node.var in sub[1].free_vars):
node = Solver.alpha(node, node.var + "'")
node.left = solve(node.left, sub)
else:
node.left = solve(node.left, sub)
return node
node = solve(node, sub)
Solver.free_vars(node)
return save
@staticmethod
def beta_reduction(node: Node, flag: bool):
def solve(node: Node):
if(node.type == "apply" and node.left.type == "lambda"):
node.left = solve(node.left)
# print(f"Before: {Solver.tree_to_string(node)}")
node = Solver.substitue(copy.deepcopy(node.left), [copy.deepcopy(node.left.var), copy.deepcopy(node.right)]).left
# print(f"After: {Solver.tree_to_string(node)}")
return node
elif(node.type == "lambda"):
node.left = solve(node.left)
return node
elif(node.type == "oper"):
node.left = solve(node.left)
node.right = solve(node.right)
if node.left.type == "num" and node.right.type =="num":
if node.op == '+':
sumthis = node.left.val + node.right.val
node = Node()
node.type = 'num'
node.val = sumthis
return node
elif node.op == '-':
subthis = node.left.val - node.right.val
node = Node()
node.type = 'num'
node.val = subthis
return node
elif node.op == '*':
multiply = node.left.val * node.right.val
node = Node()
node.type = 'num'
node.val = multiply
return node
elif node.op == '/':
if node.right.val == 0.0:
raise Exception('Arithmetic Error')
else:
div = float(node.left.val // node.right.val)
node = Node()
node.type = 'num'
node.val = div
return node
return node
elif(node.type == "apply"):
node.left = solve(node.left)
# node.right = solve(node.right)
return node
return node
prev = Solver.tree_to_string(node)
if flag:
print(f"INITIAL> {prev}")
node = solve(node)
cur = Solver.tree_to_string(node)
while(not cur.__eq__(prev)):
prev = cur
if flag:
print(f"BETA> {cur}")
node = solve(node)
cur = Solver.tree_to_string(node)
return node
# --------------------------------------------------------------------------------------------