The IsMonotonic(s) command returns the value true if s is monotonic, and the value false otherwise. A string is monotonic if the sequence of characters it comprises is non-increasing or non-decreasing, when the characters are identified with their ASCII code points.

Every string can be factored into a product (concatenation) of monotonic substrings by using StringTools[MonotonicFactors].

If s is the empty string, the command returns true.

All of the StringTools package commands treat strings as (null-terminated) sequences of $8$-bit (ASCII) characters.  Thus, there is no support for multibyte character encodings, such as unicode encodings.

$\mathrm{with}\left(\mathrm{StringTools}\right)\:$

$\mathrm{IsMonotonic}\left(''''\right)$

$\mathrm{true}$

$\mathrm{IsMonotonic}\left(''aaa''\right)$

$\mathrm{true}$

$\mathrm{IsMonotonic}\left(''abc''\right)$

$\mathrm{true}$

$\mathrm{IsMonotonic}\left(''cba''\right)$

$\mathrm{true}$

$\mathrm{IsMonotonic}\left(''cab''\right)$

$\mathrm{false}$

$\mathrm{IsMonotonic}\left(''abcba''\right)$

$\mathrm{false}$

$\mathrm{andmap}\left(\mathrm{IsMonotonic}\,\mathrm{MonotonicFactors}\left(\mathrm{Random}\left(1000\,'\mathrm{lower}'\right)\right)\right)$

$\mathrm{true}$