Step by Step solution about How to resolve the algorithm Determine if a string is numeric step by step in the Haskell programming language

Type Signatures

isInteger :: String -> Bool
isDouble :: String -> Bool
isNumeric :: String -> Bool

Pattern Matching

isInteger s = case reads s :: [(Integer, String)] of
 [(_, "")] -> True
 _         -> False

• reads attempts to parse the input string s into a list of tuples [(Integer, String)].
• Each tuple contains an Integer value and a remaining string.
• The pattern [(_, "")] matches a single tuple where the Integer is bound by the wildcard _ and the remaining string is empty.
• If the pattern matches, the function returns True indicating that the input is a valid Integer.
• Otherwise, it returns False.

Guards and Predicates

areDigits = all isDigit
isDigit  selects ASCII digits i.e. '0'..'9'
isOctDigit selects '0'..'7'
isHexDigit selects '0'..'9','A'..'F','a'..'f'

• all applies a predicate to each element of a list and returns True if all elements satisfy the predicate.
• isDigit checks if a character is an ASCII digit ('0' to '9').
• isOctDigit checks if a character is an ASCII digit from '0' to '7'.
• isHexDigit checks if a character is an ASCII digit from '0' to '9', or an uppercase or lowercase letter from 'A' to 'F'.

Combining Functions

isNumeric :: String -> Bool
isNumeric s = isInteger s || isDouble s

• isNumeric combines the isInteger and isDouble functions.
• It checks if a string s is either an Integer or a Double using || (logical OR).
• It returns True if either check succeeds, and False otherwise.

isInteger s = case reads s :: [(Integer, String)] of
  [(_, "")] -> True
  _         -> False

isDouble s = case reads s :: [(Double, String)] of
  [(_, "")] -> True
  _         -> False

isNumeric :: String -> Bool
isNumeric s = isInteger s || isDouble s


areDigits = all isDigit
isDigit  selects ASCII digits i.e. '0'..'9'
isOctDigit selects '0'..'7'
isHexDigit selects '0'..'9','A'..'F','a'..'f'