Regular expression operators

Using just the three basic regular expression operators and a few of the common extensions to them, write regular expressions for the following; You can use + or | for the union operator, but if you use +, you cannot use it as a postfix repeat factor operator. For convenience use Lambda to stand for the expression emptyset*, which denotes the language containing just the empty string. You can use the pattern language's convention for a set of individual letters, so [a-zA-Z] is the set of all Roman letters, both uppercase and lower case, which is much shorter than a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s + t + u + v + w + x + y + z + A + B + C + D + E + F + G + H + I + J + K + L + M + N + O + P + Q + R + S + T + U + V + W + X + Y + Z If you want to use + as a postfix unary operator meaning repeat 1 or more times then you must use | for +. You can use postfix ? or repeat 0 or 1 time and * for 0 or more times. If you use ?, you may not need to use Lambda, since usually that it comes up to allow optionally including a piece. Concatenation is given by juxtaposition, no operator. You can also use \s to stand for white space and \d to stand for [0-9], the set of decimal digits. All characters other than + * ? \ ( ) [ ] - | . will stand for themselves, so that cat denotes the language that has just the one string "cat" in it. The exception is that Lambda refers to the empty string. If you want to refer to any of the characters + * ? \ ( ) [ ] - | . as a character and not part of the expression, precede it with a backslash. Note, the minus sign(-) only needs this treatment inside the square brackets. If you want the set that contains - and all the digits, [\-0-9] gets it. For another example, if I want the regular expression for the language that contains the single string "(cat|dog)*" I would need \(cat\|dog\)\* to have the operators regarded as the characters. DO NOT USE ANY OTHER OF THE PATTERN LANGUAGES FEATURES. If I did not give the okay here don't use it. Some tools that use regular expressions, lex, for example, allow you to define one, and then refer to it in another. I do not see that in the Perl/JavaScript/Java pattern expression language. That's unfortunate, because it makes them more modular and easier to read and to build them up from simpler components. The exercises will allow that, except when you do the pattern string in the program below you will need to do the whole thing all at once.