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lec3.py
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lec3.py
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from logic import *
# Check if a list is empty
def isEmpty(lst):
"""
>>> isEmpty([])
True
>>> isEmpty([2,3])
False
"""
return lst == []
# Append an element to the front of a list
def cons(head, rest):
"""Construct a list from a head (A) and a rest (list of A)
>>> cons(1,cons(2,cons(3,[])))
[1, 2, 3]
"""
# We will expand upon `precondition` in next lecture
precondition(type(rest)==type([]))
return [head] + rest
# Get the head of a list
def head(lst):
"""
>>> head([1,2,3])
1
"""
precondition(not isEmpty(lst))
return lst[0]
# Get the tail of a list
def tail(lst):
"""
>>> tail([1,2,3])
[2, 3]
"""
precondition(type(lst) == type([]))
return lst[1:]
# Predicate to determine if a list is sorted
def isSorted(lst):
"""
>>> isSorted([])
True
>>> isSorted([1])
True
>>> isSorted([2,1])
False
>>> isSorted([1,2])
True
>>> isSorted([3,6,7,-5])
False
"""
if (len(lst) == 0 or len(lst) == 1): return True
if (head(lst) < head(tail(lst))):
return isSorted(tail(lst))
else: return False
def gt0(e):
return e > 0
def forall(lst,prop):
"""
>>> forall([1,2], gt0)
True
>>> forall([-1,2], gt0)
False
"""
if (isEmpty(lst)): return True
else:
return prop(head(lst)) and forall(tail(lst),prop)
def compatibleSort(lst,e):
"""
>>> compatibleSort([1],1)
True
>>> compatibleSort(["a"],1)
False
"""
if (isEmpty(lst)): return True
else:
try:
head(lst) < e
return True
except:
return False
# Insert element e into a sorted list lst
def insert(lst,e):
"""
>>> insert([1,3,8,9],4)
[1, 3, 4, 8, 9]
"""
precondition(isSorted(lst) and compatibleSort(lst,e))
return lst