Question 1:

What is the value of the following expression:

match 4 with
| S (S x) => x
| _ => 0
end.

the correct answer is answer no. 3: 2

Question 2:

What is the value of the following expression:

match 5 with
| S (S x) => x
| _ => 0
end.

Question 3:

What is the value of the following expression:

match 5 with
| S (S x) => x
| 0 => 0
end.

the correct answer is answer no. 1: Error: Non exhaustive pattern matching

Question 4:

In a context where lists have been defined, what is the value of the following expression:

match (1 :: 2 :: 3 :: 4 :: nil) with
| _ :: _ :: n :: _ =>  n
| _ => 0
end

the correct answer is answer no. 1: 3

Question 5:

What is the value of the following expression:

(fun (f : nat -> nat) => f 3) (Nat.add 2)

the correct answer is answer no. 1: 5

Question 6:

What is the value of the following expression:

match (4 + 2) with
| x + 2 => x
| _ => 0
end

the correct answer is answer no. 3: Error: Invalid notation for pattern

Question 7:

What is the value of the following expression:

match 3, 4 with x, x => x | x, y => x + y end.

the correct answer is answer no. 4: Error: the variable x is bound several times in pattern

Question 8:

What is the value of the following expression:

(fun x y => match y with 0 => true | x => false end) 3 5

Question 9:

Here is the definition of a recursive function:

Fixpoint f (x : nat) : nat :=
  match x with 0 => 0 | 1 => 0 | S p => S (f p) end.

Question 10:

Here is the definition of a recursive function:

Fixpoint f (x : nat) : nat :=
  match x with 0 => 1 | S p => p * f p end.

Question 11:

Here is the definition of a recursive function:

Fixpoint f (x : nat) : nat :=
  match x with S (S p) => S (f p) | _ => 0 end.

Question 12:

What is the value of the following expression:

fun x => match 2 + x with
| S (S x) => x
| _ => 0
end

the correct answer is answer no. 2: fun x : nat => x