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|
module pascal
/*
The Triangle of Pascal.
The result of this program is a real triangle of Pascal of height
Height, not just a list representing such a triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1 etc.
Run the program using the "Basic Values Only" option (Application options).
Use a non-proportional font for the output (e.g. Monaco 9).
*/
import StdEnv
/* A row of the triangle is represented by a list of integers,
the triangle as a list of rows:
*/
::Row :== [Int]
::Triangle :== [Row]
// Some constants
NrRows :== 18 // Number of rows to be shown.
Middle :== 40 // The middle of a 80 character line.
// Miscellaneous functions
NrOfDigits:: Int -> Int
NrOfDigits 0 = 0
NrOfDigits n = NrOfDigits (n / 10) + 1
// Calculating the Triangle.
Pascal::Triangle
Pascal = p
where
p = [[1] : [Next a \\ a <- p]]
Next x = AddRows [0:x] x
AddRows::Row Row -> Row
AddRows [a:x] [b:y] = [a + b : AddRows x y]
AddRows [a] [] = [a]
AddRows [] [] = []
// Formatting the list representing the triangle as a real triangle.
FormatRows::Triangle -> [String]
FormatRows [f:r] = [ FormatRow f +++ "\n" : FormatRows r]
where
FormatRow::Row -> String
FormatRow row
= toString (spaces (Middle - Length_new row/2 )) +++ FormatElems row
FormatElems::Row -> String
FormatElems [f:r] = " " +++ toString f +++ FormatElems r
FormatElems [] = ""
Length_new::Row -> Int
Length_new [f:r] = NrOfDigits f + Length_new r + 1
Length_new [] = -1
FormatRows [] = []
/* The Start rule: The first NrRows rows of the (infinite) triangle
returned by Pascal are taken and shown on the screen as a
triangle by means of FormatRows.
*/
Start::[String]
Start = FormatRows (take NrRows Pascal)
|
