Programming III

Question 1

What are the distinct type operators in the below function definition?

Answer 1

(,) , -> , [] , Maybe

Question 2

What are the distinct data constructors in the below function definition?

Answer 2

Nothing , Just , []

Question 3

Higher Order Function

Answer 3

A function that takes a function as an argument, or returns a function.
Example: all curried functions

Question 4

Curried function

Answer 4

A function that returns a function

Question 5

curry and uncurry

Answer 5

curry: takes function that takes a single argument, and returns that function so that it takes multiple arguments.
uncurry: takes function that takes multiple arguments, and returns that function so that it takes a single argument.

Question 6

Polymorphic function

Answer 6

A function is polymorphic if its type definition contains one or more unconstrained type variable

Question 7

zip function

Answer 7

Appends two lists together, combining values from the same index into a pair.
If one list is shorter, it truncates the longer list.
zip: [a] -> [b] -> [(a,b)]

Question 8

Alpha equivalent

Answer 8

Two terms are alpha equivalent if one can be converted to the other by alpha conversion.
* λ x -> λ y -> x y z is alpha equivalent to:
λ x -> λ w -> x w z
* λ x -> λ y -> x y z is not alpha equivalent to:
λ x -> λ z -> x z z

Question 9

Redex

Answer 9

Reducible expression:
an expression comprising a function applied to an argument expression.

Question 10

Innermost redex

Answer 10

A redex containing no other redexes

Question 11

Outermost redex

Answer 11

A redex not contained in any other redex

Question 12

Innermost evaluation

Answer 12

Innermost redexes are evaluated first

Question 13

Outermost evaluation

Answer 13

Outermost redexes are evaluated first

Question 14

Leftmost evaluation

Answer 14

Start with the leftmost redex

Question 15

Rightmost evaluation

Answer 15

Start with the rightmost redex

Question 16

Haskell evaluation strategy

Answer 16

Outmost, leftmost evaluation

Call-by-Name

Question 17

Call-by-Value reduction strategy

Answer 17

Leftmost, innermost reduction

Question 18

Call-by-Name evalution strategy

Answer 18

Leftmost, outermost evaluation

Question 19

Lambda calculus

Bound and Free variables

Answer 19

A variable is bound if given with a lambda symbol,
e.g. x is bound in λ x -> x y

A variable is otherwise free,
e.g. y is free in λ x -> x y

Question 20

Lambda calculus

Scope of a binding

Answer 20

Everything coming after the lambda definition of the variable,
e.g. e1 is the scope of x in λ x -> e1

Question 21

Lambda calculus

Scope of an abstraction

Answer 21

All values given with lambda symbols,
e.g. x is in the scope and y isn’t of λ x -> x y

Question 22

Lambda calculus

Closed term

Answer 22

A lambda calculus term with no free variables is closed

Question 23

Bind (>>=)

Answer 23

Takes a structured value and a function that may produce a structured result, and applies the latter to the former to produce a structured result:
>>= : (f a) -> (a -> f b) -> (f b)

Question 24

return

Answer 24

Takes a value of data type a, and returns the value as a Maybe data type, e.g. m a

Question 25

java.util.Stream

Intermediate operators

Answer 25

• filter
• peek
• distinct
• sorted
• iterate

Question 26

java.util.Stream

Terminal operations

Answer 26

• forEach
• toArray
• reduce (inc. max, min, count)
• collect

Question 27

Isomorphism between two data types T and U

Answer 27

An isomorphism exists if there exists are a pair of functions taking T -> U and U -> T,
and T and U have an equal size

Question 28

Monad properties

Answer 28

Associativity and Distributivity