PLQ #4

Question 1 @ 2024-02-06 19:14

Which kinds of functions do we have in our current version of the Flang language?

A First-order functions.
B First-class functions.
C Higher-order functions.
D Higher-class functions.
E None of the above, since our support for functions is premature.

Question 2 @ 2024-02-06 19:17

We know that we can drop with from the Flang language, because we can replace any of its uses:

{with {x V} B}

with a combination of call+fun:

{call {fun {x} B} V}

Is this symmetric? That is, could we similarly drop the call+fun and manage with just with?

A
Yes we can: we just need to do a similar substitution as above, only going in reverse direction.
B
The question is nonsensical: we cannot always translate a with to uses of call+fun.
C
We cannot do that: we can express more since we broke with into two independent features.
D
Of course not, since any kind of such substitution loses the original code and therefore the intended meaning that the programmer had.

Question 3 @ 2024-02-06 19:20

What is the main problem with our current Flang language implementation?

A
Our bindings are not handled correctly.
B
Function calls are slow, so we need to change the interpreter-based implementation into a compiler using de-Bruijn indexes.
C
We’re missing a way to build object values.
D
We’re missing a way to check that expressions make sense — a type checker.
E
Function calls are slow, corresponding to the function sizes.

Question 4 @ 2024-02-06 19:22

Bob wants to map a curried version of the expt function onto a list of inputs. He first writes the function currify, which takes a two argument function and returns the curried version of the function.

(define (currify f)
(lambda (x)
(lambda (y)
(f x y))))

He then writes a test using a curried expt function (Racket’s exponent):

(test (map (currify expt) '(2 3)) => 8)

What will be the result of this test?

A
It will do whatever Racket does.
B
It will pass, because (expt 2 3) evaluates to 8.
C
It will fail, because the map will evaluate to a list of numbers, not just a single number.
D
It will error, because the function (currify expt) needs to be called on an input before it is passed into map.
E
It will fail, because the map will evaluate to a list of one argument functions instead.

Question 5 @ 2024-02-06 19:27

What is a good name for the following function?

(define mystery
(lambda (f g)
(lambda (x)
(g (f x)))))

A
Trick question: this has free identifiers and therefore always an error.
B
functional-addition
C
compose
D
compose-at-point
E
reverse-compose
F
currify-3-args

PLQ #4Done on: Tuesday, February 6th

Question 1 @ 2024-02-06 19:14

Question 2 @ 2024-02-06 19:17

Question 3 @ 2024-02-06 19:20

Question 4 @ 2024-02-06 19:22

Question 5 @ 2024-02-06 19:27