Haskell - Infinite lists (1) P98957


Statement
 

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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,…].
  2. Generate the sequence of the natural numbers [0,1,2,3,4,5,6,7…].
  3. Generate the sequence of the integer numbers [0,1,−1,2,−2,3,−3,4…].
  4. Generate the sequence of the triangular numbers: 0,1,3,6,10,15,21,28,…].
  5. Generate the sequence of the factorial numbers: [1,1,2,6,24,120,720,5040,…].
  6. Generate the sequence of the Fibonacci numbers: [0,1,1,2,3,5,8,13,…].
  7. Generate the sequence of prime numbers: [2,3,5,7,11,13,17,19,…].
  8. Generate the ordered sequence of the Hamming numbers: [1,2,3,4,5,6,8,9,…]. 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,…].
  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],…].

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.

Public test cases

  • Input

    take 8 ones
take 8 nats
take 8 ints
take 8 triangulars
take 8 factorials
take 8 fibs
take 8 primes
take 8 hammings
take 8 lookNsay
take 6 tartaglia

    Output

    [1,1,1,1,1,1,1,1]
[0,1,2,3,4,5,6,7]
[0,1,-1,2,-2,3,-3,4]
[0,1,3,6,10,15,21,28]
[1,1,2,6,24,120,720,5040]
[0,1,1,2,3,5,8,13]
[2,3,5,7,11,13,17,19]
[1,2,3,4,5,6,8,9]
[1,11,21,1211,111221,312211,13112221,1113213211]
[[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1],[1,5,10,10,5,1]]
    • Information
    Author
    Albert Rubio / Jordi Petit
    Language
    English
    Translator
    Jordi Petit
    Original language
    Catalan
    Other languages
    Catalan
    Official solutions
    Haskell
    User solutions
    Haskell