REVISED: Thursday, February 8, 2024
1. INTRODUCTION
A triangle with all three sides of equal length and all angles equal to 60° is an equilateral triangle.
t n = (n * (n+1)) `div` 2
are the number of objects needed to form an equilateral triangle.
This tutorial shows a method for using Haskell to compute the Triangular Number Sequence of objects needed to form equilateral triangles:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431...
2. HASKELL PROGRAM
A Haskell program used to compute the Triangular Number Sequence is as follows:
-- C:\Users\Tinnel\Haskell2024\triangularNS.hs
import Data.List
import System.IO
main :: IO () -- Has type I/O action.
main = do { putStrLn "" -- putStrLn Has type I/O action.
; putStrLn "=========================================================="
; putStrLn ""
; putStrLn "TRIANGULAR NUMBER SEQUENCE"
; putStrLn ""
; putStrLn "h = 1 2 3 4 5"
; putStrLn " ** *** **** ***** ******"
; putStrLn " *** h**** ***** ******"
; putStrLn " **** ***** ******"
; putStrLn " h+1 ***** ******"
; putStrLn " ******"
; putStrLn ""
; putStrLn "The above rectangles are h high and h + 1 wide and contain 2 equilateral triangles."
; putStrLn ""
; putStrLn "t h is the total stars in one equilateral triangle."
; putStrLn "t h = h * (h + 1) `div` 2"
; putStrLn ""
; putStrLn "For example"
; putStrLn "t 5 = 5 * (5 + 1) `div` 2"
; putStrLn "equals 15 stars in one equilateral triangle 5 stars high."
; putStrLn ""
; putStrLn "=========================================================="
; putStrLn ""
; putStrLn "Type a positive integer representing an equilateral triangle with height of h then press Enter."
; s <- getLine -- getLine is a function, getLine :: IO String
; putStrLn ""
; putStrLn "=========================================================="
; putStrLn ""
; let h = (read s)::Integer
; putStrLn "The Triangular Number is:"
; putStrLn ""
; let z = fromIntegral(t h)
; print z
; putStrLn ""
; putStrLn "=========================================================="
; putStrLn ""
}
--
-- Haskell has different functions for integer and 'fractional' division.
-- Int is not an instance of Fractional so you can't use (/) with Int.
-- t :: Fractional a => a -> a
t :: Integral a => a -> a
t h = h * (h + 1 )`div` 2
3. GHCi RUN
*Main> :l triangularNS
[1 of 1] Compiling Main ( triangularNS.hs, interpreted )
Ok, modules loaded: Main.
*Main> main
=========================================================================
TRIANGULAR NUMBER SEQUENCE
h = 1 2 3 4 5
** *** **** ***** ******
*** h**** ***** ******
**** ***** ******
h+1 ***** ******
******
The above rectangles are h high and h + 1 wide and contain 2 equilateral triangles.
t h is total stars in one equilateral triangle.
t h = h * (h + 1) `div` 2
For example
t 5 = 5 * (5 + 1) `div` 2
equals 15 stars in one equilateral triangle 5 stars high.
=========================================================================
Type a positive integer representing an equilateral triangle with height of h then press Enter.
5
=========================================================================
The Triangular Number is:
15
=========================================================================
*Main>
4. CONCLUSION
In this tutorial you have seen a basic approach for using Haskell to compute the Triangular Number Sequence.
5. REFERENCES
Bird, R. (2015). Thinking Functionally with Haskell. Cambridge, England: Cambridge University Press.
Davie, A. (1992). Introduction to Functional Programming Systems Using Haskell. Cambridge, England: Cambridge University Press.
Goerzen, J. & O'Sullivan, B. & Stewart, D. (2008). Real World Haskell. Sebastopol, CA: O'Reilly Media, Inc.
Hutton, G. (2007). Programming in Haskell. New York: Cambridge University Press.
Lipovača, M. (2011). Learn You a Haskell for Great Good!: A Beginner's Guide. San Francisco, CA: No Starch Press, Inc.
Thompson, S. (2011). The Craft of Functional Programming. Edinburgh Gate, Harlow, England: Pearson Education Limited.
