Is the character in the string?

>>> :set -XOverloadedStrings
>>> prove $ \c -> c `elem` singleton c
Q.E.D.
>>> prove $ \c -> sNot (c `elem` "")
Q.E.D.

Is the character not in the string?

>>> prove $ \c s -> c `elem` s .<=> sNot (c `notElem` s)
Q.E.D.

The ord of a character.

Conversion from an integer to a character.

>>> prove $ \x -> 0 .<= x .&& x .< 256 .=> ord (chr x) .== x
Q.E.D.
>>> prove $ \x -> chr (ord x) .== x
Q.E.D.

Convert to lower-case. Only works for the Latin1 subset, otherwise returns its argument unchanged.

>>> prove $ \c -> toLowerL1 (toLowerL1 c) .== toLowerL1 c
Q.E.D.
>>> prove $ \c -> isLowerL1 c .&& c `notElem` "\181\255" .=> toLowerL1 (toUpperL1 c) .== c
Q.E.D.

Convert to upper-case. Only works for the Latin1 subset, otherwise returns its argument unchanged.

>>> prove $ \c -> toUpperL1 (toUpperL1 c) .== toUpperL1 c
Q.E.D.
>>> prove $ \c -> isUpperL1 c .=> toUpperL1 (toLowerL1 c) .== c
Q.E.D.

Convert a digit to an integer. Works for hexadecimal digits too. If the input isn't a digit, then return -1.

>>> prove $ \c -> isDigit c .|| isHexDigit c .=> digitToInt c .>= 0 .&& digitToInt c .<= 15
Q.E.D.
>>> prove $ \c -> sNot (isDigit c .|| isHexDigit c) .=> digitToInt c .== -1
Q.E.D.

Convert an integer to a digit, inverse of digitToInt. If the integer is out of bounds, we return the arbitrarily chosen space character. Note that for hexadecimal letters, we return the corresponding lowercase letter.

>>> prove $ \i -> i .>= 0 .&& i .<= 15 .=> digitToInt (intToDigit i) .== i
Q.E.D.
>>> prove $ \i -> i .<  0 .|| i .>  15 .=> digitToInt (intToDigit i) .== -1
Q.E.D.
>>> prove $ \c -> digitToInt c .== -1 .<=> intToDigit (digitToInt c) .== literal ' '
Q.E.D.

Is this a control character? Control characters are essentially the non-printing characters. Only works for the Latin1 subset, otherwise returns sFalse.

Is this white-space? Only works for the Latin1 subset, otherwise returns sFalse.

Is this a lower-case character? Only works for the Latin1 subset, otherwise returns sFalse.

>>> prove $ \c -> isUpperL1 c .=> isLowerL1 (toLowerL1 c)
Q.E.D.

Is this an upper-case character? Only works for the Latin1 subset, otherwise returns sFalse.

>>> prove $ \c -> sNot (isLowerL1 c .&& isUpperL1 c)
Q.E.D.

Is this an alphabet character? That is lower-case, upper-case and title-case letters, plus letters of caseless scripts and modifiers letters. Only works for the Latin1 subset, otherwise returns sFalse.

Is this an alphabetical character or a digit? Only works for the Latin1 subset, otherwise returns sFalse.

>>> prove $ \c -> isAlphaNumL1 c .<=> isAlphaL1 c .|| isNumberL1 c
Q.E.D.

Is this a printable character? Only works for the Latin1 subset, otherwise returns sFalse.

Is this an ASCII digit, i.e., one of 0..9. Note that this is a subset of isNumberL1

>>> prove $ \c -> isDigit c .=> isNumberL1 c
Q.E.D.

Is this an Octal digit, i.e., one of 0..7.

Is this a Hex digit, i.e, one of 0..9, a..f, A..F.

>>> prove $ \c -> isHexDigit c .=> isAlphaNumL1 c
Q.E.D.

Is this an alphabet character. Only works for the Latin1 subset, otherwise returns sFalse.

>>> prove $ \c -> isLetterL1 c .<=> isAlphaL1 c
Q.E.D.

Is this a mark? Only works for the Latin1 subset, otherwise returns sFalse.

Note that there are no marks in the Latin1 set, so this function always returns false!

>>> prove $ sNot . isMarkL1
Q.E.D.

Is this a number character? Only works for the Latin1 subset, otherwise returns sFalse.

Is this a punctuation mark? Only works for the Latin1 subset, otherwise returns sFalse.

Is this a symbol? Only works for the Latin1 subset, otherwise returns sFalse.

Is this a separator? Only works for the Latin1 subset, otherwise returns sFalse.

>>> prove $ \c -> isSeparatorL1 c .=> isSpaceL1 c
Q.E.D.

Is this an ASCII character, i.e., the first 128 characters.

Is this a Latin1 character?

Is this an ASCII Upper-case letter? i.e., A thru Z

>>> prove $ \c -> isAsciiUpper c .<=> ord c .>= ord (literal 'A') .&& ord c .<= ord (literal 'Z')
Q.E.D.
>>> prove $ \c -> isAsciiUpper c .<=> isAscii c .&& isUpperL1 c
Q.E.D.

Is this an ASCII Lower-case letter? i.e., a thru z

>>> prove $ \c -> isAsciiLower c .<=> ord c .>= ord (literal 'a') .&& ord c .<= ord (literal 'z')
Q.E.D.
>>> prove $ \c -> isAsciiLower c .<=> isAscii c .&& isLowerL1 c
Q.E.D.