Daily Coding Problem 5 - First-class Functions
This problem was asked by Jane Street.
cons(a, b)
constructs a pair, and car(pair)
and cdr(pair)
returns the first and last element of that pair. For example, car(cons(3, 4))
returns 3
, and cdr(cons(3, 4))
returns 4
.
Given this implementation of cons:
def cons(a, b):
def pair(f):
return f(a, b)
return pair
Implement car
and cdr
.
Solution
This is not a difficult problem, but requires that the person understand how to use functions as first-class members of the language. Admittedly, python is not a language I use often. I personally prefer statically typed languages and the compile-time goodness that comes along with them.
Regardless, the solution is quite simple. The key is that cons
returns a function that expects a function as an argument. That argument is what must, in turn, return the correct value from the pair.
First, let’s put the cons
function into scope.
def cons(a, b):
def pair(f):
return f(a, b)
return pair
Implementation of car
As the problem states, car
needs to return the first element of the pair.
def car(cns):
# Returns the first parameter passed to the function.
def fst(x, y):
return x
return cns(fst)
Implementation of cdr
cdr
needs to return the second element of the pair.
def cdr(cns):
# Returns the second parameter passed to the function.
def snd(x, y):
return y
return cns(snd)
Testing
We can perform some basic test to ensure that these implementation work correctly. Since the problem did not specify any test cases, i made some up using different types.
a = cons(1, 2)
b = cons('a', 'b')
c = cons(5.0, 6.0)
d = cons(True, False)
print ('a: ', car(a), ',', cdr(a))
print ('b: ', car(b), ',', cdr(b))
print ('c: ', car(c), ',', cdr(c))
print ('d: ', car(d), ',', cdr(d))
a: 1 , 2
b: a , b
c: 5.0 , 6.0
d: True , False
Conclusion
While this wasn’t a difficult problem by any means, it was a fun little exercise that demonstrates the use of functions as first class citizens of a language.