Haskell - Infinite lists (1) P98957

The goal of this problem is to work the definition of infinite lists. In particular, you are required to define functions that generate infinite lists to:

1. Generate the sequence of ones $[1,1,1,1,1,1,1,1,\dots]$.

2. Generate the sequence of the natural numbers $[0,1,2,3,4,5,6,7\dots]$.

3. Generate the sequence of the integer numbers $[0,1,-1,2,-2,3,-3,4\dots]$.

4. Generate the sequence of the triangular numbers: $0,1,3,6,10,15,21,28,\dots]$.

5. Generate the sequence of the factorial numbers: $[1,1,2,6,24,120,720,5040,\dots]$.

6. Generate the sequence of the Fibonacci numbers: $[0,1,1,2,3,5,8,13,\dots]$.

7. Generate the sequence of prime numbers: $[2,3,5,7,11,13,17,19,\dots]$.

8. Generate the ordered sequence of the Hamming numbers: $[1,2,3,4,5,6,8,9,\dots]$. The Hamming numbers are those that only have 2, 3 and 5 as prime divisors.

9. Generate the look-and-say sequence: $[1,11,21,1211,111221,312211,13112221,1113213211,\dots]$.

10. Generate the sequences of rows of the Tartaglia triangle (also known as Pascal’s triangle): $[[1],[1,1],[1,2,1],[1,3,3,1],\dots]$.

Specification

Define the following functions:

    ones :: [Integer]
    nats :: [Integer]
    ints :: [Integer]
    triangulars :: [Integer]
    factorials :: [Integer]
    fibs :: [Integer]
    primes :: [Integer]
    hammings :: [Integer]
    lookNsay :: [Integer]
    tartaglia :: [[Integer]]

Observation

In this problem you cannot use infinite enumerations such as $[1..]$, but you are advised to use higer-order functions such as map, scanl, iterate, filter, ...

Scoring

Each function score 10 points.