#
# a set of recursive functions
# Matt Bishop, MHI 289I, Winter 2018
#

# find the length of a string
# assumes argument passed in is a string
def length(s):
    # base case: empty string has length 0
    if s == "":
        return 0
    # now express the length as involving the length of a shorter string
    return 1 + length(s[1:])

# returns True if string is composed of letters *only*, False otherwise
# assumes argument passed in is a string
def onlyalpha(s):
    # base case: empty string is trivally composed of letters
    if s == "":
        return True
    # now see if the first is alphabetic; if so, check rest of string
    return s[0].isalpha() and onlyalpha(s[1:])

# find the maximum element of a list
# assumes argument passed in is a list and all elements in it are comparable
def largest(l):
    # base case: list of 1 element, return that element
    if len(l) == 1:
        return l[0]
    # now return the larger of the first element and the largest element
    # in the rest of the list
    lrest = largest(l[1:])
    if lrest < l[0]:
        return l[0]
    else:
        return lrest
    
# construct a string by catenating elements of a list (like ''.join(s))
# assumes argument passed in is a list of strings
def makestring(l):
    # base case: empty list gives empty string
    if l == []:
        return ""
    # otherwise, append the string formed by the rest of the list
    # to the first element
    return l[0] + makestring(l[1:])

# returns the string, reversed
# assumes argument passed in is a string
def revstr(s):
    # base case: empty list gives same reverse
    if s == "":
        return ""
    # otherwise, peel off last char, reverse rest, prepend what you peeled off
    return s[-1] + revstr(s[:-1])