Unit 1 Questions Swarat Chaudhuri amp John Greiner What do you need to do after class Do first assignment Take first quiz Sign up for tutorial section Read 10 chapters of textbook Response Counter ID: 165674
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Slide1
COMP 382Unit 1 Questions
Swarat
Chaudhuri & John GreinerSlide2
What do you need to do after class?
Do first assignment
Take first quiz
Sign up for tutorial sectionRead 10 chapters of textbook
Response CounterSlide3
List definition has how many cases?
1
2
34
Response CounterSlide4
f
unction append (x: List, y: List): List {
match x
case Empty => ???
case Cons(m, z) => ???
}
How to complete base case?
x
y
Empty
Response CounterSlide5
function append (x: List, y: List): List {
match x
case Empty => y
case Cons(m, z) => ???
}
How to complete inductive case?
Cons(m, append(x, z))
Cons(m, append(z, x))
Cons(m, append(y, z))
Cons(m, append(z, y))
Response CounterSlide6
function reverse (x: List): List {
match x
case Empty => Empty
case Cons(m, z) => ???
}
How to complete inductive case?
Cons(z, m)
a
ppend(z, m)
a
ppend(reverse(z), m)
a
ppend(reverse(z), Cons(m, Empty))
0 of 0Slide7
To prove:
is divisible by
, for
.
How many cases in inductive proof?
1
2
3
4
0 of 117Slide8
To prove:
is divisible by
, for
.
What is the inductive case?
If
, then
.
If
, then
.
Response CounterSlide9
To prove:
, for
.
What is base case?
Response CounterSlide10
< is a well-founded relation over
ℕ
.
TrueFalse
Response CounterSlide11
is a well-founded relation over
ℕ
.
TrueFalse
Response CounterSlide12
< is a well-founded relation over
ℤ
.
TrueFalse
Response CounterSlide13
Which is a well-founded relation on
ℕ×ℕ
?
iff
…
Response CounterSlide14
For chips puzzle, do induction on what?
Remove a red and anything → Put in none.
Remove two yellow → Put in 1 yellow, 5 blue.
Remove a blue and not red → Put in 10 red.Total # of chipsLex. order (#red, #yellow, #blue)
Lex. order (#blue, #yellow, #red)Lex. order (#yellow, #blue, #red)
Response CounterSlide15
Induction guarantees what for inductively-defined programs?
Termination
Correctness
Most efficient algorithmNo such general statement always holds
Response Counter