COMP**21 Principles of Programming
Term 1, 2024
Coding Quiz 3
Worth 4 marks and due Week 5 Thursday @ 9pm
Description
You are provided with a stub in which you need to insert your code where indicated without doing any
changes to the existing code to complete the task.
The current code prompts the user for an arity (a natural number) n and a word. Your task is to complete
the function is_valid(word, arity) that checks if the provided word with the given arity will
return either True if the word is valid or False if the word is invalid based on the constraints below.
Let’s call a symbol a word consisting of nothing but alphabetic characters and underscores.
The function checks if the word is valid given an arity n, that is, it satisfies the following inductive
definition:
• a symbol, with spaces allowed at both ends, is a valid word.
• a word of the form s(w1, ..., wn) with s denoting a symbol and w1, ..., wn denoting valid words,
with spaces allowed at both ends and around parentheses and commas, is a valid word.
See the test cases below for more details.
Due Date and Submission
Quiz 3 is due Week 5 Thursday 14 March 2024 @ 9.00pm (Sydney time).
Note that late submission with 5% penalty per day is allowed up to 3 days from the due date, that is, any
late submission after Week 4 Sunday 17 March 2024 @ 9pm will be discarded.
Make sure not to change the filename quiz_3.py while submitting by clicking on [Mark] button in Ed.
It is your responsibility to check that your submission did go through properly using Submissions link in Ed
otherwise your mark will be zero for Quiz 3.
2
Test Cases
$ python3 quiz_3.py
Input an arity : 0
Input a word: f_1
The word is invalid.
$ python3 quiz_3.py
Input an arity : 0
Input a word: ()
The word is invalid.
$ python3 quiz_3.py
Input an arity : 0
Input a word: function_of_arity_one(hello)
The word is invalid.
$ python3 quiz_3.py
Input an arity : 1
Input a word: f)
The word is invalid.
$ python3 quiz_3.py
Input an arity : 1
Input a word: f[a]
The word is invalid.
$ python3 quiz_3.py
Input an arity : 2
Input a word: f(a, g(b))
The word is invalid.
3
$ python3 quiz_3.py
Input an arity : 3
Input a word: constant
The word is invalid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: f((a,b,c))
The word is invalid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: f(g(a,a), f(a,b))
The word is invalid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: f(g(a,b,c),g(a,b,c),g(a,b,c)
The word is invalid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: f(a, g(a, b, f(a,b,c)), b, c)
The word is invalid.
$ python3 quiz_3.py
Input an arity : 0
Input a word: a
The word is valid.
4
$ python3 quiz_3.py
Input an arity : 1
Input a word: function_of_arity_one(hello)
The word is valid.
$ python3 quiz_3.py
Input an arity : 2
Input a word: F(g(a,a), f(a,b))
The word is valid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: ff(ff(ff(a,b,ff(aa,bb,cc)) , b , ff(a,b,c)) , b , ff(a,ff(a,b,c),c))
The word is valid.
$ python3 quiz_3.py
Input an arity : 4
Input a word: f(a, FF(a, b, fff(a, b, c, FfFf(a,b,c,d)), FfFf(a,b,c,d)), c, d)
The word is valid.
5
Some More Test Cases
Here are some more examples that may help clarify doubts about Quiz 3 requirements:
Input an arity : 0
Input a word: f()
The word is invalid.
Input an arity : 1
Input a word: f()
The word is invalid.
Input an arity : 0
Input a word: f
The word is valid.
Input an arity : 1
Input a word: f(x)
The word is valid.
Input an arity : 0
Input a word: _
The word is valid
Input an arity : 2
Input a word: f ( a , _ )
The word is valid.
Input an arity : 2
Input a word: f ( f , )
The word is invalid.
Input an arity : 2
Input a word: f ( f , a )
The word is valid.
6
Input an arity : 1
Input a word: f (f)
The word is valid.
Input an arity : 0
Input a word: f. f
The word is invalid. 
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