Question

I am new to Haskell, and programming in general. I am trying to define a function which generates the sequence of Collatz numbers from n. I have:

collatz n = (collatz' n) : 1
   where collatz' n = (takeWhile (>1) (collatz'' n))
          where collatz'' n = n : collatz'' (collatz''' n)
                 where collatz''' 1 = 1
                       collatz''' n = if (even n) then (div n 2) else ((3*2)+1)

When I run this in GHCi, I get the error:

No instance for (Num [t])
  arising from the literal `2' at <interactive>:1:7
Possible fix: add an instance declaration for (Num [t])

I don’t know what this means. The problem seems to be appending “1” to the list. This problem emerges because

collatz' n = (takeWhile (>0) (collatz'' n))

generates an infinite sequence of “1”s following the correct Collatz sequence; however,

collatz' n = (takeWhile (>1) (collatz'' n))

generates all Collatz numbers from n except “1”. What am I doing wrong?

Answer 1

ony’s answer is correct, but since you’re new to Haskell, maybe this is a clearer explanation. The : operator prepends a value to a list, so doing somelist : 7 is invalid since that’s trying to append a value to a list. That’s why (collatz' n) : 1 doesn’t compile, since the type of (collatz' n) is a list of numbers.

Try replacing the : 1 with ++ [1].